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Magnesium (Mg) alloy sheets possess several key properties that make them attractive as lightweight replacements for heavier ferrous and non-ferrous alloy sheets. However, Mg alloys need to be formed at elevated temperatures to overcome their limited room-temperature formabilities. For example, commercial forming is presently conducted at 450°C. Deformation behavior of the most commonly used wrought Mg alloy, AZ31B-H24, and two potentially competitive materials, AZ31B-HR and ZEK100 alloy sheets, with weaker crystallographic textures, are studied in uniaxial tension at 450°C and lower temperatures. The underlying physics of deformation including the operating deformation mechanisms, grain growth, normal and planar anisotropy, and strain hardening are used to construct material constitutive models capable of predicting forming for all three Mg alloy sheets at 450°C and 350°C. The material models constructed are implemented in finite-element-method (FEM) simulations and validated using biaxial bulge forming, an independent testing method. Forming limit diagrams are presented for the AZ31B-H24 and ZEK100 alloy sheets at temperatures from 450°C down to 250°C. The results suggest that forming processes at temperatures lower than 450°C are potentially viable for manufacturing complex Mg components. / text

Material failure plays an important role in human life. By investigating the failure mechanisms, people can more precisely predict the failure conditions to develop new products, to enhance product performances, and most importantly, to save lives. This work consists of three parts corresponding to three different failure mechanisms in metals, i.e., the localized necking in sheet metals, the bifurcation in bulk and sheet metals, and the ductile fracture induced by the void nucleation, growth, and coalescence. The objective of the first part is to model the localized necking in anisotropic sheet metals to demonstrate that localized geometric softening at a certain stage of deformation rather than the initial defects is the main cause of localized necking. The sheet is assumed to have no initial geometric defects. The deformation process is divided into two stages. The critical strains for a neck to form are obtained from a Considère-type criterion. The defect ratio at the neck formation is obtained using an energy-based approach. The neck evolution is considered. A novel failure criterion is proposed. Two types of necks are fond to be most competitive to cause material failure during continued deformation. The forming limit curves are hereby found to exhibit different characteristics in different region. The predicted forming limit curve for 2036-T4 aluminum is found to fit with the experimental results well. The sheet thickness, the strain hardening behavior, and plastic anisotropy are found to affect the sheet metal formability. More realistic yield criterions and strain hardening behaviors can be implemented into the proposed model. This part provides an alternative approach to modeling the localized necking in anisotropic sheet metals. The objective of the second part is to model the bifurcation in anisotropic bulk and sheet metals to couple plastic anisotropy and the strain hardening/softening behavior and also to identify different bifurcation modes in sheet metals. The material is assumed to exhibit a non-linear strain hardening/softening behavior and to obey the Hill-type Drucker-Prager yield criterion along with a non associated flow rule. The constitutive relations and the conditions for bifurcation in bulk and sheet metals are derived. The internal friction coefficient, plastic anisotropy, the terms introduced by the co-rotational stress rates, and the terms introduced by the stress resultant equilibrium are found to affect the onset of bifurcation. Two bifurcation modes are found to exist in sheet metals. More realistic material properties can be implemented into the proposed model. This part provides an applicable approach to modeling the bifurcation in anisotropic bulk and sheet metals. The objective of the third part is to derive the constitutive relations for porous metals using generalized Green’s functions to better understand the micromechanism of the ductile fracture in metals. The porous metals are assumed to consist of an isotropic, rigid-perfectly plastic matrix and numerous periodically distributed voids and to be subject to non-equal biaxial or triaxial extension. Two types of hollow cuboid RVEs are employed represent the typical properties of porous metals with cylindrical and spherical voids. The microscopic velocity fields are obtained using generalized Green’s functions. The constitutive relations are derived using the kinematic approach of the Hill-Mandel homogenization theory and the limit analysis theory. The macroscopic mean stress, the porosity, the unperturbed velocity field, and the void distribution anisotropy are found to affect the macroscopic effective stress and the microscopic effective rate of deformation field. The proposed model is found to provide a rigorous upper bound. More complicated matrix properties (e.g., plastic anisotropy) and void shapes can be implemented into the proposed model. This part provides an alternative approach to deriving the constitutive relations for porous metals.

The mechanical behaviour of the three advanced high strength steel grades, Docol 600DP, Docol 1200M and HyTens 1000, has been experimentally investigated under various types of deformation, and material models have been developed, which account for the experimentally observed behaviour. Two extensive experimental programmes have been conducted in this work. In the first, the dual phase Docol 600DP steel and martensitic Docol 1200M steel were subjected to deformations both under linear and non-linear strain paths. Regular test specimens were made both from virgin materials, i.e. as received, and from materials pre-strained in various directions. The plastic strain hardening, as well as plastic anisotropy and its evolution during deformation of the two materials, were evaluated and modelled with a phenomenological model. In the second experimental program, the austenitic stainless HyTens 1000 steel was subjected to deformations under various proportional strain paths and strain rates. It was shown experimentally that the material is sensitive both to dynamic and static strain ageing. A phenomenological model accounting for these effects was developed, calibrated, implemented in a Finite Element software and, finally,validated. Both direct methods and inverse analyses were used in order to calibrate the parameters in the material models. The agreement between the  numerical and experimental results are in general very good. This thesis is divided into two main parts. The background, theoretical framework and mechanical experiments are presented in the rst part. In the second part, two papers are appended.

Plasticity in crystalline solids is controlled by the microscopic line defects known as “dislocations”. Decisive role of dislocations in crystal plasticity in addition to fundamentals of plastic deformation are presented in the current thesis work. Moreover, major features of numerical modeling method “Discrete Dislocation Dynamics (DDD)” technique are described to elucidate a powerful computational method used in simulation of crystal plasticity. First part of the work is focused on the investigation of strain rate effect on the dynamic deformation of crystalline solids. Single crystal copper is chosen as a model crystal and discrete dislocation dynamics method is used to perform numerical uniaxial tensile test on the single crystal at various high strain rates. Twenty four straight dislocations of mixed character are randomly distributed inside a model crystal with an edge length of 1 µm subjected to periodic boundary conditions. Loading of the model crystal with the considered initial dislocation microstructure at constant strain rates ranging from 103 to 105s1 leads to a significant strain rate sensitivity of the plastic flow. In addition to the flow stress, microstructure evolution of the sample crystal demonstrates a considerable strain rate dependency. Furthermore, strain rate affects the strain induce microstructure heterogeneity such that more heterogeneous microstructure emerges as strain rate increases. Anisotropic characteristic of plasticity in single crystals is investigated in the second part of the study. Copper single crystal is selected to perform numerical tensile tests on the model crystal along two different loading directions of [001] and [111] at two high strain rates. Effect of loading orientation on the macroscopic behavior along with microstructure evolution of the model crystal is examined using DDD method. Investigation of dynamic response of single crystal to the mechanical loading demonstrates a substantial effect of loading orientation on the flow stress. Furthermore, plastic anisotropy is observed in dislocation density evolution such that more dislocations are generated as straining direction of single crystal is changed from [001] to [111] axis. Likewise, strain induced microstructure heterogeneity displays the effect of loading direction such that more heterogeneous microstructure evolve as single crystal is loaded along [111] direction. Formation of slip bands and consequently localization of plastic deformation are detected as model crystal is loaded along both directions. / <p>QC 20151015</p>