A constitutive model is developed for the transformation, reorientation and plastic deformation of shape memory alloys （SMAs）. It is based on the concept that an SMA is a mixture composed of austenite and martensite, the volume fraction of each phase is transformable with the change of applied thermal-mechanical loading, and the constitutive behavior of the SMA is the combination of the individual behavior of its two phases. The deformation of the martensite is separated into elastic, thermal, reorientation and plastic parts, and that of the austenite is separated into elastic, thermal and plastic parts. Making use of the Tanaka＇s transformation rule modified by taking into account the effect of plastic deformation, the constitutive model of the SMA is obtained. The ferroelasticity, pseudoelastieity and shape memory effect of SMA Au-47.5 at.%Cd, and the pseudoelasticity and shape memory effect as well as plastic deformation and its effect of an NiTi SMA, are analyzed and compared with experimental results.
The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element （RVE） of a particulate composite, these inclusions are separated into two groups, with volume fractions （1 -A-1）c and c/A over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as A = 1 and A = c~, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. ~klrthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced A can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.
