Probability and Statistical Modeling: Ti-6Al-4V Produced via Directed Energy Deposition

Additive manufacturing is a complex multi-parameter process. Electron beam additive manufacturing of titanium (Ti-6Al-4V), which consists of a multitude of layers of deposited metal, exhibits significant variability in many key aspects including composition, microstructure, and mechanical properties. When establishing methods to predict material properties of these builds, it is necessary to consider both geometry and microstructure. Specifically, the material property of interest is the yield stress. The constitutive equation that is used to predict the yield stress of specimens subjected to stress relief annealing in the alpha+beta phase field has been developed previously. The yield stress equation contains random variables which are modeled with appropriate cumulative distribution functions that characterize their statistical observations. Subsequently, these distributions functions are incorporated into the physically based model using standard simulation techniques. The main purpose of this integrated modeling and statistical analysis is to begin to characterize the yield stress, especially in the extreme lower tail which is critical for high reliability estimation and prediction. To manage uncertainty and improve the estimation of the yield stress, an established methodology for calibration of the distribution function for the yield stress using experimental data is applied.