Characterization of Carbon Mat Thermoplastic Composites: Flow and Mechanical Properties

Transcription

1 Characterization of Carbon Mat Thermoplastic Composites: Flow and Mechanical Properties Aaron C. Caba Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering Mechanics Prof. Romesh C. Batra, Chairman Prof. Alfred C. Loos Prof. Donald G. Baird Prof. Michael W. Hyer Prof. Saad A. Ragab Prof. Ronald D. Moffitt Sept. 14, 2005 Blacksburg, Virginia Keywords: Wetlay, squeeze flow, carbon fiber, carbon mat thermoplastic, fiber-fiber interaction. c 2005, Aaron C. Caba, ALL RIGHTS RESERVED

2 Characterization of Carbon Mat Thermoplastic Composites: Flow and Mechanical Properties Aaron C. Caba ABSTRACT Carbon mat thermoplastics (CMT) consisting of 12.7 mm or 25.4 mm long, 7.2 µm diameter, chopped carbon fibers in a polypropylene (PP) or poly(ethylene terephthalate) (PET) thermoplastic matrix were manufactured using the wetlay technique. This produces a porous mat with the carbon fibers well dispersed and randomly oriented in a plane. CMT composites offer substantial cost and weight savings over typical steel construction in new automotive applications. In production vehicles, automotive manufacturers have already begun to use glass mat thermoplastic (GMT) materials that use glass fiber as the reinforcement and polypropylene as the matrix. GMT parts have limitations due to the maximum achievable strength and stiffness of the material. In this study the glass fibers of traditional GMT are replaced with higher strength and higher stiffness carbon fibers. The tensile strength and modulus and the flexural strength and modulus of the CMT materials were calculated for fiber volume fractions of 10% 25%. Additionally, the length of the fiber (12.7 mm or 25.4 mm) was varied and four different fiber treatments designed to improve the bond between the fiber and the matrix were tested. It was found that the fiber length had no effect on the mechanical properties of the material since these lengths are above the critical fiber length. The tensile and the flexural moduli of the CMTs were found to increase linearly with the FVF up to 25% FVF for some treatments of the fibers. For the other treatments the linearly increasing trend was valid up to 20% FVF, then stiffness either stayed constant or decreased as the FVF was increased from 20% to 25%. The strength versus FVF curves showed trends similar to those of the modulus versus FVF curves. It is shown that choosing an appropriate sizing can extend the usable FVF range of the CMT by at least 5%. Published micromechanical relations over-predicted the tensile modulus of the composite by 20% 60%. An empirical fiber efficiency relation was fit to the experimental data for the tensile modulus and the tensile strength giving excellent agreement with the experimental results. Flow tests simulating the compression molding process were conducted on the CMT to determine what factors affect the flow viscosity of the CMT. The melt viscosity of the neat PP was measured using cone and plate rheometry at temperatures between 180 C 210 C and was fit with the Carreau relation. The through thickness packing

3 stress of the CMT mat was measured for FVFs of 8% 40% and was found to follow a power law behavior based on the local bending of fibers up to a FVF of 20.9%. Above this FVF the power law exponent decreases, and this is attributed to fracture of some of the fibers. Heated platens were used to isothermally squeeze the CMT at axial strain rates of s 1. The plot of the load-displacement behavior for the 10% FVF CMT was similar in shape to that for a fluid with a yield stress. For FVFs of 15% 25% the load-displacement curves showed a load spike at the beginning of the flow, then followed the curve for a fluid with a yield stress. The matrix was burned off the squeezed samples, and the remaining carbon mat was dissected and visually inspected. It was found that fiber breakage increased and fiber length decreased as the FVF of the sample was increased. iii

4 Dedication This work is dedicated to my wonderful parents, Donald and Dorothy. Their loving support over the years helped shape me into the person I am today. Their suggestion that I pursue a Ph.D. gave me the impetus and desire to reassess my life and get another degree. I also want to thank my loving wife Beth for all of her support and understanding over the years. iv

5 Acknowledgments Many people have helped with this effort. David Litchfield ran the rheometry experiments on the polymer, Joe Price-O Brien made sure the wetlay laboratory was ready to go when I needed to make more material, and kept all of the other equipment running. Danny Reed helped with manufacturing in the Composites Fabrication Laboratory. I would like to thank the Department of Engineering Science and Mechanics and the Center for High Performance Manufacturing for supporting me during my stay at Virginia Tech. v

6 Contents Contents List of Figures List of Tables List of Symbols List of Acronyms vi ix xii xiv xviii 1 Introduction Random Mat Thermoplastic Composites Wetlay Process Research Objectives Literature Review Reinforced Thermoplastic Mat Rheology Micromechanics Squeeze Flow Flow Induced Fiber Orientation Fiber Strength Micromechanics of Oriented Discontinuous Composites Shear Lag Theory Critical Fiber Length Tensile Modulus of Discontinuous Fiber Composites Elasticity Solution Area Fraction Fiber Efficiency Laminate Approximation Christensen and Waals Manera Tensile Strength of Discontinuous Fiber Composites vi

7 2.7.1 Miwa and Endo Theory Hahn Laminate Theory Chen Laminate Theory Baxter Laminate Theory Percolation Model Mechanical Testing EMI/RFI Shielding Manufacture of CMT Constituent Materials Wetlay Manufacturing Process Plaque Manufacture Conclusions Mechanical Characterization Introduction Experimental Tensile Testing Flexural Testing Density, FVF, and Void Content Results Density, FVF, and Void Content MD versus TD Testing C/PP Mechanical Testing C/PET Mechanical Testing C/PP Compared to C/PET Micromechanical Model Evaluation Specific Strength and Modulus Comparisons Comparison to Literature Results Comparison of Flexural and Tensile Test Results Fracture Surfaces Conclusions Flow Characterization Introduction Rheometry of Polypropylene Through Thickness Stress Measurement Theoretical Background Equipment Material List Experimental Procedure Results Single Fiber Pull-Out vii

8 5.4.1 Theoretical Background Equipment Material List Experimental Procedure Results Discussion Conclusions Squeeze Flow Theoretical Background Equipment Material List Procedure Results Conclusions Conclusions Contributions 108 Bibliography 110 A Fixture Schematics 120 B Wetlaid CMT Batches 122 C Manufactured Test Plaques 125 D FVF, Mass Density, Wt% and Void% Data 129 E Tensile and Flexural Data 132 E.1 Raw Data E.2 C/PP Flexural Test Results E.3 C/PET Flexural Test Results Vita 145 viii

9 List of Figures 1.1 Schematic of the wetlay line Forces at a fiber-fiber touch point Squeeze flow with: a) constant volume deformation, and b) constant area deformation Dimensions before (dark gray) and after (light gray) squeezing Fiber effective length Measured flow rates for the stock pump Picture of the mm plunger mold Picture of plaque that did not flow kn Wabash hot press Picture of the mm die mold Generic plaque molding cycle Temperature cycle during molding of a C/PP plaque C-scan of a 25 vol% C/PET panel showing the back surface reflection C-scan of a 25 vol% C/PET panel showing the mid-surface reflection Cutting templates for mechanical test samples Tension test setup Flexural test setup Chamber (left) and oven (right) for burn-off testing Typical time-temperature curve for the burn-off experiments An unburned sample, burned C/PET sample, and burned 100% PET sample showing incomplete degradation C/PET mass density and VVF C/PP mass density and VVF MD and TD strength comparison for C/PET MD and TD tensile modulus comparison for C/PET Typical tensile stress strain curves for C/PP CMT Axial tensile properties of C/PP CMT Typical tensile stress strain curves for C/PET CMT Axial tensile properties of C/PET CMT ix

10 4.15 Comparison of the tensile properties of C/PP (-3PP sized) with those of C/PET (-11 sized) Various micromechanical predictions of C/PET tensile modulus Fiber efficiency factor model for C/PET tensile strength Various micromechanical predictions of C/PP tensile modulus Fiber efficiency factor model for C/PP tensile strength Specific tensile strength comparison Specific tensile modulus comparison Specific flexural strength comparison Specific flexural modulus comparison Comparison of the ultimate tensile strength of discontinuous carbon fiber thermoplastic composites Comparison of the tensile modulus of discontinuous carbon fiber thermoplastic composites Comparison of C/PET (-11 sized) flexural and tensile results Comparison of C/PP (-3PP sized) flexural and tensile results SEM picture of fracture surface of 10% FVF C/PET, SEM picture of fracture surface of 10% FVF C/PET, SEM picture of fracture surface of 10% FVF C/PET, SEM picture of fracture surface of 15% FVF C/PET, SEM picture of fracture surface of 20% FVF C/PET, SEM picture of fracture surface of 25% FVF C/PET, SEM picture of fracture surface of 10% FVF C/PP, SEM picture of fracture surface of 10% FVF C/PP, SEM picture of fracture surface of 15% FVF C/PP, SEM picture of fracture surface of 20% FVF C/PP, SEM picture of fracture surface of 25% FVF C/PP, Viscosity of PP melt and Carreau relation fit Squeeze flow fixture mounted in MTS load frame, and closeup of the fixture LabVIEW virtual instrument used to acquire data Specimens for squeeze flow experiments Through thickness stress versus FVF for the low speed tests Through thickness stress versus FVF for the high speed tests Sketch of the fiber pull-out fixture Pull-out fixture mounted in the load frame Pull-out fixture closeup Method of obtaining a single carbon fiber Typical force versus time curve for a single fiber pull-out experiment for 10.2% C/PP CMT Force versus pulling speed for C/PP CMT x

11 5.13 Typical force versus time curve for a single fiber pull-out experiment for 15% C/PP CMT Linearly decreasing force versus time curve for the broken fiber pull-out tests Force decay results for single fiber pull-out Squeeze flow sketch Sketch of a single fiber in the flowing CMT Squeezed sample Typical measured versus expected axial strain rates for the squeeze flow experiments Load versus platen separation for the 2 mm thick, 10% FVF samples Load versus platen separation for the 4 mm thick, 10% FVF samples Load versus platen separation for the 15% FVF samples Load versus platen separation for the 20% FVF samples Load versus platen separation for the 26.2% FVF samples % FVF sample after squeezing and burn-off (scale division=1 mm) % FVF sample after squeezing and burn-off (scale division=1 mm) % FVF sample after squeezing and burn-off (scale division=1 mm) % FVF sample after squeezing and burn-off (scale division=1 mm) p versus z strain rate for the high speed testing. The theoretical stress curves were calculated using the original fiber length of 12.7 mm A.1 Fiber pull-out fixture E.1 Typical flexural stress strain curves for C/PP CMT E.2 Flexural strength of C/PP CMT E.3 Flexural modulus of C/PP CMT E.4 Ultimate flexural strain of C/PP CMT E.5 Typical flexural stress strain curves for C/PET CMT E.6 Flexural strength of C/PET CMT E.7 Flexural modulus of C/PET CMT E.8 Ultimate flexural strain of C/PET CMT xi

12 List of Tables 2.1 Calculated values of φ 1 and φ 2 for three orientations Parameters in the Halpin-Tsai equations Whitewater Chemical Concentration Wetlay line settings Plaque molding parameters Test variables Measured material density Estimated strength and modulus coefficients for the C/PET MD vs. TD tests. Fits are valid for 0.1 V f Estimated strength and modulus coefficients for the C/PET mechanical tests. Fits are valid for 0.1 V f Material Properties Used in the Micromechanics Models K σ and K E values for the fiber efficiency theory Carreau parameters of PP Parallelism of squeeze flow fixture Low speed through thickness stress samples High speed through thickness stress samples, 4 mm thick Fit constants for high speed testing Values used in Equation (2.10) High speed through thickness stress samples, 2 mm thick Calculated maximum critical fiber lengths by FVF B.1 Batches of wetlaid material C.1 Carbon/PET Plaques C.2 Carbon/PP Plaques D.1 Measured FVF, density, wt% and void% of C/PP D.2 Measured FVF, density, wt% and void% of C/PET E.1 Measured tensile properties of C/PET xii

13 E.2 Measured flexural properties of C/PET E.3 Measured tensile properties of C/PP E.4 Measured flexural properties of C/PP xiii

14 List of Symbols a minor radius of a fiber bundle (m) a T shift factor in the Carreau relation b major radius of a fiber bundle (m), linear fit parameter c n normal force vector at a fiber-fiber contact point (N) c f fiber-fiber friction force vector (N) d fiber diameter (m) e ratio of r 1 /r 2 f fiber orientation distribution f l (l) fiber length distribution function g ratio of r 1 / r 2 h platen separation or specimen height (m) h 0 initial platen separation or specimen height (m) k f friction coefficient k h hydrodynamic lubrication coefficient (m 2 ) l fiber length (m) l 0 Weibull fiber strength parameter l c critical fiber length (m) l max maximum length of a fiber in flowing CMT (m) ( ) 1/(n 1) ( ) n/(n 1) l n a function of n, l n = 4 2n+1 3(n+3) n m length fraction of fiber-matrix debonded, linear fit parameter m c mass of the composite sample (kg) m f mass of fiber (kg) m frac mass fraction of residue after burn-off test m lost mass lost during burn-off test (kg) m m mass of matrix (kg) n power law exponent of a fluid or Carreau exponent n power law exponent in the fiber packing stress equation number of fiber center points per unit volume n f n (i) p 1, p 2 number of fibers touches along a given fiber coefficients that control the shape of the fiber orientation distribution xiv

15 p orientation unit vector p average pressure (Pa) q Weibull fiber strength parameter r fiber radius (m) r 0, r 1, r 2 radii of squeezed specimen (m) r 1, r 2 change in radius of squeezed specimen (m) s Tung fiber length distribution parameter t Tung fiber length distribution parameter u closing speed of squeeze flow fixture (m/s) v fiber pulling velocity (m/s) v x, v y flow velocity components (m/s) v r, v θ, v z flow velocity components (m/s) x cross head displacement (m) x 0 cross head displacement when the fiber pulls out of the fixture (m) x i factors in the multiple linear regression analysis A f area fraction of fibers on a cross section A m area fraction of matrix on a cross section C I fiber orientation interaction coefficient DI ductility index E f fiber longitudinal Young s modulus (Pa) E m matrix Young s modulus (Pa) E max total absorbed energy (J) E perf perforation energy (J) E C randomly oriented composite Young s modulus (Pa) E F max energy absorbed until the time of the maximum force (J) E L unidirectional composite Young s modulus parallel to fibers (Pa) E T unidirectional composite Young s modulus perpendicular to fibers (Pa) E(θ) off-axis unidirectional composite modulus (Pa) E/R normalized activation energy in the Carreau relation shift factor a T (K) F squeezing force (N) F fiber pull-out force (N) F max maximum tensile force in a fiber (N) G friction force function (N) G 12 unidirectional composite shear modulus (Pa) G c critical strain energy release rate (J/m 2 ) G f fiber shear modulus (Pa) G m matrix shear modulus (Pa) randomly oriented composite shear modulus (Pa) G C xv

16 H constant in shear-lag theory, H = (2πG m )/(ln(r/r)) (Pa) K c fracture toughness (N/m 3/2 ) K E fiber efficiency factor for strength K R constant in shear lag theory K θ inclined fiber strength constant K σ fiber efficiency factor for strength L embedded length of test fiber (m) M f, M m areal moduli of a composite (Pa) N number of fiber centerlines intersecting a given volume P f Weibull fiber failure probability Q 11, Q 22, Q 12, Q 66 reduced stiffnesses of a composite lamina (Pa) R outer radius of the matrix cylinder in shear lag formulations (m) R p radius of parallel plate plastometer (m) S g local plasticity number T temperature (K) T 0 reference temperature (K) U 1, U 5 unidirectional laminate elastic invariants (Pa) V c particulate volume fraction V f fiber volume fraction, FVF V f,0 fiber volume fraction at h 0 V f,knee volume fraction where the slope of the stress vs. V f curve changes V f,max consolidated fiber volume fraction V m matrix volume fraction, VVF V p volume fraction in a fiber bundle V void void volume fraction V ol f volume of fibers V ol m volume of matrix W f weight fraction of fibers W m weight fraction of matrix α average thickness of polymer between two fibers (m) β constant in shear-lag theory, β 2 = H/(πr 2 E f ) (m 1 ) β i coefficients in the multiple linear regression analysis γ shear rate (s 1 ) γ p fiber pull-out energy (N/m) ε m far-field axial matrix strain ε xx, ε yy, ε zz components of the strain rate (s 1 ) ζ parameter in Halpin-Tsai equations η viscosity (Pa s) η complex viscosity (Pa s) xvi

17 η 0 Bingham viscosity parameter or Carreau zero shear viscosity (Pa s) κ shear strength to longitudinal strength ratio, κ = τ 12,ult /σ L λ 0 Carreau relation parameter (s) λ 1, λ 2, λ 3 extensional viscosities (Pa s) ν f fiber Poisson s ratio ν m matrix Poisson s ratio ν C randomly oriented composite Poisson s ratio ν 12, ν 21 unidirectional composite Poisson s ratios ξ parameter in Halpin-Tsai equations ρ measured mass density of composite (g/cm 3 ) ρ f mass density of the fiber (g/cm 3 ) ρ m mass density of the matrix (g/cm 3 ) σ(θ) off axis unidirectional composite strength (Pa) σ 0 Weibull fiber strength parameter (Pa) σ f axial fiber stress (Pa) σ f,ult fiber ultimate tensile strength (Pa) σ f,ult (l) average fiber axial strength as a function of length (Pa) σ f,max maximum axial stress in a fiber (Pa) σ f,ult (θ) strength of an inclined fiber (Pa) σ m axial stress in the matrix at the axial fracture strain of the composite (Pa) σ m,ult matrix ultimate tensile strength (Pa) σ p through-thickness fiber bed packing stress (Pa) σ r residual axial thermal stress (Pa) σ C randomly oriented composite strength (Pa) σ L unidirectional composite strength parallel to fibers (Pa) σ T unidirectional composite strength perpendicular to fibers (Pa) τ deb shear strength of fiber-matrix bond (Pa) τ f fiber surface shear stress parallel to the axis of the fiber (Pa) τ i fiber-matrix interfacial traction or shear strength of the matrix (Pa) τ 0 yield shear stress of a fluid (Pa) τ 12,ult unidirectional composite ultimate shear strength (Pa) φ 1, φ 2 fiber orientation functions χ 1 strength factor for fiber orientation χ 2 strength factor for fiber length ω frequency, rotation rate (rad/s) sliding direction Ψ (p, l) three dimensional orientation and length distribution function Ψ(θ) two dimensional orientation distribution function Ω(Θ, Φ) probability density function of the fiber orientation xvii

18 List of Acronyms C/PET C/PP CLT CMT DMA FVF GMT LFT MD PET PP PPP TD VVF carbon fiber and PET CMT carbon fiber and PP CMT classical lamination theory carbon mat thermoplastic dynamic mechanical analysis fiber volume fraction glass mat thermoplastic composite long fiber thermoplastic composite machine direction poly(ethylene terephthalate) polypropylene parallel plate plastometer transverse direction void volume fraction xviii

19 Chapter 1 Introduction 1.1 Random Mat Thermoplastic Composites Long fiber thermoplastic (LFT) describes a type of prepreg composite material that is composed of an inexpensive thermoplastic matrix and either chopped or continuous reinforcing fibers. Typical matrix materials include nylon, polypropylene (PP), and poly(ethylene terephthalate) (PET); typical types of reinforcing fibers include glass, aramid, organic, and carbon. The reinforcing fibers may be randomly oriented as either a continuous strand mat or as long chopped fibers which are typically 3 mm to 50 mm long. Glass mat thermoplastic (GMT) is used to describe a type of LFT that includes glass reinforcement and PP matrix [1 3]. Manufacturing with the LFT material usually employs a compression molding process. First the LFT charge is heated above the melt temperature of the matrix using either infra-red or forced hot air convection. The heated charge is then transferred to a chilled mold and the mold is closed, forcing the material to flow and fill the mold. Upon cooling, the finished part is removed from the mold. Typical cycle times of s can be achieved for production parts [4]. For short production runs, the LFT material can utilize lighter-weight tooling than that required for steel stampings, thus reducing production costs [3, 5]. These long fiber composites can offer substantial cost and weight savings over typical steel construction in new automotive applications, and automotive manufacturers have already begun to use LFT molded materials in production vehicles [4, 6 10]. To further increase the strength and reduce the weight, carbon fibers are proposed as the reinforcement material in a new carbon mat thermoplastic (CMT). Extensive characterization of GMT materials including mechanical properties [11 29] and flow properties [30 35] has been performed and reported in the literature. Models of the flow behavior of GMT have been developed that include macro- and micro-mechanical descriptions of the process [1, 34 40]. 1

20 1.2. WETLAY PROCESS 2 Figure 1.1: Schematic of the wetlay line [42]. 1.2 Wetlay Process A new, low-cost, wet-laid material is under development that will allow the use of compression molding technology to manufacture complex parts using advanced composite materials. A patented wetlay process is used to produce a discontinuous, moldable carbon fiber/thermoplastic composite prepreg. The carbon fiber can range from 6 mm to 25 mm in length, and the thermoplastic matrix can vary from cost-effective lower performance material to high-temperature/high-performance material. The wetlay process uses paper making equipment to form a wet mat of co-mingled discontinuous reinforcing fiber and thermoplastic with the reinforcing fibers either oriented randomly or aligned along a preferred axis [41, 42]. A 300 mm wide lab-scale wetlay line at Virginia Tech was used to produce readyto-mold mat from carbon and thermoplastic fibers. The line shown schematically in Figure 1.1 was used to study the formation of the mat during wetlay processing as all of the controls could be readily varied during the process. All of the material needed for this study was produced on this line, ensuring that direct control over processing variables was kept under the supervision of the researchers. The wetlay process begins by mixing the discontinuous reinforcing fibers and thermoplastic matrix together in an aqueous slurry at about 0.3% to 0.6% by weight. A

21 1.3. RESEARCH OBJECTIVES 3 high shear pulper is used to ensure that fiber bundles are broken apart into individual fibers. The slurry is diluted and pumped to the headbox where the fibers are cast onto the inclined wire, forming a mat which is subsequently de-watered using vacuum. Finally, a convection oven is used to both dry the mat and fuse the thermoplastic to the reinforcing fibers to create a porous, self-supporting mat that is easy to handle and shape. 1.3 Research Objectives Much research effort has been focused on GMT materials, including optimization of their processing capabilities and the determination of their mechanical properties. Short carbon fiber ( 2 mm long) thermoplastics have also been studied, but no research has explored the long fiber CMT material. Before the CMT material can be utilized in a production environment, its flow and mechanical properties must be quantified and laboratory scale specimens must be manufactured and tested. This research develops the knowledge base for CMT materials by performing the following four tasks: i. Manufacture the CMT material using the wetlay process. The wetlay processing characteristics of the carbon and thermoplastic fibers were investigated, including varying the lengths of carbon fibers and the resulting areal weight of the final mat. ii. Determine a processing cycle suitable for forming the material using the compression molding process. Small scale panels were manufactured to determine what combination of time, temperature, and molding pressure is necessary to produce quality parts. iii. Characterize the flow properties of the CMT material. This included measuring the flow parameters of the material under typical compression molding conditions, developing a relation that adequately describes the experimental findings, and comparing the measured characteristics of the CMT with published values of GMT. iv. Characterize the tensile strength, Young s modulus, and flexural strength and modulus as a function of fiber volume fraction. These experimental values have been compared with those derived from models available in the literature; if necessary, the available relations have been modified.

22 Chapter 2 Literature Review 2.1 Reinforced Thermoplastic Mat Typical processes to manufacture reinforced thermoplastic mat include air lay, carding, needle punching, double-belt consolidation, foamed aqueous dispersion and wetlay processing [3, 41, 43]. Various forms of random mat thermoplastic materials have been invented. The mat may be produced in rigid, partially consolidated, board-like panels such as commercial products available currently. Typically this type of product is heated to its melting point using infra-red heaters or microwave heat sources [44]. Alternatively, the mat may be produced in an air-permeable form that allows heated air to pass through the mat for faster heating; the reinforcing fibers are either randomly oriented [2, 5, 41] or partially aligned [42]. 2.2 Rheology It is important to know the viscosity of the material in order to predict flow patterns and molding forces. Different methods have been used to measure the rheology of highviscosity thermoplastic melts. Options for unfilled polymer melts include the cone and plate or parallel plate viscometer, capillary rheometer, the Ballman method, or the Meissner method. Many different relations have been proposed to predict the viscosity of polymers as a function of shear rate and temperature. Of note are the power-law, and those proposed by Ellis, Bingham, Hershel and Bulkley, and Carreau; these can be found in Baird [45]. In particular, the Carreau relation [45 47] is η(t, γ) = η 0 a T [ 1 + (λ0 a T γ) 2] n 1 2 (2.1) where η(t, γ) is the viscosity as a function of temperature, T, and the shear rate, γ, η 0 is the zero shear viscosity at the reference temperature T 0, λ 0 is approximately the reciprocal of the strain rate at the onset of shear thinning at the reference temperature, 4

23 2.2. RHEOLOGY 5 and n represents the degree of shear thinning. The shift factor a T temperature only and is given by [ ( E 1 a T = exp R T 1 )] T 0 is a function of (2.2) where E is the activation energy and R is the universal gas constant. The viscosity of polymers filled with reinforcing materials has been determined with cone and plate viscometers, tests involving bubble inflation, oscillatory shear, and squeezing flow [30 35]. Cone and plate viscometry may not provide accurate results for polymer materials filled with long fibers because the fibers tend to align with the direction of motion, while the other techniques give good results for the flow of the material Micromechanics Toll [37] proposed a relation to estimate the number of fiber to fiber contacts in a matlike structure. Consider the orientation and length distribution function Ψ (p, l) where p is an unit vector along a fiber and l is the fiber length. For a mat of mono-disperse fibers of length l and diameter d, the average number N of fibers intersecting a tube of radius d surrounding a fiber of interest is N = 2n f l 2 dφ 1 + πn f ld 2 φ 2 + πn f ld 2 (2.3) where n f is the number of fiber center points per unit volume of the mat, and the orientation functions φ 1 and φ 2 are given by φ 1 = sin p p Ψ (p, l)ψ (p, l)dp dp (2.4) φ 2 = cos p p Ψ (p, l)ψ (p, l)dp dp where p p is the angle between two fibers. orientations are listed in Table 2.1. Values of φ 1 and φ 2 for different fiber Table 2.1: Calculated values of φ 1 and φ 2 for three orientations. Orientation φ 1 φ 2 Unidirectional D random 2/π 2/π 3-D random π/4 1/2

24 2.2. RHEOLOGY 6 v α c n c f Lubricating polymer film Figure 2.1: Forces at a fiber-fiber touch point Toll and Månson [38, 48] derived equations for normal contact forces and friction forces at fiber-fiber touch points. Given a two-dimensional orientation distribution function Ψ(θ), an orientation distribution, f, was defined as f = sin(θ θ ) Ψ(θ )Ψ(θ)dθ dθ (2.5) Figure 2.1 shows forces acting at the point where two fibers touch. Assuming a well dispersed planar bed of fibers, the average normal force c n in terms of f, the FVF V f, and the longitudinal modulus of the fibers E f is given by c n = 32 5π 2 E fd 2 f 3 V 3 f (2.6) Using equation (2.6) the in-plane friction vector c f at each contact point on the fiber can be expressed as c f = G ( c n, ) (2.7) where is the sliding direction, =, and G is a friction function. Also, the packing stress σ p exerted to squeeze the planar bed of fibers through the thickness was found to be σ p = 16 π V 2 2 f f cn (2.8) d 2 Substituting for c n from (2.6) into (2.8) yields the following expression for σ p as a function of V f : σ p = 512 5π ke ff 4 V 5 4 f (2.9) In order to test the validity of equations (2.6) and (2.9) for both dry and impregnated conditions, Servais et al. [35, 36, 49, 50] devised a heated apparatus that allows one to vary the FVF and simultaneously measure the force required to pull either a single glass fiber or a fiber bundle through the mat. From these experiments they

25 2.2. RHEOLOGY 7 were able to measure both the frictional force and the hydrodynamic lubrication force at fiber-fiber contact points. The Coulomb friction law was assumed to apply. For a fiber with length L embedded in the molten material, the following relationship was obtained between the pulling force F and the pulling velocity v ( ) ( ) [ ( ) ] 2 (n 1)/2 F 256 v 8 L = k f 5π de ff 4 V 4 3 f v + k h πd fv v v f η 0 a T 1 + λ 0 a T α α (2.10) where k f and k h are unknown friction and hydrodynamic coefficients respectively, n and η 0 are the Carreau parameters of the suspending fluid, and α is the lubricating film thickness between fibers. A similar relation was determined for fiber bundles. These relations were verified by oscillatory shear measurements of the molten material Squeeze Flow Squeeze flow has been used to study high-viscosity materials. Typical flow characterization is performed using a squeeze flow viscometer or a parallel plate plastometer (PPP) that employs parallel heated platens. Usually the material to be tested is placed between two parallel plates that are driven together at constant velocity, constant force, or constant strain rate. This method of testing cannot directly produce material parameters but the resulting force-displacement curves must be fit to theoretical velocity distributions between the plates, with the material properties extracted from these fits. Either constant volume or constant area experiments are used to characterize the flow as shown in Figure 2.2. During constant volume deformation the volume of material between the plates is fixed, but the contact area between the material and the plates changes with time. Constant area experiments allow some of the material to squeeze out from between the plates, thus the area of material in contact with the plates does not change. Analytical solutions to the squeezing flow problem have been developed for a number of different types of flow and material constitutive relations including Newtonian, power law, Herschel-Bulkley, and Bingham [51 58]. Sherwood et al. [59] have studied the squeezing flow of mudcakes made from bentonite clay and water. They assumed the mudcake s material was a Bingham fluid with a yield stress. A lubrication analysis was conducted for constant area squeezing flow and the magnitude of the force required to move the plates was found to be F = 2πτ 0R 3 p 3h + 4πτ 0R 3 p 7h (2S g ) 1/2 + O (S g ) for S g 1 (2.11) where R p is the diameter of the PPP, τ 0 is the yield stress of the mudcake material, h is the platen separation, and S g is the local plasticity number defined by S g = R puη 0 h 2 τ 0 (2.12)

26 2.2. RHEOLOGY 8 Heated platens Squeezed material a) b) Figure 2.2: Squeeze flow with: a) constant volume deformation, and b) constant area deformation. where u = dh/dt and η 0 is the Bingham viscosity parameter. The experimental studies found that the measured force rose sharply as the squeezing began, then fell as the material began to flow plastically. As the platens were further closed, the force began to rise very quickly until the end of the experiment. The yield stress τ 0 of the mud cakes was found to vary with the volume fraction of clay, V c, as τ 0 (bar) = 3.9V 1.9 c (2.13) Squeeze flow of reinforced thermoplastics has been studied extensively. Typically a GMT material is squeezed isothermally between heated plates. Dweib and Ó Brádaigh [1, 34] studied the flow of GMT composed of 30 wt% discontinuous glass fibers in a PP matrix. Disks either 50 or 97 mm diameter were cut directly from the 3.7 mm thick supplied material and squeezed at a constant speed on platens of 187 mm in diameter. Squeezing speeds were varied from 0.02 mm/s up to 8 mm/s and temperatures were set at 180 C or 200 C. They assumed the flow to be either pure extensional or extensional with a shearing force at the plate walls. To produce pure extensional flow, the mold surface was lubricated with a silicone release agent. Large differences in squeezing force were found between the lubricated and the unlubricated platens. This indicates a significant shearing force between the platen surface and the GMT. Also, as the circular disk was squeezed between the plates, it was deformed into an elliptical shape as shown in Figure 2.3. The resulting major and minor radii were measured and the following relationships were defined r 1 = e r 2 (2.14) r 1 = g r 2 (2.15)

27 2.2. RHEOLOGY 9 r 2 r 2 r 1 r 0 r 1 Figure 2.3: Dimensions before (dark gray) and after (light gray) squeezing. Assuming the GMT to be an incompressible material, normal strain rates were determined to be gu ε xx = (e + g)h (2.16) eu ε yy = (e + g)h (2.17) ε zz = u h (2.18) Dweib and Ó Brádaigh used Rogers transversely isotropic incompressible Newtonian fluid model [60] and assumed full slip conditions at the material/platen interfaces. The extensional viscosities λ i were thus determined to be λ 1 = λ 3 = p (u/h) λ 2 = p ( ) e + g (u/h) 2e (2.19) (2.20) where p is the average pressure over the squeezing area. For an isotropic fluid e = g = 1 in (2.16) (2.20). Equations (2.19) and (2.20) were used to calculate the extensional viscosities in the experiments, and these results were compared to the viscosity calculated using a fully isotropic model and were found to differ by up to 20%. Kotsikos et al. [30] squeezed 50 mm diameter by 3.9 mm thick 30 wt% glass/pp GMT disks between 50 mm diameter platens heated to 180 C at axial speeds of to 2 mm/s. Their findings indicate that when squeezing force versus squeezing rate is plotted on a logarithmic chart, the relationship is generally linear, except at low

28 2.2. RHEOLOGY 10 Edge of Die Typical fiber length Effective length Ineffective length Figure 2.4: Fiber effective length. squeezing rates where the PP weeps out of the fibrous mat. As these low squeezing rates are not representative of typical industry processing, they were not included in the analysis. Two different axisymmetric flow profiles were postulated for the GMT: pure shear flow or pure extensional flow (plug flow). The experimental squeezing forces were compared with the predictions of each and it was found that the pure shear flow relations under-predicted the squeezing force by a large margin while the pure extensional flow relations matched the data much better. Kotsikos et al. [32] further developed this work by embedding pressure transducers in their squeeze flow apparatus to measure the radial pressure distribution. Mats with either continuous or discontinuous fibers in PP were studied. 150 mm diameter samples were prepared with glass content of 30% or 40% by weight. The samples were squeezed between 150 mm diameter flat plate dies at 200 C. Purely extensional flow would have a uniform pressure profile in the radial direction, while shear flow would have a parabolic profile varying from a maximum at the center to zero at the edges. While the measured pressure did drop off near the edge of the dies, it still did not agree well with either of the two profiles. They used a variational approach to estimate the flow field between the dies and found that effects of shear flow alone were not enough to account for the pressure drop. They modified their assumptions to take into account the varying length of fibers between the dies. As the mat flows out from between the dies, the effective fiber length near the edges is reduced because a part of each fiber is outside of the dies as shown in Figure 2.4. Since shorter fibers contribute less to the squeezing pressure of the material, the flow has a parabolic pressure profile, while still being dominated by extensional flow. The theories developed above were also applied to the behavior of sheet molding compound (SMC) at various temperatures [31]. SMC is typically composed of chopped glass fibers, unsaturated polyester resin, and a filler material. The pressure distribution

29 2.3. FLOW INDUCED FIBER ORIENTATION 11 of the squeezed SMC was found to lie between the profiles for pure extensional and pure shear flows, leaning toward that for a pure extensional flow. The pressure distribution seemed to drop off toward the edges of the plates as predicted by the theory. More recently researchers have begun to study non-isothermal squeezing flows. Most GMT composites are manufactured by heating the GMT to a temperature above the melting temperature of the matrix, then compression molding in a chilled tool. This has the effect of freezing a skin layer at the tooling surface while the hot material in the center continues to flow and fill the mold. Micro-rheological experiments have been used to measure the temperature dependent interactions between bundles of fibers [40]. These interactions were then fit to numerical relations and predictions of the flow and temperature histories were made. The most comprehensive model for the squeezing flow of a concentrated long-fiber suspension is by Servais et al. [50]. The fibers are assumed to be slender (d l), straight, and of uniform length l. Fiber bundles have an elliptical cross section with minor axis of length a and major axis of length b. For dispersed fibers, both a and b reduce to r, the radius of the fiber. The fibers are assumed to lie in a plane and have an orientation distribution f given by equation (2.5). The suspending matrix is assumed to be shear thinning and described by the Carreau relation. The expression found for the average pressure p over the squeezing area is ( ) l 6 l 2 p = σ p 1 + k f + k h 3a π 2 ab 2 α f V f 2 η 0 a T V p [ 1 + ( ) ] 2 (n 1)/2 l l n λa T 2α ε zz ε zz (2.21) where V p is the volume fraction of fibers in a fiber bundle which is 0.8 for square packed bundles and 1.0 for dispersed fibers, ε zz is the squeezing strain rate, and ( ) 1/(n 1) ( ) n/(n 1) 4 2n + 1 l n = (2.22) 3(n + 3) n 2.3 Flow Induced Fiber Orientation Flow of a fiber filled fluid can typically be divided into three regimes: dilute, semi-concentrated, and highly-concentrated. Fiber filled polymers can be characterized by the length of the fibers l, the diameter of the fibers d, and the FVF V f. Dilute suspensions are defined to have V f < (d/l) 2 so the typical distance between fibers is greater than l. For this case, fibers do not touch one another and can be considered to be independent of each other. Semi-concentrated suspensions are defined to have (d/l) 2 < V f < (d/l). Typical spacing between fibers is between l and d. When the FVF is in this range, the fibers will interact with each other through both hydrodynamic action and mechanical contact. Highly-concentrated suspensions occur when (d/l) < V f, and the distance between fibers is on the order of d. All composite materials of commercial interest fall in either the semi- or the highly-concentrated regime [61].

30 2.3. FLOW INDUCED FIBER ORIENTATION 12 Researchers are interested in describing a number of different flow phenomena. During the molding process the molten composite material is forced to flow and fill the mold. It is well known that this flow tends to change the orientation of fibers, thus changing the viscosity of the material and the final mechanical properties of the composite. A method to predict this orientation effect would greatly enhance the accuracy of simulations of the molding process. Folgar and Tucker [61] studied the orientation of rod-like particles suspended in a viscous fluid. Experiments with nylon and polyester monofilament fibers in silicone oil were conducted. The mixture was subjected to a simple shearing Couette flow between concentric cylinders. A theory was developed that accurately predicts the steady-state orientation distribution. In a dilute suspension the orientation of a fiber is only dependent on its initial position and the flow field. As the concentration of fibers in the suspension increases, fiber orientation will also depend on interactions among fibers. For concentrated suspensions, such as a typical reinforced thermoplastic molding material, modeling interactions among the fibers is extremely difficult. Therefore a statistical technique is used to predict the orientation distribution after the flow event. A two dimensional theory has been developed for predicting fiber orientations in the plane of the flow, or when the fiber orientations are in a single plane. A distribution function Ψ is defined such that the probability that a given fiber has the orientation between θ 1 and θ 2 is given by P [θ 1 < θ < θ 2 ] = θ 2 θ 1 Ψ(θ )dθ (2.23) To meet physical conditions, restrictions are placed on Ψ. Since a fiber oriented at an angle θ is indistinguishable from one oriented at θ + π, Ψ is assumed to be periodic with period π Ψ(θ + π) = Ψ(θ) (2.24) Therefore, the orientation of the fibers must lie between π/2 and π/2 so the distribution function must meet the following condition π/2 π/2 The evolution equation for Ψ is defined to be Ψ(θ)dθ = 1 (2.25) Ψ t = θ ( Ψ θ ) (2.26) where θ is the average angular velocity of fibers. One suggested form for θ is [61] [ θ = sin θ cos θ v x x sin2 θ v x y + cos2 θ v y x + sin θ cos θ v ] y C I γ Ψ (2.27) y Ψ θ

31 2.4. FIBER STRENGTH 13 where γ is the shear rate, v x and v y are flow velocities of the suspending fluid, and C I is an empirically determined interaction coefficient. Substituting (2.27) into (2.26) gives Ψ t = C I γ 2 Ψ θ θ [ 2 Ψ ( sin θ cos θ v x x sin2 θ v x y + cos2 θ v y x + sin θ cos θ v y y )] (2.28) Other researchers are developing a micromechanical understanding of the flow behavior of fiber filled thermoplastics. Models of individual fibers, or more generally fiber tows, have been developed that describe the rotation of these fibers in a viscous medium, and the axial stress generated in a fiber [58, 62, 63]. Many of these micromechanical relations have been incorporated in the commercial computer code Express [64 66]. This code predicts the compression molding behavior of GMT and LFT materials. It simulates the flow patterns during compression molding and computes the resulting pressure distributions. When given an initial fiber orientation in the LFT charge, it will calculate the resulting fiber orientations and the local strength of the molded part. Also, a warpage model is included that will calculate the warping of the final part due to cooling and shrinkage. 2.4 Fiber Strength The strength of the reinforcing fibers can either be assumed to be constant along the length of the fibers, or it can be allowed to vary with position. The varying fiber strength is assumed to vary as a Weibull distribution [67 70]. As fibers become longer, the cumulative number of defects in the fiber increase. The probability that a fiber of gage length l 0 will fail at an axial stress σ is given by ( ) q ] P f (σ) = 1 exp [ l 0 (2.29) σσ0 where l 0, q and σ 0 are the Weibull parameters for the fiber. 2.5 Micromechanics of Oriented Discontinuous Composites Much research has been devoted to predicting the strength and the stiffness of oriented composite materials. A good review of the existing models for stiffness is given by Tucker and Liang [71]; strength models can be found in [16, 72 79]. Shear lag theories based on oriented fibers are reviewed below and the resulting critical fiber length calculations are given.

32 2.5. MICROMECHANICS Shear Lag Theory A number of theories have been proposed to predict the stiffness of oriented discontinuous composites. One of the first approaches was the shear lag formulation of Cox [80]. A fiber in a discontinuous fiber composite can be considered to be completely surrounded by the matrix. The strain field of the matrix can be thought of as uniform with a local disturbance caused by the stiffer fiber. Shear lag theory has been developed to determine stresses in the fiber and at the fiber-matrix interface. Basic assumptions of the theory are i) the fiber is straight, slender, and cylindrical, and surrounded by a cylinder of matrix material, ii) both matrix and fiber are linear elastic and isotropic, iii) load transfer occurs through the cylindrical surface of the fiber, and iv) only two components of stress are present: an axial tensile stress σ f in the fiber and a surface shear traction τ f that acts parallel to the axis of the fiber. Assuming a perfect bond between fiber and matrix leads to the following stress distributions in a fiber of length l [19, 80] τ f = E fε m 2 [ σ f = E f ε m 1 cosh(β( 1l x)) ] 2 cosh( 1βl) 2 [ ] 1/2 [ E m sinh(β( 1 l x)) ] 2 E f (1 + ν m ) ln(r/r) cosh( 1βl) 2 (2.30) (2.31) with 0 x l, where ε m is the far-field axial strain in the matrix, r is the radius of the fiber, R is the outer radius of the matrix cylinder, E f and E m are the moduli of the fiber and the matrix, ν m is the matrix Poisson s ratio, β 2 = H πr 2 E f (2.32) H = 2πG m ln(r/r) (2.33) and G m is the shear modulus of the matrix. A number of authors have proposed different values of R for the various packing arrangements shown in Figure 4 in Tucker and Liang [71]. These can be summarized as R r = KR (2.34) V f where K R depends on the fiber packing arrangement: Cox (pseudo-hexagonal), K R = 2π/ 3 = 3.628; composite cylinders, K R = 1; hexagonal, K R = π/(2 3) = 0.907; square K R = π/4 = With an increase in stresses in the composite, debonding between the fiber and the matrix may occur over the entire length of the fiber due to the high shear stresses

33 2.5. MICROMECHANICS 15 developed at the interface between the two. In this case, the shear stress at the surface is assumed to be a constant, and the following stress state exists in the fiber [67] { 2τ i x/r 0 x l/2 σ f = (2.35) 2τ i (l x)/r l/2 < x l { τ i 0 x < l/2 τ f = (2.36) l/2 < x l τ i where the shear stress τ i is due to the friction between the fiber and the matrix. This result can also be obtained from Kelly s formulation of fiber stresses [75]. Piggott [81] assumed that debonding only occurs over a distance of ml/2 (0 m 1) from each end of the fiber. Stresses in the debonded zone are given by equations (2.35) and (2.36) for 0 x ml/2, and those in the bonded section of the fiber (ml/2 x l(1 m/2) by σ f = E f ε m τ f = rβ 2 [ E f ε m τ i l [ E f ε m τ i l r m ] [ cosh β( 1 r m l x)] 2 cosh [ (2.37) 1βl(1 m)] 2 ] [ sinh β( 1 l x)] 2 cosh [ (2.38) 1βl] 2 The non-dimensional number m depends on the shear strength of the interface. Typically, there is some debonding shear strength τ deb. Using the condition that τ f rises to the debond stress at the junction between the bonded and the debonded regions, m is given by the following implicit non-linear equation that can be solved numerically Critical Fiber Length m = E fε m 2(τ deb /β) coth [β(l/2)(1 m)] τ i l (2.39) In discontinuous fiber composites, it is well established that the strength and the stiffness of the composite depend on the length of the reinforcing fibers [74,75,82]. As fiber length is increased for a given FVF, strength and stiffness typically increase up to a point, then level off. This occurs because a fiber is not equally stressed along its length. The end portions of the fiber are less stressed than the middle of the fiber. There is a critical fiber length, l c, over which the tensile stress in the fiber rises from zero at the fiber end to its maximum in the fully stressed section in the fiber s middle. Fibers shorter than l c are not as efficient at reinforcing the composite as are fibers longer than l c. Different methods have been devised to define the critical length, and various theories have been developed to predict it from material properties. The bond strength

34 2.6. TENSILE MODULUS 16 between the matrix and the fiber plays an important role in determining the critical length. Equation (2.30) derived by Cox [80] assumes that the fibers are perfectly bonded to the matrix. In this theory, the critical length decreases with increasing axial strain, with no lower limit. This implies that any fiber, irrespective of its length, can be broken with enough strain. Kelly and Tyson [75] measured the critical lengths of fibers in composites consisting of tungsten or molybdenum wires uniaxially aligned in a copper matrix. They assumed that the interface between the fiber and the matrix can carry a maximum shear stress of τ i. Using results from both single-fiber pull-out experiments and from tensile tests on the composites, they derived the following estimate for l c l c d = σ f,ult 2τ i (2.40) where σ f,ult is the ultimate strength of the fiber and τ i is either the interface strength or the shear strength of the matrix. They defined l c /2 as the load transfer length and l c /d as the critical aspect ratio. This formulation assumes uniform fiber strength and constant interfacial stresses, and is used very often. Lacroix et al. [67] extended equation (2.40) by assuming a Weibull distribution for the fiber failure probability as given in (2.29) and allowing the interfacial stress to vary with matrix strain. The relation they obtained for the critical length is l c d = ( σf,ult (l) 2τ i (ε) ) q/(1+q) ( l d where σ f,ult (l) is the average fiber strength at length l given by ( σ f (l) = σ 0 l 1/q Γ ) q ) 1/(1+q) (2.41) (2.42) where τ i (ε) is the strain dependent interfacial shear stress and Γ is the gamma function. For a partially debonded fiber, they found an implicit equation that could be numerically solved for the critical length. 2.6 Tensile Modulus of Discontinuous Fiber Composites Elasticity Solution For fibers that are much longer than their critical length, an elasticity solution for the modulus of randomly oriented composites has been suggested by Nielsen and Chen [83]. They began with the angular dependence of the Young s modulus for a unidirectional composite, i.e., E L E(θ) = cos4 θ + E ( ) L sin 4 ET θ + 2ν 12 cos 2 θ sin 2 θ (2.43) E T G 12

35 2.6. TENSILE MODULUS 17 where E L is the Young s modulus of the composite parallel to the fibers, E(θ) is the Young s modulus of the off-axis composite, E T is the Young s modulus of the composite transverse to the fibers, G 12 is the shear modulus, and ν 12 is the major Poisson s ratio. They then used the following micromechanical relation to estimate the values for a unidirectional composite E L = E m V m + E f V f (2.44) [ ] Mf (2M m + G m ) G m (M f M m )V m E T = 2 [1 ν f + (ν f ν m )V m ] (2.45) (2M m + G m ) + 2(M f M m )V m G 12 = G m 2G f (G f G m )V m 2G f + (G f G m )V m (2.46) ν 12 = M fν f (2M m + G m )V f + M m ν m (2M f + G m )V m M f (2M m + G m ) G m (M f m m )V m (2.47) where M f = E f /2(1 ν f ), M m = E m /2(1 ν m ), V m is the matrix volume fraction, G f is the fiber shear modulus, and ν f is the fiber Poisson s ratio. Finally, an average modulus E C for the randomly oriented composite is calculated from π/2 E(θ)dθ 0 E C = E(θ) = π/2 (2.48) dθ 0 Numerical results are presented that show modulus versus FVF for different values of E f /E m Area Fraction Pan [84] derived the elastic constants of a randomly oriented composite based on an area-fraction concept. At any given cross section through a composite, the area of matrix and fiber can be calculated and the area fraction A f of the fibers and A m of the matrix can be computed. The relation between V f and A f was found to depend on the angle the fibers make with the cross section. The orientation of each fiber relative to a reference coordinate system can be described by a pair of angles (Θ, Φ) where the polar angle 0 Θ π and the base angle 0 Φ π. The area fraction of the fibers (A f ) and the matrix (A m ) on any cross section defined by the normal (Θ, Φ) satisfies A f (Θ, Φ) + A m (Θ, Φ) = 1 (2.49) Next a probability density function Ω(Θ, Φ) is defined to describe the fiber orientation distribution. The fiber area fraction A f is related to the FVF V f by The resulting equation for the tensile elastic modulus is A f (Θ, Φ) = Ω(Θ, Φ)V f (2.50) E C = E f Ω(Θ, Φ)V f + E m (1 Ω(Θ, Φ)V f ) (2.51)

36 2.6. TENSILE MODULUS 18 For a planar, randomly oriented composite, equation 2.51 reduces to ( V f E C = E f π + E m 1 V ) f π and using similar reasoning the Poisson s ratio is found to be ( V f ν C = ν f π + ν m 1 V ) f π (2.52) (2.53) Fiber Efficiency The following rule of mixtures type relation for the fiber-direction strength σ L and Young s modulus E L has been suggested [85]: σ L = K σ σ f,ult V f + σ m(1 V f ) (2.54) E L = K E E f V f + E m (1 V f ) (2.55) where K σ is the fiber efficiency factor for strength, σ m is the axial stress in the matrix at the fracture strain of the composite, and K E is the fiber efficiency factor for the modulus. Equations (2.54) and (2.55) are also applicable to randomly oriented composites [11]. Values of K σ, K E, and σ m are typically determined experimentally Laminate Approximation Halpin and Pagano [86] used the classical lamination theory (CLT) to predict the stiffnesses of randomly oriented fiber composites. They used the invariant properties of a unidirectional lamina [87, 88] to find the stiffnesses of a quasi-isotropic composite plate: E C =4U 5 (U 1 U 5 )/U 1 (2.56) ν C =(U 1 2U 5 )/U 1 (2.57) G C =U 5 (2.58) where G C is the in-plane shear modulus of a randomly oriented composite, and where U1 =(3Q Q Q Q 66 )/8 (2.59) U5 =(Q 11 + Q 22 Q Q 66 )/8 (2.60) Q 11 =E L /(1 ν 12 ν 21 ) (2.61) Q 22 =E T /(1 ν 12 ν 21 ) (2.62) Q 12 =ν 12 Q 22 = ν 21 Q 11 (2.63)

37 2.6. TENSILE MODULUS 19 Table 2.2: Parameters in the Halpin-Tsai equations. p p f p m ξ E L E f E m 2 G 12 G f G m 1 Q 66 =G 12 (2.64) The Halpin-Tsai equations [89] used to calculate the properties of a unidirectional composite are with E L = E f V f + E m V m (2.65) ν 12 = ν f V f + ν m V m (2.66) p = 1 + ξζv f p m 1 ζv f (2.67) ζ = p f/p m 1 p f /p m + ξ (2.68) where p and ξ are given in Table 2.2. Values from equations (2.65) and (2.66) were compared against literature data for boron-epoxy and nylon-rubber composites at various l/d ratios, and the agreement was good Christensen and Waals Christensen and Waals [90] studied a composite system with fibers randomly oriented in three dimensions. They began with a composite cylinder approximation to find the properties of a unidirectional composite. Then they postulated that the average modulus for the randomly oriented composite could be found by averaging the modulus while the fiber takes on all possible orientations in space. The properties for the randomly oriented composite are E C = V f 6 E f + [1 + (1 + ν m ) V f ] E m (2.69) Restricting the above three-dimensionally oriented composite to a state of plane stress allowed the calculation of the modulus for fibers restricted to a planar orientation E C = V f 3 E f + (1 + V f )E m (2.70)

38 2.7. TENSILE STRENGTH Manera Manera [91] combined CLT, laminate invariants, and a micromechanical formulation to obtain the following equations for a composite s tensile and shear moduli ( ) 16 E C = V f 45 E f + 2E m E m (2.71) G C = V f ( 2 15 E f + 2E m ) E m (2.72) 2.7 Tensile Strength of Discontinuous Fiber Composites Tensile strength models of random discontinuous fiber composites are not well developed. Due to the complex failure mechanisms of these materials, most authors use empirical equations for estimating their strength; some such equations using constituent properties are presented below. Kelly and Tyson [75] used a plastic stress-transfer theory to find the ultimate strength of unidirectional metal matrix composites and arrived at the following equations ( σ L = σ f,ult V f 1 l ) c + σ m (1 V f ) for l l c (2.73) 2l l σ L = τ i d V f + σ m,ult (1 V f ) for l < l c (2.74) where σ m,ult is the ultimate tensile strength of the matrix. Lees [16] extended the Kelly and Tyson equations to include fibers of unequal length in the unidirectional composites. Equations (2.73) and (2.74) are combined to give σ L = i σ f,ult(i) V f(i) ( 1 l c(i) 2l (i) ) + j τ i l (j) d V f(j) + σ m,ult (1 V f(j) ) (2.75) where i V f(i) + j V f(j) = V f, and the i represents those fibers for which l l c and the j represents fibers with l < l c. Equations (2.73) and (2.74) have been generalized by Fu and Lauke [82] to include efficiency factors for both the fiber length variation and the fiber orientation variation. The result is σ C = χ 1 χ 2 V f σ f,ult + V m σ m (2.76) where σ C is the strength of the composite, and χ 1 and χ 2 are the fiber orientation and the fiber length factors, respectively. For composites with uniform fiber length l, { l/(2l c ) l < l c χ 2 = (2.77) 1 l c /(2l) l l c

39 2.7. TENSILE STRENGTH 21 where l c is given by (2.40). The fiber length distribution can be described by a Tung distribution with parameters s and t and the orientation distribution is described by Ψ(θ) = f l (l) = stl t 1 exp( sl t ) for l > 0 (2.78) θmax θ min (sin(θ)) (2p 1 1) (cos(θ)) (2p 2 1) (sin(θ)) (2p 1 1) (cos(θ)) (2p 2 1) dθ (2.79) with parameters p 1 and p 2 that control the shape of the distribution. The function is valid for p 1 1/2, p 2 1/2, and 0 θ min θ θ max π/2. While this orientation distribution function provides a variety of distribution shapes, it is only defined over half of the necessary range. As shown in equation (2.25), the distribution must be defined over π/2 θ π/2. Fu and Lauke also assumed that the strength of a fiber bridging a crack varies with the angle the fiber makes to the crack surface. Fibers nearly perpendicular to the crack will contribute their full strength, while fibers that are at an angle to the crack surface will contribute very little to the strength of the composite. For brittle fibers (e.g. glass, carbon, etc.) inclined at an angle θ to the crack surface, the effective fiber strength σ f,ult (θ) is assumed to follow the relation σ f,ult (θ) = σ f,ult [1 K θ tan(θ)] (2.80) where K θ is a constant for the fiber/matrix system under consideration. For angles θ > arctan(1/k θ ), σ f,ult (θ) = 0. Taking the orientation distribution, the length distribution, and the equation (2.80) into account gives σ C = V f θmax θ min lmax Miwa and Endo Theory l min f l (l)ψ(θ)(l/l mean )σ f,ult (θ) dl dθ + σ mv m (2.81) Miwa and Endo [69] measured the strength of a composite with 9.9% FVF of randomly oriented carbon fibers in an epoxy matrix as it varied with temperature. They derived relations that predict the composite tensile strength when both the fiber length and the fiber strength have a Weibull distribution. The expression for tensile strength was given as σ C = 2τ i π σ C = 2τ i π { 2 + ln { 2 + ln [ ]} (1 lc /2l)σ f,ult σ m,ult V f + σ m,ult σ mv m σ r l l c (2.82) τ 2 i [ (l/d)σm,ult V f + σm,ult 2 V ]} m σ r l < l c (2.83) where σ r is the residual axial thermal stress. τ 2 i

40 2.7. TENSILE STRENGTH Hahn Laminate Theory Hahn [92] analyzed the problem of randomly oriented fiber composites using a lamination theory. Each unidirectional ply is randomly oriented in the plane, thus giving rise to a transversely isotropic laminate. Additionally, a gradual failure mechanism is introduced that allows transfer of load from failed plies to the remaining plies. Using the maximum stress failure criteria, Hahn found an expression for the strength of the random composite to be σ C σ T = { (4/π)κ [ ln ( σl )] κ 2 σ T κ (σ L /σ T ) 1/2 (2.84) (4/π)(σ L /σ T ) 1/2 κ > (σ L /σ T ) 1/2 where σ T is the strength of the unidirectional composite perpendicular to the fibers, κ = τ 12,ult /σ L and τ 12,ult is the shear strength of the unidirectional composite Chen Laminate Theory Chen s [73] theory is based on composite laminate theory. This formulation postulates that there are three possible failure modes for the composite and it is assumed that the failure mode is determined by the angle that the reinforcing fibers make with the loading direction. For small angles, the dominant failure mode is fiber failure. For intermediate angles, the failure occurs by shear of the matrix. At higher angles the matrix fails in plane-strain. The strength σ(θ) of the unidirectional composite for each region is given in the following relations where σ(θ) = K σσ L cos 2 θ τ i σ(θ) = sin θ cos θ σ(θ) = σ m,ult sin 2 θ 0 θ θ 1 (2.85) θ 1 θ θ 2 (2.86) θ 2 θ π 2 (2.87) θ 1 = tan 1 (τ i /σ L ) (2.88) θ 2 = tan 1 (σ m,ult /τ i ) (2.89) where τ i is the failure stress in shear at the weakest interface. Integrating through the thickness and assuming each infinitesimal ply has only one active failure mechanism gives the following for the strength of the composite σ C = 2τ i π ( 2 + ln K σσ L σ m,ult τ 2 i ) (2.90) It is noted that the strength efficiency factor K σ is characteristic of each material system.

41 2.8. MECHANICAL TESTING Baxter Laminate Theory Baxter [93] started with the same three failure modes as Chen, but instead used the Tsai-Hill failure criterion to combine the modes to obtain the strength for a material with aligned fibers, as a function of fiber orientation σ(θ) = [ ( cos 4 (θ) σl 2 τ12,ult 2 σl 2 ) ] 1/2 sin 2 θ cos 2 θ + sin4 θ (2.91) σl 2 The strength of the randomly oriented composite is then found by integrating and averaging (2.91) as follows σ C = 1 π π 0 σ(θ)dθ (2.92) This theory is compared against a number of fiber reinforced metal matrix composites with varying degrees of success. It is concluded that the interfacial strength plays a key role in the ultimate strength of the composite Percolation Model A percolation model was developed to estimate the strength of a random glass/pp composite [28] using the finite element method. First, a computer code uses a Monte- Carlo method to generate a composite with varying fiber lengths and orientations over a 2-D grid of elements. The mechanical properties of each element are calculated using a micro-mechanical theory that translates the fiber and the matrix properties into unidirectional composite properties. The structure is slowly loaded uniaxially until individual elements reach a failure criteria, and these elements have their properties reduced. Loading continues until the failed elements create a bridge from one edge to the other. This is the calculated failure load of the composite. Their results agree fairly well with published data up to about 30 wt% (13% FVF) of fibers. After that, the experimental data shows a leveling off of ultimate strength while the model predicts continued linear increase with reinforcement fraction. The stated reason for this leveling off of the experimental data is that at higher FVFs the fibers begin to touch each other, and the interfacial strength between fiber-fiber touches is much less than that between the fiber and the matrix. The model does not take this into account. 2.8 Mechanical Testing Extensive mechanical testing of continuous and discontinuous glass and organic fiber reinforced polymer composites has been performed [11 28, 77, 94, 95]. Most of the test results are for injection molded specimens [96]. It has been shown that molding specimens this way results in 33% to 90% of the fibers oriented along a particular axis and the rest of the fibers oriented according to the flow history near

42 2.8. MECHANICAL TESTING 24 the edges of the mold [15, 16, 76, 97]. While these studies can provide a starting point for the analysis of long-fiber reinforced composites, the very short oriented fibers in injection molded specimens makes comparison difficult at best. Blumentritt et al. [11,85] determined the tensile strength of a carbon fiber reinforced composite with the matrix being either an ionomer (DuPont Surlyn 1558 type 30), or a high-density polyethylene (Alathon 7140), or a polycarbonate (General Electric Lexan ), or a poly(methyl methacrylate) (PMMA) (DuPont Lucite 47). Fiber efficiency factors were calculated using equations (2.54) and (2.55). Typical modulus factors, K E, ranged from , and strength factors, K σ from The modulus and strength factors decreased with an increase in the reinforcement FVF. The stated reason for this was that packing defects decreased the fiber-efficiency at the higher FVFs. Crosby and Drye [13] studied nylon 6,6 reinforced with glass, PAN carbon, and aramid fibers. The materials were prepared via extrusion compounding and long fiber pultrusion to produce a range of fiber lengths. Tensile, Izod impact, and falling dart impact tests were conducted. Most theories of strength and modulus of discontinuous fiber composites only take the length and orientation distributions into account. It has been shown by Mehan and Schadler [98] that local fiber-fiber interactions may also play a significant role in determining the strength of the composite. High-modulus carbon fibers in an epoxy matrix were studied using Micro-Raman Spectroscopy to measure strains in individual fibers. It was found that stress concentrations at fiber ends can lead to increased stresses in neighboring fibers that result in damage development. They gave an example where a strength theory is modified to take into account the fiber-end stress concentration factors. Impact properties of short carbon fiber/nylon 6,6 composites were studied by Ishak and Berry [99] by using an instrumented falling weight impact fixture. Fracture parameters G c and K c were determined for FVF of carbon fiber from 0 27%. The value of G c was increased by a factor of 3 and K c by a factor of 4 over those for the unreinforced nylon. Both pull-out energy, γ p, and matrix toughness contribute to the fracture behavior of the composite. Theoretical values of G c are given by where G c (theory) = G c (matrix) (1 V f ) + γ p (2.93) γ p = V fτ i l 2 12d γ p = V fτ i l 3 c 12dl for l l c (2.94) for l > l c (2.95) Very good agreement between predicted and the experimental results was found. The long term creep and mechanical behavior of long carbon fibers in a thermoplastic matrix was studied by Bockstedt and Sajna [100]. Mechanical properties from

43 2.9. EMI/RFI SHIELDING 25 static tests leveled off when the fiber length exceeded 3 mm. Elevated temperature creep and dynamic mechanical analysis (DMA) data showed a marked improvement when the fiber length was increased from 1 mm to 12 mm. DMA of carbon fiber reinforced nylon 6,6 has been performed at strain rates of min 1 [101]. Test coupons were loaded as simply supported beams, with controlled displacement and frequency. In this manner, S-N curves were generated for materials reinforced with both long and short carbon fibers. The endurance limit for the material was found to occur when the strain rate was below 30 min 1 with strain levels below mm/mm. The long fiber composite was found to have a longer life than the short fiber composite, possibly because the long fibers were low modulus carbon with a rougher surface than the high modulus short carbon fibers. Impact testing of glass PP was conducted by Czigány and Karger-Kocsis [14]. An instrumented falling weight impact tester with a 40 mm diameter clamping unit and 20 mm diameter impactor was used to test eleven experimental products with different mat structures, matrix characteristics, and fiber/matrix coupling agents. The glass reinforcement was either continuous or discontinuous. The experimental results were analyzed using the perforation energy E perf and ductility index DI defined as follows E perf = E max h (2.96) DI = E max E F max E max (2.97) where E max is the total absorbed energy and E F max is the energy absorbed until the time of the maximum force. Reported results include total absorbed energy, perforation energy and maximum recorded force. Effects of the different matrix and interface characteristics could not be distinguished in this study and it was theorized that the high speed of this test may have masked those effects. A marked difference existed between the continuous and the discontinuous reinforcements with the continuous reinforcement outperforming the discontinuous one. 2.9 EMI/RFI Shielding While molded thermoplastics provide reasonable strength and mechanical properties, they are inherently transparent to electromagnetic interference (EMI) and radio frequency interference (RFI). Electromagnetic interference can be found across the entire frequency spectrum from less than 1 Hz for DC currents to over Hz for gamma rays. Radio frequency interference is typically limited to the range of 25 khz to 10 GHz, which is the range of conventional audio and radio frequencies. Increasing the inherent conductivity of the molded thermoplastic components will increase their shielding effectiveness [102]. To increase the electrical conductivity of the plastics, either conductive surface coatings are applied or conductive fillers are compounded into the material. Surface

44 2.9. EMI/RFI SHIELDING 26 coatings can be applied by conductive sprays, zinc-arc spraying, electro-plating, or electrolysis-plating. Conductive fillers can take the form of conductive metal particles, flakes, fibers, and metal coated glass or carbon fibers. Additionally, conductive polymers may be added to the mixture to further enhance the conductivity [ ]. Typically, conductive fibers are added to the polymer by compounding through an extruder. While this is an effective and economical mixing method, it can result in fiber breakage [102]. Experimental studies have shown that both the shape and the aspect ratio of the fillers affect the shielding capability of the material. Jou et al. [103] found that for identical weight percentages of carbon fiber in nylon 6,6, 5.0 mm carbon fiber outperformed 1.0 mm carbon fiber. The material was compounded in a twin screw extruder, pelletized, and injection molded into a circular disk. No information was given about fiber attrition during the mixing process. To improve the conductivity of carbon fiber composites, Charbonneau [102] has studied the effect of coating the fibers with metal and embedding them in a thermoplastic polycarbonate matrix. The metal coated fibers tested were of two types: the first type had approximately wt% nickel and wt% carbon and the second type of fiber had a tri-layer coating consisting of 10 wt% nickel, 30 wt% copper and 10 wt% nickel with the remainder carbon fiber. Two different blending methods were used to compound the final material. The first method results in low fiber attrition and breakage, but requires greater technical skill to achieve good fiber dispersion in the final part. The second method requires less skill, but results in higher fiber attrition. It was found that the first method showed a step increase in EMI attenuation between 5 and 10 wt%, while the second method showed an increase between 10 and 15 wt%. Additionally, attenuation at the same concentrations was greater in the first method versus the second method. The conclusion is that the first method performs better, probably due to the increased fiber length in the final part.

45 Chapter 3 Manufacture of CMT The first objective of the manufacturing portion of this research was to find acceptable manufacturing conditions for the CMT using the apparatus in the Virginia Tech- DuPont Random Wetlay Composite Laboratory located in the Virginia Tech Corporate Research Center. The second objective was to find a combination of molding cycle and presses to mold plaques of the CMT. Manufacturing runs were made at the Wetlay Laboratory and tested for acceptable mat formation during the wetlay process. Parameters in the wetlay process include initial fiber concentration in the white water, concentration of chemicals in the white water, speed of the backwater and stock pumps, speed of the wire, and temperature of the drying oven. These parameters were varied until the mat formation and subsequent drying/bonding produced a usable mat at the end of the wetlay line. Parameters that were measured included qualitative mat appearance and areal weight. Volume fractions of reinforcement varied from 10% 25%. Acceptance of the manufactured mat was judged on its qualitative appearance and smoothness or lumpiness of the mat. A total of 70 batches of material were manufactured for this study and a list of these batches by lot number is given in Appendix B. The mat varied from being very smooth to very lumpy, depending on the batch. Fifty-one different plaques were molded using heated platen hot presses. Temperature cycles were tested that allowed the mold to quickly come up to the desired temperature, while maintaining a reasonably constant temperature across the face of the plaque. Molding pressures were found that made the CMT flow and completely fill the mold. 3.1 Constituent Materials The carbon fiber chosen for this research was Zoltek (St. Louis, MO) PANEX with tensile strength 3.80 GPa, mass density 1.81 g/cm 3, diameter 7.2 µm, and length of either 12.7 mm or 25.4 mm. Two types of carbon fibers, PANEX33 and PANEX35, that differ only in the tensile modulus were used; PANEX33 fibers have a modulus of 27

46 3.2. WETLAY MANUFACTURING PROCESS GPa (33 Msi) and PANEX35 fibers 242 GPa (35 Msi) [105,106]. To aid the bonding between the fiber and the matrix, a finish or sizing, which is usually proprietary with only general information available, is applied to the fiber by the fiber manufacturer. The sizings tested in this work are the -11, -21, -3PP, and unsized types. The -11 and -21 sizings are multi-compatible with epoxy and vinyl ester resins, and the -3PP is an experimental one designed for PP [107]. Two different matrix materials have been chosen for this study. The first is Fibervisions (Covington, GA) polypropylene (PP) Type 158. The fibers are 15 denier, no crimp, no draw, and chopped to 5 mm in length, with a mass density of 0.90 g/cm 3. Since a typical GMT is manufactured with PP, this will give a direct comparison of mechanical properties of GMT and CMT. The second matrix is a poly(ethylene terephthalate) (PET) resin consisting of DuPont (Wilmington, DE) Chrystar 4434 with 1 wt% Ethanox 330 as an anti-oxidant. The PET fibers are manufactured at 16 denier with no crimp, no draw, and chopped to 6.35 mm long, with a mass density of 1.37 g/cc. PET is a higher performing matrix, and will show what, if any, strength improvements are available over PP. 3.2 Wetlay Manufacturing Process A schematic of the wetlay line is shown in Figure 1.1 on page 2. The first step of the wetlay manufacturing process was to prepare the white water with three types of chemical additives. A thickener was used to increase the viscosity of the white water, a surfactant was used to reduce the surface tension, and an anti-foam was used to reduce the amount of foaming during processing. Typical concentrations of these chemicals are listed in Table 3.1. Table 3.1: Whitewater Chemical Concentration. Type Trade Name Concentration (ppm, weight) Thickener Nalco Surfactant Rhodameen VP-532 SBP 250 Anti-foam Nalco Approximately 1200 L of white water was used to fill the wetlay system; 800 L was placed in the dilution water tank and 400 L in the pulper. Polymer fiber was added to the pulper and pulped for 5 minutes at a setting of 5 which ran the pulper at a speed about one-half of its maximum speed. The carbon fiber was then added to the pulper and the mixture was pulped at a setting of 5 for an additional 5 minutes. The total mass of fiber added to the pulper was either 500 or 1000 g resulting in an effective

47 3.2. WETLAY MANUFACTURING PROCESS Measured flow rate (l/min) Stock pump setting Figure 3.1: Measured flow rates for the stock pump. concentration of the stock of 0.12% or 0.25% by weight. After pulping, the stock was pumped to the stock tank and agitated to keep the fibers in suspension. As the stock was pumped from the feed tank to the head box it was further diluted with water from the dilution storage tank. Since the backwater pump was fixed at a speed of 240 l/min the concentration in the head box could be varied by adjusting the flow rate of the stock pump between settings of to give various flow rates as shown in Figure 3.1. Thus, the stock was diluted to between 10% to 20% of its original concentration upon entering the head box. The resulting concentration of fibers in the head box ranged between 0.012% 0.050% by weight, depending on the batch. Trial runs indicated that having a concentration of fibers in the head box that was too high caused the resulting mat to have a very lumpy appearance and poor uniformity. To reduce the concentration, either the initial batch size was reduced or the stock pump was set to a lower speed. Typical processing parameters are listed in Table 3.2. Once the mat had formed in the head box, it was de-watered using suction and passed through the oven which was set at 182 C for the PP and 249 C for the PET. The oven served as the final de-watering stage and also fused the carbon fibers and thermoplastic into the final mat. The line speed chosen for all manufacturing runs was 1.1 m/min which allowed for complete drying of the web in the oven and fusing of the polymer to the carbon fibers. A full description of the wetlay line used in this process can be found in Lu [17].

48 3.3. PLAQUE MANUFACTURE 30 Table 3.2: Wetlay line settings. Fiber Length Batch Size Carbon Stock Pump (mm) (g) Volume % Setting Figure 3.2: Picture of the mm plunger mold. 3.3 Plaque Manufacture Two series of test plaques were manufactured from the CMT to test the formability of the material and to provide coupons for the mechanical testing. The first series were molded in a 107 kn hot press using the mm mm plunger mold shown in Figure 3.2. Sheets of both the carbon/pp (C/PP) and carbon/pet (C/PET) CMT were cut to 127 mm 127 mm and placed in the mold. The mold was heated to C above the melt temperature of the thermoplastic material, and full load of 107 kn was applied. After the cycle was complete, it was found that the fibers had failed to flow and the charge did not fill the mold resulting in a molded plaque which remained about 127 mm 127 mm as shown in Figure 3.3. The pressure applied to the plaques by the 107 kn press was approximately 4.6 MPa, about 3-4 times lower than the peak stress reported in Section 5.5. It was decided that a higher tonnage press would be needed

49 3.3. PLAQUE MANUFACTURE 31 Figure 3.3: Picture of plaque that did not flow. Squeezed out resin can be seen along all four edges. to mold the plaques. The second series of plaques were manufactured using the 667 kn press in the Composites Fabrication Laboratory at Virginia Tech, shown in Figure 3.4. Over a mm mm mold, this press is capable of generating up to 28.7 MPa pressure. Two molds were tried in this series with the first attempt using the plunger mold; however, due to the low stiffness of the mold side panels and the high loads generated by this press, 30% of the CMT material was squeezed out of the mold during the consolidation step. This indicated that the material would flow under adequate pressure, but a different mold was required. The remaining panels fabricated in the Composites Fabrication Laboratory used an enclosed die mold, shown in Figure 3.5, to contain the material upon consolidation. A total of 99 test plaques were manufactured: 52 C/PET panels and 47 C/PP panels. A complete list of these panels is given in Appendix C. Tests were run using either 127 mm 127 mm or 146 mm 146 mm preforms. The 127 mm preforms were used during initial testing to ensure that the material was flowing and filling the mold. The 146 mm preforms were used in subsequent testing so that different areas of the plaque did not undergo different flow histories. The platen temperature was ramped from room temperature to the desired molding temperature at the press s maximum heating rate of 8.9 C/min and the platens were held at this temperature until the mold and the CMT reached the desired molding temperature. At this time, the pressure was increased from touch pressure to the molding pressure and was held until the end of the molding cycle. The platens were cooled at their maximum rate of about 11 C/min using first air cooling until the platens reached 175 C, then water cooling to room temperature. The molded plaques were visually inspected to ensure that the CMT has completely filled the mold cavity. The cycle used to manufacture each plaque is shown in Figure 3.6 and the molding

50 3.3. PLAQUE MANUFACTURE 32 Figure 3.4: 667 kn Wabash hot press. Figure 3.5: Picture of the mm die mold.

51 3.3. PLAQUE MANUFACTURE 33 Temperature Pressure Molding Temp Molding Pressure Room Temp Touch Pressure Heat-up Hold Cool down Time Figure 3.6: Generic plaque molding cycle. Table 3.3: Plaque molding parameters. Matrix Molding Temp. Ramp Rate Hold Time Molding Pressure ( C) C/min (min) (MPa) PP PET temperature and pressure are listed for each type of matrix in Table 3.3. A typical temperature cycle measured during the manufacture of a C/PP plaque is shown in Figure 3.7. The platen temperatures stayed within 5 10 C of each other, so only the temperature of the top platen is shown. The mold temperature was measured by a thermocouple probe inserted into a thermocouple well in the bottom half of the mold with its tip approximately at the center of the plaque, 6 mm away from the CMT/mold interface. After the panels were manufactured, the integrity of the consolidated panel was checked using a C-scan technique on C/PET panels ranging from 10% 25% FVF. The best results were found using a 15 MHz transducer with a focal length of 12.7 mm. A scan increment of 0.15 mm in both the X and the Y directions was used. Results for

52 3.4. CONCLUSIONS Set Point Platten Mold Temp (C) Time (min) Figure 3.7: Temperature cycle during molding of a C/PP plaque. the 25% FVF panel are shown in Figures 3.8 and 3.9. These results are typical for all FVFs tested. The back surface reflection, Figure 3.8, shows some evidence of flow patterns in the lower left and right corners, but rest of the panel has a speckled pattern that does not give much information about the quality of the panel. After tensile samples were cut from this panel and tested to failure, the broken samples were reassembled and laid on top of Figure 3.8 and the location of the tensile failure was visually compared to the image. No correlation between break location and the image was found. It is believed that the random orientation of fibers in the CMT scatters the ultrasound in a random manner and prevents this method from finding any small flaws in the manufactured panel. Large flaws such as flow lines near the corners can be detected. 3.4 Conclusions Parameters for the wetlay line were found that produced acceptable quality mat based on visual inspection for uniformity and absence of substantial lumps. Good quality mats were used for all subsequent experiments. It was found that a larger hot press than initially thought was needed to mold the higher FVF panels due to the high through-thickness stresses required to make the CMT flow in the mold. Further discussion of this phenomenon can be found in Chapter 5. The tonnage of the press was increased to compensate for the actual

53 3.4. CONCLUSIONS 35 Figure 3.8: C-scan of a 25 vol% C/PET panel showing the back surface reflection. flowability of the CMT. The temperature cycle of the press was adjusted in order to achieve complete melting of the CMT prior to molding. Nondestructive evaluation of the CMT panels was attempted using ultrasonic C- scan techniques. Due to the random orientation of fibers, the reflected sound waves seemed scattered and gave generally poor images of the panels. Nevertheless, large defects such as orientation of fibers near flow lines into the corners could be detected.

54 3.4. CONCLUSIONS 36 Figure 3.9: C-scan of a 25 vol% C/PET panel showing the mid-surface reflection.

55 Chapter 4 Mechanical Characterization 4.1 Introduction A new class of inexpensive composites has been developed for various applications in the automotive and aerospace industries. Long fiber thermoplastic (LFT) describes a type of prepreg composite material that is composed of an inexpensive thermoplastic matrix and either chopped or continuous reinforcing fibers. These long fiber composites offer substantial cost and weight savings over typical steel construction in new automotive applications and automotive manufacturers have already begun to use LFT molded materials in production vehicles [4, 6 8]. The current technology is called glass mat thermoplastic (GMT) and uses glass fiber as the reinforcement and polypropylene as the matrix. GMT parts have limitations due to the maximum achievable strength and stiffness of the material. To further increase the strength and stiffness of manufactured parts, a new carbon mat thermoplastic (CMT) material has been developed at Virginia Tech in which glass fibers of traditional GMT are replaced by higher strength and stiffness carbon fibers. Lighter and stronger parts help automotive manufacturers achieve better fuel economy, reduce the overall cost of their product, and stay competitive in the world market. The new CMT material was manufactured at Virginia Tech using the wet-lay paper making process and then formed into test panels. Novel test methods were devised to measure the flow properties of the material during manufacturing, and the strength and the stiffness of finished panels were measured. The mechanical properties of randomly oriented discontinuous fibers have been shown to be a function of the fiber sizing, matrix, and FVF. 4.2 Experimental In order to assess the strength properties of the CMT, tensile and flexural mechanical tests were performed on consolidated panels. Testing was performed in both the ma- 37

56 4.2. EXPERIMENTAL 38 Table 4.1: Test variables. Variable Range Fiber length 12.7 mm or 25.4 mm Sizing none, -11, -21, or -3PP Fiber type PANEX33 or PANEX35 Matrix PP or PET Orientation Machine or Transverse Carbon FVF 10% 25% chine and transverse direction of the material to test for orthotropicity of the material. Additionally, pieces from each panel were subjected to resin burn-off tests to determine the actual fiber and void content of each panel. It was desired to test the effects of the following variables on the strength of the CMT material: fiber length, sizing, matrix, FVF, and orientation. The ranges of the variables are listed in Table 4.1. C/PET was tested with three sizing conditions: none, -11, and -21 while the C/PP was tested with all four. Testing was performed to determine differences in material properties in the machine and the transverse directions. Test plaques were molded using heated compression molding wherein a closed diemold was placed in a heated press, and the temperature was ramped at the maximum rate of 8.9 C/min from room temperature to 180 C for the PP or 275 C for the PET. The press applied approximately 17.2 MPa over the mm mm mold. The press was then cooled at maximum rate. The produced panels were about 3.1 mm thick. In order to test for any orthotropicity of the material, two plaques were manufactured from each batch of material with one plaque having specimens cut parallel to the machine direction of the material and the other plaque being cut transverse to the machine direction. Cutting was performed on a computer controlled saw using a diamond grit blade according to the cutting templates shown in Figure 4.1. Cutting fluid was used to cool the blade and panels while cutting. The cut surface was deemed acceptable for testing, and no further polishing of the samples was performed Tensile Testing Tensile testing was performed according to the ASTM D 3039/D 3039M [108] standard with coupons cut to 12.7 mm wide 152 mm tall. An Instron 4468 load frame was used to test specimens with a cross-head speed of 2 mm/min while a 222 kn load cell measured the load applied to the specimen. Two extensometers were used on the specimens: a 25.4 mm gage length, 4% extensometer was used to measure the axial

57 4.2. EXPERIMENTAL 39 Figure 4.1: Cutting templates for mechanical test samples. The asterisk (*) indicates pieces cut from the flexural specimens and used in the burn-off tests. strain and a 12.7 mm gage length, 15% extensometer was used to measure transverse strains. Six specimens from each panel were tested and strength, modulus, and axial strain at failure were calculated. Figure 4.2 shows a tension sample and the mounted extensometers Flexural Testing Flexural testing was performed according to the ASTM D 790 [109] standard with coupons cut to 12.7 mm wide 76 mm long. An Instron 4204 load frame with a 1 kn load cell was used to test specimens in three-point bend at a cross-head speed of 1.35 mm/min. The diameters of the loading nose and the supports were 7.93 mm. Eight specimens from each panel were tested, and the strength, modulus, and strain at failure were calculated. A slight modification of the flexural specification was allowed: the span length of the specimen was fixed at 50.8 mm for all samples, regardless of the actual depth Density, FVF, and Void Content Once the mechanical tests were completed, the unstressed ends of the flexural samples were cut off and used to determine the FVF and void volume fraction (VVF) of the

58 4.2. EXPERIMENTAL 40 Strain gage extensometers Sample Grips Figure 4.2: Tension test setup. Figure 4.3: Flexural test setup.

59 4.2. EXPERIMENTAL 41 molded plaques. Four specimens, each approximately mm long, were cut from the ends of flexural specimens numbered 1, 3, 5 and 7 in Figure 4.1. First, the mass density ρ of each sample was measured using Method A (water displacement) of ASTM D792 [110]. Two deviations from the standard were allowed: the specimens masses were only g as compared to the recommended 1.0 g minimum mass, and the sample dimensions of approximately 12 mm 12 mm 3 mm resulted in a smaller sample volume than the recommended volume of 1,000 mm 3. The temperature of the water was recorded to the nearest 0.1 C, and the mass density of the composite was calculated to four significant figures. Average value and standard deviation of the mass density were calculated. Additionally, three samples of consolidated PP and four of PET were measured for density. The virgin fibers were placed in an aluminum weigh pan coated with release agent. The pan was placed in a vacuum oven and the fibers were melted under vacuum in order to remove any air from the samples. ASTM standard D2734 [111] was followed to calculate the VVF in the samples. In order to find the mass fraction of the fibers and resin in the samples a resin degradation procedure was devised to heat the sample to at least 450 C for a minimum of 30 minutes. Since the carbon fiber would degrade and oxidize in air at this temperature, the procedure was performed in a nitrogen atmosphere. Up to 18 samples were placed inside an aluminum chamber (18.4 cm 18.4 cm 9.53 cm) having a volume of 3.23 L, shown in Figure 4.4. The chamber was placed inside a convection oven and the temperature was ramped from room temperature to 475 C, held for 45 min, then cooled to room temperature. Nitrogen was flowed through the chamber at a rate of 0.94 L/min for the first 20 min to ensure good purge of the chamber, then the flow rate was reduced to 0.47 L/min for the remainder of the cycle. A typical temperature cycle is shown in Figure 4.5 After the samples were burned the final remaining mass was recorded. Figure 4.6 shows an unburned sample, burned sample, and burned PET resin. While the PP degraded completely using this temperature cycle, the PET did not. Four samples of unprocessed PET fibers were subjected to the same temperature cycle as above and the mass of the residue was measured. The mass fraction m frac of the residue was calculated: mass remaining m frac = (4.1) original resin mass In order to calculate the mass of the resin m m in the composite samples it was necessary to correct for the incomplete degradation of the PET, so the following relation was used: m m = m lost (4.2) 1 m frac where the m lost was the measured mass loss after burning the composite. The weight fractions of the constituent components in the composite were found using W f = m c m m m c (4.3)

60 4.2. EXPERIMENTAL 42 Figure 4.4: Chamber (left) and oven (right) for burn-off testing. 600 Temperature (C) Oven Air Inside Chamber Time (min) Figure 4.5: Typical time-temperature curve for the burn-off experiments.

61 4.3. RESULTS 43 Figure 4.6: An unburned sample, burned C/PET sample, and burned 100% PET sample showing incomplete degradation. W m = m m m c (4.4) where W f is the weight fraction of the fibers, W m is the weight fraction of the matrix, and m c is the original mass of the specimen. The VVF, V void, was calculated per ASTM D2734 [111] ( Wm V void = 100 ρ + W ) f (4.5) ρ m ρ f where ρ m and ρ f are the mass density of the matrix and fiber, respectively. The mass of the fiber, m f, is given by m f = m c m m (4.6) and the total volume of each constituent is given by The FVF is calculated using 4.3 Results Density, FVF, and Void Content Vol f = m f ρ f (4.7) Vol m = m m ρ m (4.8) Vol f V f = (1 V void ) (4.9) Vol f + Vol m The mass density of the carbon fiber and the measured mass densities of the PP and PET are listed in Table 4.2 and they are within the range of published values.

62 4.3. RESULTS 44 Table 4.2: Measured material density. Material Density Std. Dev. Published Values (g/cm 3 ) PP [45, 112] PET [45, 113] Carbon Fiber 1.81 [105] Using the burn-off test described above, it was found that the PP degraded completely to ash and left no detectable residue. The PET did not degrade completely at this temperature. The mass of the residue was about 20% of the original mass after 30 min. Holding another sample of PET at 475 C for 90 min showed no additional mass loss. Four samples of unprocessed PET fibers were degraded and the average mass ratio left was found to be with a standard deviation of The mass density, FVF, and VVF of the composite panels are shown in Figures 4.7 and 4.8. For the C/PET the VVF decreases monotonically as the FVF increases. The density of the 10% FVF material is actually lower than the density of the unreinforced polymer due to the high void content of 4 7%. The C/PP panels show a non-monotonic decrease of VVF with increasing FVF. The manufacturing conditions in the wetlay process for the 10% FVF material may have been different than those for the 15% 25% FVF, thus causing the mat to behave differently during molding and causing the low FVF material to have more voids. Another possibility is that the molding conditions from one panel to another may have been different because the process cycle was controlled by time, not temperature. Different panels may have had molding at temperatures varying by ±1 2 C, and this may have affected the VVF. Complete data is listed in Appendix D MD versus TD Testing Tensile and flexural testing was run in both the MD and the TD of C/PET panels for both 12.7 mm and 25.4 mm long fibers. The fibers were PANEX33 sized with type -11 sizing. Tensile strength and modulus results are shown in Figures 4.9 and 4.10, where the error bars show ± one standard deviation. Statistical analysis was performed on the results using the XLStats package [114] and Microsoft Excel. A multiple-linear regression analysis was performed to estimate the effects of the fiber length and the test direction on the tensile strength and the modulus of the CMT. The equation used to fit the data was of the form y = β 0 + β 1 x 1 + β 2 x β n x n (4.10)

63 4.3. RESULTS % Mass Density (g/cc) % 6% 3% Void Volume Fraction PET 10 v% 15 v% 20 v% 25 v% 1.1 0% 5% 10% 15% 20% 25% 30% Fiber Volume fraction 0% Figure 4.7: C/PET mass density (open symbols) and VVF (solid symbols) % Mass Density (g/cc) % 12% 8% 4% Void Volume Fraction PP 10 v% 15 v% 20 v% 25 v% 0.7 0% 5% 10% 15% 20% 25% 30% Fiber Volume Fraction 0% Figure 4.8: C/PP mass density (open symbols) and VVF (solid symbols).

64 4.3. RESULTS Axial Tensile Strength (MPa) MD, 12.7 mm MD, 25.4 mm TD, 12.7 mm TD, 25.4 mm Fit 0 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.9: MD and TD strength comparison for C/PET. Axial Tensile Modulus (GPa) MD, 12.7 mm MD, 25.4 mm TD, 12.7 mm TD, 25.4 mm Fit 0 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.10: MD and TD tensile modulus comparison for C/PET.

65 4.3. RESULTS 47 where y is either the strength or the modulus, β i are the coefficients, and x i are the factors. The factors for this analysis were x 1 = V f, x 2 = T D = 0 for machine direction or 1 for transverse direction, and x 3 = LEN25 = 0 for 12.7 mm long fibers or 1 for 25.4 mm long fibers. The regression analysis gave the following relation to estimate the strength: σ C = ( V f T D 6.63 LEN25) MPa (4.11) The effect of testing direction was found to be statistically insignificant (level of significance (p=0.328, T test, two tailed), indicating that the wetlay line is providing a near random dispersion of the fibers in the mat. Though fiber length was not expected to have any effect because both lengths exceed the critical fiber length, increasing the fiber length from 12.7 mm to 25.4 mm actually seems to decrease the strength of the composite by about 5 10%. While this decrease is statistically significant (p=0.013), the magnitude of the change is still within one standard deviation of the measured strengths, so it will be considered insignificant (see Appendix E for complete test results). Eliminating these factors gives a new estimate of the strength as σ C = ( V f ) MPa (4.12) The same argument can be used to show that the tensile modulus only depends on the FVF and not the test direction or the fiber length. A listing of the coefficients for the strength and modulus relations can be found in Table 4.3. Using similar arguments it can be shown that the flexural modulus also depends only on the FVF. However, flexural strength was found to depend on the test direction of the test piece. It is concluded from this analysis that the both the test direction and fiber length have a negligible effect on the strength and the modulus of the CMT. Further testing was only performed on MD samples. It will be assumed that the fiber length does not have a significant effect on the properties, so the 12.7 mm and 25.4 mm fibers will be used interchangeably in the following tests C/PP Mechanical Testing Carbon fiber and PP panels were manufactured at FVFs ranging from 10% 25%. Based on the results of the previous section, only tests in the MD were run and the strength, modulus, and strain at failure were calculated. Tensile test results are shown in Figures 4.11 and Unlike unidirectional composites whose strength and modulus increase with an increase in the FVF, for randomly oriented composites the strength and the modulus reach their peak values at about 20% 40% FVF; subsequently their values decrease with an increase in the FVF [11, 17, 22]. Typical axial stress-axial strain curves for the C/PP material are shown in Figure Increasing the FVF enhances both the modulus and the ultimate tensile strength until about 20% FVF, but decreases the axial strain at failure. At 25% FVF,

66 4.3. RESULTS 48 Table 4.3: Estimated strength and modulus coefficients for the C/PET MD vs. TD tests. Fits are valid for 0.1 V f 0.3. Property Factor Original coefficients Reduced coefficients Coeff. Std. p-value Coeff. Std. p-value Err. Err. Tensile V f < <0.001 Strength Constant < <0.001 (MPa) T D LEN Tensile V f < <0.001 Modulus Constant (GPa) T D LEN Flexural V f < <0.001 Strength Constant < <0.001 (MPa) T D < <0.001 LEN Flexural V f < <0.001 Modulus Constant < <0.001 (GPa) T D <0.001 LEN the curve becomes distinctly non-linear at a strain of about 0.5%; this feature has been reported in the literature [85, 97]. The decrease in the secant modulus indicates that the efficiency of the fibers in resisting the load is decreasing, and, as the test proceeds, more fibers may fail thus reducing the modulus even further. Another possibility is that the increased stress in the composite may reduce the effective fiber length because the fiber ends, where the stress is concentrated, will break their bond with the matrix while the majority of the composite stays intact. The non-linear relationship between axial tensile strength and FVF of the C/PP material is shown in Figure Blumentritt et al. [11] have suggested that higher FVFs increase the amount of voids in the composite. As shown in Figure 4.8, the void fraction in the current composite decreases with increasing FVF. While it is possible that more fibers interact with voids in the higher FVF material, and thus weaken the material, this does not seem likely. It is also possible that fiber breakage during

67 4.3. RESULTS 49 Axial Tensile Stress (MPa) vol% vol% vol% vol% Axial Tensile Strain (%) Figure 4.11: Typical tensile stress strain curves for C/PP CMT. molding may have reduced the length of the fibers to a value below the critical length, but fiber length after molding was not measured so this hypothesis is unproven. Further discussion of fiber length after manufacturing is found in Section 5.5. The sizing on the fibers also affects the ultimate strength of the composite. The -3PP sizing outperforms the others both in increasing the strength for a given FVF, and in delaying the drop-off in properties as the FVF is increased. As the FVF is increased from 20% to 25%, the strength of the composite manufactured with the -3PP sized fibers stays level at about 175 MPa while the strength of the composites manufactured with fiber that have other sizings decreases significantly. These results indicate that the fiber-matrix bond is critical for achieving strength at higher FVFs. Effects of using different sizings are also seen in the tensile moduli results reported in Figure CMT manufactured with -3PP sized fibers shows a linear increase in modulus as the FVF is increased from 10% 25%. Material manufactured with fibers that have other sizings follows a linear trend up to a FVF of 20%. As the FVF is increased to 25% the modulus is either the same as, or less than what it was at 20%. Axial tensile strain at failure is shown in Figure As with the tensile strength and tensile modulus results, the strains at failure for CMT manufactured with different fiber sizings are very similar to each other for FVFs between 10% 20%. Only in the 25% FVF material does the sizing seem to come into play. The -3PP sizing achieves the highest failure strain of 1.06%, while the -11, -21, and unsized have failure strains of 0.95%, 0.68%, and 0.50% respectively. The fibers sized with the -3PP material perform

68 4.3. RESULTS % 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% PP -non 5% 15% 25% 35% Fiber Volume Fraction PP -non 5% 15% 25% 35% Fiber Volume Fraction PP -non 5% 15% 25% 35% Fiber Volume Fraction Axial Tensile Strain at Failure Axial Tensile Strength (MPa) Axial Tensile Modulus (GPa) a) b) c) Figure 4.12: Axial tensile properties of C/PP CMT: a) failure strain, b) strength, c) modulus.

69 4.3. RESULTS Axial Stress (MPa) vol% 20 vol% 15 vol% 10 vol% Axial Tensile Strain (%) Figure 4.13: Typical tensile stress strain curves for C/PET CMT. better at higher FVF than fibers with other sizings. Sizing the fibers so they are compatible with the matrix is most important when the FVF is near the critical FVF when the properties start to degrade. The right sizing can extend the usable range of FVF at least 5%, as indicated by this experiment. The results of the flexural tests paralleled the tensile test results and are included in Appendix E C/PET Mechanical Testing A typical axial stress-axial strain curve for the C/PET material is shown in Figure Unlike the C/PP, the curves remain linear up to a FVF of 25%. This may indicate that the effective length of the fiber is unaffected by the molding process, or that the bond between the fiber and the matrix is much stronger in the C/PET than in the C/PP. Figure 4.14 shows the tensile strength results for the C/PET CMT, with the error bars representing ± one standard deviation. For all three sizing treatments, the strength increases with an increase in the FVF. Unlike the C/PP, there is no fall-off in strength above 20% FVF and the linear trend continues through the maximum tested FVF of about 28%. A multiple factor linear regression analysis was used to fit the data [114] with Equation (4.10). The factors in the analysis are x 1 = V f, x 2 = SIZ11 = 1 when sized with -11 and 0 for other sizings, and x 3 = SIZ21 = 1

70 4.3. RESULTS % 1.3% 1.2% 1.1% 1.0% 0.9% 0.8% 0.7% non 5% 15% 25% 35% Fiber Volume Fraction none 5% 15% 25% 35% Fiber Volume Fraction Axial Tensile Strain at Failure Axial Tensile Strength (MPa) none Axial Tensile Modulus (GPa) 5% 15% 25% 35% Fiber Volume Fraction a) b) c) Figure 4.14: Axial tensile properties of C/PET CMT: a) failure strain, b) strength, c) modulus.

71 4.3. RESULTS 53 Table 4.4: Estimated strength and modulus coefficients for the C/PET mechanical tests. Fits are valid for 0.1 V f 0.3. Property Factor Coeff. Std. Err. p-value Tensile V f <0.001 Strength Constant <0.001 (MPa) SIZ <0.001 SIZ <0.001 Tensile V f <0.001 Modulus Constant (GPa) SIZ <0.001 SIZ <0.001 Flexural V f <0.001 Strength Constant <0.001 (MPa) T D <0.001 LEN <0.001 Flexural V f <0.001 Modulus Constant (GPa) SIZ SIZ <0.001 when sized with -21 and 0 for other sizings. Regression coefficients are shown in Table 4.4. The -11 sizing slightly outperforms the -21 sizing, and both outperform the unsized treatment. The variation of the tensile modulus with FVF in the C/PET is shown in Figure 4.14 and a linear relationship between the modulus and the FVF is indicated. The CMT manufactured with -21 sized fibers proved to be stiffer than that manufactured with the -11 sized fibers, and the CMT with unsized fibers showed the lowest stiffness of the three treatments. Coefficients for the fitted lines are given in Table 4.4. Axial tensile strain at failure as a function of FVF is shown in Figure 4.14 with tensile strain ranging from a high of 1.2% for the 10% FVF CMT to a low of 0.9% for the 28% FVF CMT. This is typical of LFT and has been extensively reported in the literature [11 17, 19 28, 77, 85, 94, 99]. Similar results are seen in the flexural data, included in Appendix E.

72 4.4. C/PP COMPARED TO C/PET Axial Tensile Strength (MPa) C/PET Strength C/PP Strength C/PET Modulus C/PP Modulus Tensile Modulus (GPa) 0 0 5% 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.15: Comparison of the tensile properties of C/PP (-3PP sized) with those of C/PET (-11 sized). 4.4 C/PP Compared to C/PET In order to compare the performance of the C/PP CMT with the C/PET CMT, the sizing treatment that gave the highest strength for each one was chosen: the -3PP sizing for the C/PP and the -11 sizing for the C/PET. Figure 4.15 shows the tensile strength results of the C/PP (-3PP sized) and the C/PET (-11 sized) on a single plot. Since the strength and the modulus of the composite are fiber dominated, the coincidence of the experimental data for the two CMTs is not a surprise. While the mechanical strength and the modulus of the C/PP may be similar to those of the C/PET, the PP has much lower melting (T m =165 C) and glass transition (T g = C) temperatures than the PET (T m =265 C, T g =68 80 C), allowing for possible use of C/PET under the hood of automobiles and other hot environments [45, 113, 115]. 4.5 Micromechanical Model Evaluation Various theories have been proposed in the literature to estimate the tensile strength and the tensile modulus of composites with randomly oriented discontinuous fibers. Many of these require that the unidirectional properties of the composite be known, while others only require properties of the constituents. While unidirectional elastic properties can be estimated from various micro-mechanical equations, no good esti-

73 4.5. MICROMECHANICAL MODEL EVALUATION 55 Table 4.5: Material Properties Used in the Micromechanics Models. Material Tensile Shear Poisson s Tensile Modulus Modulus Ratio Strength (GPa) (GPa) (MPa) PP [112] PET [113] Carbon Fiber [105] , Axial Tensile Modulus (GPa) % 15% 20% 25% 30% Fiber Volume Fraction Manera Christensen & Waal Halpin-Tsai Area Fraction Avg. K E Fit K E Nielsen & Chen Experiment Figure 4.16: Various micromechanical predictions of C/PET tensile modulus. mate of the unidirectional strength is available. The unidirectional strength data is not available, and is not likely to become available for the composite system under consideration. Properties of PP, PET, and carbon fiber used in the following calculations are listed in Table 4.5. Results of the area fraction theory, Equation (2.52), Christensen and Waals Equation (2.70), and Manera s Equation (2.71) are shown in Figure All of these relations over-predict the tensile modulus by about 30% 64%, except for Nielsen and Chen s equation which underpredicts it by 12% 30%. The fiber efficiency factor equations (2.54) and (2.55) were used to fit the data shown in Figures 4.16 and It was found that the fiber efficiency factors K σ and K E were not constant, but varied almost linearly with the FVF. K σ varied from 0.18 to 0.21, while K E varied from 0.21 to 0.24, thus both factors are functions of the FVF

74 4.5. MICROMECHANICAL MODEL EVALUATION 56 Table 4.6: K σ and K E values for the fiber efficiency theory. CMT Variable Average Linear Fit Type Value m b C/PET K E K σ σ m (MPa) C/PP K E K σ σ m (MPa) and equations (2.54) and (2.55) become: σ C = K σ (V f ) σ f,ult V f + σ m(v f ) (1 V f ) (4.13) E C = K E (V f ) E f V f + E m (1 V f ) (4.14) where the K s and the σ m have the form: f(v f ) = mv f + b. The values of the fit constants are given in Table 4.6. Equations (4.13) and (4.14) were used to fit the C/PET strength and modulus data, and the results are plotted in Figures 4.16 and The curves plotted using these equations show a much better fit to the data than the curves plotted using equations (2.54) and (2.55). Similar results for the C/PP are shown in Figures 4.18 and In this case the strength drops off more sharply than that for the C/PET, and the strength estimate using equation (4.13) shows a good fit to the curve Specific Strength and Modulus Comparisons The specific strength and modulus of the CMT are compared to other material s data available in the literature. For the C/PP CMT the -3PP sized fibers were chosen since the composite made from it had the best properties, and the C/PET data shown is for the -11 sized fibers, again because of its higher performance when made into a composite. In particular, comparison is made with the GMT data of Lu [17] because the same manufacturing line and polymers were used in that work, hence the substitution of carbon for glass can be directly studied. Additionally, data for commercially available GMT from Azdel (Southfield, MI) [116] are included. The specific properties of the composites were calculated as the property divided by the mass density. Figures 4.20 and 4.21 show the specific tensile strength and the specific modulus, respectively, as a function of the FVF. The CMT outperforms the GMT by a factor of about 2 in specific strength, and by a factor of 2 4 in specific modulus. This is to be expected since the carbon fiber

75 4.5. MICROMECHANICAL MODEL EVALUATION Axial Tensile Strength (MPa) Experiment Avg. Ks Fit Ks 0 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.17: Fiber efficiency factor model for C/PET tensile strength. Axial Tensile Modulus (GPa) Manera Christensen & Waal Halpin-Tsai Area Fraction Average Fit K E K E Nielsen & Chen Experiment 0 5% 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.18: Various micromechanical predictions of C/PP tensile modulus.

76 4.5. MICROMECHANICAL MODEL EVALUATION Axial Tensile Strength (MPa) Experiment Average Ks Fit Ks 0 5% 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.19: Fiber efficiency factor model for C/PP tensile strength. is much stiffer and stronger than the glass fiber, while being only 75% as heavy. The C/PP CMT outperforms the C/PET on a specific basis because the PP is only 65% as dense as the PET, and at the low FVF used in this study, the matrix is the major component of the composite. The major advantage of PET is its resistance to higher temperature environments. Results for the flexural tests depicted in Figures 4.22 and 4.23 follow the same pattern as the tensile test results Comparison to Literature Results The current results are compared to results from other researchers in Figures 4.24 and Data is taken from Bader and Bower [117] with 6 mm carbon fiber in nylon 6,6, Blumentritt et al. [11] with 9.5 mm fiber in various reinforcements, Bockstedt and Sajna [100] with 1 12 mm long fiber in nylon 6,6, Brandl et al. [118] with functionalized vapor grown carbon fibers (carbon nano-tubes) in PP, Crosby and Drye [13] with >3 mm carbon fibers extruded with nylon 6,6, and Curtis et al. [97] with 0.5 mm long carbon fibers in nylon 6,6. The CMT produced during this study shows a much higher strength and stiffness than the carbon/thermoplastic composites produced by extrusion compounding (Blumentritt, Bockstedt, and Brandl); extruding the material results in fiber attrition and short fibers below l c, thus reducing the effectiveness of the reinforcement. Bader s, Curtis, and Crosby s long fiber carbon/thermoplastic composites tended to perform better than the CMT manufactured in this study.

77 4.5. MICROMECHANICAL MODEL EVALUATION Specific Strength (N m/kg) C/PP C/PET G/PP G/PET Azdel GMT 0 0% 10% 20% 30% 40% 50% Fiber Volume Fraction Figure 4.20: Specific tensile strength comparison. 20 Specific Modulus (10 3 N m/kg) C/PP C/PET G/PP G/PET Azdel GMT 0 0% 10% 20% 30% 40% 50% Fiber Volume Fraction Figure 4.21: Specific tensile modulus comparison.

78 4.5. MICROMECHANICAL MODEL EVALUATION Specific Strength (N m/kg) C/PP C/PET G/PP G/PET Azdel GMT 0 0% 10% 20% 30% 40% 50% Fiber Volume Fraction Figure 4.22: Specific flexural strength comparison. 16 Specific Modulus (10 3 N m/kg) C/PP C/PET G/PP G/PET Azdel GMT 0 0% 10% 20% 30% 40% 50% Fiber Volume Fraction Figure 4.23: Specific flexural modulus comparison.

79 4.5. MICROMECHANICAL MODEL EVALUATION Maximum Axial Stress (MPa) Fiber Volume Fraction Bader Brandl Curtis Crosby Bockstedt Blumentritt, Ionomer Blumentritt, PE Blumentritt, PC Blumentritt, PMMA Caba Figure 4.24: Comparison of the ultimate tensile strength of discontinuous carbon fiber thermoplastic composites. 35 Tensile Modulus (GPa) Brandl Curtis Crosby Blumentritt, Ionomer Blumentritt, PE Blumentritt, PC Blumentritt, PMMA Caba Fiber Volume Fraction Figure 4.25: Comparison of the tensile modulus of discontinuous carbon fiber thermoplastic composites.

80 4.6. COMPARISON OF FLEXURAL AND TENSILE TEST RESULTS Strength (MPa) Modulus (GPa) Flexural Strength Tensile Strength Tensile Modulus Flexural Modulus % 15% 20% 25% 30% Fiber Volume Fraction Figure 4.26: Comparison of C/PET (-11 sized) flexural and tensile results. 4.6 Comparison of Flexural and Tensile Test Results For fiber reinforced composites, it is well known that tensile and flexural tests give different values for a material s strength and modulus. Figures 4.26 and 4.27 show this to be true for the C/PET and the C/PP respectively. The strength measured in the CMT by three-point-bending is higher than that measured by tensile testing because the maximum tensile and compressive stresses occur along a line on the top and the bottom surfaces of the flexural specimen, while the stress in the tension test is (ideally) uniform throughout the specimen. Since flaws are distributed throughout the material, the tensile sample will fail at a cross-section with the lowest strength, regardless of where that cross-section is located. In the flexural sample, the chance of a critical flaw occurring exactly where the stress state is highest is small, thus the sample will carry more load before failure. Conversely, the modulus measured in the tension test is typically higher than that measured in the flexural test due to the method each test standard uses to calculate it. The flexural test standard uses classical beam theory and does not account for shear deformations that tend to reduce the apparent modulus of the sample. Since the fibers are oriented in a plane, the out-of-plane shear modulus is relatively low and these shear deformations may be significant.

81 4.6. COMPARISON OF FLEXURAL AND TENSILE TEST RESULTS Strength (MPa) Modulus (GPa) Flexural Strength Tensile Strength Tensile Modulus Flexural Modulus % 10% 15% 20% 25% 30% Fiber Volume Fraction Figure 4.27: Comparison of C/PP (-3PP sized) flexural and tensile results.

82 4.7. FRACTURE SURFACES 64 Figure 4.28: SEM picture of fracture surface of 10% FVF C/PET, Fracture Surfaces A scanning electron microscope (SEM) was used to image the fracture surfaces of tensile test specimens; failed ends of C/PP and C/PET samples with FVFs of 10% 25% were scanned. The C/PET samples were manufactured with fibers sized with the -11 sizing, while fibers in the C/PP samples were sized with the -3PP sizing. These two sizings were chosen as they provided the highest mechanical properties for the composites fabricated and tested in this work. Figures show pictures of the 10% FVF C/PET sample at increasing magnifications of 150, 400, and 1000, respectively. The assumption that the fibers are oriented in a plane is confirmed by these pictures. On the fracture surface, there is some fiber pull-out, and the fibers have resin adhered to them, indicating a good fiber-matrix bond. Figures show scanning electron micrographs at 1000 for C/PET at FVFs of 15%, 20%, and 25%, respectively. These also show resin bonded to the fibers, and a small amount of fiber pull-out. It appears that the -11 sizing provides a good bond between the fiber and matrix as was indicated in the afore mentioned mechanical tests. Even at 1000 magnification there is no clear demarcation between adjacent plies suggesting thereby that the tensile loading did not cause any delamination, and that the compression molding process produced good quality samples.

83 4.7. FRACTURE SURFACES 65 Figure 4.29: SEM picture of fracture surface of 10% FVF C/PET, 400. Figure 4.30: SEM picture of fracture surface of 10% FVF C/PET, 1000.

84 4.7. FRACTURE SURFACES 66 Figure 4.31: SEM picture of fracture surface of 15% FVF C/PET, Figure 4.32: SEM picture of fracture surface of 20% FVF C/PET, 1000.

85 4.7. FRACTURE SURFACES 67 Figure 4.33: SEM picture of fracture surface of 25% FVF C/PET, 1000.

86 4.8. CONCLUSIONS 68 Figure 4.34: SEM picture of fracture surface of 10% FVF C/PP, 150. Pictures of the C/PP fracture surfaces look very different from those of the C/PET. In Figures 4.34 and 4.35, the fracture surface of a C/PP sample at 10% FVF is shown at 150 and The fibers still show a planar orientation, but the length of the fiber pulled out of the matrix is much longer than that pulled out of the C/PET samples. Also, there is no evidence of matrix adhering to the fiber. Figures are for FVFs of 15%, 20, and 25%, respectively, and show the same fiber pull-out phenomenon and the absence of matrix particles adhered to the fiber. This, combined with the long length of the pulled out fibers indicates that the fiber-matrix bond was much weaker in the C/PP as compared to that in the C/PET. Improving this bond by using additives to the PP, by functionalizing the surface of the carbon fiber, or by using a different sizing that further improves the bond would strengthen the C/PP material. 4.8 Conclusions Mechanical properties of CMT were determined using tension and three-point flexural test data. The void fraction in the CMT composite was found to be maximum of about 7% for the 10% FVF CMT and this reduced to 3 5% as the FVF was increased to 25%. The results show that for the range of FVF (10% 25%) and fiber lengths (12.7 mm or 25.4 mm) tested, the tensile and flexural results are independent of testing direction and the length of fibers. This indicates that the wetlay process used to produce the

87 4.8. CONCLUSIONS 69 Figure 4.35: SEM picture of fracture surface of 10% FVF C/PP, Figure 4.36: SEM picture of fracture surface of 15% FVF C/PP, 1000.

88 4.8. CONCLUSIONS 70 Figure 4.37: SEM picture of fracture surface of 20% FVF C/PP, Figure 4.38: SEM picture of fracture surface of 25% FVF C/PP, 1000.

89 4.8. CONCLUSIONS 71 CMT provides good fiber dispersion and a random orientation. It was found that different fiber sizings affect the measured strengths and moduli of the CMT. For the C/PP the sizing has a small but noticeable effect on the measured values of the strength and modulus which extended the usable FVF range. The -11, -21, and unsized fibers showed a marked deviation from the linear increase of strength with the FVF for FVF above 20%. In contrast, for the -3PP sizing the strength continued to increase with an increase in the FVF even for the FVF greater than 20%. Thus the choice of an appropriate sizing can increase the usable FVF range of the composite by at least 5%. For the C/PET the sizing or lack thereof also affects the strength and the modulus. Of the three sizing treatments tested (-11, -21, and none), the only one that showed significant difference was the unsized treatment. C/PET manufactured with unsized fibers had a lower strength and modulus than those made from -11 and -22 sized fibers, while composites from fibers sized with the latter two treatments had essentially the same mechanical properties. It is possible that a difference between their properties may manifest itself at a FVF greater than 25%. Various micromechanical theories were tested to see if their predictions matched the experimental data. Some of these require properties of the unidirectional composite, but this data was not available, and is not likely to become available for the composite system under consideration. Theories that used only constituent properties all overpredicted the tensile modulus by 20% 60% with one exception, which under-predicted it. Theories that take into account the finite length of the fibers and possible non-ideal bonding with the matrix were either inaccessible due to lack of input parameters or were not found in the literature. A fiber efficiency relation was fitted to the experimental data and gives excellent agreement. It was found that by allowing the fiber efficiency factors to vary with the FVF, the equations could be adjusted to fit the data. Finally, specific strength and modulus data was presented. It is seen that on a specific basis, the C/PP CMT outperforms both the laboratory produced GMT and a typical industrial GMT by a factor of about two. However, the PET is better able to withstand high temperature environments such as those under the hood of an automobile, so both materials are useful and have possible applications.

90 Chapter 5 Flow Characterization 5.1 Introduction Suspensions of long fibers have been studied extensively as they relate to composite materials. The flow of a fiber filled viscous media is controlled mainly through the interactions of fibers at fiber-fiber touch points. A mathematical description of this phenomenon is described by Servais et al. [35,36,49] who assumed that all interactions occur at fiber-fiber touch points and can be formulated as a combination of Coulomb friction between the fibers and hydrodynamic lubrication due to the thin film of liquid between the fibers. These two aspects are typically orders of magnitude greater than the viscosity of the suspending fluid alone [50], so the viscosity of the matrix is disregarded. The three types of experiments described in this chapter are designed to gain a better understanding of factors that affect the flow viscosity of the CMT. The first type of experiment measured the viscosity of the PP over a range of 180 C 210 C using a cone and plate rheometer in frequency sweep mode. The parameters in the Carreau relation were found by fitting predictions from it to the data. The second experiment used heated platens to simulate the compression molding environment. Samples of C/PP CMT were squeezed isothermally between heated platens and the resulting force and the platen separation distance were measured. Tests were run at low squeezing speed (0.005 mm/s) where the matrix was allowed to weep out of the mat, thus allowing the measurement of the packing stress of the mat. Tests run at high squeezing speed ( mm/s) were used to measure the bulk flow of the CMT. At the high speeds the fibers and the matrix flowed together as they would in a manufacturing environment. In the third type of experiment, a single carbon fiber was sandwiched between two pieces of molten C/PP CMT, and the force required to pull the fiber through the mat was measured at various speeds. Fiber-fiber frictional coefficients were calculated for use in the Servais et al. relations [50]. A force decay experiment was also run using the fiber pull-out fixture in which the fiber was pulled through the CMT as before, but it was stopped and the force was allowed to decay. From this the Coulomb friction 72

91 5.2. RHEOMETRY OF POLYPROPYLENE η (Pa s) 180C 190C 200C 210C ω (rad/s) Figure 5.1: Viscosity of PP melt and Carreau relation fit. coefficient was estimated. The single fiber pull-out and force decay experiments provide insight into the micromechanical sources of flow stresses. The data from the low speed and single fiber tests were used to find values of material parameters in the Servais et al. constitutive relation, and its predictions are compared to the results of the high speed tests. 5.2 Rheometry of Polypropylene The complex viscosity, η, of the PP was measured using a cone and plate setup over frequencies between rad/s on a RMS-800/RDSII rheometer from Rheometrics, Inc. (Piscataway NJ). The cone has an angle of 0.1 rad, diameter of 25 mm, and a plate separation distance of 0.05 mm. The Cox-Merz rule [45] states that the shear viscosity, η, and complex viscosity, η, are identical when evaluated at the same values of γ and ω respectively, i.e.: η( γ) = η (ω) ω= γ (5.1) The Carreau Equations (2.1) and (2.2) were fit to the measured data as shown in Figure 5.1. The Carreau constants were shifted to 180 C and are listed in Table 5.1.

92 5.3. THROUGH THICKNESS STRESS MEASUREMENT 74 Table 5.1: Carreau parameters of PP. Parameter Value Units E/R 5922 K T K η Pa s n λ s Through Thickness Stress Measurement As the CMT material is compressed in the thickness direction the fiber bed will elastically resist the compression. Finding a relation that relates this transverse normal stress to the FVF of the composite is important as an input to the micro-mechanical relations used later in this chapter Theoretical Background The following assumptions are made when measuring the through thickness stress of the CMT: 1. Fibers are oriented in a single plane. The wetlay process used to produce the CMT results in a thin web ( mm thick) of material. Since the 12.7 mm fibers are much longer than the thickness of the material, this assumption is reasonable. 2. The material is statistically homogeneous. In the wetlay process the chopped carbon fibers are introduced as bundles of fibers that are broken apart by the process down to single fibers. While some bundles are not completely broken apart, visual inspection of the mat indicates that the fibers are well dispersed. 3. There are a large number of fiber touches along each fiber. For a FVF of 10%, it can be shown that there are, on average, more than 100 fibers touching a single 12.7 mm fiber. This will tend to prevent any out-of plane movement of the fibers. 4. The compression is quasi-static and allows the matrix to weep out while the fibers do not move in-plane. 5. Fibers do not slide relative to each other during compaction. The squeezing stress, σ p, was calculated assuming constant area and the measured load. Toll and Manson [48] found the analytical solution for the elastic compression of

93 5.3. THROUGH THICKNESS STRESS MEASUREMENT 75 a disperse planar fiber network to be: σ p = 512 5π 4 E ff 4 V 5 f (2.9) This equation is slightly modified when it is fit to experimental data to allow for nonideal arrangement of fibers by changing the exponent on V f to an adjustable parameter, n. σ p = 512 5π E ff 4 V n 4 f (5.2) Equation 5.2 can be fit to experimental data by adjusting both f and n. Assuming that the squeezing speed is slow enough, the frictional force between the fibers will keep them in place and allow the matrix to weep out. The in-plane dimensions of a sample are constant while the height changes. Therefore, the current fiber FVF of the sample, V f, can be calculated from V f = h 0 h V f,0 (5.3) where V f,0 is a known FVF at an initial thickness h 0, and h is the current sample thickness. If assumption number 4 is violated, Equation (5.3) will still apply while the sample is debulking. It can be assumed that no bulk flow of the CMT takes place until the sample is fully debulked. It will be seen that this assumption holds for moderate squeezing rates, but becomes less applicable for high squeezing rates Equipment A heated squeeze flow fixture, shown in Figure 5.2, was designed and built. The platens are mm mm 38.1 mm (6 in 6 in 1.5 in) and each is heated using four 150 mm long by 12.7 mm diameter, 250W, cartridge heaters. Zircar (Florida, NY) 25.4 mm thick insulation board, type RSLE-57, was mounted on the back and sides of each platen and the platens were then mounted in a ball-bearing die set to help ensure parallelism. Attached to the die set is an LVDT capable of measuring 0 10 mm displacement. The temperature of each platen is independently controlled using a digital PID temperature controller. The fixture was mounted in a 444 kn MTS servo-hydraulic load frame with hydraulic grips that limited the maximum loading to the 222 kn load range. A routine was written in the MTS TestStar language to control the motion of the actuator during the setup and testing and this routine was run on the computer that controlled the MTS frame. A separate computer running LabVIEW recorded load, displacement, and temperature data at a rate of Hz. A LabVIEW Virtual Instrument, shown in Figure 5.3, was designed to interface with the fixture and the load frame to record the data. The parallelism of the platens was measured by squeezing 3.1 mm diam. 20 mm long cylindrical pieces of lead-tin solder between the platens at room temperature.

94 5.3. THROUGH THICKNESS STRESS MEASUREMENT 76 Figure 5.2: Squeeze flow fixture mounted in MTS load frame, and closeup of the fixture. Figure 5.3: LabVIEW virtual instrument used to acquire data.

95 5.3. THROUGH THICKNESS STRESS MEASUREMENT 77 Table 5.2: Parallelism of squeeze flow fixture. Load Measured Solder Thickness (mm) (kn) Avg. Max. Min. Difference Table 5.3: Low speed through thickness stress samples. Total Constituent Mass (g) FVF Lot No. Mass (g) Fiber Matrix Nine pieces of solder were placed on the platens, laying down, in a 3 3 grid. The thickness of the solder was measured at three values of the axial load: 15 kn, 45 kn, and 150 kn, and the maximum differences in thickness occurred at opposite corners of the square platens as listed in Table 5.2. Based on this, the squeezing experiments in this study were run with plate separations above 0.5 mm to ensure that the platens were plane to within 12% of the sample thickness Material List Through thickness stress experiments were conducted on C/PP CMT at slow (quasistatic) and fast squeezing speeds. Slow speed compression tests were run on 10% 26.2% FVF CMT consisting of 12.7 mm long PANEX35 fibers in PP. Sheets mm square were cut from the roll of material and stacked with the MD aligned to form each sample with the number of sheets being varied so all of the samples contained approximately the same mass of fibers. The five samples that were tested are listed in Table 5.3. High speed tests used 10% 26.2% FVF CMT with 12.7 mm long PANEX35 fibers in PP. The samples were 50.4 mm in diameter, and the number of sheets was chosen so that at full consolidation the sample height equaled 4 mm. The sheets were once again stacked with the MD aligned. Each sample was tested at closing speeds of 0.1,

96 5.3. THROUGH THICKNESS STRESS MEASUREMENT 78 Table 5.4: High speed through thickness stress samples, 4 mm thick. V f Lot No. Sample No. Speed (mm/s) Mass (g) H 0 (mm) ACC3.181N ACC3.181M ACC3.181L ACC3.181K ACC3.181J ACC3.181I ACC3.181H ACC3.181AG ACC3.181AF ACC3.181AE ACC3.181AD ACC3.181AC ACC3.181AB ACC3.181AA ACC3.182H ACC3.182I ACC3.182J ACC3.182K ACC3.182L ACC3.182M ACC3.182N ACC2.099L ACC2.099D ACC2.099E ACC2.099F ACC2.099G ACC2.099H ACC2.099I , 0.5, 1.0, 2.0, 5.0, or 8.5 mm/s, for a total of seven samples per FVF as listed in Table 5.4. A picture of the samples before testing is shown in Figure Experimental Procedure Testing was conducted in two speed regimes, low (0.005 mm/s) and high ( mm/s). Different samples were used for each range, and the testing procedure for each range

97 5.3. THROUGH THICKNESS STRESS MEASUREMENT 79 Figure 5.4: Specimens for squeeze flow experiments; left figure shows the disks as cut from the CMT, and the right figure shows the stacked disks ready for squeezing. was slightly different as described below. Low Speed Testing Before the testing started, the platens of the squeeze flow fixture were treated with the release agent Frecote 700-NC to prevent the samples from sticking to the platens. The platens were pre-heated and allowed to come to a uniform temperature of 200 C, then the empty fixture was closed and held at 1 kn load so the zero reference for the platen separation could be set. The fixture was opened and a sample was inserted, then the MTS program closed the platens to a separation of 10 mm and the samples were held for at least 9 minutes to allow them to be heated to the temperature of the platens. This was sufficient time for the center of the stack to heat to within 0.1 C of the set temperature. Each test began with the load cell on its 44 kn range. The data acquisition was started at a rate of 0.25 Hz and the platens were driven together at a constant speed of mm/s. The program that controlled the load frame continued until the load reached 40 kn where the motion of the actuator was stopped to allow the load cell range to be manually changed from the 44 kn range to the 222 kn range. Then the test proceeded until a limiting load of 220 kn was reached. After the maximum load was reached the overall load was reduced to 4 kn and the platens were held a fixed distance apart while the fixture cooled. When the temperature was below 130 C the fixture was opened and readied for the next sample.

98 5.3. THROUGH THICKNESS STRESS MEASUREMENT 80 High Speed Testing The platens were coated with Frecote 700-NC before each batch of seven samples. Before testing each individual sample, the platens were also sprayed with Miller Stephenson MS-122 Teflon release agent in an attempt to reduce sliding friction between the platens and the sample. The platens were pre-heated to 180 C and the zero separation reference was found as above. The sample was inserted into the fixture, then the fixture was closed so the platens were 10 mm apart and held there for 9 minutes to allow the samples to come to thermal equilibrium. Depending on the loads expected during the test, the load cell range was set to either 44, 88, or 222 kn before each test. After the hold time was complete the data acquisition system was started and the MTS control program was run to drive the platens together at a constant speed of mm/s and each sample was squeezed to approximately 25% of its original thickness. Once the maximum load was reached, the load was reduced to 4 kn and the platens were held a fixed distance apart until the fixture cooled to 130 C when the fixture was opened and prepared for another sample Results For the low speed testing the experimentally measured transverse normal stress versus FVF is shown in Figure 5.5. The curves for the 15%, 20% and 25% FVF material are all coincident with the curve appearing bi-linear in the log-log plot with a knee at V f = Equation (5.2) was used to fit both sections of the curve with the left portion of the curve was fit with f = and n = while the right portion was fit with f = and n = The f value of is not very close to the analytical value for randomly oriented fibers of f = 2/π = , but the exponent, n, is close to the theoretical value of 5 suggesting that there is some preferential alignment of the fibers in the CMT. The presence of the knee in the data is qualitatively predicted by Toll [119]. For brittle fibers such as carbon, he suggests that above a certain FVF a loss of stiffness is expected as fibers begin to fracture. Since some fiber segments will be carrying a high load while others will have a low load, there should be a transition from purely elastic to inelastic behavior. The results for the 10% FVF material differed dramatically from those for the other three FVFs. The recorded load signal from the two 10% FVF samples was erratic and jumped around significantly while the load for the other three FVFs steadily increased, as shown in Figure 5.5. Also, the calculated stresses were about 7 times larger than those for the other samples. Fitting Equation (5.2) to the data yields f = and n = This value of f is much closer to the theoretical value for randomly oriented fibers. It is probable that there was a manufacturing difference between the 10% FVF material and the other materials. The higher FVF material may have more fiber alignment or bundles of fibers that were not dispersed as well as those in the 10% FVF material.

99 5.3. THROUGH THICKNESS STRESS MEASUREMENT 81 1.E+08 Stress (Pa) 1.E+07 1.E+06 1.E+05 1.E+04 Consolidated FVF: 10 vol.% 15 vol.% 20 vol.% 25 vol.% Power law fits 1.E Fiber Volume Fraction Figure 5.5: Through thickness stress versus FVF for the low speed tests. High speed testing showed trends that were similar in nature to those in the slow speed testing, but depended on both the FVF and the closing speed. Plots of σ p versus V f are shown in Figure 5.6. The general trend is a slow increase in stress as the material debulks, followed by a sharp stress rise as the material nears its fully consolidated V f, then the stress levels off or drops as the material begins to flow. On the log-log scale, the through thickness stresses follow a bi-linear trend until the material begins flowing. Equation (5.2) was fit to the linear regions and the fit lines are shown in the Figure 5.6. The coefficients f and n are listed in Table 5.5 for fits in the figure. The n values for the left hand slope are reasonably close to the value of calculated during the low speed tests. The difference is most likely due to the dynamic nature of the current tests. The steep slope shows a much higher n of which occurs just before the CMT reaches full consolidation. The interactions between fibers, the matrix, and air is very complex here. One possibility is that the air flow channels become pinched-off and the resulting pressure rise is due to the compression of the air. Alternately the load could be rising to the yield stress of the material. The very large f values do not have physical significance in the steep slope region; they should be considered curve fit constants.

100 5.3. THROUGH THICKNESS STRESS MEASUREMENT 82 Log 10 (σp ) mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Fit (1)-(4) 7 6 V f,max =10% 5 Log 10 (σp ) mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Fit (1)-(4) V f,max =15% Log 10 (V f ) Log 10 (V f ) Log 10 (σp ) mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Fit (1)-(4) Log 10 (V f ) V f,max =20% Log 10 (σp ) Log 10 (V f ) V f,max =26.2% 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Fit (1) Figure 5.6: Through thickness stress versus FVF for the high speed tests.

101 5.4. SINGLE FIBER PULL-OUT 83 Table 5.5: Fit constants for high speed testing. V f < V f,knee V f V f,knee V f,max V f,knee f n f n N/A N/A Single Fiber Pull-Out The frictional forces that exist between touching fibers during the compression molding process were studied. A heated fixture was constructed to measure the force per unit fiber length required to pull a single fiber longitudinally through the molten CMT Theoretical Background The fibers are assumed to be straight uniform cylinders of diameter d and length l. The fibers may be considered slender since l d, and they are assumed to be randomly distributed in a single plane. Measuring the pulling speed and force allows for the calculation of the frictional coefficient k f, the hydrodynamic coefficient k h, and the film thickness α in Equation (2.10). That equation will be used to fit the data in this study Equipment The equipment used to perform these tests is listed below: 0.5 N load cell mounted in an electro-mechanical test frame. Single fiber pull-out fixture, 10 mm gage length. Oven: 150 mm 150 mm 150 mm outside, 75 mm 75 mm 75 mm inside dimensions. Digital PID temperature controller (Omega Engineering, model CN132). Type K thermocouple, attached to the fixture. Infra-red quartz heater: 200 W, 120 V, 150 mm long 12.7 mm diam., 75 mm heated length (Glo-Quartz Inc., model LHP-2A6).

102 5.4. SINGLE FIBER PULL-OUT 84 Adjusting screw Traction fiber CMT F Parallel plate Extra fiber 10 mm Figure 5.7: Sketch of the fiber pull-out fixture. Stereo optical microscope, magnification. Data acquisition computer running LabVIEW software. A sketch of the fixture is shown in Figure 5.7 and a detailed plan for the fixture is shown in Appendix A. The oven was mounted in the load frame as shown in Figure 5.8. A close-up of the fixture in Figure 5.9 shows how the thermocouple was mounted and the aluminum plates and wire clips that were fashioned to constrain the heated sample within the fixture. Temperature was controlled by switching the heater power on and off with a maximum duty cycle of 70% on, 30% off over 5 seconds to prevent the IR heater from overheating and burning out. Temperature control to within ±0.5 C was achieved using this setup. Since the heating was by IR and the furnace box was not air tight, the air temperature lagged behind the fixture temperature by a significant margin, therefore the controlling thermocouple was attached directly to the metal fixture. Heating the fixture to 180 C took about 10 minutes Material List The materials used in this experiment are a single 7.2 µm carbon fiber and consolidated panel of C/PP CMT. Carbon fibers were extracted from a 48K tow of unsized Zoltek PANEX33. The 3 mm thick C/PP panel was manufactured from unsized PANEX33, 12.7 mm long, with FVF of 10%, wetlay lot number Pieces 10 mm 19 mm were cut from the consolidated panel to fit in the pull-out fixture. In order to maintain consistency in testing, CMT pieces were placed in the fixture so the side of the panel that was on the bottom of the mold sandwiched the traction fiber. All testing had the traction fiber pulled in the transverse direction of the panel.

103 5.4. SINGLE FIBER PULL-OUT N Load Cell Fixture IR Heater Temperature Controller Figure 5.8: Pull-out fixture mounted in the load frame. Thermocouple (under screw) Aluminum plate to hold sample in fixture Wire to keep plates parallel Aluminum heat reflector Figure 5.9: Pull-out fixture closeup.

104 5.4. SINGLE FIBER PULL-OUT 86 a) b) Figure 5.10: Method of obtaining a single carbon fiber: a) trimming all but one fiber; b) pulling extra fibers through empty fixture Experimental Procedure First, a small bundle of carbon fibers about 60 cm long was separated from the 48K tow and it was loaded through the fixture then taped onto the load-cell hanger using office tape. Fibers were trimmed away as shown in Figure 5.10 until a single fiber was left as verified with an optical microscope. After the single fiber was positioned in the fixture, pieces of consolidated CMT were placed in the fixture, sandwiching the single fiber between them. The adjusting screws on the side of the fixture were screwed in until the parallel plates just held the CMT in place and the aluminum plate and wire retaining clips were secured to hold the sample in place. The oven door was closed and the temperature was raised to 180 C at which point the adjusting screws were slowly tightened to compress the CMT to the desired FVF. Once the FVF was set, one of two different types of experiments was performed. The first was a constant speed experiment where the cross-head on the load frame was raised at various speeds and the force required to pull the fiber through the fixture was measured. The fiber was pulled at speeds of mm/s and the force was recorded. The system was allowed to equilibrate at each speed for about 120 s allowing any waves in the traction fiber to straighten. Typically the force reached equilibrium after about s. The force was averaged over the 100 s after equilibrium was reached. The second type of experiment was a force-decay experiment. After the fiber had reached equilibrium in the constant-speed experiment, the cross-head motion was stopped and the force on the traction fiber was allowed to decay to a constant value which was used to find the friction coefficient k f. Typically the force decayed very quickly, usually within 5-10 seconds. The cross-head was held in position for at least 60 s and after equilibrium was reached, the average force was calculated from the

105 5.4. SINGLE FIBER PULL-OUT Force Speed 1 Force (mn) Speed (mm/s) Time (sec) Figure 5.11: Typical force versus time curve for a single fiber pull-out experiment for 10.2% C/PP CMT. experimental data Results Testing was completed for PP CMT at 10.2% 15% FVF. A typical force-versus-time curve is shown in Figure The time up to 1000 s includes the heat up time (about 600 s) and the initial settling time, from s where the fiber was pulled at mm/s until the force leveled out. Any slack in the fiber was removed and the traction fiber was pulled straight during this time. Typically, 10 mm of fiber was pulled through the fixture to ensure equilibrium. Once the measured force leveled out, the pulling speed was steeped between mm/s. Additionally, part way through the test, at about 1225 s, the direction of the cross head was reversed to completely unload the traction fiber. From this, any offset in the load signal could be measured and subsequently removed during data analysis. As the pulling speed was stepped up ( s), the measured force was seen to increase. At each speed below 0.5 mm/s, the measured force remained constant over time whereas at speeds of 0.5 mm/s and above, the measured force showed a spike at the beginning of each new speed, then the force decayed to a varying value. This can clearly be seen in the data collected at both the 0.5 mm/s and 1.0 mm/s speeds. All of the traction fiber had been pulled through the fixture at 2195 s.

106 5.4. SINGLE FIBER PULL-OUT Normalized pull-out force (N/m) vol% Fit 15.0% 12.1 vol% Fit 12.1% 11.3 vol% Fit 11.3% 10.2 vol% Fit 10.2% Pull-out speed (mm/s) Figure 5.12: Force versus pulling speed for C/PP CMT. Open points are from constant speed experiments, filled points are estimated from broken fiber experiments. Table 5.6: Values used in Equation (2.10). Parameter Value Units d 7.2 µm E f 228 GPa f n α µm k f k h mm 2 The average of the force over each speed was calculated and was normalized to a force per unit length, and results from runs at 10.2% to 15% FVF are shown in Figure Equation (2.10) was fit to the data using constants in Table 5.6. A least squares method was then used to find the parameters k f, k h, and α. Only data at speeds less than 1.0 mm/s were used in the data fit because the average force could not be calculated with certainty for the higher speeds. Results for the 15% FVF material were harder to obtain. Instead of the traction fiber pulling smoothly through the CMT, the fiber tended to break when load was

107 5.4. SINGLE FIBER PULL-OUT Force Speed Constant force region 0.1 Force (mn) Fiber break 0.01 Speed (mm/s) Time (sec) Figure 5.13: Typical force versus time curve for a single fiber pull-out experiment for 15% C/PP CMT. applied. A typical force-versus-time curve is shown in Figure The first 900 s of the experiment were used to bring the fixture up to 180 C and obtain equilibrium with an equilibrium force being measured from 927 s to 997 s. At 997 s, the load dropped and it is assumed that the fiber broke somewhere within the fixture. At about 1240s a second break event occurred. The remaining fiber was completely pulled out of the CMT at 1380 s. A total of six tests were attempted with the 15% FVF CMT material. Only one of the experiments exhibited a region where a steady force was measured, and that only lasted for about 70 s before the fiber broke. All of the other experiments had the fiber break and no steady force regions were observed. Even when the traction fiber breaks inside the fixture, it is still possible to estimate the length of the remaining fiber and estimate the force per unit length on the fiber, F/L. In Figure 5.14 two linearly decreasing regions are highlighted. A linear equation can be fit to these regions: F = mx + b (5.4) where m is the slope, x is the cross head displacement, and b is the y-intercept. A least squares method was used to find m and b. It is assumed that when the fiber pulls out of the CMT, the resulting force will be zero. Thus the cross head displacement x 0

108 5.4. SINGLE FIBER PULL-OUT Force (mn) Force Linearly decreasing force regions Cross head displacement (mm) Figure 5.14: Linearly decreasing force versus time curve for the broken fiber pull-out tests. when the fiber pulls out is given by x 0 = b m (5.5) The length of fiber L left in the CMT at a given cross head position is found from L = x 0 x (5.6) Substituting (5.6) into (5.4) gives the following estimate for the normalized pulling force F = m (5.7) L These estimated F/L values are plotted in Figure 5.12 as solid circles. Results from the force-decay experiment are shown in Figure Equation (2.10) was fit to the data with v = 0 and k f = was found using a least squares method, which is close to the value found from the constant speed experiments Discussion Working with a single carbon fiber proved challenging. Fiber breakage during setup of each experiment is always a problem. The fibers are fragile, and the fact that they

109 5.4. SINGLE FIBER PULL-OUT Normalized Force (N/m) Experiment 0.2 Fit % 11% 12% 13% Fiber Volume Fraction Figure 5.15: Force decay results for single fiber pull-out. cannot be seen with the unaided eye makes the setup that much more difficult. Often it is not known if the single fiber has survived until the sample is heated to its melt point and the test is begun. Results from the % FVF C/PP CMT material were fit with Equation (2.10) very well, as shown in Figure 5.12 for pulling speeds of mm/s. At greater speeds the experimental data was difficult to interpret (see Figure 5.11). When the speed was stepped up, the measured force showed a peak then dropped-off to an unsteady value. Since the fiber bed and traction fiber should have been at equilibrium due to the slower speed testing, it is possible that there is rearrangement of the fiber bed when the speed is >0.5 mm/s. As the fiber bed changes configuration, the load would change, making the test invalid. The 15% FVF samples were more difficult to work with than the lower FVF samples as the traction fiber tended to break rather than smoothly slide through the CMT. This is due to the higher FVF that leads to both a larger number of fibers touching the traction fiber, and a higher normal force at each fiber-fiber touch point. Equation (2.10) predicts a five fold increase in the static friction force when the FVF is increased from 10% to 15%. Even with these difficulties, the 15% FVF data appears to be reasonable and brackets the predictions of Equation (2.10). The extra scatter in the 15% FVF data seems reasonable since the remaining fiber length must be estimated.

110 5.5. SQUEEZE FLOW 92 Moving Platen z Squeezed material Fixed Platen h u = constant r Figure 5.16: Squeeze flow sketch Conclusions A single fiber pull-out fixture was successfully designed, built, and used to measure the fiber-fiber frictional coefficients in CMT. These coefficients will be used in relations to estimate the bulk flow of the CMT in the next section. 5.5 Squeeze Flow Manufacturing of CMT will be performed using the compression molding technique, so it is important to understand the bulk flow properties of the material. This information could be used to estimate the closing forces required to fabricate parts and to predict the flow patterns of the CMT inside the mold. Compression molding can be approximated as squeezing flow between parallel plates. In order to measure the bulk flow properties of the CMT a heated squeeze flow fixture was built. This fixture was used to measure the squeezing force on samples of CMT as a function of sample thickness Theoretical Background During squeeze flow the resultant of the frictional forces on each individual fiber may generate an axial stress in that fiber that exceeds its strength, causing it to break into shorter pieces. A simple way to estimate the maximum stress in a fiber in the flowing CMT is presented now. A purely extensional flow field with no friction between the platens and the CMT material is shown in Figure The flow is assumed to be incompressible and axisymmetric about the z-axis and satisfies v = 0 (5.8) v r = v r (r, z) (5.9) v θ = 0 (5.10) v z = v z (r, z) (5.11)

111 5.5. SQUEEZE FLOW 93 r f f + f h (r) Figure 5.17: Sketch of a single fiber in the flowing CMT. where v r, v θ, and v z are the components of the velocity field v in cylindrical coordinates. Using Equation (5.10), Equation (5.8) in cylindrical coordinates is 1 r r (rv r) + v z z = 0 (5.12) In order to satisfy Equation (5.12), the velocity field is assumed to have the following form v r = f(r) (5.13) v z = uz/h (5.14) Substituting equations (5.13) and (5.14) into equation (5.12) gives ( ) 1 d u r dr (rf(r)) + = 0 (5.15) h Equation (5.15) is integrated with respect to r and solved for f(r): f(r) = ru 2h + C 1 r (5.16) where C 1 is a constant of integration. Since v r must be finite at r = 0, C 1 = 0. Thus the velocity field between the plates is v r = ru 2h v z = uz h (5.17) (5.18) A single fiber in the flow is shown in Figure The circles represent other fibers that are contacting the fiber under consideration. To an observer sitting on any fiber, the flow field will look the same, therefore we consider the fiber with its center located at r = 0. The following assumptions are made:

112 5.5. SQUEEZE FLOW 94 The number of fiber touches n (i) is known (e.g. n (i) = 5 in Figure 5.17). The fiber touches are equally spaced along the fiber. The velocity of each contacting fiber is along the axis of the main fiber. The velocity at each contact point equals v r (r). The forces at each contact point will be based on the average contact force. Since the fiber mat is randomly oriented the actual contact problem is much more complicated than what is assumed here. These assumptions will allow a first order approximation of the forces on an individual fiber in the flowing CMT. The average number of fiber-fiber interactions along a given fiber is given by Toll [37] as: n (i) = 8l πd fv f (5.19) The force at a given fiber-fiber touch point is the sum of the frictional and the hydrodynamic forces where F = f f + f h (5.20) f h = k h η f f = k f c n v v [ ( 1 + λ v ) ] 2 (n 1)/2 v α α (5.21) (5.22) where c n is given by Equation (2.6) on page 6. The maximum force in each fiber will occur at the fiber s center. Summing one half of the forces on the fiber gives the maximum force F max F max = n(i) n (i) /2 2 f f + f h (r = ja) (5.23) where a = l/n (i) is the average spacing between touches. The maximum axial stress in each fiber is given by Equipment j=1 σ f,max = F max πd 2 /4 The squeeze flow fixture described in Section was used for these experiments. (5.24)

113 5.5. SQUEEZE FLOW Material List Squeeze flow experiments were conducted on 10% 26.2% FVF C/PP CMT material. The CMT consisted of 12.7 mm long PANEX35 fibers, sized with type -21 sizing, in PP. A 50.4 mm diameter punch was used to cut disks from the CMT. This diameter is four times the fiber length and should help reduce edge effects [50]. Disks were stacked into each sample with the MD aligned, to achieve either a 2 mm or 4 mm consolidated thickness. The 4 mm thick samples are listed in Table 5.4 on page 78 and the 2 mm thick samples are listed in Table 5.7. Photographs of the samples before testing are shown in Figure 5.4 on page Procedure The test procedure in Section on page 80 (High Speed Testing) was used to test these samples. After the samples had been squeezed, the burn-off procedure in Section on page 39 was used to remove the PP from the samples so the carbon fibers could be visually inspected Results Figure 5.18 shows a typical sample after squeezing. The originally circular disk has been deformed into an elliptical disk. The black concentric circles in the middle of the sample were drawn on the top disk before testing. If there was no friction between the sample and platens, the circles would have deformed into ellipses along with the rest of the sample. Since the circles are still the same size and shape as they were before testing, a no-slip condition between the platen and the sample prevails. The squeezing strain rate ɛ zz of the sample is calculated as ɛ zz = u h (5.25) where h is the platen separation and u is the closing speed. The tests were to be run at constant velocity. It was found that the load frame could maintain a constant closing speed until the squeezing force was too high. The experimental strain rate and the expected strain rate for each test are plotted in Figure For closing rates of 2 mm/s and below the experimental strain rate matches the expected strain rate through the end of each test. When the closing speed is 5 mm/s and above, the machine is unable to provide enough force quickly enough to maintain the desired strain rate, and the measured strain rate peaks then falls. Figures 5.20 and 5.21 show the force versus displacement curves for the 10% FVF C/PP material. The shape of the curves is qualitatively the same as that of the low FVF GMT and SMC [30 32, 120]. The force is very low as the platens approach h 0, then near h 0 the force rises quickly while the material is consolidated. As squeezing continues the force shows a plateau, then increases sharply near the end of the test.

114 5.5. SQUEEZE FLOW 96 Table 5.7: High speed through thickness stress samples, 2 mm thick. FVF Lot No. Sample No. Speed Mass H 0 (mm/s) (g) (mm) ACC3.181G ACC3.181F ACC3.181E ACC3.181D ACC3.181C ACC3.181B ACC3.181A ACC3.181V ACC3.181U ACC3.181T ACC3.181S ACC3.181R ACC3.181Q ACC3.181P ACC3.182G ACC3.182F ACC3.182E ACC3.182D ACC3.182C ACC3.182B ACC3.182A ACC2.099A ACC2.099B ACC2.091D ACC2.091E ACC2.091F ACC2.091G ACC2.091H

115 5.5. SQUEEZE FLOW 97 Figure 5.18: Squeezed sample. Squeezing Strain Rate (1/s) 10 Expected Experiment mm/s 5.0 mm/s 2.0 mm/s 1.0 mm/s mm/s 0.2 mm/s 0.1 mm/s Elapsed Time (s) Figure 5.19: Typical measured versus expected axial strain rates for the squeeze flow experiments.

116 5.5. SQUEEZE FLOW 98 Force (kn) h 0 = 2 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Force (kn) h 0 = 2 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Platen separation, h/h 0 Platen separation, h/h 0 Figure 5.20: Load versus platen separation for the 2 mm thick, 10% FVF samples; the left figure shows entire range and the right figure shows a zoomed in region. Force (kn) mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) h 0 = 4 mm Platen separation, h/h 0 Figure 5.21: Load versus platen separation for the 4 mm thick, 10% FVF samples.

117 5.5. SQUEEZE FLOW 99 Force (kn) h 0 = 2 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Force (kn) h 0 = 4 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Platen separation, h/h 0 Platen separation, h/h 0 Figure 5.22: Load versus platen separation for the 15% FVF samples. The 15% FVF material behaves similar to the 10% FVF material. Results from the 2 mm and the 4 mm thick samples are shown in Figure The 20% and the 26.2% FVF materials show a different behavior (Figures 5.23 and 5.24, respectively) than the lower FVF material. As the platens approach h 0, the load rises quickly to a local maximum, then drops as the squeezing continues. As the test progresses the load begins to climb again. This behavior has not been reported in the literature for any other fiber filled polymer. The cause of this initial load spike was determined to be breaking of the fibers. It has been known anecdotally that the maximum fiber length in a GMT part is limited both by the distance the material must flow during molding and by its FVF. The GMT used in other studies [30, 34, 36, 39] is about 8% 13% FVF while the CMT shows the load spike beginning at 15% FVF. It is possible that glass fibers do not exhibit this trait, or researchers have not tested GMT s with high enough FVF. Two squeeze-flow samples at each FVF had the matrix burned off after the squeezing test. Dissection and visual inspection of the resulting carbon fiber mats found an increasing amount of very short (<1-4 mm) fibers as the FVF of the sample increased. Photographs of the dissected specimens are shown in Figures For the 10% FVF sample (Figure 5.25), the mat had very few visibly broken fibers and the mat had structural integrity from the many layers of long overlapping fibers. The 15% FVF (Figure 5.26) sample showed some very short (<1 mm long), fibers that are visible in Figure 5.26 against the white background. When the FVF was increased to 20%

118 5.5. SQUEEZE FLOW 100 Force (kn) h 0 = 2 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Force (kn) h 0 = 4 mm 8.5 mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Platen separation, h/h 0 Platen separation, h/h 0 Figure 5.23: Load versus platen separation for the 20% FVF samples. Force (kn) h 0 = 2 mm 8.5 mm/s (7) 2.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) Force (kn) mm/s (7) 5.0 mm/s (6) 2.0 mm/s (5) 1.0 mm/s (4) 0.5 mm/s (3) 0.2 mm/s (2) 0.1 mm/s (1) h 0 = 4 mm Platen separation, h/h 0 Platen separation, h/h 0 Figure 5.24: Load versus platen separation for the 26.2% FVF samples.

119 5.5. SQUEEZE FLOW 101 Figure 5.25: 10% FVF sample after squeezing and burn-off (scale division=1 mm). Figure 5.26: 15% FVF sample after squeezing and burn-off (scale division=1 mm).

120 5.5. SQUEEZE FLOW 102 Figure 5.27: 20% FVF sample after squeezing and burn-off (scale division=1 mm). Figure 5.28: 25% FVF sample after squeezing and burn-off (scale division=1 mm).