Durability of Polymer Composite Materials. Liu Liu

Transcription

1 Durability of Polymer Composite Materials A Thesis Presented to The Academic Faculty by Liu Liu In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy School of Aerospace Engineering Georgia Institute of Technology December 2006

2 Durability of Polymer Composite Materials Approved by: Professor Holmes, John W. Schoof of Aerospace Engineering Georgia Institute of Technology Professor Feron, Eric Schoof of Aerospace Engineering Georgia Institute of Technology Dr. Makeev, Andrew Schoof of Aerospace Engineering Georgia Institute of Technology Professor Ruzzene, Massimo Schoof of Aerospace Engineering Georgia Institute of Technology Professor Haj-Ali, Rami School of Civil Engineering Georgia Institute of Technology Date Approved: September 15, 2006

3 To my beloved husband Wei, and my parents, Xianchong and Zhongxian, for their constant encouragement and support over the years. iii

4 ACKNOWLEDGEMENTS First of all, I would like to thank my advisor, Prof. John Holmes, and the other members of my thesis committee: Prof. Eric Feron, Prof. Massimo Ruzzene, Dr. Andrew Makeev from the School of Aerospace Engineering and Prof. Rami Haj-Ali from the School of Civil Engineering. It is my pleasure to pursue my graduate studies in the School of Aerospace Engineering, Georgia Tech, where I had the opportunity to work directly with and learn from a group of very talented people. In particular, Dr. John Holmes provided me with an exceptional model of an experimental scientist. John is a great experimentalist. His abilities allow him to generate many good ideas and possible pathways towards them almost simultaneously, as well as to debug some difficulties in laboratory. John is also a very good, patient and helpful advisor. He provided me time to clear my mind and room for creativity. I always have freedom to work in an area that I like to contribute on. As a graduate student of John, I shall never forget the time he spent to teach me how to perform delicate experiments, work, and talk professionally. He gives me opportunity to diversify my research. He encouraged me to learn more material science to understand material behavior, which opened another door for my future. Dr. Holmes brought an amazing store of knowledge to our lab, from him I gained a clear understanding of material behaviors from point of view of a material scientist. As a good experimentalist with strong material science background, I learned a lot from him to strengthen my material background. He made me understand that to be a good engineer, it is important to make an idea feasible in a real world. As a good advisor, John helped me to built my confidence, that is another gift I obtained from Georgia Tech. I would like to express my deep appreciation to professor Jeff Jagoda. He was the first faculty iv

5 member I met in Georgia Tech, his trust and help made me feel warm. As a graduate coordinator, he is a big supporter for gradate students. I would like to acknowledge the other three graduate students in our group, Wendy Hynes, Huimin Song and Di Yang. Wendy graduated in Summer, Although Wendy and I did not collaborate in a same research topic, the numerous discussions with her are delightful and helpful. She is a very brilliant engineer and taught me a lot. I remember that Wendy corrected my English and gave me all kinds of good advice for my presentations with patience. She encourages and supports me. I want to appreciate her contribution to the web page of our lab (Materials & Advanced Structural Testing). Song is my classmate since 1994 in BUAA (Beijing University of Aero. & Astro.). We are very good friends and had a lot of discussions about engineering problems and non-engineering problems. I had the unique opportunity to collaborate on a variety of problems with Song. She is a very good collaborator and contributed to the work in this thesis. She gave me a lot help for FEA modelling. Di is a kind and out-going student full of energy, who also graduated from BUAA. She helped me perform fatigue test of ultra thin Ti foil specimen using the magnetic drive machine. Good destiny brought us together and I will cherish the time with these girls in Georgia Tech. Although my time working with them was short, I am sure that they will do great work in the years ahead in Georgia Tech, since both of them are smart, hard working and Dr. Holmes is one of best advisors in the world. Our research group is much like a big family and everyone enjoys life spent in the group. I wish I could work with people like them in the future. I would like to thank undergraduate student Marc Anderson and graduate student Gregory Lantoine for their collaboration and help in the past three years. I want to express my thanks to the ones who are important to me, but are not directly related to my graduate studies. My parents and husband constantly encourage v

6 me to pursue my goals and support my own decisions. They shared all my experiences in the past five years. I feel their generous love. My father is an exceptional model of a good engineer. In his entire career, he shows me integrity, responsibility and hard-work. In particular, I would like to thank Dr. Wei Zhang, my husband, for his intellectual support as a talented physicist. He helps me build a physical picture to understand engineering problems. He gave me very useful advice to improve my presentations. I would also like to appreciate Xiaoguang Yang, my Master thesis advisor in BUAA. He gave me great support and encouragement for pursuing my PhD abroad, which are very useful for my future career. Finally, I would like to thank Zonta International Foundation for their generosity to provide me financial support and gave me opportunity to present my work in conferences. vi

7 TABLE OF CONTENTS DEDICATION iii ACKNOWLEDGEMENTS iv LIST OF TABLES ix LIST OF FIGURES x SUMMARY xvi I INTRODUCTION Behavior of FRP composites under combined thermal and mechanical loading Shear Fatigue and Interface Fracture of Polymeric Composite Sandwich Structure Summary II THERMAL BUCKLING OF A FIRE-DAMAGED COMPOSITE COLUMN EXPOSED TO A UNIFORM HEAT FLUX Introduction Theoretical Development Temperature Distribution Thermal Buckling Analysis Results and Discussion Conclusions III EXPERIMENTAL WORK Post-Fire Compressive Behavior of Fiberglass Reinforced Polymeric Composite Columns Material, experimental apparatus and procedure Experimental results and discussion Integrity of Fiberglass Reinforced Polymeric Composite Column Under Simultaneous High Heat Flux Exposure and Compressive Loading Material, specimen geometry and experimental apparatus.. 62 vii

8 3.2.2 Experimental results and discussion Summary IV MONOTONIC SHEAR AND SHEAR FATIGUE OF FOAM-CORE COMPOSITE SANDWICH STRUCTURES Introduction Specimen Geometry, Test Apparatus and Instrumentation Finite Element Modelling Proof-of-concept Experiments Summary V CONCLUSIONS AND FUTURE WORK Conclusions Future work and suggestions APPENDIX A DIRECT SHEAR APPARATUS - ASSEMBLY DRAWING APPENDIX B DESIGN OF TEST APPARATUS FOR MODE-I FATIGUE TESTING OF THIN FOILS REFERENCES VITA viii

9 LIST OF TABLES 2.1 Material properties for a burnt composite column Typical properties of fiberglass-reinforced vinyl-ester composite laminate Time-to-failure (t f ) for fiberglass-reinforced vinyl-ester composite columns subjected to simultaneous surface heating and axial compressive loading Mechanical properties of the PVC H80 foam core used ix

10 LIST OF FIGURES 1.1 (a) char layer, (b) interface between the char layer and unburnt composite, (c) delamination cracks, and (d) a resin-rich region in the unburnt composite The schematic diagram of the simple-to-use two-layer model Experimental set-up for fire exposure under constrained compressive load using a calibrated propane burner A standard two-rail diagonally loaded shear test specimen (ASTM D4255/D4255M-01). A rectangular specimen is bonded between loading plates that are attached to clevises. As shown by the dashed line, loading takes place along a diagonal between the clevises located at each end of the loading plates The four-point bending set-up configuration Definition of the geometry for a fire-damaged laminated column under a uniform heat flux Q The effect of temperature on the elastic modulus of E-glass/Vinyl-Ester composites The relationship between the slope of the deflected angle and the equivalent shear angle γ eq, where θ is the rotation of the cross section due to bending Definition of the geometry for a original laminated column under the heat flux Q Temperature distribution of the burnt column subjected to a heat flux Q = 10 kw/m Temperature distributions for the charred and the original columns subjected to a heat flux Q = 5 kw/m Axial constraint force, P con, vs. exposure time t for the burnt column subjected to a heat flux Q = 10 kw/m Mid-point transverse deflection, w m, vs. exposure time t for the burnt column subjected to heat flux Q = 10 kw/m 2 (constrained, immovable ends case) The thermal moment, M T z, vs. exposure time t for the burnt column subjected to heat flux Q = 10 kw/m 2 (constrained, immovable ends case) x

11 2.10 Mid-point deflection, w m, vs. exposure time, t, under a constant applied axial force, P (ends free to move axially, unconstrained case). Each curve represents the column response under a constant heat flux, Q= 10 kw/m 2 and axial force P Mid-point deflection, w m, vs. exposure time, t for the column with axial force P = 250 lb and 3000 lb respectively under a constant heat flux Q = 10 kw/m 2 for comparison (ends free to move axially, unconstrained case) Applied axial force vs. midpoint transverse deflection for a burnt column subjected to a heat flux Q = 10 kw/m 2 at different times t (ends free to move axially, that is, unconstrained case) Axial constraint stress σ con xx vs. time for the burnt and the original column subjected to heat flux Q= 5 kw/m 2 (constrained, immovable ends case) Test coupons with [(0/45/90/ 45/0) s ] 2 ply layup were machined from a composite panel with a nominal thickness of 12.5 mm (a) Cone calorimeter arrangement showing position of 5000 W electric cone heater used to generate single-sided surface heat fluxes in the range of 25 kw/m 2 to 100 kw/m 2. (b) Close-up showing sample position beneath surface of cone heater Experimental arrangement used to perform monotonic compressive tests on a servo hydraulic load frame. The grip faces measure 100 mm square. The specimen ends fit within a 4 mm deep cavity and are in contact with a hardened steel insert. The axial LVDT measures displacement between the grip faces and the transverse LVDTs are located at the mid-points of the specimen length and width. All tests were performed at a displacement rate of 1 mm/min Normalized char thickness versus exposure time for a heat flux 50 kw/m 2. The post ignition time refers to the elapsed time after surface ignition is detected (t 0 = time to surface ignition). Beyond approximately 800 s, the char layer depth penetrates the entire specimen thickness, which we define as 100 % charred Normalized char thickness versus surface heat flux Q for a fixed postignition exposure time of 325 s Plot of axial compressive stress σ versus axial compressive strain ε for a sample without heat exposure. The average tangent modulus (between 0 and 200 MPa) was 17.4 GPa and the failure strength was approximately 297 MPa xi

12 3.7 Effect of heat exposure time (0 to 1800 s) on the residual compressive stress-strain behavior of fiberglass/vinyl-ester composites, which had been exposed to a heat flux of 50 kw/m 2. For an exposure time of 600 s, the residual strength was approximately 14 MPa; after 900 s, the residual strength was below 4.0 MPa a,b. (a). Normalized post-fire compressive strength σ c /σ 0 versus heat exposure time t. The data trend can be approximated by a first order exponential decay curve. The average compressive strength of unexposed samples (σ 0 ) was 297 MPa. (b). Normalized post-fire compressive modulus E c /E 0 versus heat exposure time t. The data trend can be approximated by a first order exponential decay curve. E 0 = 17.5 GPa Digital images showing failure modes of samples which had been subjected to a heat flux 50 kw/m 2 for exposure times of 0 s to 1200 s. As the exposure time increases, the failure mode switches from shear failure (fiber kinking) of the undamaged (without char) layers to global buckling (for 600 s and longer exposure times) Digital images showing progressive compressive deformation of fiberglassreinforced vinyl-ester specimen, which had been exposed to a surface heat flux of 50 kw/m 2 for total exposure time 600 s Photographs of the failure modes of samples exposed to heat fluxes of 25 kw/m 2, 50 kw/m 2 and 75 kw/m 2 for a fixed post-ignition exposure time of 325 s Photographs of deformation of the sample, which had been exposed to a heat flux of 75 kw/m 2 for a post-fire ignition exposure time of 325 s The Southwell plot Schematic of loading module used to mechanically load specimens during high heat flux thermal exposure in the cone calorimeter. An LVDT was used to measure axial displacement of the test specimens. The cooling manifold is used to keep linear bearings and the load cell at constant temperature (a) A close-up view of the specimen and grip arrangement used for the combined fire and compression tests. (b) A load cell mounted at one end of the load frame was used to monitor specimen load level. (c) H-block and linear bearings races Digital image of a 100 mm specimen (74 mm heated length) exposed for 100 s to a heat flux of 50 kw/m 2 under a compressive load of 7.0 MPa xii

13 3.17 Digital images comparing failure modes of 150 and 100 mm long specimens (100 mm heated length and 74 mm heated length, respectively) tested at the same heat flux intensity of 50 kw/m 2 and compressive load of 7.0 MPa. (a) 100 mm specimen; (b) 150 mm specimen; (c) fiber kinking observed in a specimen without heat exposure and tested to failure under a monotonically compressive load at room temperature Digital images showing failure modes of 150 mm long specimens (100 mm heated length between grips) for various thermal and axial compressive loads: (a) 25 kw/m 2 and compressive load of 5.25 MPa (1.66 kn). (b) 50 kw/m 2 and compressive load of 5.25 MPa (1.66 kn). All specimens failed by global buckling Experimental arrangement showing the LVDT located used to measure mid-point transverse deflection. The LVDT contacted the unexposed surface of the specimen Mid-point transverse displacement of the unexposed surface of specimens subjected to a heat flux of 50 kw/m 2 and an applied axial compressive load of 7.00 MPa (2.22 kn). For comparison, the transverse deflection of a specimen (74mm exposed length), subjected to the same heat flux, but with zero axial load, is shown Axial displacement of specimens exposed to a heat flux of 25 kw/m 2 under constant compressive loads from 1.11 to 3.34 kn. The initial compressive displacement decreased due to thermal expansion; the subsequent increase in compressive axial displacement is due to a decrease in specimen stiffness Axial compressive displacement u x versus axial applied compressive P under the same heat flux of 50 kw/m 2 with different heat exposure times (5, 10, and 50 s) Axial compressive displacement u x versus axial applied compressive load P under the same heat flux of 50 kw/m 2 with different heat exposure times (5 and 100 s) Axial compressive displacement versus heat flux for 150 mm long specimens subjected to a compressive force of 1.11 kn (250 lb). Data is plotted for heat exposure times from 0 to 150 s Specimen geometry and loading plates used for shear testing of sandwich materials. The face-sheets are adhesively bonded to the loading plates xiii

14 4.2 (a) Shear apparatus mounted on a 100 kn servohydraulic load frame. (b) Close-up of LVDT brackets. (c) Schematic of shear apparatus with key components identified. (1) sandwich specimen, (2) specimen loading plates, (3) U-shaped guide plates, (4) vertical linear bearing rails (5) horizontal plate with attached linear bearing races, (6) horizontal linear bearing rails, (7) upper plate fixed rigidly to hydraulic load frame, (8) lower plate fixed rigidly to hydraulic load frame. The left specimen attachment plate is fixed rigidly to the frame. The right plate is displaced vertically to develop shear in the specimen. As the specimen is displaced, the vertical linear bearings guide the vertical movement while the horizontal linear bearings allow transverse displacement to accommodate transverse contraction of the specimen. (d) Illustration of specimen deformation during shear loading Shear test apparatus with a furnace installed for elevated temperature tests. The U-shaped guiding plates and the extension arms used for the LVDTs are water-cooled Geometry of the dual LVDT setup (a) 3D finite element model for sandwich specimen in ASTM two-rail shear technique. (b) Stresses components along the center line of the specimen (a) 3D finite element model for sandwich specimen in the new directshear technique. (b) Stresses components along the center line of the sandwich structure Stress distribution contours in the modified two-rail new direct-shear technique (a) 2D finite element model of specimen geometry proposed for Mode II fracture toughness testing. (b) Shear stress τ 12 distribution around the crack tips. (c) Normal stress σ 22 distribution around the crack tips Monotonic shear behavior of a fiberglas/pvc foam-core sandwich specimen. The inset shows a specimen after testing. In all cases, failure occurred by fracture at the face-sheet/pvc-core interface Influence of maximum shear stress on the room temperature fatigue life of fiberglass/pvc foam sandwich specimens. The maximum fatigue stress was normalized with respect to the average monotonic shear strength (0.78 MPa) xiv

15 4.11 Typical stress-strain behavior observed during room temperature shearfatigue testing of fiberglass/pvc sandwich specimens. The data shown was obtained at loading frequency of 1 Hz and a stress ratio (τ min /τ max ) of Failure occurred by cyclic growth of interface cracks along the facesheet/core interface Shear modulus G degradation with fatigue cycles A.1 Direct shear apparatus B.1 The configuration of the new mode-i ultra thin foil fatigue machine B.2 The front side of the new mode-i ultra thin foil fatigue machine B.3 The new mode-i ultra thin foil fatigue machine xv

16 SUMMARY The purpose of this research is to examine structural durability of advanced composite materials under critical loading conditions, e.g., combined thermal and mechanical loading and shear fatigue loading. A thermal buckling model of a burnt column, either axially restrained or under an axial applied force was developed. It was predicted that for a column exposed to the high heat flux under simultaneous constant compressive load, the response of the column is the same as that of an imperfection column; the instability of the burnt column happens. Based on the simplified theoretical prediction, the post-fire compressive behavior of fiberglass reinforced vinyl-ester composite columns, which have been exposed to high heat flux for a certain time was investigated experimentally, the post-fire compressive strength, modulus and failure mode were determined. The integrity of the same column under constant compressive mechanical loading combined with heat flux exposure was examined using a specially designed mechanical loading fixture that mounted directly below a cone calorimeter. All specimens in the experiments exhibited compressive instability. The experimental results show a thermal bending moment exists and has a significant influence on the structural behavior, which verified the thermal buckling model. The trend of response between the deflection of the column and exposure time is similar to that predicted by the model. A new apparatus was developed to study the monotonic shear and cyclic-shear behavior of sandwich structures. Proof-of-concept experiments were performed using PVC foam core polymeric sandwich materials. Shear failure occurred by the extension of cracks parallel to the face-sheet/core interface, the shear modulus degraded with the growth of fatigue damage. Finite element analysis was conducted to determine xvi

17 stress distribution in the proposed specimen geometry used in the new technique. Details for a novel apparatus used for the fatigue testing of thin films and face sheets are also provided. xvii

18 CHAPTER I INTRODUCTION 1.1 Behavior of FRP composites under combined thermal and mechanical loading Fibre reinforced thermoset polymer (FRP) composites are used extensively in aerospace, marine, high speed train and automotive industry. For example, the worldwide consumption of glass-reinforced isophthalic polyester laminates by the boat and ship building industry currently exceeds 300, 000 tonnes per annum. FRP may be used in marine craft because of their relatively low cost, light-weight, excellent durability in sea-water, and good mechanical properties. Composites used in these applications are usually made of glass, carbon or Kevlar fibres with a polyester, vinyl ester, epoxy or phenolic resin matrix. A limitation on the use of FRP composites is that they can ignite soon after being exposed to a high-temperature fire; as the resin matrix is consumed large amounts of heat, smoke and fumes are released. In-flight fire is the fourth most common cause of aircraft fatalities. Because of the critical importance of fire properties, extensive work has been performed to study fire performance of composites for naval vessels including flame spread index, smoke obscuration, ignitability, heat release and so on [1]. For example, as reported by Gibson and his colleagues [2], the fire characteristics of polyester, vinyl ester and epoxy laminates were similar, but phenolics gave much lower heat release, longer time to ignition and reduced smoke; All laminates showed a useful thickness effect, with reduced heat release, heat transmission and slow burn-through above a critical thickness. The use of composites in marine craft has been hindered by the reduction in their mechanical properties during fire. Large reductions to the stiffness and strength 1

19 can occur when a composite is heated above the glass transition temperature of the resin. It is during a fire that the mechanical properties of composites are the most severely degraded. After the fire has been extinguished, the mechanical properties of composites may also be lower than their original values due to thermal degradation and combustion of the resin matrix. Studies have shown that the post-fire tension [3], interlaminar shear [3] and flexure strength [4, 5, 6, 7, 8, 9] of burnt composites can be much lower than the original strengths. Sorathia [5, 6, 7, 8, 9] studied the post-fire mechanical properties of thin composite panels. They found that composites with a thickness of about 5 mm can lose more than 75 % of their flexural strength after being exposed for 20 min to a heat flux of 25 kw/m 2, which is equivalent to the heat emitted from a low-to-medium intensity fire. Sorathia et al. [5] also found that the reduction in strength could be minimized by protecting the composite from the radiant heat with a thermal barrier material such as phenolic coating, silicone foam or intumescent mat. Mouritz et al. [10, 11, 12] investigated the effect of radiant heat on the mechanical properties of a glass-reinforced isophthalic polyester composite (GRP), which is typical of the glass-reinforced polymer used in marine craft. The GRP was exposed to various incident heat fluxes from 25 kw/m 2 to 100 kw/m 2. Reductions to the post-fire tension, compression, flexure and interlaminar shear properties caused by increasing heat flux and heat exposure time were determined, and related to damage caused by the radiant heat. The high heat flux the composites were exposed to caused charring, -i.e, thermal degradation and combustion of the polymer matrix. In scanning electron micrographs (Fig. 1.1, adapted from Ref. [11]) of the char layer, interface region between the char layer and unburnt composite, Mouritz et al. observed delamination cracks and a resin-rich region in the unburnt composites. It was found the post-fire tension, compression and flexural and interlaminar shear properties decrease rapidly with increasing heat-exposure time and heat flux due mostly to 2

20 (a) (b) (c) (d) Figure 1.1: (a) char layer, (b) interface between the char layer and unburnt composite, (c) delamination cracks, and (d) a resin-rich region in the unburnt composite combustion of the polymer matrix. Mouritz [13] proposed that the post-fire properties of uniformly burnt composites can be determined with simple-to-use models that are based on rule-of-mixtures analysis. The only data needed to calculate the post-fire properties using the models is the original mechanical properties of the composite and the char thickness. The basic assumption of the models is that the mechanical properties of the char and unburnt regions can be combined using rule-of-mixtures analysis to obtain the bulk stiffness and strength of a fire-damaged composite. A schematic diagram of the model is shown in Fig. 1.2 (adapted from Ref. [13]) The key simplifying assumptions include (i) the char region in the fire-damaged composite has a uniform thickness (defined as d c in Fig. 1.2); (ii) the tension, compression and flexure properties of the char are constant throughout the char region; the mechanical properties of the char region are negligible because of thermal decomposition of the polymer matrix; (iii) the tension, compression and flexure properties of the unburnt region are the same as the mechanical properties of the original (unburnt) composite; the mechanical properties of the 3

21 Fire Char d c Unburnt Layer Delaminations d Combustion Front Figure 1.2: The schematic diagram of the simple-to-use two-layer model unburnt region are constant throughout, and are not affected by excessive heating of the resin matrix or by the small delamination cracks. Based on the simplifications, the post-fire properties of burnt composites can be determined. For instance, they proposed that the tensile stiffness (S t ) of an evenly burnt composite can be estimated using the simple expression: S t ( d d c ) S o + ( d c d d ) S c (1.1) where d c is the thickness of the char region; d is the original thickness of the composite, and S c and S o are the tensile stiffness of the char and unburnt (original) material, respectively. If it is assumed that the tensile stiffness of the char is negligible, then the second term to Eq. 1.1 can be ignored and the expression reduces to: S t ( d d c ) S o (1.2) d Similarly, other post-fire properties can be determined by the rule-of-mixtures. The key of the calculation is to determine the thickness of the char region after fire exposure. In order to determine the post-fire mechanical properties with the model proposed by Mouritz, it is necessary to determine the thickness of char region. Gibson developed 4

22 a thermal model for the decomposition of composite laminates in fire [14, 15, 16, 17]. The model predicts the evolution of the temperature and resin content in the laminate with time for any surface condition. Application of the model requires knowledge of the decomposition process of the resin, which can generally be acquired through thermo-gravimeytic analysis (TGA). They also proposed a simple criteria for determining the position of the boundary between heat-affected and undamaged material in two-layer model, this boundary corresponds to a remaining resin content (RRC) of 80 %, a criterion that applies to all the resin types tested. Further, Gibson et al. [18] studied the laminate composites under mechanical loading (tension and compression) in fire. It was found that compressive loading caused more degradation than tensile loading. For polyester laminates under compressive load in fire, buckling failure appears to correspond to the point where the resin reaches 170 o C, In tensile loading, significant strength is retained, because of the residual strength of the glass reinforcement. The key conclusion of their work is that failure times in fire are short and that composite structures are especially prone to local compressive failure. In summery, Gibson et al. contributed extensively to the fire related FRP composites both analytically and experimentally. The temperature distribution and residual resin content (RRC) distribution along the thickness of the laminated composite with time variation was given theoretically; they also proposed a simple criteria for determining the position of the boundary between heat-affected and undamaged material. For the residual mechanical properties of FRP after fire, they proposed a simple two-layer model. However the model does not take into account the interface region with delamination between heat-affected and undamaged layers. In another series of experiments, laminates were tested under compression load in fire; the experimental set-up is shown in Fig. 1.3 (adapted from Ref. [18]). In order to achieve higher compressive stresses, nearer to the design stresses that might be used 5

23 Testing machine Propane burner Rear face insulation Specimen Temperature measured 'Boeing' test jig Anti-buckling guides Figure 1.3: Experimental set-up for fire exposure under constrained compressive load using a calibrated propane burner in some composite structures, additional constraint was provided to delay the onset of buckling ( Anti-buckling guides in Fig.1.3). It was found that an excellent way of accomplishing this, while still allowing a substantial region of the specimen to be subjected to heat flux, was to use a test jig with anti-buckling guides similar to the well-known Boeing compression test [19], but with a square, rather than rectangular sample. Boeing compression test was proposed by Boeing Specification Support Standard for advanced composite compression tests. The aim of the Boeing test with anti-buckling guides was to generate measurements at stresses typical of design stresses in composite structures. Failure in the constrained tests took place 6

24 by local buckling. However the Boeing test cannot characterize the behavior of a structure under compressive loading in fire since many composite structures without constraints under compression in fire will fail by global buckling. Therefore It is important to understand the combined mechanical and thermal loading effect on composite structures. The purpose of this research work was to investigate the response of FRP composite columns under simultaneous high heat flux exposure and compressive loading. The most important part of this research is to design a new test fixture to investigate the thermal bending (global buckling) of a heat-exposed axially restrained column. Testing, which simulated fire exposure and compressive loading on laboratory size test samples was performed to determine the damage modes that occurred during fire exposure. Knowledge of the post-fire mechanical residual strength of these materials was obtained from fire and post-fire mechanical tests. 1.2 Shear Fatigue and Interface Fracture of Polymeric Composite Sandwich Structure In addition to the FRP composite, sandwich construction is used in many applications because of the high stiffness and strength to weight ratio. Therefore, an important topic investigated in this thesis is the shear behavior of polymer sandwich materials. The sandwich structures typically consist of two thin face sheets and a thicker lightweight core. The face sheets are generally composite laminates reinforced with kevlar, carbon or glass fibers, while the core may be made of honeycomb, cellular foams or balsa wood. Examples of their successful use include primary aircraft structures, building materials, automobile parts and refrigerated transport containers [20]. Sandwich composites are also being used increasingly in wind turbines, pleasure boats, commercial ships and naval vessels [21]. These applications all have in common that they are subjected to fatigue loads, which can cause failure as a 7

25 A Figure 1.4: A standard two-rail diagonally loaded shear test specimen (ASTM D4255/D4255M-01). A rectangular specimen is bonded between loading plates that are attached to clevises. As shown by the dashed line, loading takes place along a diagonal between the clevises located at each end of the loading plates. result of a gradual, build up of damage or the growth of a flaw to a critical dimension. When a sandwich structure is subjected to in-plane or bending loads, the core material is mainly loaded in shear. Crack initiation, propagation and failure behavior in sandwich structures under the shear fatigue loading is still a relatively open field, especially basic knowledge of the shear fatigue test apparatus design. Much attention has been concentrated on the shear properties of sandwich structures and there exist various test standards for evaluation. For example, in the two-rail shear technique (ASTM D4255/D4255M-01 [22]), developed for polymeric 8

26 sandwich composites, a rectangular specimen is bonded between two metallic loading plates which are loaded axially at their ends, as shown in Fig. 1.4 (adapted from Ref. [23]). Garcia et al. [24] presented the results from an experimental and analytical investigation of the stress distributions occurring in a rail shear test; the effects of nonuniform stresses induced by differential thermal expansion, rail flexibility and specimen aspect ratio on measured shear modulus and ultimate strength of composite laminates were shown. Hussain and Adams [25] modified the ASTM D-4255 standard two-rail test method (Fig. 1.4) by using a multiple-bolt C-clamp to grip the specimen to thermal- sprayed (gritted) rails. They also used 3D finite element modelling to analyze a range of specimen configurations in order to optimize the specimen geometry of composite laminates in two-rail shear testing [26]. In addition to the two-rail shear technique, 3-point or 4-point flexure of rectangular beams are also widely used experimental methods to study the shear behavior of sandwich structures. ASTM C [27] outlines the use of 3 and 4-pt bending for room temperature shear testing of sandwich specimens. M. Burman and D. Zenkert [28] used a modified four-point bending test method to address the shear fatigue characteristics of two cellular foam core materials. The flexural experimental configuration is shown in Fig 1.5 (adapted from Ref. [28]). Nitin Kulkarni et al. [29] found that the first visible sign of damage initiation was a core-skin debond parallel to the sandwich beam axis (experiments were performed in a 3-point flexure mode utilizing a newly designed fixture such that localized indentation damage was minimal). Roosen [30] performed fatigue tests with X-PVC, PEI and PMI cored sandwich beams using a 4-point bending rig. Fracture loads, displacements, shear strengths and S/N diagrams of the sandwich beams were determined. However it should be noted in the ASTM standard C393-94, failure in the compression facing may occur by actual crushing, yielding causing large deflection, wrinkling of the facing into the core or the facing popping off the core for thin 9

27 Figure 1.5: The four-point bending set-up configuration face-sheet sandwich structure in flexure testing. Therefore the use of flexural techniques can not be reliably applied to thin face-sheet sandwich structures to determine shear strength and shear modulus. The ideal test technique for investigating shear response of sandwich structures should provide a uniform shear region with minimal normal stress. In addition to permitting various specimen sizes and material types to be studied, the technique should allow direct measurement of the shear stress-strain response at both ambient and elevated temperatures. Ideally, the technique allows for monotonic, fatigue and creep testing. With these requirements in mind, a goal of my research is to develop a new shear testing method that can be applied to a variety of sandwich structures, 10

28 including polymers, metals and ceramics. An improvement of the new testing apparatus is the reduction in normal stress and the ability to provide a large region of pure and uniform shear by allowing the specimens expansion and contraction, which none of previous testing methods considered. Another important design objective was to develop a technique that could be used to study the fracture behavior of interfaces and adhesives under direct Mode II (shear) loading. 1.3 Summary A summary of the contents of each chapter is given here. Chapter 2 describes thermal buckling of a fire-damaged composite column, which is exposed to heat flux from one side. It predicted that a thermal moment exists for a composite column exposed to a heat flux under compressive mechanical loading. The behavior of the burnt column under the compressive load is the same as that of an imperfection column. The instability of the burnt column happens. For the thermal buckling analysis, the mechanical properties of the fire-damaged region (char) are considered negligible; the degradation of the elastic properties with temperature in the undamaged layer (especially near the glass transition temperature of the matrix) is accounted for by using experimental data for the elastic modulus of the glass/vinylester material as a function of temperature. To simplify the thermal conduction problem, it is modelled as a one-dimensional problem in the thickness direction. Chapter 3 describes the experimental work performed to study the effect of simultaneous high heat flux surface heating and compressive loading on the failure time and failure mode of fiberglass-reinforced vinyl-ester matrix polymeric composites. The experiments also verified the thermal bending moment existence and its effects for the burnt column under simultaneous compressive loading, which has been predicted by the thermal buckling model in chapter 2. To characterize the residual compressive strength and failure mode of composites after exposure to high heat fluxes, specimens 11

29 were exposed to various heat fluxes in a cone calorimeter, followed by room temperature compression testing in a servo-hydraulic load frame. These experiments were performed to determine how heat flux intensity and exposure time affect the residual compressive behavior of the composite. Further, the effect of simultaneous high heat flux surface heating and compressive loading were investigated using a specially designed mechanical loading fixture that mounted directly below a radiant cone heater. The effect of surface heat fluxes from 25 to 75 kw/m 2 and compressive loads from 3.5 to 10.5 MPa on failure time and failure mode were examined. Monotonic shear and shear-fatigue loading are important loading modes for many composite sandwich structures. In order to study the monotonic shear and shearfatigue behavior of composites and sandwich structures at ambient and elevated temperatures, a new shear test apparatus, which allows direct core shear loading, was developed. Chapter 4 describes the new shear test technique, which can be used to study monotonic shear, shear-fatigue and shear-creep of various thin face-sheet sandwich structures. It can also be used to study the Mode II fracture behavior of interfaces in sandwich materials. Experimental results are provided for the monotonic shear and shear fatigue testing of a polymeric composite sandwich structure (glass-fiber/epoxy face-sheets with a 50 mm thick PVC foam core). Chapter 5 summarizes the significant results of this thesis. The appendix contains some details for the design of the new direct shear apparatus as well as the design of a new magnetic driven apparatus for mode I fatigue testing of ultra-thin metallic foils and lap-shear testing of adhesives. 12

30 CHAPTER II THERMAL BUCKLING OF A FIRE-DAMAGED COMPOSITE COLUMN EXPOSED TO A UNIFORM HEAT FLUX 2.1 Introduction Polymer-based composites and sandwich panels with composite face sheets are increasingly being used for structural applications in naval vessels, aircrafts, space vehicles, and high-speed trains. These materials are also being used for lightweight bridge structures and storage containers. In the case of naval vessels and aircrafts, the effect of high intensity fires on the structural response of composites is of great concern. Predictions for structural response, both during and after fire exposure, are needed to ascertain structural safety, in particular the possibility of structural collapse. Information regarding the effect of exposure time on structural response is also needed to establish time constraints for fire fighting crews and automated firefighting equipment. In the case of heavily loaded structures, such as bridges, the effect of vehicle fires on structural safety is of paramount concern. The resulting effect of catastrophic events such as fire or explosions on the integrity of structures is of considerable concern. There is little research done on the structural behavior and integrity during and following exposure to fire. Still, the combined effect of simultaneous mechanical loading and thermal (fire) loading has not been studied. It is of interest to know the structural behavior and integrity of composite columns during and following exposure to fire using Bernoulli-Euler beam theory, which is addresses in this chapter. 13

31 When a heat flux is applied to one side of a column, a non-uniform temperature distribution develops through the thickness direction of the column. Since the modulus of elasticity of polymeric composites depends on temperature, this non-uniform temperature results in a non-uniform distribution of stiffness through the thickness. A thermal moment is also developed, which causes bending of the column from the very start of heat exposure when only the slightest change of temperature occurs. This chapter examines this issue theoretically for compressive loading, which for otherwise purely mechanical loading (no fire) would lead to bifurcational buckling for a perfect column. The model includes the effect of char (resin decomposed layer) which has a significant influence on the temperature distribution and also on the resulting structural response. As far as the undamaged layer, the temperature distribution still induces a considerable spatial change in stiffness, therefore the layer is essentially a non-homogeneous material. For fiber reinforced polymeric composites, an increasing in temperature causes a gradual softening of the polymer matrix material with a profoundly significant effect near the glass transition temperature, T g. Data from recent experiments on E-glass vinyl ester composites, conducted by Kulkarni and Gibson [31], are used in the analysis as a basis for including the effect of temperature on the nonuniform stiffness distribution. When fire is applied on one side of a column, two things happen simultaneously: a char (damaged) layer appears and a nonuniform temperature develops through the thickness of the undamaged layer. These effects result in a nonuniform distribution of stiffness through the thickness. In addition, a thermal moment is developed, which causes bending of the column from the very start of fire when only the slightest change of temperature occurs. Thus, the column bends like a beam (even if it is initially perfect) and cannot buckle in the classical Euler (bifurcation) sense. In this chapter, the general bending response of a column that is pinned at both 14

32 ends, with an applied axial force is investigated. Two cases are considered: one case is a column with immovable ends, which would result in axial reaction forces due to the thermal loading; the other is a column with ends free to move axially under the action of an applied axial load. Details of the formulation are outlined next. However, As a simplified model, the model does not consider the charred layer thickness varies with the heat exposure time dynamically, which influences the structural response including temperature distribution definitely. Since the model does not incorporate the charred layer formation information with heat exposure time, the heat flux intensity used in the numerical calculation is defined much lower than the heat flux, which can be used to simulate fire, therefore the temperature increase by the heat exposure in the calculation is controlled and much lower than the temperature which can induce the charred layer. Because of these, the prediction given by the model for the behavior of the column is only qualitative and can not be verified quantitatively by the experiments in lab. 2.2 Theoretical Development Temperature Distribution A fire-damaged laminated burnt composite column consisting of an undamaged layer and a fire damaged layer is considered, as show in Fig The length and thickness of the column are represented by L and H respectively. Coordinate axes x and y are chosen, as shown in Fig. 2.1 A. The fire-damaged column is exposed to a constant heat flux from the damaged surface and the undamaged surface has radiation boundary condition with the surrounding media. In order to simplify the analysis, the temperature of the surrounding air at the undamaged surface is denoted by T 0. The column is assumed to be initially at T 0 and the thermal boundary conditions at x = 0 and x = L are assumed to be adiabatic, so the heat conduction problem becomes a one-dimensional problem governed by coordinate y. 15

33 L H l a A x Undamaged layer Damaged layer T 0 y Q L l B x' Undamaged layer y Figure 2.1: Definition of the geometry for a fire-damaged laminated column under a uniform heat flux Q 16

34 K 1, κ 1, h 1 and T 1 represent conductivity, diffusivity, relative heat transfer coefficient and temperature for the undamaged composite column in the region l y 0 and K 2, κ 2 and T 2 are the corresponding quantities for the fire damaged layer in the region 0 y a. The differential equations to be solved are: 2 T 1 y 1 T 1 2 κ 1 t 2 T 2 y 1 T 2 2 κ 2 t = 0 for l y 0, t > 0 (2.1a) = 0 for 0 y a, t > 0 (2.1b) If we assume there is no contact resistance at the surface of the interface between the fire-damaged and the undamaged layer, x = 0, then the conditions at that interface are: K 1 T 1 y = K 2 T 2 y at y = 0, t > 0 (2.2a) T 1 = T 2 at y = 0, t > 0 (2.2b) For the composite column described above, with T 0 being the initial temperature, the initial conditions can be written as: T 1 = T 2 = T 0 for l y a, t = 0 (2.3) the boundary conditions of impending heat flux, Q at the fire-damaged side, K 2 T 2 y = Q at y = a, t > 0 (2.4) and T 1 y = h 1(T 1 T 0 ) at y = l, t > 0 (2.5) If we denote: T 1 = T 1 = T 1 T 0 T 2 = T 2 = T 2 T 0 17

35 T 1 and T 2 satisfy Eq.(2.1),(2.2), and (2.4) as well; but the initial and other boundary conditions should be rewritten as: T 1 = T 2 = 0 for l y a, t = 0 (2.6) T 1 y = h 1 T 1 at y = l, t > 0 (2.7) With the aid of the Laplace transformation for time t, the temperature change governed by Eq.(2.1a) and (2.1b) can be analyzed. Denoting the Laplace transform of F (t) as F (p) and taking into account the initial condition Eq.(2.6), the fundamental equations for the temperature variation in the transformed domain become: d 2 T1 dy 2 q2 T 1 1 = 0 for l y < 0 (2.8a) d 2 T2 dy 2 q2 T 2 2 = 0 for 0 < y a (2.8b) where q 1 = (p/κ 1 ) 1 2, q 2 = (p/κ 2 ) 1 2. These have to solved with A solution of Eq.(2.8) is d K T 1 d 1 = K T 2 2 at y = 0 (2.9a) dy dy T 1 = T 2 at y = 0 (2.9b) d T 2 dy d T 1 dy = Q K 2 p at y = a (2.9c) = h 1 T1 at y = l (2.9d) T 1 (y, q 1 ) = A 1 cosh(q 1 y) + B 1 sinh(q 1 y) (2.10a) T 2 (y, q 2 ) = A 2 cosh(q 2 y) + B 2 sinh(q 2 y) (2.10b) The notation κ = κ1 κ 2 and K = K 2 K 1 are used, therefore q 2 can be replaced by κq 1. A 1, B 1, A 2 and B 2 are unknown constants, which should be determined so as to satisfy the boundary conditions Eq.(2.9). Substituting Eq.(2.10) into the relations of Eq.(2.9), these unknown constants can be determined from: q 1 B 1 Kκq 1 B 2 = 0 (2.11a) 18

36 A 1 A 2 = 0 [κq 1 sinh(κq 1 a)]a 2 + [κq 1 cosh(κq 1 a)]b 2 = Q K 2 p (2.11b) (2.11c) [ q1 sinh(q 1 l) h 1 cosh(q 1 l) ] A 1 + [ q 1 cosh(q 1 l) + h 1 sinh(q 1 l) ] B 1 = 0 (2.11d) These equations can be represented in matrix form: 0 0 a 13 a 14 A 1 1 a 21 a B 1 = Q 0 a 31 0 a 33 0 A K 2 2 p 0 0 a 42 0 a 44 B 2 0 (2.12) where the nonzero elements a kl among the coefficient matrix [a kl ] are given as follows: a 13 = κq 1 sinh(κq 1 a) a 14 = κq 1 cosh(κq 1 a) (2.13a) a 21 = q 1 sinh(q 1 l) h 1 cosh q 1 l a 22 = q 1 cosh(q 1 l) + h 1 sinh q 1 l (2.13b) a 31 = 1 a 33 = 1 (2.13c) a 42 = q 1 a 44 = Kκq 1 (2.13d) The temperature solution in the transformed domain can be expressed as: T 1 (y, p) = Q A 1 cosh(q 1 y) + B 1 sinh(q 1 y) K 2 p T 2 (y, p) = Q A 2 cosh(q 2 y) + B 2 sinh(q 2 y) K 2 p (2.14a) (2.14b) where = a kl = det(a kl ). From the Inversion Theorem, the solution is found to be: T 1 (y, λ) = Q K 2 γ+i γ i T 2 (y, λ) = Q K 2 γ+i γ i A 1 cosh(q 1 y) + B 1 sinh(q 1 y) e λt dλ λ A 2 cosh(q 2 y) + B 2 sinh(q 2 y) e λt dλ λ (2.15a) (2.15b) λ is written in place of p in Eq.(2.14) to emphasize that the behavior of T 1 and T 2 is regarded as a function of a complex variable in Eq.(2.15). 19

37 Using the residue theorem, the inverse Laplace transformation of Eq.(2.15) can be accomplished; the temperature solution T 1 and T 2 are given by the summation of the residues. The single-value poles of Eq.(2.15), corresponding to λ = 0 and the roots of = 0, in which the residue for λ = 0 gives a solution for steady state, are treated separately. If we denote λ n = κ 1 α 2 n; q 1 = iα n ; λ n = κ 1 q 2 1, n = 1, 2, 3... (2.16) where ±α n, n = 1, 2, 3... are the roots (all real and simple) of = 0 (2.17) The transient part of the temperature solution T 1 and T 2 is given as: T 1 = Q K 2 + n=1 T 2 = Q K 2 + n=1 2e κ 1q 2 1 t q 1 [A 1 cosh(q 1 y) + B 1 sinh(q 1 y)] q1 =iα n (2.18a) 2e κ 1q 2 1 t q 1 [A 2 cosh(q 1 y) + B 2 sinh(q 1 y)] q1 =iα n (2.18b) is defined as the derivative of the determinant (λ) with respect to λ. Finally T 1 and T 2 can be written as functions of t and y in terms of α n. Next, we evaluate the steady temperature solution T 1 and T 2. From Eq.(2.1), the fundamental equations for T 1 and T 2 are 2 T1 y 2 = 0 for l y < 0, t > 0 (2.19a) 2 T2 y 2 = 0 for 0 < y a, t > 0 (2.19b) The fundamental solution of T 1 and T 2 can be written in the following form: T 1 = Ā1y + B 1 (2.20a) T 2 = Ā2y + B 2 (2.20b) 20

38 where Ā and B are unknown constants determined so as to satisfy boundary conditions. The temperature solution T 1 and T 2 can be expressed as, T 1 = T 2 = ( Q K 1 y h 1l h 1 ( Q K 2 y h 1l h 1 ) Q + Q 2e κ 1q 2t[ 1 A 1 cosh(q 1 y) + B 1 sinh(q 1 y) ] K 2 q 1 K 1 n=1 ) Q + Q 2e κ 1q 2t[ 1 A 2 cosh(q 1 y) + B 2 sinh(q 1 y) ] K 2 q 1 K 1 n=1 q1 =iα n (2.21a) q1 =iα n (2.21b) The first part of the equation represents the the solution for the steady state and the second part of the equation represents the transient solution. In theory, a numerical solution of the above problem provides the convergence factor exp( κ 1 α 2 nt), which is uniformly convergent for any interval of y, when t > 0; and regarded as a function of t, it is uniformly convergent when t t 0 0, t 0 being any positive number. The form of solution is suitable for moderate and large values of t. Alternative solutions of the same problem can be obtained which are suitable for very small values of t Thermal Buckling Analysis The analysis of the thermal bending of a burnt column is based on the assumptions made by A. Mouritz [13], which assumed that the mechanical properties of the charred (fire-damaged) layer are negligible because of the thermal decomposition of polymer matrix; the mechanical properties of the undamage region are not influenced by small delamination cracks. I consider only the undamaged layer in the thermal buckling analysis. The temperature distribution which was determined earlier for the undamaged region is used in the analysis. A quasi-static assumption is made (at each different time, the column is in an equilibrium state and the temperature distribution at that time can be used in the static buckling analysis). Regarding the stiffness, E of the undamaged composite column, it is well known that the modulus of a polymer depends strongly on the temperature and especially 21

39 Figure 2.2: The effect of temperature on the elastic modulus of E-glass/Vinyl-Ester composites on how close the temperature is to its glass transition temperature, T g. For composites with polymeric matrices, it is logical to expect that the stiffness E depends on temperature. A recent paper by Kulkarni and Gibson [31] studied the effects of temperature on the elastic modulus of E-glass/Vinyl-Ester composites as shown in Fig. 2.2 (adapted from Ref. [31]). They provided measurements of temperature dependence of the elastic modulus of the composite in the range of 20 o C to 140 o C. The glass transition temperature of the matrix is T g = 130 o C. Near this temperature the elastic modulus shows a significant decrease, but below T g the variation is small. The variation of the modulus in Kulkarni and Gibson [31] fits a 3 rd order polynomial equation very well. If we denote E 0 as the modulus at room temperature, T 0 = 20 o C, then the modulus E is a function of the temperature T : E E 0 = 1 a 1 ( T T 0 T g T 0 ) + a 2 ( T T 0 T g T 0 ) 2 a 3 ( T T 0 T g T 0 ) 3 = 1 a 1 ( T 1 T g ) + a 2 ( T 1 T g ) 2 a 3 ( T 1 T g ) 3 (2.22) 22

40 For the present E-glass/Vinyl-Ester, E 0 = 20.6 GPa and a 1 = 0.348, a 2 = and a 3 = The composite studied has a fiber volume fraction of and consisted of four sub-layers with the orientation of each sub-layer [0/90/ + 45/ 45/Random]. Eq.(2.22) captures the physics of the non-linear dependence of the composite on the glass transition temperature of the matrix T g. The temperature distribution in the undamaged layer T 1 can be determined from Eq.(2.21a). In order to simplify the formulations in the thermal buckling analysis, the axis x is translated to the midsurface of the undamaged layer y = l, as shown in Fig. 2.1B. 2 In the new coordinate system, I define an average modulus E av and a first and second moment of the modulus with respect to the mid-surface y-axis, E m1 and E m2 respectively by: E av A = A EdA ; E m1 la = A EydA ; E m2 I = A Ey 2 da (2.23) where A is the cross sectional area, l is the thickness of the undamaged layer; and I is the moment of inertia (I = A y2 da). The integral is evaluated numerically (a simple closed-form expression can not be obtained). Due to the nonuniform modulus, the neutral axis of the column is not at the midsurface. The distance, e, of the neutral axis from the mid-surface axis, is determined from: which, by use of Eq.(2.23) leads to: A E(y)(y e)da = 0 (2.24) e = E m1 l/e av (2.25) Assuming the thermal expansion coefficient, α, is independent of temperature, the thermal force is: Nx T = Eα T 1 da which can be evaluated numerically by use of Eq.(2.21a) and (2.22). A (2.26a) 23

41 The thermal force develops due to the constraints at both ends of the column, which may cause buckling. However, the problem is not one of bifurcation buckling because a thermal moment also develops. The thermal moment (with respect to the neutral axis of the column) is given by: Mz T = Eα T 1 (y e)da The thermal moment will induce bending of the column. A (2.26b) The problem now is to determine the response of the column under the influence of both N T x and M T z, which change the characteristic of the problem from bifurcation buckling to a bending problem. That is, if the applied axial load is large enough to constrain the column at both ends, the column will bend as M T z is applied. Of course, the applied force P could cause failure if it is large enough. As the load increases, the column mid-span transverse deflection, w, increases until the column fails due to the bending. I consider two cases: case I is a column constrained by the two ends, which can not move; the other is a column under a certain constant applied load P. First of all, for case I, it is assumed that the external support force P, which develops due to the boundary conditions is large enough to constrain the column and both ends of the column are immovable. The axial force N x does not vary with the axial position x (Simitses [32]). So it can be seen N T x equal to P, due to the axial equilibrium. However, unlike the case of a uniformly heated column, the force P is less than Nx T because the thermal moment Mz T. The column bends away from its original straight configuration due to the thermal moment Mz T, which relieves some of the external support force at the immovable ends. From the analysis, it is known that P is a derived quantity, not a controlled quantity in case I; the controlled quantity is the thermal loading due to the fire; and the response quantity is the mid-span transverse deflection of the column. Denoting the displacements along the x and y directions on the neutral axis as 24

42 Figure 2.3: The relationship between the slope of the deflected angle and the equivalent shear angle γ eq, where θ is the rotation of the cross section due to bending. u 0 and w 0, and θ as the rotation of the cross section due to bending, the nonlinear strain at the neutral axis becomes: ɛ 0 (x) = u 0,x θ2 (2.27) In the following I account for transverse shear following the procedure used in Ref. [33]. In particular, it is set: dw dx = sin(θ + γ eq) (2.28) where γ eq is the equivalent shear angle, i.e., the difference between the slope of the deflected column neutral axis and the rotation angle θ of the cross section due to bending, as shown in Fig It is reasonable to assume the shear modulus, G, varies with temperature in the same manner as the elastic modulus, E. The shear modulus G can be expressed as: [ G(T ) = G 0 1 a 1 ( T T 0 ) + a 2 ( T T 0 ) 2 a 3 ( T T ] 0 ) 3 T g T 0 T g T 0 T g T 0 = G 0 [ 1 a 1 ( T 1 T g ) + a 2 ( T 1 T g ) 2 a 3 ( T 1 T g ) 3 An effective shear modulus, Ḡ is now defined based on the shear compliance as: ] (2.29) l l/2 Ḡ = dy l/2 G(y) (2.30) 25

43 The equivalent shear angle, γ eq, is defined as: γ eq = βp sin θ ḠA (2.31) where β is the shear correction factor which accounts for the nonuniform distribution of shear stresses throughout the entire cross section. Further, the strain at an arbitrary point, ɛ(x, y), can be represented by: ɛ(x, y) = ɛ 0 (x) (y e) d(θ + γ eq) dx (2.32) When the resulting force from Eq.(2.31) is integrated through the section, the resultant should equal P + N T x, i.e., By use of Eq.(2.27), (2.31) and (2.33), it becomes: E av A (u 0,x + 12 ) ( ) ( θ2 + E av e E m1 l A 1 + By use of Eq.(2.25), Eq.(2.34) reduces to: A E(y) ɛ(x, y)da = P + N T x (2.33) ) βp cos θ θ,x = Nx T P (2.34) ḠA u 0,x = N T x P E av A 1 2 θ2 (2.35) which can be integrated over the length of the column subject to the boundary conditions that the ends are restrained in the axial direction, i.e., u 0 (0) = 0 and u 0 (L) = 0. Therefore, the following is obtained: ( ) L Nx T P E av A 1 2 L 0 θ 2 dx = 0 (2.36) which is applicable for the entire loading range of the column and is a constraint equation expressing the condition that the overall change in displacement between the end supports must be zero because the two ends of the beam are immovable, which induces a support load P. 26

44 The bending rigidity, (EI) eq of the column, is likewise influenced by the nonuniform stiffness and is defined by: (EI) eq = A E(y)(y e) 2 da (2.37) The column equation is modified to consider the thermal loading including thermal force and moment and moderately large deflection. Transverse shear is also be included. In doing so, the equations developed in Ref. [33] are modified. The moment including the thermal effect is given by: M = (EI) eq dθ dx M T z (2.38) From equilibrium, taking into account the (compressive) applied force, P at both ends, the moment at any position is given by: M = P w + M 0 (2.39) where M 0 is the moment at x = 0. Differentiating Eq.(2.38) and (2.39) with respect to x and using Eq.(2.28) and (2.31) with the additional assumption that the shear angle is sufficiently small that sin γ eq γ eq and cos γ eq 1 are valid. This assumption results in: ( ) d 2 θ βp (EI) eq dx + P sin 2θ + sin θ + dm z T 2 2AḠ dx = 0 (2.40) At each end (simple supports), we have the moment boundary conditions: (EI) eq dθ dx (0) M T z = 0 ; (EI) eq dθ dx (L) M T z = 0 (2.41) 27

45 Linear Analysis Consider the fact that the temperature variation T 1 is not so high before the polymeric matrix is charred, the deflection of the column due to the thermal force N T x and thermal moment M T z is sufficiently small, therefore it is reasonable to linearize the differential equation Eq.(2.40). Taking into account the fact that the thermal moment, M T z, is independent of x, and linearizing, sin θ θ, results in the differential equation: ( ) d 2 θ βp (EI) eq dx + P 2 AḠ + 1 θ = 0 with boundary conditions given by Eq.(2.41). If we set λ 2 = P βp 2 + (EI) eq (EI) eq AḠ then the solution can be expressed as: θ(x) = M [ z T (1 cos λl) λ(ei) eq sin λl ] cos λx sin λx (2.42a) (2.42b) (2.42c) Notice that the symmetry condition θ(l/2) = 0 is satisfied automatically by Eq.(2.42c). The constraint equation of Eq.(2.36), again linearizing, cos θ 1, becomes: ( ) L Nx T P E av A (M ( z T ) 2 (1 cos λl) L 2[(EI) eq λ] 2 sin λl sin λl 1 ) = 0 (2.42d) λ The vertical deflection of the column is obtained for the linear problem by using Eq.(2.28) and (2.31) and integrating: ( w(x) = 1 + βp ) x θ(ξ)dξ ḠA Substituting Eq.(2.42c) gives: w(x) = M ( z T 1 + βp ) [ (1 cos λl) (EI) eq λ 2 ḠA sin λl 0 sin λx + (cos λx 1) ] (2.42e) (2.42f) Notice from Eq.(2.42f) that the deflection w(x) at each end is zero (as should be), w(0) = w(l) = 0. The mid-point deflection, w(l/2) = w m, is: w m = M ( z T 1 + βp ) [ ] 1 (EI) eq λ 2 ḠA cos(λl/2) 1 (2.42g) 28

46 which tends to infinity for λl = π (the Euler load of the column) If the thermal loading is prescribed via the heat exposure time t, then N T x and M T z can be determined for any time and the only unknown in Eq.(2.42d) is P [or λ from Eq.(2.42b)]. The transcendental Eq.(2.42d) for P can be solved to obtain the relationship between the heat exposure time t and the transverse deflection w. This relationship is obtained for constrained columns only, which means the support reaction force P provided by both ends is large enough to prevent the column moving along the x direction under effects of the thermal force N T x and the thermal moment Mz T. In this case, P, which is obtained by Eq.(2.42d), is the support reaction. For the second case (case II), the constraint condition of immovable supports is released and P is a constant applied load; hence the relationship between the mid-point deflection w m and the applied load P can be obtained from Eq.(2.42g). Note that for zero Mz T, the constraint Eq.(2.42d) reduces to N T x = P, i.e., the solution for a uniform column. 2.3 Results and Discussion To show the influence of the fire-damaged layer on the temperature distribution and mechanical response, numerical results are presented for a burnt column including fire-damaged and undamaged layers and an original column without any fire damage. It is considered that two columns with the same dimensions: one is a burnt column made of two different materials, undamaged (original) layer and fire-damaged layer respectively, which have different material properties as show in Table 2.3 (for the fire-damaged layer, the thermal properties are taken from Dr. Brian Y. Lattimer s experimental measurements, the mechanical properties are given at room temperature). The second column is the original column without a fire-damaged layer. All these columns are assumed to be made of E-glass/Vinyl-Ester. The two columns are shown in Fig. 2.1 and Fig It is assumed that a column of length, L = 0.15 m, thickness, H = m and width b = m. For the burnt column, the thickness 29

47 L T 0 H x Undamaged layer y Q Figure 2.4: Definition of the geometry for a original laminated column under the heat flux Q Table 2.1: Material properties for a burnt composite column Material Condition Property undamaged fire damaged κ i, m 2 /s K i, W/m.K h i, W/m α i, 1/ o C E i, P a G i, P a of the fire-damaged (charred) layer is a = H/4 as shown in Fig In Fig. 2.5, the temperature distribution of the burnt column with a char layer is shown at different times t; the column is subjected to a constant external heat flux Q = 10kW/m 2. It is obvious that the temperature increases with time t. Although part of the resin decomposes and creates a charred (fire-damaged) layer, the temperature in the undamaged layer is lower than that in the damaged layer. In order to present the influence of the fire-damaged (charred) layer and, in particular, the difference of the temperature distributions for the burnt (damaged) and the original (undamaged) columns, I show the temperature distributions for both columns in Fig It is clear that under the same heat flux Q = 5kW/m 2, the temperature 30

48 Charred layer 150 Undamaged layer Figure 2.5: Temperature distribution of the burnt column subjected to a heat flux Q = 10 kw/m 2. T-T 0 original column burnt column 300 s 260 s 220 s 180 s 140 s 100 s 60 s 20 s y / H Figure 2.6: Temperature distributions for the charred and the original columns subjected to a heat flux Q = 5 kw/m 2. 31

49 0.30 Axial constraint force P/P Euler Time, s Figure 2.7: Axial constraint force, P con, vs. exposure time t for the burnt column subjected to a heat flux Q = 10 kw/m 2. in the undamaged layer of the burnt column is much lower than the temperature in the original column without the fire-damage (charred) layer. The reason for such a difference is that the char acts as an insulating front. Furthermore, the net temperature variation in the burnt column is smaller than that in the original one, which has a direct influence on the resulting thermal moment and the transverse deflection of the column. Figure 2.7 shows the axial constraint force, P con as a function of time t for the burnt column, which is pinned at both ends (immovable) and subjected to a heat flux Q = 10 kw/m 2. The force P con is normalized with the Euler critical load, P Euler, of the column at room temperature, which is assumed to be a constant. In Fig. 2.7, a quasi-static assumption is made, so the temperature distribution in the undamaged layer can be determined at each fixed time from Eq.(2.21a). It can be seen that 32

50 0.008 Mid-point deflection wm /L Time, s Figure 2.8: Mid-point transverse deflection, w m, vs. exposure time t for the burnt column subjected to heat flux Q = 10 kw/m 2 (constrained, immovable ends case). the axial constraint force increases with time t. However the slope of the curve decreases for t > 240 s. The variation of the axial constraint force P con with time is nonlinear, which is due to the material properties degradation and temperature increasing simultaneously with exposure time. The response of the burnt column is governed by two factors: one is the thermal force and the thermal bending moment, which both increase with exposure time; the other is the change in material properties e.g., E av and Ḡav, which decrease with exposure time. These two factors compete with each other and result in a nonlinear variation of the axial constraint force P. Based on the axial support force P con, the mid-point deflection w m is calculated from Eq.(2.42g). Fig. 2.8 shows the variation of the mid-point deflection w m with exposure time t, where w m is normalized by the length of the column L. It is obvious that w m increases nonlinearly with exposure time. As shown in Fig. 2.8, the mid-point 33

51 5 Thermal moment, M T z, N.m Time t, s Figure 2.9: The thermal moment, M T z, vs. exposure time t for the burnt column subjected to heat flux Q = 10 kw/m 2 (constrained, immovable ends case). deflection is very small compared with the length of the column, which indicates the cross section rotation angle θ is very small (less than 1 o ). Thus, the deflection w of the constraint column under the heat flux Q = 10 kw/m 2 is sufficiently small that the linear assumption used to simplify Eq.(2.40) is valid. From the derivation of Eq.(2.42g), the mid-point deflection is related to the thermal induced bending moment Mz T. To understand the variation of w m, it is helpful to show the variation of the thermal moment in Fig. 2.9 (the deflection w is determined by the thermal bending moment Mz T ). It can be seen the thermal moment increases with exposure time t; after reaching a peak value, it begins to decrease, but the direction of the moment does not switch. The thermal moment is determined by the temperature distribution, T 1 and the elastic modulus E. At the beginning of the 34

52 Mid-point deflection w m, mm 1.2 P = 250 lb P = 375 lb 1.0 P = 500 lb P = 750 lb P = 1000 lb Time t, s Figure 2.10: Mid-point deflection, w m, vs. exposure time, t, under a constant applied axial force, P (ends free to move axially, unconstrained case). Each curve represents the column response under a constant heat flux, Q= 10 kw/m 2 and axial force P. heat exposure, the elastic modulus E does not change very much as shown in Fig. 2.2; thus, the temperature variation dominates the thermal moment, which increases with exposure time. As the exposure time increases further, E decreases rapidly as the temperature approaches the glass transition temperature T g ; M T z is influenced by both T 1 and E and decreases from its peak value near 175 s. In Fig and 2.11, the mid-point deflection, w m, vs. exposure time, t, is shown for different levels of the constant applied axial force, P. Each curve represents the column response under a constant heat flux, Q = 10 kw/m 2 and a constant axial force P. The end of the column can move freely in the axial direction (unconstrained 35

53 Mid-point deflection w m, mm P = 250 lb P = 3000 lb Time t, s Figure 2.11: Mid-point deflection, w m, vs. exposure time, t for the column with axial force P = 250 lb and 3000 lb respectively under a constant heat flux Q = 10 kw/m 2 for comparison (ends free to move axially, unconstrained case). case). In this case, the constraint boundary conditions are released, and the constraint condition Eq.(2.36) is not applicable; instead, P is a variable now. This case differs significantly from the constraint case. In Fig and 2.11, for each curve, P is kept constant from the beginning to the end of exposure, which is similar to the experimental arrangement described in Sec The mid-point deflection, w m, can be determined from Eq.(2.42g). It can be seen that the mid-point transverse displacement, w m, increases nonlinearly with the heat exposure time for the column under the constant axial force P. For higher applied axial force P, the rate of variation of the mid-point deflection increases with heat exposure time (Fig. 2.11). The reason 36

54 for the behavior can be explained by Eq.(2.42g). The column deflection is initially governed by the thermal moment Mz T. The initial deflection induces a mechanical moment P w in Eq.(2.39) under the axial compressive load P. With increasing exposure time, the deflection increases, and the moment P w increases, which leads to an instability of the deflection. With small load, the thermal moment and the moment P w control the column response; however with a much higher load, e.g., P = 3000 lb, the moment P w dominates the behavior of the column and the instability happened quickly. For a very high compressive load (e.g., P = 3000 lb in Fig. 2.11), the trend of the mid-point deflection is very similar with the experimental result shown in Fig. 3.20, which shows the behavior of a column for a constant heat flux Q = 50 kw/m 2 and an axial compressive load P = 500 lb. Although the load in the experiment is not large (P = 500 lb), the heat flux is much higher (Q = 50 kw/m 2 ) than that in the analysis. Thus, the material degradation rate and char formation rate are much higher. Since the thermal moment induced deflection w dominates, even with low applied compressive load P, the moment term P w is large for the column in the experiment and causes instability as well, as shown in Fig Figure 2.12 gives plots of P vs. w m at each fixed time t. The relationship between P and w m is determined from Eq.(2.42g). The end of the column can move freely; hence, the constraint boundary conditions are released, and the initial w m can be calculated from the linear analysis. In Fig. 2.12, the applied axial force is normalized by the Euler critical load P Euler at room temperature and w m is normalized by the length of the column. This figure shows that at the beginning of heat exposure (e.g., t = 20 s curve), the temperature of the column is relatively low and the axial force P increases initially with only a small bending deflection; as P approaches P Euler, the deflection increases rapidly with P becoming asymptotic to P Euler. The bending moment influence is insignificant at the beginning of heat exposure. With increasing time, the load-deflection curve bends over much earlier in the response, and the 37

55 P/ P E value t = 20 s t = 60 s t = 140 s t = 180 s t = 220 s t = 100 s 0.6 t = 260 s 0.4 t = 300 s 0.2 W m / L Figure 2.12: Applied axial force vs. midpoint transverse deflection for a burnt column subjected to a heat flux Q = 10 kw/m 2 at different times t (ends free to move axially, that is, unconstrained case). 38

56 Axial constraint stress con xx, MPa original column burnt column Exposure time t, s Figure 2.13: Axial constraint stress σ con xx vs. time for the burnt and the original column subjected to heat flux Q= 5 kw/m 2 (constrained, immovable ends case). beam behavior is the same as that of an imperfect column. Eventually, in all cases, the axial force approaches P Euler as the midspan transverse deflection becomes large. The temperature variation through the thickness has effectively an analogous role for the column as that of an imperfection on a mechanically loaded column. That is, both a temperature change through the thickness and an initial imperfection would cause a moment that bends the column from the instant that any load, whether thermal or mechanical, is applied. From Fig. 2.6, it can be seen the temperature in the undamaged layer of the burnt column is lower than that of the original column without the fire-damaged layer. It is helpful to compare the axial stress for the burnt and the original column. The constraint axial stress σ con xx vs. time for both the original and the burnt columns, is shown. The two columns are constrained at both ends and exposed to a heat flux 39

57 Q = 5 kw/m 2. For the burnt column, with 1/4 of the entire thickness fire-damaged (char layer), the axial constraint stress is lower than in the original column, although the mechanical properties of fire-damaged material are neglected in the analysis. In addition, it is observed that for the original column without a fire-damaged layer, the axial constraint force increases with time t for t 280 s; but for t > 240 s, P con decreases with exposure time. The variation is non-linear, which is due to the material properties degrading nonlinearly with exposure time, as well the fact that the ends are restrained. Therefore, beyond a certain level of deformation, the structure starts to pull from the ends rather than push against the ends. However for the burnt column, this variation does not occur. 2.4 Conclusions The thermal bending problem of a burnt, axially restrained composite column or with an axial applied force was analyzed. The mechanical response of the firedamaged (charred) layer was neglected in the analysis. In order to understand the influence of the fire-damaged layer (char layer) on the temperature distribution and the thermal buckling response, the same problem for the original (unburnt) column was also solved. A Quasi-static assumption is made for the buckling response. The heat flux was assumed to be low enough that the resin material did not decompose before 300 s; the structure had enough time to respond and be in equilibrium. Since a linear analysis was used to simplify the governing equations, validity of the solution was checked from the numerical results. From the results the following can be concluded: 1. The temperature in the undamaged layer of the burnt column is much lower than the original column due to the thermal protection of the fire-damaged layer; and the net temperature variation in the undamaged layer is lower. 2. For a column under heat exposure with constraint, the response is the same 40

58 as that for an imperfect column. It can be proven that the temperature distribution through the thickness acts in an analogous role as that of an imperfection on a mechanically loaded column. 3. If both columns are restrained at both ends, the axial restraint stress of the burnt column is less than that of the original column. 4. For a column under a high constant applied axial force, P, without constraint at the ends, the rate of increase in the mid-point deflection increases with heat exposure time. In addition, instability of the column happened quickly. 41

59 CHAPTER III EXPERIMENTAL WORK According to the prediction of the simplified thermal buckling model, it was concluded that because of existence of the thermal bending moment, for a column under a high constant applied axial force, the deflection increases with the heat exposure time and the rate of variation increases with heat exposure time. Instability of the column happened quickly if the column is under a high compressive axial load as shown in Fig Also because of the thermal moment, for the column under heat exposure with constraint, the response is the same as that for an imperfect column. It can be proven that the temperature distribution through the thickness induces the thermal moment and it acts in an analogous role as that of an imperfection on a mechanically loaded column. The purpose of experimental work in this chapter is to verify the predication of the thermal buckling model qualitatively; on the other side, it is to characterize the failure time and failure mode for the composite column under simultaneously thermal and mechanical loadings. 3.1 Post-Fire Compressive Behavior of Fiberglass Reinforced Polymeric Composite Columns There is a significant amount of literature that addresses the effects of fire intensity on the fire ignition time and heat release rates of polymeric composite materials as we reviewed in the section 1.1. These studies show that polymeric composites could ignite quickly when subjected to heat fluxes greater than approximately 50 kw/m 2. With ignition, a layer of char forms at the surface; the char layer depth increases with increasing heat flux and exposure time. During and after a fire, the mechanical 42

60 Side 100 mm 12.5 mm y Top 25.4 mm x Figure 3.1: Test coupons with [(0/45/90/ 45/0) s ] 2 ply layup were machined from a composite panel with a nominal thickness of 12.5 mm. properties of polymeric composites can be severely degraded due to combustion of the resin and the conversion of load bearing material to a weaker layer of char. In recent work by Mouritz et al. [10, 11, 12] with fiber-reinforced thermoset polymeric composites it was observed that the tension, compression, and flexure properties decreased rapidly with increasing heat flux and heat-exposure time. These decreases have been modelled using two-layer theory [13] that assumed negligible strength and stiffness within a char layer. The goal of the initial experimental investigation was to characterize the residual compressive strength and failure mode of a fiberglass-reinforced polymeric composite after a high heat flux exposure in a cone calorimeter. A glass/vinyl-ester composite laminate was used in the experiments. This composite is representative of the facesheet material used in Naval sandwich composites. Specimens were exposed to various heat fluxes in the cone calorimeter followed by room temperature compression testing in a servo-hydraulic load frame. These experiments were performed to determine the degree to which how heat flux intensity and exposure time affect the residual compressive behavior of the composite. 43

61 Table 3.1: Typical properties of fiberglass-reinforced vinyl-ester composite laminate Properties Thermal diffusivity (m 2 /s) κ Thermal conductivity (W/m o C) K Thermal expansion coefficient (1/ o C) α The compressive Young s modulus (GPa) E 20.6 The shear modulus (GPa) G Material, experimental apparatus and procedure Test sample geometry. Fiberglass-reinforced vinyl-ester matrix (Derakane 510A) composites with twenty plies were obtained from Seemann Composites Inc. in the form of a mm (24 inch) mm (24 inch) panel. The panel, which had a nominal thickness of 12.5 mm thick with a fiber volume fraction of 48 %, had a [(0/45/90/ 45/0) s ] 2 ply layup. Test samples, which is shown in Fig. 3.1, were machined dry from the panel using carbide tooling. The material properties of the laminate are listed in Table 3.1. The test sample had an overall length of 100 mm and a cross section of 12.5 mm 25.4 mm. Fire test apparatus. In order to perform post-fire mechanical tests, the test samples were exposed to different heat flux intensities using a cone calorimeter equipped with a 5000 W electric heater, as shown in Fig. 3.2a and b. The electric cone heater provided a uniform heat flux of 100 kw/m 2 and lower for samples with a maximum surface area of 100 mm 100 mm. In the current investigation a sample length of 100 mm and width of 25 mm was selected to facilitate post-fire compressive testing. The test samples were placed on top of a low density alumina-silica plate located beneath the cone-heater (Fig. 3.2a). The sides of the test samples were insulated from the heat source by using alumina-silica plates placed along both specimen edges Gulfport, MS Information provided by Dr. Brian Lattimer, Hughes Associates. Fire Testing Technology Limited, P.O. Box 116, East Grinstead, West Sussex, RH19 4FP, U.K. 44

62 (Fig. 3.2b). The distance between the surface of the 5000 W cone heater and the surface of the test samples was fixed at 25 mm. In the first group of experiments, samples were exposed to a heat flux of 50 kw/m 2 for exposure times ranging from 325 s to 1800 s. In a second group of experiments, samples were exposed to incident heat fluxes typical of low intensity fires (25 kw/m 2 ) and high intensity fires (100 kw/m 2 ); a fixed post-ignition time of 325 s was selected as being representative of the response time for a fire-fighting crew to begin extinguishing a fire on a small-to-medium sized naval vessel. For all experiments, an electric spark source was used to ignite the gaseous compounds that form during decomposition of the polymer matrix. For both specimen groups, reductions in compressive strength and details concerning the failure mode were related to heat flux intensity and exposure time. Post-fire compression testing. Monotonic compression testing of samples after exposure in the cone calorimeter was conducted on an MTS Model 810 servo hydraulic load-frame. The ends of the samples were fixed between two rigid grips designed for the compressive loading experiments, as shown in Fig The ends of the samples fit within a 4 mm deep cavity in the center of the grip; the bottom of the cavity had a hardened steel insert. The insert for the cavity could be adjusted to clamp the specimen ends over the 4 mm embedded length. To eliminate the effect of machine compliance on the measured axial displacement, the axial displacement of the test samples was measured using an axial LVDT mounted between the grip faces. It is well known that axial compressive loading can induce buckling instability of long or slender beams. For the specimen dimensions used in the present investigation, the original ratio of length to width would not be expected to cause buckling of the unexposed composite samples (this was verified by testing of an unexposed test sample). However, because a lower-stiffness char layer formed during heat exposure, MTS Systems Corp., Minneapolis, MN 45

63 (a) 5000 W Cone Heater specimen igniter insulation ceramic Q 100 mm 12.5 mm 25.4 mm (b) Figure 3.2: (a) Cone calorimeter arrangement showing position of 5000 W electric cone heater used to generate single-sided surface heat fluxes in the range of 25 kw/m 2 to 100 kw/m 2. (b) Close-up showing sample position beneath surface of cone heater. 46

64 Figure 3.3: Experimental arrangement used to perform monotonic compressive tests on a servo hydraulic load frame. The grip faces measure 100 mm square. The specimen ends fit within a 4 mm deep cavity and are in contact with a hardened steel insert. The axial LVDT measures displacement between the grip faces and the transverse LVDTs are located at the mid-points of the specimen length and width. All tests were performed at a displacement rate of 1 mm/min. 47

65 lateral displacement and bending were possible failure modes for the fire-exposed samples. For this reason, LVDTs were used to measure the transverse displacements on either side of the specimen. The LVDTs were installed at the mid-point of the unburnt and burnt sides of the specimens (see Fig. 3.3). This data was also required for future analytical modelling used to determine the post-fire deformation behavior of fire-exposed composites. All compression tests were performed at room temperature under displacement control at a nominal displacement rate of 1 mm/min. During the compression tests, a video camera (30 Hz Frame rate) was used to continuously record the deformation and failure mode of the sample Experimental results and discussion Fire damage Char depth The high heat flux that the samples were exposed to in the cone calorimeter caused considerable charring, in particular for heat fluxes of 50 kw/m 2 and above. The thickness of the heat damaged (charred) layer was estimated by optical microscopy and is plotted versus exposure time for samples exposed to a fixed heat flux of 50 kw/m 2 in Fig As would be expected, the char thickness increases and the growth rate decreased with increasing exposure time. As discussed in detail by Mouritz and Mathys [11], the rate of char formation was controlled by the rate of transport of oxygen to the combustion front, which slowed with increasing char thickness. The data in Fig. 3.4 can be fit to a first order exponential model relating char thickness d to post-ignition heat exposure time, d = e t t 0 a (3.1) where d is the char thickness, t is the total heat exposure time, t 0 is the ignition time and the constant a is associated with the material (a = s for this composite). If the exposure time was sufficiently long (> 1200 s), the char layer penetrated completely through the specimen thickness. Similar phenomena were observed for 48

66 Normalized char layer thickness, % Heat flux Q: 50 kw/m 2 Model: 1st order Exp d = e -(t-t 0 )/a +1.0 a = s Post ignition time t- t 0, s Figure 3.4: Normalized char thickness versus exposure time for a heat flux 50 kw/m 2. The post ignition time refers to the elapsed time after surface ignition is detected (t 0 = time to surface ignition). Beyond approximately 800 s, the char layer depth penetrates the entire specimen thickness, which we define as 100 % charred. 100 Normalised char layer thickness, % Exposure time: post ignition 325 s 40 Model:Power law equation d = a (Q-b) c 20 a b c Heat flux Q, kw/m 2 Figure 3.5: Normalized char thickness versus surface heat flux Q for a fixed postignition exposure time of 325 s. 49

67 glass-reinforced isophthalic polyester laminates [11]. In Fig. 3.5 the normalized char thickness d versus the incident heat flux Q is shown for the group of samples subjected to heat fluxes between 25 kw/m 2 to 100 kw/m 2 with a fixed post-ignition time of 325 s (i.e., the tests were terminated 325 s after ignition was detected). The char layer thickness increases with increasing heat flux level and the data can be represented by a power-law equation Post-fire compressive properties Unexposed specimen The compressive stress-strain behavior of an unexposed original composite sample is shown in Fig The nominal compressive stress is determined by the load divided by the original cross sectional area and the corresponding engineering strain is determined by the axial displacement from the grip-mounted LVDT, divided by the original length of the sample (nominal length = 100 mm). As noted earlier, the grip mounted LVDT eliminates the elastic compliance in the load frame and grips and provides a more accurate compressive modulus. Prior to failure, the compressive response is linear with a compressive modulus (E 0 ) of 17.4 GPa. Near the failure load, non-linear compressive response is observed. The compressive stress at failure (σ 0 ) was approximately 297 MPa. The failure mode involves kinking of the glass fiber tows with no obvious signs of global buckling. Effect of heat-exposure time at a constant heat flux The effect of exposure time on post-fire compressive behavior is shown in Fig. 3.7 for samples with heat-exposure times from 0 s to 1800 s at a constant heat flux of 50 kw/m 2. The post-fire compressive failure load decreases with increasing exposure time. For all samples, the initial compressive stress-strain behavior is approximately linear; close to the failure load, nonlinear response occurs. In Fig. 3.8a and b, the normalized post-fire compressive strength σ c /σ 0 and normalized compressive modulus 50

68 Figure 3.6: Plot of axial compressive stress σ versus axial compressive strain ε for a sample without heat exposure. The average tangent modulus (between 0 and 200 MPa) was 17.4 GPa and the failure strength was approximately 297 MPa. 51

69 Figure 3.7: Effect of heat exposure time (0 to 1800 s) on the residual compressive stress-strain behavior of fiberglass/vinyl-ester composites, which had been exposed to a heat flux of 50 kw/m 2. For an exposure time of 600 s, the residual strength was approximately 14 MPa; after 900 s, the residual strength was below 4.0 MPa. 52

70 (a) (b) Figure 3.8: a,b. (a). Normalized post-fire compressive strength σ c /σ 0 versus heat exposure time t. The data trend can be approximated by a first order exponential decay curve. The average compressive strength of unexposed samples (σ 0 ) was 297 MPa. (b). Normalized post-fire compressive modulus E c /E 0 versus heat exposure time t. The data trend can be approximated by a first order exponential decay curve. E 0 = 17.5 GPa. 53

71 0 s 325 s 450 s 600 s 1200 s 12.5 mm a b c d e Figure 3.9: Digital images showing failure modes of samples which had been subjected to a heat flux 50 kw/m 2 for exposure times of 0 s to 1200 s. As the exposure time increases, the failure mode switches from shear failure (fiber kinking) of the undamaged (without char) layers to global buckling (for 600 s and longer exposure times). E c /E 0 are plotted versus heat exposure time t (the data is normalized by the compressive strength and modulus of an unexposed sample). The compressive strength drops significantly after heat exposure; for exposure times exceeding 900 s, the residual strength of the samples decreases to approximately 4 MPa. From Figs. 3.7, 3.8a and b, the normalized char layer thickness, compressive strength and modulus all decreased with increasing exposure time t; as noted above, in all cases data trends can be fit to a first order exponential decay model approximately. Thus, if the total exposure time is known, the char layer thickness, post-fire residue strength and modulus can be predicted. The different compressive failure modes of the samples which had been exposed to a heat flux 50 kw/m 2 for exposure times from 0 s to 1800 s, are shown in Fig. 3.9ad. The sample without heat exposure failed due to kinking of the glass fiber tows under compressive loading. As exposure time increases, the mechanical properties and 54

72 burnt side burnt side burnt side burnt side 12.5 mm a b c d Figure 3.10: Digital images showing progressive compressive deformation of fiberglass-reinforced vinyl-ester specimen, which had been exposed to a surface heat flux of 50 kw/m 2 for total exposure time 600 s. failure modes change due to thermal degradation of the resin matrix. For an exposure time of 325 s (Fig. 3.9b), the charred layer on the heat exposed side was delaminated at the beginning of loading due to resin decomposition; the sample failed due to kinking of the glass fiber tows without obvious global buckling, which was the same with the specimen without heat exposure. As the exposure time increased, the failure modes changed. For an exposure time of 450 s (Fig.3.9c), global buckling failure was observed. As the exposure time increased to 600 s (Fig.3.9d), global buckling was observed obviously and the specimen failed due to buckling. For the sample with a heat exposure time 1200 s (Fig.3.9e), the char layer penetrated the entire specimen thickness; the residual strength of this sample was 4.0 MPa. At 1800s, the compressive strength had decreased to approximately 1.5 MPa. For all samples, the glass-fibers remain embedded in the char layer (the various plies were still held together, albeit weakly, by the char), under axial compression, the composite does retain a limited 55

73 amount of strength and stiffness. For example, even after 1200 s of exposure at 50 kw/m 2, a 1.5 kn load was required to fail the 12.5 mm x 25 mm cross section of the composite. Fig. 3.10a-d shows the progressive compressive deformation of a sample (50 kw/m 2, t = 600 s) during the monotonic compressive test. Local buckling, attributed to delamination growth in the interfacial region between the charred layer and undamaged region of the sample occurred (as shown in Fig. 3.10b). For the test conditions imposed, global buckling was the final failure mode. Effect of heat flux with a constant post-ignition time. The effect of heat flux on the post-fire compressive properties was investigated. In a second series of experiments, composites columns were exposed to heat fluxes from 25 kw/m 2 to 100 kw/m 2 with a constant post ignition heat exposure time of 325 s, followed by post-fire monotonic compressive tests at room temperature. The post-fire compressive strength and modulus decreased with increasing heat flux. For example, at 100 kw/m 2, the post-fire compressive strength had decreased to approximately 15 MPa. The different failure modes of the samples which had been exposed to heat fluxes from 25 kw/m 2 to 75 kw/m 2, and a post-ignition exposure time of 325 s, are shown in Figs. 3.11a-c. The failure modes for heat fluxes of 25 kw/m 2 to 50 kw/m 2 are similar. The charred layer delaminated from the unaffected material at the beginning of loading; the samples failed by fiber kinking [34] in the undamaged layer without obvious global buckling. However, the post-fire mechanical response of the sample tested at a heat flux of 75 kw/m 2 is different with those exposed to heat fluxes from 25 kw/m 2 to 50 kw/m 2 for 325 s post-ignition time. The progressive deformation of the specimen is shown in Figs. 3.12a-d. At the beginning of loading, the charred layer delaminated (as shown in Fig. 3.12b); due to delamination in the interfacial region, local buckling and delamination growth under the compressive load were observed clearly. The sample failed by global buckling eventually. 56

74 (a) (b) burnt burnt burnt (c) side side side burnt side burnt 12.5 side mm 25 kw/m 2 50 kw/m 2 75 kw/m 2 B Figure 3.11: Photographs of the failure modes of samples exposed to heat fluxes of 25 kw/m 2, 50 kw/m 2 and 75 kw/m 2 for a fixed post-ignition exposure time of 325 s. burnt side a b c d burnt side burnt side burnt side 12.5 mm Figure 3.12: Photographs of deformation of the sample, which had been exposed to a heat flux of 75 kw/m 2 for a post-fire ignition exposure time of 325 s. 57

75 Transverse displacement and Southwell plot. Buckling failure was observed in the samples after they had been exposed to the heat fluxes. Buckling failure can be observed for the specimens as shown in Figs 3.9d, 3.10d, 3.11c and 3.12d. In order to measure the transverse deflections of the samples, two transverse LVDTs were installed in later tests as shown in Fig The specimen with buckling failure can be treated as an imperfect column in the compressive tests. Although the material properties are not uniformly distributed along the thickness, the rigid loading fixture can provide uniform axial compressive displacement, which is related with the engineering strain by ε x = u x l 0, therefore the axial compressive stress was not uniformly distributed along the thickness, and the resultant compressive force was applied at the position of the neutral axis. The behavior of the post-fire column with non-uniform material properties distribution under a uniform axial compressive strain is the same as that of an imperfect column under an axial compressive force applied at the neutral axis. Southwell [35] noted that the equations developed for the theory of a simple column with hinged supports could be used to predict the Euler load of a real column by the use of a load-deflection plot made for loads smaller that the Euler load itself. This technique has been applied to numerous structural forms other than simple columns. The mid-point deflection and load can be written as: δ = P cr δ P + A 1 (3.2) Based on the Southwell plot and its generalization [36, 37], we can obtain the theoretical Euler critical load of a burnt column. Fig shows the relationship between δ/p and the mid-point deflection δ for the test specimen exposed to 75 kw/m 2 with a post-ignition exposure time of 325 s. By a linear fit of the data, the theoretical Euler load can be obtained. For instance, the theoretical Euler load P cr = 7796N for the specimen exposed to the heat flux 75 kw/m 2 for a post-ignition exposure time of 325 s, is consistent with the failure load P failure = 8011N measured 58

76 Figure 3.13: The Southwell plot in the compressive test. Therefore if it is known that the relationship between δ/p and δ is linear through experimental measurement, the failure of the specimen is governed by buckling and the Euler buckling load can be obtained by use of a Southwell plot. However, if the linear relationship can not be determined in the Southwell plot, the failure of the specimen is complicated and could include buckling, fiber kinking and so on as shown in Figs. 3.11a and b. Based on results obtained from compression testing of single-sided high heat flux exposure of vinyl-ester/fiberglass composites, the following remarks can be made: (1) Char layer depth is a function of fire intensity. For instance, the char depth was approximately 6.25 mm after 325 s exposure at 50 kw/m 2. After 1200 s, the char layer extended completely through the specimen thickness. (2) The compressive behavior and failure modes are strongly influenced by heat flux intensity and total exposure 59

77 time. For a heat flux of 50 kw/m 2 with an exposure time of 600 s, the residual strength was approximately 14 MPa; after 900 s, the residual strength was below 4 MPa. The residual compressive strength and Young s modulus decrease with increasing heat flux intensity and heat exposure time. (3). Based on the experiments performed, it is shown that the compressive strength and modulus are very low within a char layer and can be negligible as a simplification, which is consistent with the two-layer model proposed by Mourize[13] (4). However the small delamination cracks in the interfacial region between the char region and unburnt region can not be neglected for the post-fire properties of the burnt composite column; the assumptions that the mechanical properties of the unburnt region are constant throughout and are the same as the mechanical properties of the original composite are oversimplified. (5). When the char layer depth is small, the failure is dominated by fiber kinking in the undamaged portion of the composite, and no obvious deflection can be observed in the compressive tests. As the char layer depth increases, obvious transverse displacement occurs on the undamaged side of the specimens with local and global buckling response. (6). if it can be determined that the relationship between δ/p and δ is linear through experimental measurements, the failure of the specimen is governed by buckling and the Euler buckling load can be obtained by a Southwell plot. This approach can be used to predict or measure the compressive failure load of burnt specimen. On the other hand, if the relationship is not linear, failure is governed by other modes, including fiber kinking, buckling, delamination growth and so on. 60

78 3.2 Integrity of Fiberglass Reinforced Polymeric Composite Column Under Simultaneous High Heat Flux Exposure and Compressive Loading The effects of heat flux intensity and exposure time on the post-fire mechanical behavior of fiberglass reinforced polymeric composite column were discussed in Section 3.1. These studies showed that polymeric composite columns, subjected to surface heating, can quickly ignite. During heat exposure, a layer of char (from decomposition of the polymer matrix) forms at the surface; the depth of the char layer increases with both heat flux intensity and total exposure time. The compressive behavior and failure modes of a burnt column are strongly influenced by heat flux intensity and total exposure time. The compressive strength and compressive modulus decrease dramatically after heat exposure. However, very little information is available concerning the more realistic situation of simultaneous mechanical loading and fire exposure on overall structural response and time-to-failure. In a pioneering study, Gibson et al. [18] investigated the effects of compressive and tensile loading on the failure time of composite specimens subjected to surface heat fluxes between 25 and 75 kw/m 2. For a 0/90 fiberglass-reinforced vinyl-ester matrix composite panels, the time-to-failure was found to be strongly influenced by the heat flux intensity and applied load level. The purpose of the present study was to develop an experimental approach that could be used to study the mechanical response of materials simultaneously exposed to high heat flux surface heating and compressive axial loading. To meet goal, a mechanical loading device was designed and installed on an electric cone calorimeter that was capable of producing controlled surface heat fluxes up to 100 kw/m 2. In many practical applications, composites will be subjected to mechanical compressive loading (e.g., decks and aircraft structures). Thus, it is important to include 61

79 simultaneous compressive mechanical loading during fire testing. In order to analyze the response of the test samples and compare the experimental data with theoretical results, the axial displacement and mid-point transverse displacement of specimens were measured during the experiments Material, specimen geometry and experimental apparatus Material, specimen geometry, and grips The test coupons were machined from the same panel as that described in the post-fire experiments (Sec ). Machining was performed without a liquid coolant using carbide tooling. The specimen geometry is the same with that used in the post-fire compressive tests as shown in Fig The top and bottom surfaces of the specimen were left in the as-received condition of the panels. The x y coordinates refer to axial and thickness directions. Two different specimen lengths, 150 and 100 mm, were utilized in the experiments. For both specimen lengths, the nominal thickness was 12.5 mm and the width was 25.4 mm. In the experiments, one of the broad faces (25.4 mm dimension) was exposed to the heat source. Grips for specimen loading were machined from a Ni-base alloy (Inconel 718). The grips have rectangular, flat-bottomed cavities to hold the specimen ends (the cavities were machined by electro-discharge-machining). Each grip has a fixed cavity depth of 25 mm. For the 150 mm long specimens, the heated and clamped length was 100 mm (this corresponds to the distance between the grip faces). For the 100 mm long specimens, inserts were placed in the grip cavities to provide a heated specimen length of 74 mm. To minimize heat loss from the specimen to the grips, the portion of the specimens located within the grips was insulated with a thin ( 0.4mm) ceramic layer (Zircar Inc., Alumina Cement). Inconel 718 shims between the sides of the specimen and the grip cavity were used to firmly fix the specimen within the grips 100 mm was the maximum length over which uniform heating could be obtained in the cone calorimeter. 62

80 and minimize any transverse specimen movement and rotation in the grips. For the fixtures used, the specimens can be treated approximately as clamped end conditions in a theoretical analysis. Experimental apparatus The cone calorimeter described earlier was used as the heat source for the combined high heat flux exposure and compressive loading tests. In the present investigation, the region of uniform heat flux limited the maximum length of test specimens to 100 mm. Although larger specimen widths were possible, a 25.4 mm specimen width was chosen to reduce the size of the test fixtures and actuator required to apply the axial compressive load. To minimize heating of the specimen sides, a thin (0.3 mm mm thick) alumina ceramic coating was applied to both sides of the specimens (12.5 mm 150 mm faces). The initial trial tests were undertaken to determine the effect of surface insulation on time-to-failure. Several experiments were conducted using 150 mm (100 mm heated length) long specimens with and without surface coating on the unexposed specimen surface (bottom surface 25.4 mm 150 mm). The experimental results showed that coating the unexposed surface of the specimen did not significantly affect time-to-failure or failure mode. Therefore, all remaining experiments discussed in Sec. 3.2 were performed with specimens that were coated only on their sides (12.5 mm 150 mm faces). For all tests, the distance between the exit of the cone heater and the specimen surface was maintained at 25 mm. In the experiments, the applied heat flux varied from 25 to 75 kw/m 2. These heat fluxes represent the heat flux of typical low, low-to-medium, and medium-to-high intensity fires on transportation vessels. Prior to testing, a heat flux meter was used to verify the heat flux applied to the surface of the specimens. To investigate the effect of simultaneous axial compressive loading and high intensity surface heating, a load frame with pneumatic actuator was designed to fit directly beneath the cone heater as shown in Fig The load frame and frame 63

81 Figure 3.14: Schematic of loading module used to mechanically load specimens during high heat flux thermal exposure in the cone calorimeter. An LVDT was used to measure axial displacement of the test specimens. The cooling manifold is used to keep linear bearings and the load cell at constant temperature. 64

82 (a) Grip Cone heater Specimen Grip Connected wth load cell Transverse Connected LVDT wth air cylinder (b) (c) load cell mechanical stop mechanical stop cooling manifolds cooling manifolds linear bearing H-block linear bearing Figure 3.15: (a) A close-up view of the specimen and grip arrangement used for the combined fire and compression tests. (b) A load cell mounted at one end of the load frame was used to monitor specimen load level. (c) H-block and linear bearings races. 65

83 used to attach it to the cone calorimeter, were machined from 6061 aluminum. A close-up view of the specimen and grip arrangement is shown in Fig. 3.15a. A load cell, mounted at one end of the load frame, was used to monitor specimen load level (Fig. 3.15b). To minimize transverse and axial deformations that can occur with low stiffness load cells, a load cell with very high axial and lateral stiffness was utilized (110 kn capacity, Interface Inc., Model 120AF- 25K). The grip at the left end of the specimen was rigidly attached to the load cell. As shown in Fig. 3.15c, the grip at the right end of the specimen was attached to an aluminum H-block that was mounted to a linear bearing system; this arrangement permitted axial motion only. For compressive loading, the end of the pneumatic actuator rod contacted the H-block through a spherical pad. Although the specimen grip could be connected directly to a pneumatic or hydraulic actuator, the use of a linear bearing arrangement to axially guide the H-block provided several important advantages: First, the actuator is isolated from the hot portion of the apparatus; second, the linear bearing mounts and the H-block connecting the bearings can be readily adjusted to ensure precise specimen alignment (specimen alignment is obtained by use of a strain gage instrumented steel bar of the same dimensions as the test coupons); third, the connecting members between the linear bearing rails permit various end-conditions to be used during the tests (e.g., the effect of pinned end and eccentric loading on buckling behavior can be studied). For example, to study the effect of fixed-end clamped condition on specimen failure time, the pneumatic cylinder used for specimen loading can be removed and replaced by a threaded rod (between the end of the load frame and the H-block). This experimental arrangement would allow fixing a specimen between two approximately rigid ends and could be used to examine the effect of thermally generated axial compressive load on failure time. Cooling manifolds, connected to an isothermal water bath (maintained at 25 o C ± 1 o C), were used to keep the linear bearings and the load cell at a constant temperature. As noted earlier, the ends of the composite specimens fit firmly into 66

84 flat-bottom cavities. In addition to the high temperature capability of the Ni-base grips, the high elastic modulus of Ni-base alloys minimizes lateral deflection of the load train during axial loading, this is of particular concern since the end-condition (e.g., pinned, free, clamped, etc.) of a composite structure or test specimen will influence the buckling behavior. For all experiments, a LVDT was used to measure the axial displacement of the specimen. The tip of the axial LVDT was in contact with the cold-end of the H-block. However, based upon analysis of the failure modes observed during initial trial experiments, it was decided to include a second LVDT for several experiments to measure the mid-point transverse deflection. As discussed later, this information also provides insight into the existence of a thermally generated moment. For the tests that included transverse displacement measurements, a 100 mm long hollow Al 2 O 3 ceramic rod (low heat conduction and thermal expansion) was used between the mid-point of the unheated (backside) specimen surface and the LVDT. Test procedure One of the goals of the experiments was to determine the material response for exposure times beyond 300 s (which is a typical response time to ship board fires). For this reason, compressive load levels in the range of 1.11 to 3.34 kn were selected to provide specimen failures that would include the desired time range. The experiments were performed using surface heat fluxes of 25, 50, and 75 kw/m 2, which, as discussed earlier, are representative of the heat fluxes expected for small to high fire intensities aboard naval vessels. Because of material limitations, only one specimen was tested for each experimental condition. However, by performing tests at multiple load levels and heat fluxes, it was possible to utilize a limited number of specimens to determine general trends in the time-to-failure versus heat flux and mechanical loading, and to investigate the failure mode under different test conditions. The test procedure involved bringing the cone heater to the desired temperature 67

85 Table 3.2: Time-to-failure (t f ) for fiberglass-reinforced vinyl-ester composite columns subjected to simultaneous surface heating and axial compressive loading. Specimen Axial compressive stress (MPa) Heat flux heated length (kw/m 2 ) (mm) t f =2549 s t f = 660 s t f = 366 s t f = 251 s (used to establish a given heat flux level), and allowing it to stabilize for 30 min, after which the exit shutters were closed. Next, a specimen (with attached grips) was installed into the loading module and loaded to the desired compressive load level. Within 10 s of applying the load, the shutters shielding the test specimen from the heat source were opened. The compressive loads of 1.11 to 3.34 kn that were used in the experiments, which provided nominal compressive stresses between 3.5 and 10.5 MPa. During the experiments, the axial displacement of the specimen, load level, and elapsed time were continuously recorded until specimen failure (data was gathered using an 18-bit data acquisition board). When the specimens failed, the H-block hit the mechanical stops (as shown in Fig. 3.15c) to limit complete collapse of the specimens, which would obscure the failure modes. After specimen failure, the shutters were immediately closed and the specimens removed from the loading fixture. All experiments were videotaped (30 Hz Frame rate) to document the failure mode of the specimen. The time-to-failure of the specimen was documented by a timer on the cone calorimeter and was further verified by examination of the videotape of each test Experimental results and discussion Time-to-failure and failure mode The time-to-failure data (time period between the onset of exposure to the heat 68

86 source and total specimen collapse) is summarized in Table 3.2. The time-to-failure was readily determined since all specimens exhibited collapse with significant axial deformation. Analysis of the video recordings from experiments showed that, for all specimens, the final failure event was exceedingly rapid (the transition from an intact, load bearing specimen, to collapse was less than 50 ms). It should be noted that the sudden unexpected failure occurred without any observable bending deformation, and it was different with what was found for specimens that had been exposed to fire (without mechanical load) and then compressively loaded to failure at room temperature. For post-fire compressive loading of composites columns, bending deformation, that increased gradually (in a controlled fashion) until final specimen failure, can be directly observed and is typical of the behavior found during the compressive loading of other materials. For a heat flux of 25 kw/m 2, time-to-failure ranged from approximately 2549 s at 3.5 MPa to 251 s at 10.5 MPa; At 50 kw/m 2, time-to-failure was considerably shorter, 404 s at 3.5MPa and 131 s at 10.5 MPa; for the highest heat flux used, 75 kw/m 2, time-to- failure was much shorter, 191 s at 3.5MPa and 123 s at 7.0 MPa. The relationship between time-to-failure and axial applied load is nonlinear, which is most likely caused by char formation and degradation of the material properties. As noted above, for all heat flux intensities and load levels studied, both 150 mm (100 mm heated length) and 100 mm (74 mm heated length) long specimens failed in an unexpected fashion. Examination of the videotapes taken for each experiment showed that, prior to failure, there was not any obvious delamination or discernable transverse deformation in the uncharred portion of the specimens. This was further verified by direct examination of a specimen from an experiment that was stopped prior to failure. The specimen was exposed to a heat flux of 50 kw/m 2 under a compressive load of 7.0 MPa. The test was interrupted at an exposure time of 100 s to check for damage and possible delaminations within the specimen. As shown 69

87 Figure 3.16: Digital image of a 100 mm specimen (74 mm heated length) exposed for 100 s to a heat flux of 50 kw/m 2 under a compressive load of 7.0 MPa. in Fig. 3.16, the specimen showed no evidence of damage or delamination, however the same specimen collapsed at an exposure time of 133 s, which suggests that the process of damage initiation and delamination propagation happens quickly. Digital images comparing failure modes of 150 and 100 mm specimens tested at the same heat flux of 50 kw/m 2 and compressive load of 7.0 MPa are shown in Figs. 3.17a and b. Fiber kinking in a specimen without heat exposure and tested to failure under a monotonically increasing compressive load at room temperature is shown in Fig. 3.17(c) (for comparison, the compressive failure strength of this specimen was 297 MPa). As discussed below, the failure modes of the 150 and 100 mm specimens were significantly different. Although the failure modes differed, the time-to-failure for the shorter specimens was only slightly less than that of the longer specimens (Table 3.2). Global buckling did not occur for the shorter specimens; instead, the samples failed by local kinking of the glass fiber tows as shown in Fig. 3.17(a). This type of failure occurred rapidly, with no obvious changes in specimen appearance or transverse deflection for the majority of the exposure time. A similar failure mode was observed during the room 70

88 (a) (b) (c) Fiber kinking (local buckling) Fiber kinking (local buckling) Figure 3.17: Digital images comparing failure modes of 150 and 100 mm long specimens (100 mm heated length and 74 mm heated length, respectively) tested at the same heat flux intensity of 50 kw/m 2 and compressive load of 7.0 MPa. (a) 100 mm specimen; (b) 150 mm specimen; (c) fiber kinking observed in a specimen without heat exposure and tested to failure under a monotonically compressive load at room temperature. temperature monotonic compressive loading of unexposed material (removed from the same panel) as shown in Fig. 3.17(c) and for composite panel used by Gibson in the Boeing tests [18]. Therefore, the geometry of the composite structure influences the final failure mode. However, the time-to-failure is not significantly affected by the geometry. Figs. 3.18a and b show the typical failure modes of the 150 mm specimens exposed to different heat fluxes with compressive axial loads from 3.5 MPa (250 lb) to 10.5 MPa (750 lb), respectively. All specimens failed by global buckling. It is interesting to note that for most specimens, the unexposed side of the specimen deflected away from the heat source. When defining the overall failure mode of the specimens, only the uncharred (remaining) layer was taken into account because the stiffness and modulus of charred material are negligible and does not support the compressive mechanical load [13]. The buckling occurred in an unexpected catastrophic fashion. As noted earlier, final collapse was, for all practical concerns, instantaneous and 71

89 (a) (b) Figure 3.18: Digital images showing failure modes of 150 mm long specimens (100 mm heated length between grips) for various thermal and axial compressive loads: (a) 25 kw/m 2 and compressive load of 5.25 MPa (1.66 kn). (b) 50 kw/m 2 and compressive load of 5.25 MPa (1.66 kn). All specimens failed by global buckling. 72

90 occurred in less than 50 ms (determined by examination of videos). Prior to failure the amount of transverse deflection was very limited, but increased dramatically as the specimen approached failure. The catastrophic buckling collapse of specimen observed during combined thermal and compressive loading was much different than that found in earlier post-fire compression testing of the same composite. In the postfire compressive experiments, specimens were subjected (without load) to the same heat flux intensities used in the present study before mechanical loading. During postfire monotonic compression testing at room temperature, specimens failed by global buckling with a gradual increasing in transverse deflection until specimen failure. Compared with the post-fire experimental results, there are several features which could cause the different buckling failure for specimens in the combined thermal and mechanical loading tests. First of all, the response in the combined tests is dynamic. Material property degradation varies with time, which influences the delamination growth rate between the undamaged region and charred region. Secondly, there exists a thermal bending moment due to the non-uniform temperature and material property distribution along the thickness of a specimen. A thermal moment can develop from the onset of heat exposure. The resultant moment can be expressed in the form: E l α l T (y e)da (3.3) A where, E l and α l are the axial (longitudinal direction in Fig. 3.1) modulus and axial thermal expansion coefficient of the composite column respectively, T is the temperature change of the specimen between the beginning of heat exposure and the time of interest, e is the eccentric distance between the geometric center and the neutral axis of the cross section (if we assume as an approximation isotropic behavior), A is the area of the cross section, and y is the coordinate in the thickness direction (see Fig. 3.1). Both axial compressive Young s modulus E l and the temperature T are functions of the through-thickness coordinate y and exposure time t. In addition, 73

91 Specimen Ceramiccoating TransverseLVDT Figure 3.19: Experimental arrangement showing the LVDT located used to measure mid-point transverse deflection. The LVDT contacted the unexposed surface of the specimen. the thermal expansion coefficient changes as the matrix decomposes and transforms to char. However, to simplify the model, the thermal expansion coefficient αl was assumed to remain constant. Transverse deflection and thermal moment After initial axial loading, transverse displacement of a specimen can be induced by thermal expansion (in the thickness direction) or by a thermal bending moment arising from the non-uniform temperature and differing material properties along the through thickness direction. To verify our expectation of small transverse displacement induced by the thermal moment, and determine if a thermal bending moment could influence specimen failure, the transverse deflection was measured for several specimens. These tests were performed with a heat flux of 50 kw/m2 and an axial compressive load of 7.0 MPa (2.22 kn). The transverse deflection was measured 74

92 by use of a second LVDT in contact with the mid-point of the unexposed (backside) surface of the test specimens as shown in Fig To estimate the amount of transverse displacement that could be attributed to thermal expansion only, the transverse displacement of an unloaded specimen (100 mm heated length) without axial compressive load was measured during exposure to a heat flux of 50 kw/m 2 for comparison. For this experiment, a specimen was placed in the loading module beneath the cone calorimeter in an identical way to the axially loaded specimens, but the air cylinder was disconnected from the apparatus to eliminate the axial compressive load (note that the linear bearing arrangement still constrains the overall motion of the specimen to the axial direction only). Since the specimen could expand freely along the axial direction, a thermal bending moment cannot be induced. Indeed, as shown in Fig. 3.20, negligible transverse displacement occurred during heating of the unloaded sample (the small amount of transverse displacement observed is due to through-thickness thermal expansion of the specimen). Also plotted in Fig is the transverse displacement measured for 150 mm long specimen (100 mm heated length) under the same thermal loading (50 kw/m 2 ) but subjected to a simultaneous axial compressive load of 2.22 kn. It is noticed the mid-point deflection rate increased dramatically as the heat exposure time exceeded 120 s, which indicated instability happened for this column. Comparison of the two curves shows that, from the onset of heat exposure, the mid-point transverse displacement of the compressively loaded specimens exceeds that of the unloaded specimen. At the onset of heating, the transverse displacement of the unloaded specimen increased linearly with heat exposure time, which, as noted above, arose from the through thickness thermal expansion. For the compressively loaded specimens, the relationship between transverse displacement and exposure time becomes increasingly nonlinear with increasing exposure time and instability occurred for the structure. There are several factors that contribute to the increase in transverse displacement in the beginning of heat exposure and the 75

93 2.5 Q = 50 kw/m 2 Mid-point deflection w, mm P = 2.22 kn P = 0 kn Exposure time t, s Figure 3.20: Mid-point transverse displacement of the unexposed surface of specimens subjected to a heat flux of 50 kw/m 2 and an applied axial compressive load of 7.00 MPa (2.22 kn). For comparison, the transverse deflection of a specimen (74mm exposed length), subjected to the same heat flux, but with zero axial load, is shown. instability behavior prior to specimen failure, including char layer formation and the non-uniform temperature distribution in the thickness direction, which can induce a thermal bending moment. In addition, the decrease in compressive axial modulus E l in the unburnt region with increasing temperature also leads to a softer specimen and larger transverse displacement. From the comparison of the mid-point transverse displacement discussed above for loaded and unloaded specimens, it can be concluded that a thermal bending moment is generated during single-sided high-heat flux loading, which causes the specimen to deflect from the onset of heat exposure. Measurement of the mid-point transverse deflection shows that a thermal moment exists, which has a profound effect on the 76

94 compressive behavior of a structure subjected to simultaneous surface heating and compressive loading. In effect, the transverse deflection from the beginning of heat exposure causes a specimen or structure to behave much like an imperfect column. The thermal moment varies with the exposure time and increases in a nonlinear fashion with time. The results also point to a wealth of information that can be obtained from measurement of transverse displacement and it is also suggested that future testing must include both axial and transverse displacement measurements. Further numerical and analytical investigations are required to relate thermal bending moment to specimen failure. Axial displacement Figure 3.21 shows the axial displacements of specimens exposed to a heat flux of 25 kw/m 2 under constant compressive loads from 3.5 MPa (1.11 kn) to 10.5 MPa (3.34 kn). The initial displacement is from elastic deformation prior to heat exposure. Immediately after exposure to the heat source, thermal expansion of the specimen caused an increase in specimen length (axial compressive displacement decreased in Fig. 3.21). A similar phenomenon has been observed in tests performed by Bausano et al. [38]. The decrease in compressive displacement continued until the temperature induced char formation and stiffness loss overcame the effect of thermal expansion. In order to explain the variation of the axial compressive displacement versus axial load, the simplest 1D model, which does not consider transverse deflection, can be used. Although the transverse deflection of specimens under combined loading occurs, based on our measurements, the deflection does not become significant until close to specimen failure. Therefore, for short exposure times, the thermal force can be written as: Nx T = E l (t, y)α l T (t, y)da (3.4) A 77

95 Axial compressive displacement u, mm Q = 25 kw/m 2 P = 3.34 kn (750 lb) P = 2.22 kn (500 lb) P = 1.67 kn (375 lb) P = 1.11 kn (250 lb) Exposure time t, s Figure 3.21: Axial displacement of specimens exposed to a heat flux of 25 kw/m 2 under constant compressive loads from 1.11 to 3.34 kn. The initial compressive displacement decreased due to thermal expansion; the subsequent increase in compressive axial displacement is due to a decrease in specimen stiffness. 78

96 The total axial force applied at the neutral axis is, N x = P N T x = P E l (t, y)α l T (t, y)da (3.5) A So the axial strain is written as: ε x = N x = P E A l(t, y)α l T (t, y)da (3.6) AE av AE av where, E av is the longitudinal (axial direction along x axis in Fig. 3.1) average modulus, which can be expressed as E av (y, t) = A E l(y, t)da, where A is the area of the cross section of the specimen and T (y, t) is the difference between the temperature of the specimen and initial temperature before heat exposure. Both E av and T are functions of the elapsed exposure time t. If the thermal force and the total axial strain ε x do not vary with the axial position, the total axial displacement u x can be written as: u x = l 0 ε x dx = P L α l( E A l(y, t) T (y, t)da)l (3.7) AE av AE av The first term in Eqn. 3.7 is associated with the mechanical response of the specimen to the external applied force P ; the second term is associated with the thermal force, which is dependent on the heat flux intensity and exposure time. If the specimen is exposed to the same heat flux with the same total exposure time, we make a simplifying assumption that the degradation in material properties is associated with heat intensity and exposure time only. If the material response is independent of loading history, we would expect the axial displacement u x is linearly related to the applied force P. With this assumption, the slope (s) can be written as s = L AE av, which is dependent only upon heat flux and exposure time t and is not a function of the applied load. However the axial displacement u x versus applied compressive load P is plotted for specimens exposed to a heat flux of 50 kw/m 2 with exposure times for 5, 10, and 50 s in Fig During the initial stages of heat exposure (e.g., the curves for exposure times t = 5 and 10 s in Fig. 3.22) the axial displacement is 79

97 Experimental measured axial compressive displacement u, mm x t = 5 s t = 10 s t = 50 s linear fit curve 3rd order polynormial fit curve Q = 50 kw/m Axial applied compressive force P, kn Figure 3.22: Axial compressive displacement u x versus axial applied compressive P under the same heat flux of 50 kw/m 2 with different heat exposure times (5, 10, and 50 s). linearly related to the applied load P, which is consistent with Eqn The slope is governed by the material longitudinal average modulus E av, which is dependent on heat flux intensity and exposure time; the decrease in axial compressive displacement is caused by thermal expansion of the specimen (note that the pneumatic loading actuator allows axial displacement while maintaining a constant load). The slope is the same for specimens exposed for 5 s and 10 s, which means the average modulus E av does not change very much in the initial stage of heat exposure. Examination of Fig also shows that, for all applied load levels from 1.11 to 3.34 kn, the axial compressive displacement change for specimens at the start of the tests is the same (exposed for 5 and 10 s), which indicates that the axial displacement variation due to 80

98 thermal expansion is the same even though they are under different axial compressive loads. Therefore the second term in Eqn. 3.7 is not dependent on the applied force P. The two curves also indicate that the material stiffness does not change significantly at the beginning stages of heat exposure since the slope does not change significantly. As the heat exposure time increases further (t = 50 s in Fig. 3.22), the relationship between axial displacement and applied load becomes nonlinear; the slope increases with load. This is verified by Fig. 3.23, which shows the axial compressive displacement u x versus compressive load for specimens with heat exposure times of 5 and 100 s. With an exposure time of 5 s, the relationship between axial displacement and axial load is linear. For an exposure time of 100 s, the relationship is nonlinear and the slope varies significantly with external applied load. Thus, the simplifying assumption made in Eqn. 3.7, that the deflection of the column under combined thermal and compressive loading can be neglected in the 1D model, and in this model the slope between the axial compressive displacement and the axial compressive load is dependent only on the heat flux intensity and heat exposure time, are an oversimplification. There are several possible reasons for the interrelation between heat flux, heat exposure time, and applied compressive load: 1. Material stiffness loss is dependent on heat flux intensity and heat exposure time, but it might also depend upon the applied compressive load. 2. A thermal moment exists; its influence increases with load level and can not be neglected for long heat exposure times. 3. The column bends due to the thermal moment and the bending deformation is significant for columns with long heat exposure times. 4. The growth of delaminations is influenced by load level. Of these, it is thought that the decomposition of the epoxy resin, which results in material stiffness loss is the most important mechanism. In Fig. 3.24, the axial displacement is plotted versus heat flux for a constant 81

99 Experimental measured axial compressive displacement u, mm x t = 5 s t = 100 s 3rd order polynormial fit curve Axial applied compressive force P, kn Q = 50 kw/m 2 linear fit curve Figure 3.23: Axial compressive displacement u x versus axial applied compressive load P under the same heat flux of 50 kw/m 2 with different heat exposure times (5 and 100 s). 82

100 Experimental measured axial compressive displacement u, mm x P = 1.11 kn (250 lb) t = 0 s t = 5 s t = 50 s t = 100 s t = 150 s Heat flux Q, kw/m 2 Figure 3.24: Axial compressive displacement versus heat flux for 150 mm long specimens subjected to a compressive force of 1.11 kn (250 lb). Data is plotted for heat exposure times from 0 to 150 s. force of 1.11 kn and heat exposure times from t = 0 s to t = 150 s. The variations of the curves can be qualitatively explained with reference to Eqn The axial compressive displacement variation is associated with the thermal expansion and the material stiffness loss due to the heat damage. The axial compressive displacement decreases due to thermal expansion, which corresponds to the second term in Eqn. 3.7; simultaneously the compressive displacement increases under a constant applied load due to a decrease in axial modulus; the two factors compete with one another. At the beginning of a test (e.g., up to 50 s), when microstructural damage is limited, thermal expansion dominates the variation of axial compressive displacement. The curves at t = 5 s and t = 50 s show that for the same axial compressive load, the influence 83

101 of material stiffness loss on the specimens exposed to higher heat fluxes is greater than the influence of thermal expansion. With increasing heat exposure time (e.g. 100 and 150 s) the axial displacement variation of specimens with the higher heat flux exposure is dominated by the material stiffness loss, causing the net compressive displacement to increase. 3.3 Summary Based on the experiments performed with the cone calorimeter, I studied both the post-fire compressive behavior of fiberglass reinforced vinyl-ester composite column, which has been exposed to high heat flux for a certain time, and the integrity of the same column under constant compressive load combined with heat flux exposure. The high intensity heating, used to simulate fire exposure, was obtained by a cone calorimeter. Composite specimens used for post-fire mechanical tests were subjected to heat fluxes of 25 kw/m 2 to 100 kw/m 2 for exposure times up to 1800 s. After exposure, the compressive behavior and failure mode of the composite were determined. The degree of strength and modulus degradation increased with increasing heat flux and total exposure time. Without heat exposure, the compressive strength of the composite was approximately 297 MPa. For a fixed heat flux of 50 kw/m 2, the residual compressive strength was approximately 14 MPa after 600 s of heat exposure and decreased to only 4 MPa after 900 s of heat exposure. When the char layer depth due to heat exposure was small, the failure was dominated by fiber kinking in the undamaged portion of the composite column. As the char layer depth increased, obvious transverse displacement occurred on the undamaged side of the specimen with local and global buckling response. With large charred layer depth, the failure of specimens was governed by global buckling of the undamaged portion, and the Southwell plot can be used to determined the critical buckling load experimentally for the burnt column. 84

102 The small delamination cracks in the interfacial region between the char region and unburnt region can not be neglected for the post-fire properties of the burnt composite column; the assumptions that the mechanical properties of the unburnt region are constant throughout and are the same as the mechanical properties of the original composite are oversimplified. In order to verify the prediction of the simplified thermal buckling model and show the existence of thermal bending moment, the effect of simultaneous axial compressive loading on the time-to-failure and failure mode of the vinyl-ester/fiberglass composite column exposed to single-sided surface heat fluxes between 25 and 75 kw/m 2 was examined using a modified cone calorimeter. Compressive loading of specimens during heat exposure was achieved by using a specially designed mechanical loading fixture that mounted directly below the radiant cone heater. Using specimens with a heated lengths of 74 and 100 mm, the effect of surface heat fluxes from 25 to 75 kw/m 2 and compressive loads from 3.5 to 10.5 MPa on failure time and failure mode were studied. Based upon the experimental results, for the range of heat fluxes and compressive stresses studied, all specimens exhibited compressive instability. Global buckling was observed for the specimens with a heated length of 100 mm. Failure occurred by local fiber kinking for specimens with a shorter heated length of 74 mm. The relationship between time-to-failure and axial applied load was nonlinear. For specimens with a heated length of 100 mm and subjected to a heat flux of 25 kw/m 2, the failure time ranged from 2549 s at 3.5 MPa to 251 s at 10.5 MPa. At 75 kw/m 2, the highest heat flux studied, the failure time of the same specimens ranged from 191 s at 3.5 MPa to 123 s at 7.0 MPa. The time-to-failure of the shorter specimens was slightly less than that of the longer specimens. There existed a thermal bending moment for all specimens, which caused transverse deflection from the onset of heat exposure. Due to the existence of thermal moment and the degradation of material property, the deflection of specimens increased dramatically for long heat exposure 85

103 time and instability occurred for all specimens tested. The thermal moment has a more significant influence on the mechanical response of the longer specimens under higher compressive load than that of the shorter specimens. Material stiffness loss might depend not only on the heat flux intensity and heat exposure time, but also on the level of applied compressive load. 86

104 CHAPTER IV MONOTONIC SHEAR AND SHEAR FATIGUE OF FOAM-CORE COMPOSITE SANDWICH STRUCTURES 4.1 Introduction For sandwich materials, composites and adhesive joints, shear can be a critical failure mode. With the increased use of sandwich structures in wind-turbines, aircraft and in high speed rail systems, techniques are required to more accurately study the shear behaviour of these materials under monotonic, fatigue and creep loading. Various test methods and engineering standards exist for evaluating the shear behaviour of sandwich materials and composites [22, 27, 39, 40]. For example, the two-rail shear technique [22] is often used to determine the shear strength of polymeric sandwich composites. The two-rail technique utilizes a rectangular specimen bonded between two metallic loading plates that are loaded through clevises at each end (Fig. 1.4). Because of the manner in which the load is applied, the stress state developed in the specimen is not pure shear and the stress-strain behavior and failure mode can be influenced by the normal stresses developed during loading. Garcia et al. [24] performed extensive finite element analysis and laboratory experimentation, to examine the differences in two-rail shear tested laminated composite specimens. Analytical results indicated that large normal stresses can develop in the test materials. Advances in shear testing have primarily involved the design of new clamping methods and specimen geometries. For instance, Hussain and Adams [25] modified the ASTM D-4255 standard two-rail test method (Fig. 1.4) by using a multiple-bolt C-clamp to grip the 87

105 specimen to thermal- sprayed (gritted) rails. They also analyzed a range of specimen configurations in order to optimize the specimen geometry of composite laminates in two-rail shear testing by linear three-dimensional finite element modeling [26]. Their analysis found that shear stresses distributed uniformly over a large region in the specimen gage section for most of the specimen configurations, but were accompanied by significant transverse and axial normal stresses. Previous investigation using the two-rail technique has been primarily concerned with the shear behavior of laminated composites, however shear strength, modulus and shear fatigue of sandwich structures are relatively unexplored by this approach because with thick sandwich structure configuration, large normal stress develops, which can have a significant effect on the shear behavior of specimens. Three-point and four-point flexure of rectangular beams are also widely used to study the monotonic shear and shear fatigue behaviour of sandwich structures. For example, ASTM C [27] outlines the use of 3-pt and 4-pt bending for room temperature shear testing of sandwich specimens. In flexural testing a pure shear stress state is not developed within a test specimen, normal stresses, which also present during flexure testing, influence the damage initiation and failure mode. Because of the complicated stress state, a combination of failure modes may be observed. In addition, the direct measurement of in-plane shear modulus and shear stress-strain behavior cannot be made. It should also be noted in the ASTM standard C [27], failure in the compression facing may occur by actual crushing, yielding causing large deflection, wrinkling of the facing into the core or the facing popping off the core (for thin face-sheet sandwich structures). Therefore, the use of flexural techniques can not be reliably applied to thin face-sheet sandwich structures to determine shear strength and shear modulus. Techniques used to study shear fatigue behavior have focused primarily on composites. Eilers et al. [41, 42] analyzed the ASTM standard three-rail shear test specimen 88

106 to locate and reduce high-magnitude localized stresses that influenced the fatigue life. Notches, inserted at the stress concentrations, improved the shear strength and fatigue life of the test specimen. The technique, however, is not suitable for sandwich structures or for elevated temperature testing. Previous shear fatigue research has also examined different loading modes such as torsional loading or axial cyclic loading of angle-ply composite laminates [43, 44, 45, 46, 47]. The ideal test method for investigating the shear behavior of sandwich structures and lap-joints should provide a region uniform shear with minimal normal stress. In addition to permitting various specimen sizes and material types to be investigated, the technique should allow direct measurement of the shear stress-strain response at both ambient and elevated temperatures. Ideally, the technique allows for monotonic, fatigue and creep testing. With these requirements in mind, the goal of the present study was to develop a new shear testing method that could be applied to a variety of sandwich structures, including polymers and metals. Another important design objective was to develop a technique that could be used to study the fracture behavior of interfaces and adhesives under direct Mode II (shear) loading. Details of the new apparatus will be discussed in this chapter. In order to show the improvement of the new shear technique compared with the ASTM standard two-rail shear technique for sandwich structures, linear three-dimensional finite element analysis was conducted to evaluate various shear testing techniques for a sandwich specimen configuration. Using the new shear apparatus, the shear behavior of a thin face-sheet sandwich structure composed of glass-fiber/epoxy face-sheets with a 50 mm thick PVC foam core was investigated. The monotonic shear and shear fatigue test results at room temperature are presented in this chapter. 89

107 4.2 Specimen Geometry, Test Apparatus and Instrumentation Specimen geometry. The specimen geometry with attached loading plates is shown in Fig.4.1. Specimens were adhesively bonded to the loading plates. Although longer specimens (or wider) can be accommodated, the specimen used in the current investigation was mm long 38.1 mm wide 57.5 mm thick. The specimen loading plates, machined from a low-carbon steel, were 380 mm length with a width of 38.1 mm and a thickness of 25.4 mm. Test apparatus. Details of the test apparatus are shown in Figs 4.2a-d. For the experiments described here, the shear apparatus is installed on a 100 kn servohydraulic load frame (Fig 4.2a). Schematics showing the principle of operation of the shear apparatus and specimen deformation are shown in Figs 4.2c and d. For sandwich specimens, the face-sheets are bonded between two parallel loading plates. One of the loading plates is rigidly attached to the test frame. The other plate is attached to two vertically movable U-shaped guiding plates (part 3 in Fig. 4.2c) that can travel vertically on guide rods (part 4 in Fig. 4.2c) by use of linear bearings. The purpose of the U-shaped guiding plates is to guide the shear deformation and constrain bending deformation of the specimen during shear loading (the guide plates are U-shaped to increase the heated length of specimens during elevated temperature testing). A key requirement of the design was to minimize transverse constraint of the specimen (which leads to generation of normal stresses) as a specimen is loaded in shear. To accomplish this, the U-shaped guiding plates are attached to horizontally movable plates (part 5 in Fig. 4.2c) that run on linear bearings fixed to the base plate and top plate (part 6 in Fig. 4.2c). This arrangement accommodates transverse specimen expansion and contraction during shear loading (this also allows free To bond the fiberglass reinforced epoxy face-sheets to the loading plates, a high shear strength adhesive with a room temperature cure was utilized (Master Bond Inc., No. EP31). 90

108 139.7 mm Face-sheet 57.5 mm Loading plate Loading plate PVC core Bonding surfaces Figure 4.1: Specimen geometry and loading plates used for shear testing of sandwich materials. The face-sheets are adhesively bonded to the loading plates. 91

109 expansion of a specimen during heating for elevated temperature testing), thereby minimizing the development of normal stresses (the transverse deformation of the specimen under the shear loading arises from Poisson s ratio effect). Ideally, normal stress values of zero are desired throughout the specimen. However, the transverse constraint and the presence of the free edges cause normal stresses to develop in the specimen. So far there is no appropriate rail shear testing technique that takes into account transverse deformation. The uniqueness of this arrangement is that it allows transverse deformation of the specimen by four horizontal linear bearings (part 6 in Fig. 4.2c), which can minimize the normal stress developed in the sandwich specimen. To develop shear loading, an axial load is applied through the lower cross arm which is attached to the specimen loading plate. In this manner, shear loads can also be applied to the specimen while not constricting the horizontal movement of the sample. This arrangement has been successfully used for the testing of PVC foam core honeycomb specimens with thicknesses up to 50 mm. Instrumentation. A load cell is used to measure the axial force applied to the moveable side of the specimen. The experimental arrangement and specimen design allows direct measurement of shear displacement. This capability is important for the characterization of shear stress-strain behavior and for determining shear-creep extension during elevated temperature testing. For elevated temperature testing, a furnace is designed to fit around the specimen and attached loading plates. The U- shaped guiding plates are machined with water-cooling passages to keep heat away from the linear bearings and guide rails. The extension arms used for the LVDTs, which are machined from a nickel base alloy (Inconel 718), also contain water passages to keep the LVDTs at a constant temperature (Fig. 4.3). Based on the instrumentation, the shear strain can be calculated from LVDT measurements, and the shear stress can be calculated from the applied load. In order to eliminate the effect of misalignment of the loading plates on the displacement 92

110 a 7 b c d Y Figure 4.2: (a) Shear apparatus mounted on a 100 kn servohydraulic load frame. (b) Close-up of LVDT brackets. (c) Schematic of shear apparatus with key components identified. (1) sandwich specimen, (2) specimen loading plates, (3) U-shaped guide plates, (4) vertical linear bearing rails (5) horizontal plate with attached linear bearing races, (6) horizontal linear bearing rails, (7) upper plate fixed rigidly to hydraulic load frame, (8) lower plate fixed rigidly to hydraulic load frame. The left specimen attachment plate is fixed rigidly to the frame. The right plate is displaced vertically to develop shear in the specimen. As the specimen is displaced, the vertical linear bearings guide the vertical movement while the horizontal linear bearings allow transverse displacement to accommodate transverse contraction of the specimen. (d) Illustration of specimen deformation during shear loading. 93

111 Furnace Figure 4.3: Shear test apparatus with a furnace installed for elevated temperature tests. The U-shaped guiding plates and the extension arms used for the LVDTs are water-cooled. measurements, two LVDTs were utilized to find the displacement. (Fig. 4.4). The inner and outer LVDT readings were each zeroed at the beginning of the run and multiplied by a scaling factor calculated during calibration to give the displacements, U i and U o. u = U il o U o L i L o L i (4.1) where u is the actual displacement, U i is the displacement read by inner LVDT, U o is the displacement read by outer LVDT, L i is the distance from core center to inner LVDT, L o is the distance from core center to outer LVDT. 94

112 Figure 4.4: Geometry of the dual LVDT setup. For the LVDT arm, L i = mm and L o = mm. Shear strain was then calculated for the core by taking the ratio of the actual axial displacement, u and the specimen thickness, t. γ = u t (4.2) Shear stress,τ, is calculated in accordance with ASTM C273 [40], as the ratio of load, P and the area of the specimen. τ = P Lb (4.3) where, L is the specimen length and b is the specimen width. 4.3 Finite Element Modelling In order to show the improvement obtained with the new shear test technique, finite element modelling was used to compare the stress states for four-point bending (ASTM C393-62), two-rail shear (ASTM D4255/D4255M-01), and the new shear testing arrangement. The FEM analysis was conducted for sandwich specimens in 4-point flexural testing by Burman and Zenkert [28]. The results showed that shear stress distribution between the inner and outer supporters as shown in Fig. 1.5 is not uniform. It was 95

113 also seen the zone of maximum shear stress is slightly off the neutral axis. Further more, there were locally high stresses in the vicinity of the load supports. As observed by Burman and Zenkert [28], an initial crack formed along the neutral axis during fatigue. As a visible macro crack, parallel the face sheets, propagated further, the crack kinked out towards the face sheets, which indicates that this does not provide uniform Mode II shear loading at the crack tip. Fatigue failure of the test coupon was dominated by the combined shear stress and normal stress in the core area. Richard et al. [48] reviewed extensive experimental techniques for Mode-II fracture and fatigue tests and pointed out that the flexural testing method showed a pronounced overlapping of crack edges and a remarkable negative K I at the crack tip, indications of strong compressive normal stresses. It can be concluded that the flexural testing technique is not an optimal method to determine K IIC for sandwich specimen. [48]. One concern for two-rail shear testing (ASTM D4255/D4255M-01 [22]) is the transverse (the thickness direction) constraint of the test specimen, which induces large normal stress component. Under pure mode II loading, specimens will contract along the thickness direction (due to Poisson ratio effect). The contraction of the specimen is not accommodated by two-rail shear testing technique, which results in a normal stress component in the sandwich specimen. In addition, it would be difficult to apply combined loading (shear and normal) to a specimen since the specimen would rotate about the joint connection at point A as shown in Fig Standard two-rail testing can not be used at elevated temperatures due to the creep deformation of the loading plates. In order to understand the stress distribution developed in a specimen during two-rail testing, a preliminary linear 3D finite element analysis was conducted. The dimension of the specimen is the same as that used in the 4-point flexural analysis. The meshed model is given in Fig. 4.5(a) and the stress distribution along the longitudinal direction (length direction) on the center-line of the specimen is given 96

114 (a) (b) Figure 4.5: (a) 3D finite element model for sandwich specimen in ASTM two-rail shear technique. (b) Stresses components along the center line of the specimen. 97

115 (a) (b) Figure 4.6: (a) 3D finite element model for sandwich specimen in the new direct-shear technique. (b) Stresses components along the center line of the sandwich structure. 98

116 in Fig. 4.5(b). As shown by Fig. 4.5b, the shear stress distribution is more uniform than that obtained with 4-point bending. However, σ 11 and σ 22 also exist. Thus, the standard 2-rail test approach does not provide pure shear. Direct Shear Technique significantly reduces the transverse constraint of the sandwich specimen by use of four horizontal linear bearings (Fig. 4.2c part 6). Creep deformation of the loading plates is also reduced allowing to be applied at the elevated temperature to study shear creep behavior of metallic sandwich panels [23]. Results of the 3D finite element analysis (Fig. 4.6a and b) shows that the shear stress distribution of the sandwich specimen is much more uniform and the normal stress components are much lower in the core region compared with other techniques. The geometry used in the FEM analysis is the same with that used for the two-rail test analysis. It is noticed from the stress distribution contour in fig. 4.7 that the shear stress distribution τ 12 is uniform in the entire core region and the normal stress σ 22 concentration occurs at two free edges of the specimen, which can not be avoided totally since the dimension of the specimen is always finite with free edges. The new technique provides a pure shear field in the middle region of the core material, which is a necessary characteristic for performing mode-ii fatigue or fracture tests. Accordingly, the new shear testing technique provides a reliable method to perform mode-ii fatigue or fracture tests with a center crack in the middle of the core region. The proposed specimen geometry for mode-ii shear fracture testing is shown in Fig. 4.8a, a single crack along the longitudinal direction is located in the center of core region with a crack length of 55 mm. The 2D finite element model of a sandwich structure with a center crack was constructed to calculate the stress intensity factor at the crack tips. The shear stress τ 12 and normal stress σ 22 distributions around the two crack tips are shown in Fig. 4.8b and c. The shear stress τ 12 is the dominating stress component; the normal stress σ 22 is much smaller and uniformly distributed around the crack tips. The mode I stress intensity factor K I and the mode 99

117 "Free" edge "Free" edge Figure 4.7: Stress distribution contours in the modified two-rail new direct-shear technique. 100

118 1 2 (a) (b) (c) Figure 4.8: (a) 2D finite element model of specimen geometry proposed for Mode II fracture toughness testing. (b) Shear stress τ 12 distribution around the crack tips. (c) Normal stress σ 22 distribution around the crack tips. 101

119 II stress intensity factor K II are 38.2 and MP a m respectively, which also indicates that at the crack tip, mode II fracture dominates the crack propagation, and no compressive stresses at the crack tip (positive stress intensity factor K I ). The compressive stress can cause the crack to close up and its surfaces to be compressed. The friction occurring leads to a reduction or even complete prevention of shear deformation [48]. Hence for the mode II fracture test specimen, it is required that there is no compressive normal stress component at the crack tip to make sure mode II cracks growth continuously. The above result indicated that the new direct shear technique should be used for obtaining the mode II fracture toughness of sandwich structure. 4.4 Proof-of-concept Experiments Material The sandwich construction used in the proof-of-concept experiments is composed of fiberglass-reinforced vinyl-ester matrix composite face-sheets and H80 PVC foam core. The layer-up schedule of the face-sheet is [0/ + 45/0 + 45/0] with the total thickness (each side) mm (0.12 in); the core material (Divinycell H80) investigated was provided by Seemann Composites Inc.(Sec ). The H80 core material is a partially cross-linked, structural cellular material expanded manufactured using a CFC free process. The thickness of the core was 50.8 mm (2 in). Some basic mechanical properties of the foam core material are listed in Table 4.1. The configuration of the specimen bonded to the loading plates is shown in Fig The most common usage of the Divinycell PVC (H-quality) foam is as a core material in sandwich constructions in the shipbuilding industry. It is widely used in sailing and cruising boats and also in high speed vessels. PVC foam core is also increasingly used for cabins The analysis assumed frictionless clevis pins in the two-rail technique and friction-free bearings (free transverse movement) in the direct-shear technique. The data is provided by DIAB [49] 102

120 Table 4.1: Mechanical properties of the PVC H80 foam core used Material Density Tensile Tensile Shear Shear Cell modulus strength modulus strength size H80 80 kg m 3 80 MPa 2.2 MPa 31 MPa 1.0 MPa 0.5 mm and rotor blades of latest generation wind turbines. Monotonic shear strength The room temperature monotonic shear response of the sandwich composite was investigated using the new shear technique. Shear strength, shear modulus and shear failure mode of the PVC foam core specimens were obtained. Because of the large width (57.5 mm) of the structure studied, the axial load was applied along the centerline of the specimen loading plate which was attached to the U-shaped guide-plates (to provide additional rotational freedom, a clevis was used to attach the linkage to the load cell). The monotonic shear tests were run under load control mode with the loading rate 22.2 N/s (5 lb/s). Since the shear modulus of the face-sheet is very high compared with the PVC foam core material, the shear deformation was dominated by the foam core, thereby, it can be considered that the shear stress-strain behavior obtained by the sandwich structure is also the shear stress-strain behavior of the foam core material. The monotonic stress-strain behavior is shown in Fig Failure occurred by rapid crack extension along the face-sheet/pvc-core interface, which indicates that the weakest region for the sandwich construction is the adhesive interface between the face-sheet and core material under pure mode II loading for the entire structure. The failure mode observed by the direct shear technique is different with that observed by the flexural tests. For example, the similar sandwich configuration with H100 as the core material did not actually fracture in shear in the 4-point bending test [28]. The damage initiated at the two free edges due to the normal stress concentration as shown in Fig Prior to the initial interfacial damage, the stress-strain response is linear with the constant shear modulus G, with the interfacial 103

121 Figure 4.9: Monotonic shear behavior of a fiberglas/pvc foam-core sandwich specimen. The inset shows a specimen after testing. In all cases, failure occurred by fracture at the face-sheet/pvc-core interface. crack occurrence and growth, the shear modulus deceased and the shear stress-strain behavior became non-linear. Based upon eight monotonic experiments, the failure strength was approximately 0.78 MPa, which is smaller than the value given by the manufacturer. The reason is that the strength provided by the the manufacturer is based on the ASTM C 273 [40] technique and the failure of the sandwich structure is dominated by combined stresses. The average shear modulus was approximately 26 MPa (calculated by a linear curve fit between shear strains of 0.1 % and strain of 0.8 %). 104

122 max Normalized maximum shear stress / R = 0.16 ~ 0.19 f = 1 Hz Number of cycles, N Figure 4.10: Influence of maximum shear stress on the room temperature fatigue life of fiberglass/pvc foam sandwich specimens. The maximum fatigue stress was normalized with respect to the average monotonic shear strength (0.78 MPa). Shear-fatigue. Shear fatigue experiments with the same specimen geometry were performed at room temperature at a sinusoidal loading frequency of 1 Hz. The stress ratio (σ min /σ max ) varied between 0.16 and The experimental arrangement for the fatigue experiments was identical to that used for the monotonic shear tests. The influence of maximum shear stress on fatigue life is shown in Fig Fig shows the typical cyclic stress-strain behavior observed during the fatigue experiments. The initial stress strain behavior is linear. However, with additional fatigue cycles, interface cracks initiate at the face-sheet/core interface (in all cases, interface cracks formed on both sides of the specimen). The cracks extended along the interface and 105

123 Shear stress, MPa max = 0.61MPa R = 0.17, f = 1 Hz Shear strain, arc Figure 4.11: Typical stress-strain behavior observed during room temperature shearfatigue testing of fiberglass/pvc sandwich specimens. The data shown was obtained at loading frequency of 1 Hz and a stress ratio (τ min /τ max ) of Failure occurred by cyclic growth of interface cracks along the facesheet/core interface. caused a progressive decrease in cyclic shear modulus and increase in stress-strain hysteresis. The shear modulus degradation with fatigue cycles is shown in Fig Similar shear modulus degradation was observed in all fatigue tests. In the initial stage of shear fatigue, the shear modulus degradation was gradual; with crack growth along the interface, the shear modulus decreased further. Once the modulus decreased below 21 MPa approximately, the growth of fatigue damage was dramatic and final fatigue happened quickly. 106

124 28 Shear modulus G, MPa max = 0.61 MPa max = 0.54 MPa Number of fatigue cycles, N Figure 4.12: Shear modulus G degradation with fatigue cycles 4.5 Summary A new apparatus was developed to study the monotonic shear and cyclic-shear behavior of sandwich structures. Proof-of-concept experiments were performed using polymeric sandwich materials. For the fiberglass-epoxy/pvc foam-core sandwich material investigated, shear failure occurred by the extension of cracks parallel to the face-sheet/core interface, the shear modulus degraded with the fatigue damage growth. The results showed reproducible specimen behavior. The technique is readily adaptable to elevated temperature shear testing, including studies of the core shear creep behavior of sandwich structures and adhesives. 107

125 CHAPTER V CONCLUSIONS AND FUTURE WORK 5.1 Conclusions Thermal Buckling of a Fire-Damaged Composite Column Exposed to A Uniform Heat Flux To better understand the response of a composite column under simultaneous compressive mechanical loading and high heat flux, a theoretical thermal bending model of a burnt column, either axially restrained or with an axial applied force was developed. From the calculation, the important conclusions obtained from the analysis are: The temperature in the undamaged layer of a burnt column is much lower than the original column. Due to the existence of thermal bending moment, for a burnt column exposed to a high heat flux under simultaneous constant axial compressive loading, the response of the column is the same as that for an imperfection column. Integrity of Composite Columns Under Simultaneous High Heat Flux Exposure and Compressive Loading The effect of combined high heat flux and mechanical loading on the integrity of a fiberglass-reinforced vinyl-ester matrix (Derakane 510 A) thermoset composites was investigated. A modified cone calorimeter was used to obtain surface heat flux levels between kw/m 2. The first part of the investigation examined the post-fire compressive behavior and failure mode of composite columns. The second part investigated the effect of combined thermal and mechanical loading on failure 108

126 time and failure mode. The key conclusions of the post-fire compressive tests are: The degree of post-fire compressive strength and modulus degradation increased with increasing heat flux and total exposure time. When the char layer depth due to heat exposure was small, failure was dominated by fiber kinking in the undamaged portion of the composite column. As the char layer depth increased, obvious transverse displacement occurred on the undamaged side of the specimen with local and global buckling response. With larger charred layer depth, failure was governed by global buckling of the undamaged portion. Southwell plots can be used to determined the critical buckling load for the burnt columns. The small delamination cracks in the interfacial region between the char region and unburnt region can not be neglected for the post-fire properties of the burnt composite column. The assumptions that the mechanical properties of the unburnt region are constant throughout and are the same as the mechanical properties of the original composite are oversimplified. The key conclusions of the combined thermal-mechanical experiments are: All specimens exhibited compressive instability. Global buckling was observed for the specimens with a heated length of 100 mm. Failure occurred by local fiber kinking for specimens with a shorter heated length of 74 mm. A thermal bending moment was developed for all specimens, which caused transverse deflection from the onset of heat exposure, which verified the prediction of the thermal buckling model. The instability mode of the burnt column that was observed from the tests was 109

127 the same as that obtained from the thermal buckling model. The thermal moment has a more significant influence on the mechanical response of the longer specimens under higher compressive load than that of the shorter specimens. An Improved Technique for Shear Testing of Sandwich Structures To investigate the monotonic shear and shear fatigue of foam-core composite sandwich structures and reduce the normal stress components, a new shear technique was developed and proof-of-concept experiments were performed using polymeric foam core sandwich specimens. The key conclusions are: By accommodating transverse contraction, the new technique provided lower normal stresses and a uniform shear stress distribution. The technique can be easily extended to elevated temperature. For the foam core sandwich studied, failure occurred by the extension of cracks parallel to the face-sheet/core interface. 5.2 Future work and suggestions Future work should have the following objectives: Shear-fatigue and creep are important loading modes for composites and sandwich structures. Significant practical and theoretical contributions can be made in this area. Mode-II fracture and shear fatigue research should be expanded to include the effect of combined shear and normal load on the fatigue behavior of polymers, in particular in various environments where time dependent deformation (viscoelasticity) will occur. An important application of this work is in the area of wind turbine design and reliability analysis. In addition, the effect of stress concentration on the shear fatigue life of sandwich structures with various notch geometries under shear loading should be explored. 110

128 Further investigations of high heat flux thermal degradation of polymeric composite materials. In the theoretical modelling, the time dependent char layer formation and the viscoelastic material response at elevated temperature should be considered. In addition, the sandwich construction response under combined simultaneous thermal and mechanical loading is another area that should be explored in greater detail. 111

129 APPENDIX A DIRECT SHEAR APPARATUS - ASSEMBLY DRAWING Figure A.1: Direct shear apparatus. 112

130 APPENDIX B DESIGN OF TEST APPARATUS FOR MODE-I FATIGUE TESTING OF THIN FOILS Thin metallic foils, with a thickness less than 0.3 mm, are used in a variety of applications including seals in gas turbines, face-sheets of metallic honeycomb panels used for metallic thermal protection systems of space vehicles. Investigations of the fatigue crack growth behavior of foil-thickness materials are becoming increasingly important. However, currently there is very little information available in the literature concerning the test procedures and specimen geometries required; even less is know about the fatigue crack growth behavior of thin foils. I designed a new test apparatus driven by magnetic force. Because the axial force that the new machine can produce is very low, and can be adjusted by the distance between the magnet and the specimen, the apparatus can be used to test ultra thin foil with a thickness as small as 5 µm. The prototype of the new apparatus is shown in Figs. B.1 - B

131 Figure B.1: The configuration of the new mode-i ultra thin foil fatigue machine. Figure B.2: The front side of the new mode-i ultra thin foil fatigue machine. 114

132 Figure B.3: The new mode-i ultra thin foil fatigue machine. 115