Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites

In this paper a new numerical procedure by Gusev, for predicting the elastic and thermoelastic properties of short fibre reinforced composites, is described. Computer models, comprising 100 non-overlapping aligned spherocylinders, were generated using a Monte Carlo procedure to produce a random morphology. Periodic boundary conditions were used for all the generated structures. Where necessary, the generated microstructures were based on measurements of real materials: for example a measured fibre length distribution was used to seed the Monte Carlo generator to produce a computer model with an equivalent fibre length distribution (FLD). The generated morphologies were meshed using an intelligent 3 dimensional meshing technique, allowing the elastic and thermo-elastic properties of the microstructures to be calculated. The numerical predictions were compared with those from three commonly used micromechanical models, namely those attributed to Halpin/Tsai, Tandon/Weng and Cox (shear lag). Firstly, the effect of volume fraction and aspect ratio were investigated, and the numerical results were compared and contrasted with those of the chosen models. Secondly, the numerical approach was used to investigate what effect a distribution of fibre lengths, as seen in real materials, would have on the predicted mechanical properties. The results were compared with simulations carried out using a monodispersed fibre length, to ascertain if the distribution of lengths could be replaced with a single length, and whether this length corresponded to a particular characteristic of the distribution, for example the first moment or average length.

[1]  Suresh G. Advani,et al.  The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites , 1987 .

[2]  J. Whitney,et al.  The Laminate Analogy for 2 and 3 Dimensional Composite Materials , 1971 .

[3]  I. Ward,et al.  Modelling the elastic properties of fibre-reinforced composites: II theoretical predictions , 1993 .

[4]  G. P. Tandon,et al.  The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites , 1984 .

[5]  A. Wilczynski,et al.  A basic theory of reinforcement for unidirectional fibrous composites , 1990 .

[6]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[8]  M. Taya,et al.  The Effect of Variable Fiber Aspect Ratio on the Stiffness and Thermal Expansion Coefficients of a Short Fiber Composite , 1987 .

[9]  A. A. Gusev.  Representative volume element size for elastic composites: A numerical study , 1997 .

[10]  I. Ward,et al.  Modulus of short carbon and glass fiber reinforced composites , 1971 .

[11]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[12]  Andrei A. Gusev,et al.  Numerical Identification of the Potential of Whisker- and Platelet-Filled Polymers , 2001 .

[13]  Andrei A. Gusev,et al.  Fiber packing and elastic properties of a transversely random unidirectional glass/epoxy composite , 2000 .

[14]  Charles L. Tucker,et al.  Stiffness Predictions for Unidirectional Short-Fiber Composites: Review and Evaluation , 1999 .

[15]  Marc S. Ingber,et al.  A parallel‐supercomputing investigation of the stiffness of aligned, short‐fiber‐reinforced composites using the Boundary Element Method , 1997 .

[16]  Richard Schapery.  Thermal Expansion Coefficients of Composite Materials Based on Energy Principles , 1968 .

[17]  M. Taya,et al.  Thermal Expansion Coefficients and Thermal Stresses in an Aligned Short Fiber Composite With Application to a Short Carbon Fiber/Aluminum , 1985 .

[18]  J. Halpin.  Stiffness and Expansion Estimates for Oriented Short Fiber Composites , 1969 .

[19]  H. L. Cox.  The elasticity and strength of paper and other fibrous materials , 1952 .