A 3D constitutive equation for large elastoplastic deformation is derived by taking into account the energy stored in the residual microstress fields in plastically deformed material and its effect on subsequent plastic deformation: this model may be used to describe the non-linear behaviour of material at the onset of loading and unloading. Non-linear mixed isotropic and kinematic hardening, and the effects of temperature and strain rate on material properties, are also considered. Expressions with and without a yield surface are provided. A numerical algorithm which corresponds to the constitutive equation without a yield surface is proposed and the material-user-subroutine UMAT is programmed and embedded in the commercial software ABAQUS. The analyses of necking, upsetting and extrusion were used to validate the proposed constitutive model and the corresponding numerical approach in metal forming analysis.

The effect of heating-rate and its history on the thermomechanical behavior of aluminum alloy LY12 is investigated with a Gleeble 1500 thermal–mechanical material testing system. It was found that the material experiencing higher heating-rate histories possesses lower rupture strength, and the pre-stressed material fails at a lower temperature when it is heated at a higher heating-rate. The SEM observation shows that, in general, there are more defects in the material subjected to higher heating-rates or higher heating-rate histories. The concept of local thermal inconsistency is introduced to account for the effect of heating-rate on mechanical properties, such as hardening and damage. A constitutive model is proposed for the description of the behavior of the materials subjected to thermomechanical loading incorporating fast heating, which can take into account the effect of plastic deformation, temperature and its rate, and recrystallization on the mechanical property, hardening and damage of the material. The constitutive behavior of LY12 subjected to uniaxial thermomechanical loading incorporating fast heating is described, and the comparison with the experimental results demonstrates the validity of the proposed model.

Laser-aided stamping of copper work-material was simulated using the FE code ABAQUS, by which temperature distributions and the stamping forces under different heating conditions were investigated. The simulation results showed that laser-heating can provide a satisfactory distribution of temperature at the shear-zone of the work-material, which will substantially reduce the maximum stamping force and enable stamping with larger aspect ratios. A high heating rate may also be achievable so that the desired stamping-temperature can be reached within a heating period that can match the requirement of industrial applications.

Based on the concept of local thermal inconsistency, a constitutive model was developed for the description of the behaviors of metallic materials subjected to thermomechanical loading with fast heating, with reference to heating-assisted forming applications. The model considers effect of plastic deformation, of temperature as well as heating-rate and of recrystallization, on the mechanical property, hardening and damage of the materials. It can account for the reduction of the rupture strength of metallic materials subjected to high heating-rates or heating-rate histories, and the reduction of failure temperature of pre-stressed metallic materials heated at high heating-rates. The constitutive behavior of brass H62 subjected to uniaxial thermomechanical loading with fast heating is described and compared with experimental results. The satisfactory agreement between the computed and the experimental results shows the validity of the proposed model.

Two classes of experiments were conducted with a Gleeble 1500 thermal–mechanical testing system to investigate the effect of heating-rate and its history on the mechanical behavior of aluminum alloy LY12. In the first class of experiment, specimens were heated at different heating-rates to prescribed temperatures and then stretched until fracture. It was found that the specimen heated with higher heating-rate possesses lower rupture strength. In the second class of experiment, the specimens were preloaded and then heated at different rates until fracture. It was found that the higher the heating-rate was, the lower the failure temperature would be. Metallographical analysis showed that there are more defects in the specimens undergoing higher heating-rate. It was conjectured that higher heating-rate may cause stronger local thermal inconsistency due to the heterogeneous nature of the material. It may then cause local residual microstress fields, which, together with external thermal-mechanical load, may result in the changes in the microstructure of the material, such as recovery, recrystallization, nucleation and growth of microdefects, accounting for the changes in the macroscopic mechanical properties including hardening/softening, damage and failure, etc. A numerical simulation was performed, in which the mechanisms of local thermal inconsistency and the effect of the influencing factors were investigated.

A simplified continuum damage mechanics model is proposed to describe the inelastic behavior of concrete reinforced with randomly distributed short fibers. The constitutive and damage behavior of such a concrete usually involves anisotropic damage, unilateral effect, coupled volumetric and deviatoric inelastic deformation and complicated failure mechanisms due to its heterogeneous morphology. In order to avoid the analytical and computational complexity, a scalar damage variable is adopted, while the anisotropy and unilateral effect of damage corresponding to different states of stress and stress histories are described through introducing the Lode parameter lr. The proposed model can take into account the effect of fiber content on damage development and the effect of volumetric stress on deviatoric inelastic response. The validity of the proposed model is demonstrated by comparing the theoretical and experimental results for plain and fiber-reinforced concrete specimens subjected to triaxial stress histories. The in uence of fiber content on the response of concrete subjected to cyclic loading histories and on the fatigue life is also analyzed.

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 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.

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.

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.