Extraction of Mechanical Properties of Shape Memory Alloys From Instrumented Spherical Indentation

Abstract An approach to infer mechanical properties of shape memory alloys (SMAs) from instrumented spherical indentation records of indenter tip loading force, P, versus the resultant indentation depth, h, during indentation loading and unloading is proposed. The approach is based on (i) a finite element (FE) model for describing the forward problem of determining the indentation response, i.e., the P−h curve, for a given set of SMA mechanical properties, (ii) a computationally efficient Gaussian process surrogate model to replace the costly FE one, and (iii) an iterative solution strategy, which approximates the unknown model parameters from an experimentally determined P−h record and their corresponding probability densities via a Bayesian inference framework and a Markov Chain Monte Carlo sampling strategy. The efficacy of the proposed approach is demonstrated using numerical experiments, i.e., indentation curves generated by evaluating the FE model at points in the parameter space.