Uncertainty Quantification of Metallic Microstructures with Analytical and Machine Learning Based Approaches

Uncertainty in the microstructures has a significant influence on the material properties. The microstructural uncertainty arises from the fluctuations that occur during thermomechanical processing and can alter the expected material properties and performance by propagating over multiple length scales. It can even lead to the material failure if the deviations in the critical properties exceed a certain limit. We introduce a linear programming (LP) based method to quantify the effects of the microstructure uncertainty on the desired material properties of the titanium–7 wt % aluminum alloy, which is a candidate material for aerospace applications. The microstructure is represented using the orientation distribution function (ODF) approach. The LP problem solves for the mean values and covariance of the ODFs that maximize a volume-averaged linear material property. However, the analytical procedure is not applicable for maximizing nonlinear material properties where microstructural uncertainties are present. Therefore, an artificial neural network based sampling method is developed to estimate the mean values and covariance of the ODFs that satisfy design constraints and maximize the volume-averaged nonlinear material properties. A couple of other design problems are also illustrated to clarify the applications of the proposed models for both linear and nonlinear properties.