Based on a nonclassical hardening law and the Hill s self-consistent scheme, a new approach is proposed for the analysis of polycrystal nonproportional cyclic plasticity. A novel parameter related to the plastic dissipation on each slip system is proposed and embedded in the Bassani s definition of cross-hardening. The tangential elastoplastic tensor relating the increments of stress and strain in a single crystal is derived and the corresponding numerical algorithm for polycrystal plasticity is developed. The elastoplastic response of 316 stainless steel subjected to typical biaxial nonproportional strain cycling is analyzed, and the main features are well replicated. The validity of the proposed approach is demonstrated by the satisfactory agreement between the computed results and experimental observation.

The response of the work-material during forward extrusion and the subsequent unloading process was analysed with a view to examining differences in prediction of component-form errors, when different constitutive models are used. Two types of constitutive models were adopted for the analysis-classical theory of plasticity (CP) with isotropic hardening and non-classical theory of plasticity (NCP). When compared the results of the CP model with the NCP model, the latter shows a slightly smaller maximum punch-force requirement, smaller diameter of the extrudate and larger contraction of the die during unloading. The significant difference in the predicted final dimensions of the extrudate with different constitutive models suggests that more accurate constitutive descriptions on the work-material have to be used for the analysis of component-form errors in precision forming, if more accurate results are to be achieved.

A constitutive description is proposed for a single pearlitic colony based on its composition of lamellas of ferrite and cementite with a very thin interlamellar spacing. Both phases are assumed to be elastoplastic. The relationship between the increments of overall stress and strain is derived and the corresponding numerical algorithm is developed. The mechanical behavior of the colony subjected to proportional or non-proportional loading is investigated, and it shows that the overall response is anisotropic. Finite element analysis is conducted to analyze the influence of the interlamellar spacing on the mechanical response of the colony. It shows that the proposed model can not only describe the behavior of the pearlitic colony with extremely small interlamellar spacing, but also work with sufficient accuracy in the case of moderate interlamellar spacing. The constitutive response of each phase in a colony can be obtained simultaneously, which is an important step towards developing theories of microstructure-based damage and failure analysis.

Making use of the microstructure-based constitutive equation for a single dual-phase pearlitic colony and the KBW's self-consistent scheme, a description of dual-phase pearlitic steel is performed. It is based on the assumption that a representative element of the material is an aggregate of numerous spherical pearlitic colonies with randomly distributed orientations, and each colony is composed of many parallel fine lamellas of ferrite and cementite. The corresponding numerical algorithm is developed. The cyclic plasticity of single-phase hard-drawn copper and dual-phase pearlitic steel BS11 subjected to asymmetrically cyclic loading is analyzed and compared with the experimental results. The nonproportional cyclic plasticity of the two materials is also analyzed, in which stress develops along a semi-circle in biaxial tension/compression and shear stress plane, as is experienced by the surface elements in a rolling and sliding contact. The local responses of ferrite and cementite for prescribed orientations are investigated simultaneously. The developed approach can describe the main characteristics in the cyclic plasticity of the dual-phase materials. The corresponding numerical algorithm shows successful stability concerning convergence and accuracy at a large number of cycles.

A comprehensive description for the constitutive behavior of polycrystalline shape memory alloys (SMAs) is proposed based on the concept that a SMA is dynamically composed of austenite and martensite, the constitutive behavior of which is a dynamic combination of the individual behavior of each of the two phases. In the interested ranges of stress and temperature the behavior of austenite is assumed to be linearly elastic while that of martensite elastoplastic. The main features of SMAs such as ferroelasticity at lower temperature, shape memory effect (SME), pseudoelasticity at higher temperature and other typical features can be successfully replicated with the proposed constitutive model. The ferroelasticity, pseudoelasticity and SME of SMA Au-7.5 at.% Cd subjected to uniaxial forward and reverse loading and the pseudoelasticity of Cu Alan Mn SMA polycrystal subjected to proportional and nonproportional complex stress or strain histories are analyzed and compared with the experimental results.