A novel inverse methodology for the extraction of bulk elasto-plastic tensile properties of metals using spherical instrumented indentation

Abstract

This paper presents an inverse methodology relying on finite element simulation based optimization to extract material constitutive parameters from a single spherical indentation, which are used to estimate its bulk true stress–true strain curve. Methods of this type usually assume that the tensile curve of the studied material can be modelled by a power-law involving, for example, Young’s modulus, yield stress and a hardening coefficient. Since the tensile behaviour of some materials cannot be adequately fitted by such models, our approach rather relies on an optimization procedure which extracts a group of six points on the true stress–true strain curve, distributed as per a geometric progression in the strain space, as well as the elastic modulus. A direct search black-box optimization algorithm is used and is shown to be capable of eluding local minima. A surrogate step is introduced in the methodology, which is a simplified version of the inverse problem, to find a suitable starting point. The performance of the method is first investigated in a numerical study in which the estimated true stress–true strain curves lie within a maximum error of 5.7% from the corresponding target tensile curves, for four materials with different hardening behaviours. The maximum errors on the extracted elastic modulus and yield stress are 0.5% and 11.1%, respectively. A study of the convergence behaviour of the proposed method demonstrates an expected significant increase in computational times as compared to when using a hardening model. Finally, an experimental application of the method to two materials with a plastic plateau leads to true stress–true strain curves estimations with average differences of 3.9% and 0.9% with the macroscopic experimental tensile curve, respectively. The method is thus found to be accurate even in the presence of modelling and experimental errors.