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 distr ibuted spherical particulate inclusions is investigated using both numerica l 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 o f materials undergoing both elastic and plastic deformation using elastic m ethods is investigated. It is compared with the classical axisymmetric cell model as well as with a 3D-embedded finite element model. The models are f irst 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 m uch the same strengthening for 50% inclusion but at higher volume fractions differ significantly. The axisymmetric model predicts a very strong compos ite response due to particles nearly impinging on each other in contrast to the other models considered where more realistic boundary conditions are i mposed 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 har d inclusion in a relatively soft matrix. In the elastic regime and during t he early stages of plastic deformation all models are seen to give a good e stimate of the composite response. However, at higher strains, the response predicted by the 3D-embedded cell model fits closest to the experimental r esults. It is seen that the much simpler and so computationally much quicke r modified Oldroyd model also gives valid results for a wide band of inclus ion 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, th e 3D-axisymmetric cell model and the previously published Duva model for ri gid inclusions in a variety of elastic-plastic hardening matrices shows sig nificant differences between the models. For materials with high strain har dening exponents the benefit of using the 3D-embedded cell model is increas ed. Finally, comparison is further made with experiments where both phases are capable of elastic-plastic deformation. Again at higher strains the 3D-embe dded cell model is seen to give the best indication of the composite respon se. 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.