Failure analysis of serial pinned joints in composite materials

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 18, April 2011, pp Failure analysis of serial pinned joints in composite materials Alaattin Aktaş* Department of Mechanical Engineering, Uşak University, Uşak 64300, Turkey Received 23 July 2010; accepted 17 February 2011 In this paper, failure load and failure mode of woven glass epoxy composite plates with one and two serial pinned joints are analyzed experimentally and numerically. Two variables are investigated during analyses; the distance from the free edge of the plate to the diameter of the first-hole (E/D) ratio, and the width of the specimen to the diameter of the holes (W/D) ratios. Experiments are carried out according to the ASTM D Numerical study is performed by means of ANSYS finite element analysis program. Yamada Sun failure criterion is used for failure analyses. Mechanical properties of the composite material are obtained from the ASTM standards. The results showed that maximum failure load is obtained at E/D=4 and W/D=4. A good agreement is found between experimental results and numerical predictions. Keywords: Serial-pinned joint, Bearing strength, Failure mode One of the applications of pinned-joints is the construction of fiber reinforced composite structures. These joints are potential problem regions to the designers due to stress concentrations, and therefore, the strength of such a structure is dependent on the strength of its joints. This aspect of pinned-joints has attracted attention from many researchers Among them, Karakuzu et al. 2 investigated the effects of the distance between two holes-to-hole diameter ratio on the failure load and the failure modes in laminated woven-glass vinyl ester composite plates with two circular holes in serial. The failure analysis was performed numerically and experimentally. The LUSAS commercial finite element software was used for numerical analysis however; the failure mode was not predicted properly because, LUSAS program has not been improved for mechanical purpose. It has been improved for civil engineering problems. Aktas et al. 3 investigated the failure load and failure mode of glass-epoxy composite plates with one and two parallel pinned joint experimentally and numerically. The numerical study was performed by means of ANSYS finite element analysis program and good agreement was found between numerical and experimental study. Aktas and Dirikolu 4 studied the effect of stacking sequence of carbon epoxy composite laminates, with (0 /45 /-45 /90 ) S, and (90 /45 /-45 /0 ) S configuration, on pinned joint. For both configurations, the bearing strength reaches the maximum value at W/D=4 and E/D=4 geometric configuration. Sheng et al. 5 experimentally studied the * alaattin.aktas@usak.edu.tr pinned-joint for various stacking sequences of a T80011/ carbon-epoxy composite plate and also determined the maximum bearing strength and the failure mode. Okutan et al. 6 studied the bearing strength of pin loaded Kevlar-epoxy laminates experimentally. Shokrieh and Lessard 7 developed a three-dimensional non-linear finite element code to analyze the effects of material nonlinearity and the edge effects on the state of stress and failure prediction near the stress concentrations of a pinloaded graphite-epoxy laminated composite plate. Dano et al. 8 discussed influence of failure criteria and the inclusion of geometric and shear non-linearity. Ahn et al. 9 performed a nonlinear finite element analysis to consider the contact and friction between the pin and the laminate for unidirectional and woven composite laminated joints of an aircraft control rod. Pierron et al. 10 studied the behavior of woven glass fiber epoxy pin joints both numerically and experimentally, with particular attention given to the sensitivity of the model to different parameters such as clearance, friction, and material nonlinearity. This study is the continuity of the previous work of Aktas et al. 1 in which, the authors compared the single and parallel pin joints experimentally and numerically. However, in this study, the effects of E/D and W/D ratios on failure mode and failure load are investigated in the laminated woven glass fiber composite plate with one and two serial circular holes. The behavior of pin loaded composite plates was observed experimentally and numerically with various dimensions. The numerical study

2 AKTAS: FAILURE ANALYSIS OF SERIAL PINNED JOINTS IN COMPOSITE MATERIALS 103 was performed using ANSYS commercial software. Yamada-Sun failure criterion is used to obtain failure load and failure mode of the laminated plates. Problem Definition In this study, two types of pin joint plates are analyzed. One has single and the other has two serial holes as shown in Fig. 1a and 1b, respectively. The specimen with single hole of diameter (D) is located along the centerline of the plate (Fig. 1a). The center of the hole is located at distance (E) from one end. A uniform tensile load (P) is then applied to the plate, and this load is resisted by a rigid pin. The load is parallel to the plate and is symmetric with respect to the centerline. In the serial pin specimen, the distance between the two serial holes is taken 24 mm so that the failure mode gives the bearing mode 3. Since this mode gives the highest strength in pinnedjoint uses, the uniform tensile load (P) is then applied to the plate with the procedure of the single hole. In general, there are three basic pinned joint failure modes related to composites: These are net tension, shear-out, and bearing. Combination of these, i.e., mixed modes, may also appear as shown in Fig. 2. Net tension occurs catastrophically and presents the least strength. Designers are required to obtain the optimum E/D and W/D ratios to get the bearing mode, which shows the highest strength in pinned-joint uses. The behavior of the joint could be influenced by four groups of parameters 11 : (i) Material parameters: Fibre types and form, resin type, fibre orientation and laminate stacking sequence; (ii) Geometry parameters: Specimen width, W, or ratio of width to hole diameter, W/D, edge distance, E, or ratio of the edge distance to hole diameter E/D and specimen thickness (t); (iii) Fastener parameters: Fastener type, clamping area, hole size and fastener diameter; and (iv) Design parameters: Loading type, loading direction and failure criteria. Clearly, there are many variables involved in practical joints; therefore, complete characterization of joints is highly dependent on the hole geometry of the connection, including the edge distance, and the width. Experimental Procedure The fiber reinforced composite materials used in this study were manufactured from the 120 g/m 2 woven fabric, epoxy resin (Bisphenol ACY-225) and hardener (Anhydride HY-225). A hot lamination press was used for fabrication of composite plates. Laminated plates were retained at a constant pressure (250 kpa) and 130 C during 2 h for the curing process, and then the composite plate was cooled to room temperature at the same pressure. The nominal thickness and weight of the composite plates were obtained as 3.14 mm and 610 g/m 2, respectively. Specimen Preparation Woven glass-epoxy composite blanks, (0º) 4, are cut into rectangle shapes with a water-cooled diamondtipped rotary wheel for two types of testing. All cut edges were finished using a fine silicon carbide paper to remove any edge defects. The holes, typical in size of fasteners used in many airframe assemblies, were drilled using by a modified high-speed steel drilling tool with three sharp contact points to prevent fuzzy edges (Fig. 3). In this way, 6.5 mm diameter holes are Fig. 2 Three basic failure planes for pinned joints Fig. 1 Specimens dimensions Figure 3. Drill bits (a) standard, (b) modified

3 104 INDIAN J ENG. MATER. SCI., APRIL 2011 obtained on the specimens (Fig. 1). Specimens for each type were produced in the following manner: While keeping the E/D ratio as 4, the W/D ratio is varied as 2, 3, 4, and 5; and maintaining W/D as 4, E/D is changed as 2, 3, 4, and 5. Three specimens were prepared for each configuration. Material characterization In order to find the values of the longitudinal modulus, E 1, the Poisson s ratio (v 12 ), and the longitudinal tensile strength (X t ), a flat piece of woven plate, the principal axis of which coincides with the loading direction, was taken, and two strain gauges perpendicular to each other were stuck on. One of them was on principal and the other was on transverse direction. The specimen was loaded step by step up to rupture by means of a 50 kn loading capacity testing machine at a speed of 1.5 mm/min, and for all steps ε 1 and ε 2 were measured by an indicator. The same procedure was performed for the determination of transverse modulus (E 2 ), and the transverse tensile strength (Y t ). To define the respective longitudinal and transverse compressive strengths (X c ) and (Y c ), a flat piece of woven plate, the principal axis of which coincides with the loading direction was taken, and it was subjected to compressive loading up to failure. To obtain the shear modulus (G 12 ); a plate whose principal axis was on 45 was taken. Then, a strain gauge was stuck along the loading direction. The specimen was loaded step by step up to rupture and (G 12 ) was calculated by measurement of ε x, which is the strain in the tensile direction. To obtain the railshear strength (S), a series of specimens were tested. These tests were performed by placing the rail shear fixture into the testing machine and by applying compressive load. The rail-shear strength is obtained by dividing the ultimate failure load of the laminate by the sheared cross-section. The ASTM standards used for determination of the mechanical properties are given in Table 1, and the mechanical properties of the composite plate determined by the above method are given in Table 2. Testing procedures Table 1 Summarize of the ASTM standards The tests were conducted with reference to ASTM D953-D 2 at room temperature of ~20 C. One for single hole and two for serial holes through-hardening steels, 42CrMo4, hardened (by heating at 850ºC for 2 h and then quenched in oil at room temperature) and then polished pins were later inserted in holes nearly no clearance. Then, experiments were performed by Test type Determination of Specimengeometry ASTMStandard E Tensile test specimen, 1 (MPa) ASTM 12 ν Uniaxial direction X ç (MPa) Tensile test specimen, Transverse direction to fiber Shear modulus specimen Off-axis uniaxial loading E 2 (MPa) ν 21 Y ç (MPa) G 12 (MPa) ASTM [12] ASTM Shear test specimen Uniaxial direction S (MPa) Reference 14 Compressive test Uniaxial direction X b (MPa) ASTM Compressive test Transverse direction to fiber Y b (MPa) ASTM Table 2 Mechanical properties of the woven glass-epoxy composite plate E 1 =E 2 (GPa) G 12 (GPa) ν 12 X t =Y t (MPa) X c =Y c (MPa) S (MPa) R ot (mm) R oc (mm) Fiber [%]

4 AKTAS: FAILURE ANALYSIS OF SERIAL PINNED JOINTS IN COMPOSITE MATERIALS 105 means of custom fixtures on the 50 kn loading capacity universal machine with a speed of 1.5 mm/min. Characteristic lengths Characteristic length for tension (R ot ) In this study, the characteristic length for tension was determined by applying point stress criterion to the tensile specimen with a hole. This criterion has been suggested by Whitney and Nuismer 16. Figures 4a and 4b show the description of the point stress criterion and its specimen, respectively. In this criterion, failure has been said to occur when the tensile stress (σ y ) in the load direction is equal to unnotched laminate strength (σ 0 ) at some distance (R ot ) from the edge of the hole. R ot has been called characteristic length for tension 11 (Table 2). Characteristic length for compression (R oc ) In order to find the characteristic length for compression, (R oc ) bearing failure test was used (Fig. 4c). The specimen containing a machined half circle, 6.5 mm diameter, is at the center. The bearing failure test was applied by the hardened steel jig, 6.5 mm diameter. The bearing failure test was conducted at cross head speed of 1.5 mm/min. The dimension of the thickness (t) was chosen as 3.14 mm and (E) and (W) were 26 mm so that the failure mode gives the bearing mode. Since this mode gives the highest strength in pinned-joint uses, the failure load (P failure ) was measured by the bearing failure test. The point stress criterion was applied to the results obtained from the bearing failure test and the characteristic length for compression was obtained as shown in Fig. 4d. In this criterion, failure occurs when the compressive stress in the load direction equaled bearing strength (σ b ) at some distance from the arc edge. In this study, the compressive stress distribution at P failure was calculated by using finite element method (FEM) and R oc was obtained from those results and given in Table 2. Numerical Study Failure criterion In order to determine the failure loads and the failure modes, a failure criterion must be applied. In this investigation, the Yamada-Sun failure criterion is used. This criterion is quadratic theory. Involving the shear stress (τ 12 ) and the longitudinal stress (σ 1 ) along the fibers, and the following criterion for laminate failure is proposed. σ 1 2 τ ( ) + ( ) = e e 1 X S Failure e< 1 no failure... (1) Fig. 4 Description of point stress criterion

5 106 INDIAN J ENG. MATER. SCI., APRIL 2011 where, σ 1 is longitudinal stress along the fibers, X is longitudinal tensile strength of ply, τ 12 is shear stress along the fibers and S is the rail shear strength. The failure criterion (Eq. 1) only predicts whether the pin joint failed or not. It does not predict the failure mode. To obtain the failure mode the characteristic curve must be drawn. This curve is specified by Eq. (2). R c( θ) = D/ 2 + ROT + ( ROC - ROT )cosθ (2) Figure 5 shows the description of the characteristic curve. Failure occurs when e is equal to unity at any point on the characteristic curve. The calculation procedure described above also provides the location (angle θ fail showing in Fig. 5) at which e is equal to unity on the characteristic Fig. 5 Description of the characteristic curve for double serial holes curve. Knowledge of θ fail provides an estimate of the failure mode of failure, as follows 14, 0 f < θ < 15 : Bearing Failure 30 <θ f < 60 : Shear-out failure (3) 75 <θ f < 90 : Net-tension failure At intermediate values of θ fail, failure may be caused by combination of these modes. Finite element analysis Ansys TM finite element package has been used in the numerical analyses. Whether or not a joint fails under a given condition is determined by the finite element analysis as follows: (i) The geometry of the problem is modeled for single and serial holes using SHELL91 elements with the characteristic curve. The composite plates were modeled as a half model because of the symmetry of loading, geometry and material with respect to x-axis the displacements of the symmetry surface are zero in y direction (Fig. 5). (ii) In order to simulate the rigid pins, radial displacement constraints were used on the lefthand sides of the holes as shown in Fig. 6. The load was applied to the nodes of the laminate positioned at right hand side of the model. Fig. 6 Flow chart for failure load and failure mode procedure

6 AKTAS: FAILURE ANALYSIS OF SERIAL PINNED JOINTS IN COMPOSITE MATERIALS 107 (iii) The stresses (σ x, σ y and τ xy ) are calculated using the finite element method. (iv) If e equals or exceeds unity in any ply along the characteristic curve, the joint is decided to have failed. The procedure outlined above is used to numerically predict whether or not failure occurs under a given load (P). The calculated stresses are linearly proportional to the applied load. A relationship is employed to determine the maximum load (P max ), which can be imposed on the joint. For a given load (P) values of e are calculated on the characteristic curve for two cases as discussed above. The highest value of e (e 0 ) is determined, and the maximum load is calculated by the expression: P P max = (4) e 0 In order to find the failure mode, the criterion of Eq. (3) used. The procedure outlined above is shown as a chart in Fig. 7. However, in serial case, the failure loads are calculated for each hole numerically and these two loads (Let P 1 be the load available in the hole far from the free edge and P 2 be the load available in the other hole) are sum up, and then the load P 1 is divided to the sum of the loads, i.e. P P 1 = P + P 1 2 (5) Finally, failure load which occurs at each holes are calculated from Eq. (4) using the load obtained from Eq. (5) for serial pin case. The percentage of the loads which occurs at the hole far from the free edge of the specimen was given in Table 3. Results and Discussion Failure loads and failure modes of composite specimens with single and double serial holes which are subjected to reaction force by two rigid pins are investigated experimentally and numerically. In order to obtain the optimum geometry for two cases, the ratio of the edge distance to the pin diameter (E/D), Fig. 7 The effect of E/D ratio on failure load for single and serial pinned-joints

7 108 INDIAN J ENG. MATER. SCI., APRIL 2011 E/D=4 W/D=4 Table 3 The percentage of loads which occur at the hole far from the free edge of the specimens and the ratio of the specimen width to the pin diameter (W/D) have systematically been varied during analyses. Custom made fixtures on a testing machine and Ansys TM finite element package has respectively been used for pinned joint experiments and numerical solutions. Three tests were conducted for each type of specimen and average bearing load values were calculated. W/2 W/3 W/4 W/5 %88 %81 %69 %66 E/2 E/3 E/4 E/5 %69 %73 %69 %60 Failure load In serial case, the maximum failure load was calculated numerically from the procedure described in the finite element analysis section, and experimentally by multiplying the percentage of the hole far from the free edge given in Table 3 with the load obtained from the test. In this table, for example, in case of W/D=2 and E/D=4 (Table 3), while the hole far from the free edge of the specimen resists the 88% of the total applied load, on the other hand, the other resists 12%. The bearing loads with respect to E/D (W/D=4 is constant) for one and two serial pinned joints are shown in Fig. 8. When E/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases both experimentally and numerically however, the maximum and minimum values of the failure loads are close to each other. The results from both analyses show nearly the same trends. An interesting result is that the failure load for the serial hole is less than the single one. The reason for this may be that the most of load are carried by the hole far from the free edge of the specimen (Table 3). The bearing loads with respect to W/D (E/D=4 is constant) for single and serial pinned joints are shown in Fig. 9. When W/D is equal to 2 and 4, the failure loads takes its minimum and maximum value, respectively for two cases both experimentally and numerically. But the minimum and maximum values of loads are considerably far to each other because when W/D is equal to 2 the failure mode is net tension. Net tension occurs catastrophically and presents the least strength. The failure load of serial case is less than the single case as shown in Fig. 8. The reason is that the most of load are carried by the hole far from the free edge of specimen. In two Fig. 8 The effect of W/D ratio on failure load for single and serial pinned-joints Fig. 9 FEM and experimental results of failed specimens for serial pinned-joints figures the maximum failure loads are reached at E/D=4 and W/D=4. Failure mode In case of two holes in serial, only two types of photographs and FEM results of failure modes are given in Fig. 10. Since two types of these modes occur merely for the pins loaded in serial. One is net tension which shows least strength for W/D=2 (Fig. 10a), and the other is bearing mode, which shows the highest strength for W/D=4 (Fig. 10b). The other configurations of E/D and W/D give bearing mode. Failure occurs firstly in the pin hole far from the free edge of the specimens, because this pin hole is subjected to the highest stress (Table 3).

8 AKTAS: FAILURE ANALYSIS OF SERIAL PINNED JOINTS IN COMPOSITE MATERIALS 109 Figure 11 shows that when E/D and W/D is equal to 2 and 4, respectively, failure mode is net tension in the pin hole far from the free edge and shear out in the pin hole near the free edge of the specimen. Failure mode gives bearing mode in other configurations of E/D and W/D. In case of single hole, a photograph and FEM result are shown in Fig. 12a for the configuration of W/D=2 (E/D=4 is constant). In this figure, it is clear that failure mode is net tension. Another photograph and FEM result are shown in Fig. 12b for E/D=4 and W/D=4. In this configuration, the failure mode is bearing mode. An experimental and numerical result is shown in Fig. 13 for E/D=2 and W/D=4. It can be shown from the figure that the failure mode is mixed mode. It can be seen from figures that failure modes obtained from the experimental and numerical results are very close. Fig. 10 FEM and experimental results of failed specimens for serial pinned-joints (E/D=2 and W/D=4) Fig. 12 FEM and experimental results of failed specimens for single pinned-joints (E/D=2 and W/D=4) Fig. 11 FEM and experimental results of failed specimens for single pinned-joints Fig. 13 FEM and experimental results of failed specimens for single pinned-joints (E/D=2 and W/D=4)

9 110 INDIAN J ENG. MATER. SCI., APRIL 2011 Conclusions In the present paper, failure strength and failure mode of glass-epoxy composite plates with single and serial pinned joints has analyzed experimentally and numerically. Two variables were investigated during analyses; the distance from the free edge of plate to the diameter of the first hole (E/D) ratio (2,3,4,5), and the width of the specimen to the diameter of the holes (W/D) ratios (2,3,4,5). Experiments were carried out according to the ASTM D953-D 1. The numerical study was performed by means of ANSYS finite element analysis program. The following results are obtained from the numerical and experimental studies: In case of a serial hole (i) Minimum failure load is obtained W/D is equal to 2 when E/D=4 and W/D is equal to 2 when W/D=4. (ii) Maximum failure load is obtained at E/D=4 and W/D=4. (iii) Failure starts firstly at the hole far from the free edge since maximum failure load occurs at this hole. Therefore, when designers design their connections, they must take into account this failure load occurred at this hole. (iv) Failure modes give bearing mode at all geometrical configurations except, W/D=2 (E/D=4) and E/D=2 (W/D=4). In case of a single hole (i) Minimum failure load is obtained when W/D=2 (E/D=4) and E/D=2 (W/D=4). (ii) Maximum failure load is obtained when E/D and W/D is equal to 4. (iii) Failure modes give net tension and mixedmode when W/D=2 (E/D=4) and E/D=2 (W/D=4), respectively but other geometrical configurations give bearing mode. References 1 ASTM D 953-D, Standard test method for bearing strength of plastics, ASTM Designation, Karakuzu R, Çalışkan R, Aktas M & Icten B, Compos Struct, 82 (2008) Aktas A, Imrek H & Cunedioglu Y, Compos Struct, dio: /j. compstruct Aktas A & Dirikolu M H, Compos Struct, 62 (2003) Sheng H, Hung C & Chang F K, J Compos Mater, 30 (1996) Okutan B, Aslan Z & Karakuzu R, Compos Sci Technol, (2001) Shokrieh M M & Lessard L B, J Compos Mater, 30 (1996) Dano M L, Gendron G & Piccard A, Compos Struct, 50 (2000) Ahn H S, Kweon J H & Choi J H, J Reinforce Plastic Compos, 24(7) (2005) Pierron F, Cerisier F & Grediac M, J Compos Mater, 34 (12) (2000) Aktas A & Dirikolu M H, Compos Sci Technol, 64 (2004) ASTM D , Standard test method for tensile properties of fiber resin composites, American Society for Testing and Materials, ASTM D , Standard test method for in-plane shear response of polymer matrix composite materials by tensile test of a ±45 laminate, Aktas A & Karakuzu R, Mech Compos Mater Struct, 6 (1999) ASTM D , Standard test method for compressive properties of unidirectional or cross-ply fiber resin composites, American Society for Testing and Materials, Whitney J M & Nuismer R J, J Compos Mater, 8 (1974)