The energy approach recently proposed by Qiu and Weng (1992) is introduced to estimate the equivalent stress of the ductile matrix in Tohgo and Chou’s (1991) incremental damage theory for particulate-reinforced composites containing hard particles. In such a composite debonding of the particle-matrix interface is a significant damage process, as the damaged particles have a weakening effect while the intact particles have a reinforcing effect. In Tohgo-Chou’s theory, which describes the elastic-plastic behavior and the damage behavior of particulate-reinforced composites, it was assumed that the debonding damage is controlled by the stress of the particle and the statistical behavior of the particle-matrix interfacial strength, and that the debonded (damaged) particles are regarded as voids, resulting in an increased void concentration with deformation. On the other hand, Qiu-Weng’s energy approach provides a reasonable equivalent stress of the matrix in the porous material and particulate-reinforced composite even under a high triaxiality. The incremental damage theory developed here enables one to calculate the overall stress-strain response and damage evolution of the composite under high triaxial tension. The stress-strain relations for porous material obtained by the present incremental theory are completely consistent with that obtained by Qiu and Weng. The influence of the debonding damage on the stress-strain response is demonstrated for particulate-reinforced composites.

Composites containing NiTi shape memory alloy (SMA) long-fiber, short-fibers or Ti long-fiber in a Polycarbonate (PC) matrix have been fabricated by the injection molding technique. Also, prestrained SMA long-fiber/Epoxy matrix composites have been fabricated. The fracture behavior and thermo-mechanical deformation behavior are examined; (1) Fracture behavior – uniaxial tensile tests up to fracture for SMA long-fiber and short-fiber composite (SMAC). (2) Thermomechanical deformation behavior – tensile loading–unloading tests for Pseudoelastic (PE) long-fiber/PC matrix composites. Several thermo-mechanical loading tests for Shape Memory Effect (SME) long-fiber/PC matrix and SME long-fiber/Epoxy matrix composites were used. The obtained results are as follows: (1) The stress–strain relation up to the final fracture of the Shape Memory Alloy Composites (SMACs) showed the repeated up-and-down of the stress which corresponds to the necking of the specimen, fiber fracture, and matrix fracture. The strain for the initiation of necking and the strain for the fiber or matrix fracture in the SMACs were higher than those in the Ti composite. This is attributed to the unique stress–strain relations accompanied by the stress-induced martensitic transformation of the SMA fibers. (2) The SMAC containing PE fiber and PC exhibited the pseudoelastic-like deformation under tensile loading–unloading. (3) The SMAC containing SME fiber and PC exhibited the large contraction by heating after tensile loading–unloading, but the compressive residual stress in the matrix expected in this process was not remarkable. However, compressive residual stress in the matrix may become greater by embedding prestrained fiber in the matrix.

This paper deals with a constitutive model of particulate-reinforced composites which can describe the evolution of debonding damage, matrix plasticity and particle size effects on deformation and damage. An incremental damage model of particulate-reinforced composites based on the Mori-Tanaka's mean field concept has been extended to consider the particle size effects by using the Nan-Clarke's simple method. The particle size effect on deformation is realized by introducing dislocation plasticity for stress-strain relation of in-situ matrix in composites, and the particle size effect on damage is described by a critical energy criterion for particle-matrix interfacial debonding. For composites containing particles of various sizes, the effects of particle size distribution is incorporated into the model. Influence of debonding damage, particle size and particle volume fraction on overall stress-strain response of composites is discussed based on numerical results.

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In recent years, some researchers have studied about shape memory alloy composites (SMACs) which consist of a shape memory alloy (SMA) reinforcement and polymer or metal matrix. In particular, considerable attention has been paid to the creation of internal stress in a matrix of SMAC. Internal stress in a matrix can be created when a deformed SMA fiber recovers its original shape in a composite. On the other hand, deformation of the composite appears when internal stress is created in matrix. Therefore, an interaction exists between the creation of internal stress in the matrix and deformation of the composite. The main purpose of the present research is to investigate the effect of fiber volume fraction and aspect ratio (l/d: length divided by diameter of fiber) on the creation of internal stress in the matrix and deformation for a short-fiber SMA reinforced composite (S-SMAC) under thermal loadings. In the present paper, a constitutive relation of S-SMAC is proposed on the basis of the shear-lag model. Then, the effects of fiber volume fraction and aspect ratio on the creation of internal stress in the matrix and deformation of the composite are investigated by using the proposed constitutive relation for S-SMAC under thermal loadings. The main conclusions are as follows: composite shrinkage and compressive residual stress in the matrix increase with increasing aspect ratio and fiber volume fraction after heating. Also, the composite strain history and residual stress history in the matrix are different according to the fiber volume fraction and aspect ratio during heating. The change of aspect ratio has a small effect on the creation of internal stress in the matrix and deformation of the composite. The performances of S-SMAC come close to that of long-fiber SMA reinforced composite (L-SMAC) when the aspect ratio is >25. Also, residual stresses in the fiber and matrix before heating influence the creation of internal stress in the matrix and deformation of the composite during heating.