Uncertainty analysis of damage evolution computed through microstructure-property relations

Uncertainties in material microstructure features can lead to variability in damage predictions based on multiscale microstructure-property models. In this paper, we present an analytical approach for uncertainty analysis by combining a dimension reduction technique for evaluation of statistical moments of a random response, such as damage, with probability distribution fitting based on the extended generalized lambda distribution. This approach is used to analyze the effects of uncertainties pertaining to structure-property relations of an internal state variable plasticity-damage model that predicts failure. Using an un-notched A356 cast aluminum alloy tension specimen as an example, the predictions for damage uncertainty based on the proposed approach are compared with those found using the first order Taylor series approximation and direct Monte Carlo simulation. In particular, the spatial variabilities in microstructural properties, the constitutive model parameter sensitivities, and the effect of boundary condition uncertainties on the damage evolution and final failure are examined. The results indicate that the higher the strain the greater the scatter in damage, even when the uncertainties in the material plasticity and microstructure parameters are kept constant. For A356, the mathematical sensitivity analysis results related to damage uncertainty are consistent with the physical nature of damage progression. At the very beginning, the initial porosity and void nucleation are shown to drive the damage evolution. Then, void coalescence becomes the dominant mechanism. And finally when approaching closer to failure, fracture toughness is found to dominate the damage evolution process.