Mapping Nanoindentation to Stress-Strain Response: A Bayesian Approach

Shape memory alloy (SMA) research and development is challenged with efficiently traversing a large design space involving composition, synthesis, and training to design functional materials with desired thermomechanical properties. Nanoindentation provides an avenue to statistically probe material response at multiple length scales with minimal sample preparation. However, indentation imposes a complex stress and deformation state that combines competing elastic, plastic, and transformation mechanisms which calls into question conventional indentation analysis. To circumvent this, Bayesian inference is applied to train on finite element simulations of SMA nanoindentation. This creates a framework that can map indentation curves to fundamental SMA properties while furnishing uncertainties in SMA properties quantified. Additionally, the framework includes cross-correlation in the variation of one property to another property. This approach also incorporates multi-modal indentation using more than one tip shape or repeated indentation to improve statistical mapping of SMA properties. This Bayesian indentation framework can expedite the characterization of key SMA stress-strain properties over a broad design space.