Modelling of pseudoplastic deformation of carbon/carbon composites with a pyrocarbon matrix

Abstract

An engineering micromechanical model for carbon/carbon composites with a pyrocarbon (PC) matrix is presented. The model of the matrix plays an essential role in modelling of the material. This model takes into account the structural heterogeneity of the PC matrix and the anisotropy of the carbon fibres. The PC matrix is considered as a polycrystalline aggregate of anisotropic PC grains (or crystallites) with random shapes and orientations. The carbon fibres are homogeneous and anisotropic. The mathematical foundation for the model is a homogenization procedure for a multicomponent heterogeneous medium with a stochastic structure, anisotropic components and variable volume fractions of the components. The stochastic structure of the matrix generates fields of fluctuating microstresses and stochastic fractures of individual PC grains. Due to the anisotropy, the PC grains can fracture or become partially damaged via several fracture modes with different probabilities depending on the macrostress state of the material. The model allows calculation of the full stress–strain diagram for the carbon/carbon composite with arbitrary multiaxial loads and to forecast the appropriate strength limits. As an application of the model, numerical results are presented for a three-point bending of a short beam made of unidirectional materials. The calculated interlaminar shear strength matches the available experimental data.