Title: Numerical Modeling of Shear Banding and Dynamic Fracture in Metals
Description: Understanding the failure of metals at high strain rate is of utmost importance in the design of a broad range of engineering systems. Numerical methods offer the ability to analyze such complex physics and aid the design of structural systems. The objective of this research will be to develop reliable finite element models for high strain rate failure modelling, incorporating shear bands and fracture. Shear band modelling is explored first, and the subsequent developments are extended to incorporate fracture. Mesh sensitivity, the spurious dependence of failure on the discretization, is a well known hurdle in achieving reliable numerical results for shear bands and fracture, or any other strain softening model. Mesh sensitivity is overcome by regularization, and while details of regularization techniques may differ, all are similar in that a length scale is introduced which serves as a localization limiter. This dissertation contains two main contributions, the first of which presents sev- eral developments in shear band modeling.

The importance of using a monolithic nonlinear solver in combination with a PDE model accounting for thermal diffusion is demonstrated. In contrast, excluding one or both of these components leads to un- reliable numerical results. The Pian-Sumihara stress interpolants are also employed in small and finite deformation and shown to significantly improve the computational cost of shear band modelling. This is partly due to the fact that fewer unknowns than an irreducible discretization result from the same mesh, and more significantly, the fact that convergence of numerical results upon mesh refinement is improved drastically. This means coarser meshes are adequate to resolve shear bands, alleviating some of the computational cost of numerical modelling, which are notoriously significant. Since extremely large deformations are present during shear banding, a mesh to mesh transfer algorithm is presented for the Pian Sumihara element and used as part of a remeshing strategy. A practical application of the numerical formulation developed is modelling the shear band failure of a friction stir welded aluminum joint under high rate loading.

The energy absorption capacity of these joints are subse- quently analyzed and found to be significantly weaker than untreated aluminum due to the nonhomogeneous material properties of the joint. The second contribution is extending the shear band model described previously to account for fracture by way of the phase field method. The phase field method is modified to account for the contribution of inelastic deformation to the creation of fracture surfaces, which results in a rate and temperature dependent theory for fracture, due to the rate and temperature dependence of plasticity. The combined fracture and shear band model is shown to be capable of representing a wider spectrum of strain rates than either the phase field model or the shear band model alone.