Investigation of the strengthening of particulate reinforced composites using different analytical and finite element models

The limit flow stress of composite materials reinforced with randomly distributed spherical particulate inclusions is investigated using both numerical and finite element (FE) models. Comparison is made between the different models and with experiments. The recently published modified Oldyrod model, an analytical numerical method which predicts the stress-strain response of materials undergoing both elastic and plastic deformation using elastic methods is investigated. It is compared with the classical axisymmetric cell model as well as with a 3D-embedded finite element model. The models are first compared with each other for the ideal case of a rigid inclusion in an elastic-plastic nonhardening matrix. It is found that all models predict much the same strengthening for 50% inclusion but at higher volume fractions differ significantly. The axisymmetric model predicts a very strong composite response due to particles nearly impinging on each other in contrast to the other models considered where more realistic boundary conditions are imposed by surrounding the cell with actual material, Comparison is then made between the different 3D-models and experiment for a 58 vol% martensite-austenite composite, This represents the case of a hard inclusion in a relatively soft matrix. In the elastic regime and during the early stages of plastic deformation all models are seen to give a good estimate of the composite response. However, at higher strains, the response predicted by the 3D-embedded cell model fits closest to the experimental results. It is seen that the much simpler and so computationally much quicker modified Oldroyd model also gives valid results for a wide band of inclusion volume fractions. The exact location of this band is seen to vary with the hardening exponent of the matrix material. A comparison between the modified Oldroyd model, 3D-embedded cell model, the 3D-axisymmetric cell model and the previously published Duva model for rigid inclusions in a variety of elastic-plastic hardening matrices shows significant differences between the models. For materials with high strain hardening exponents the benefit of using the 3D-embedded cell model is increased. Finally, comparison is further made with experiments where both phases are capable of elastic-plastic deformation. Again at higher strains the 3D-embedded cell model is seen to give the best indication of the composite response. However, it is seen that the modified Oldroyd model can also be used to give useful results for the investigated materials. (C) 1999 Published by Elsevier Science B.V. All rights reserved.