Uncertainty Quantification and Sensitivity Analyses of the Nonlinear Behavior of Heterogeneous Material Microstructures: Applications to Dynamic Response of Energetic Materials and Cyclic Response of a Titanium Alloy
This dissertation is concerned with understanding the uncertainty and variability in the failure and nonlinear response of materials with heterogeneous microstructures at fine scales (i.e., micrometers to millimeters). In the microscale simulations with uncertainty in the complex morphologies and material behaviors, characterization of the relative roles of the competing and interacting deformation and failure mechanisms is achieved by the proposed uncertainty quantification and sensitivity analysis frameworks. Two separate material systems subjected to two different loading conditions are investigated. In the first case, the dynamic response of energetic materials in the form of particulate crystals embedded in a polymer matrix and in polycrystalline form are investigated. In the second case, the probabilistic characterization of nucleation of microcracks in a titanium alloy subjected to cyclic loading is performed. This dissertation particularly focuses on the identification of the critical microstructural mechanisms and parameters that lead to the onset of failure at this scale.