Quantifying The Evolution Of Crystal Stresses During Monotonic And Cyclic Loading Using Finite Element Simulations

Abstract

The focus of the current work is on investigating the orientation dependent micromechanical response of face-centered cubic (fcc) polycrystals using crystal-based elastoplastic finite element simulations. This dissertation contains three related studies examining the evolution of the lattice strains and the crystal stresses in fcc polycrystalline aggregates subjected to monotonic and cyclic loading. These three studies, which can be read independently, are presented in Chapters 1, 2 and 3. Chapter 1 contains an investigation into the evolution of the orientation dependent lattice strain response in fcc polycrystals under monotonic tensile loading, particularly in the elastic-plastic transition regime leading up to fullydeveloped plasticity. The lattice strains, when plotted as a function of the macroscopic stress, begin to deviate from linear behavior in the elastic-plastic transition regime when certain sets of crystals begin yielding before others. It is demonstrated that the progression of yielding in different sets of crystals is influenced by a combination of the single crystal elastic and plastic anisotropies, which can be quantified by the directional strength-to-stiffness ratio [1]. Chapter 2 examines the evolution of the lattice strains and the crystal scale stress distributions in fcc polycrystals under fully-reversed, strain-controlled cyclic loading with respect to the concepts of the directional strength-to-stiffness ratio [1] and the vertices of the single crystal yield surface [2], which have previously only been applied to monotonic tensile loading. These two concepts are derived from the single crystal elastic and plastic anisotropic properties and are used to explain observed behaviors in the lattice strain response such as the size and shape of the lattice strain hysteresis loops. Chapter 3 presents a coordinated approach to quantifying the evolution of lattice strains in an AA7075-T6 aluminum alloy under in situ zero-tension cyclic loading using high-energy synchotron x-ray diffraction experiments and crystal-based finite element simulations. This dissertation involves only the computational aspect of this coordinated approach. Lattice Strain Pole Figures (SPFs) are constructed from both measured and computed lattice strains and comparisons are made at the same macroscopic stress on several cycles in the loading history. Trends in the evolution of crystal quantities such as the crystal stresses, slip system activity and the slip system strengths, which are available from the simulation data, are examined and explained in a consistent manner with respect to the single crystal yield surface topology. The final chapter, Chapter 4, is a brief summary of the preceding chapters highlighting the main contributions of this dissertation