Modeling Different Failure Mechanisms in Metals

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 Consid?re-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.