Study of plastically deformed region underneath the ball in indentation tests and evaluation of mechanical properties of materials through finite element simulation and a hybrid algorithm

Abstract

Ball indentation technique has been studied extensively in literature and it has been widely applied to determine mechanical properties of different materials because of simplicity and minimal requirement of material for the tests. Originally, the material deformation was represented in terms of a representative strain, which is a non-dimensional form of indentation diameter and a representative stress, which again is the instantaneous mean pressure multiplied by some empirical factors. It is known that the state of deformation as well as stress beneath the ball is multiaxial in nature in a ball indentation test. In this work, a new hybrid algorithm for estimation of equivalent stress and equivalent plastic strain during the process of indentation in the most stressed location beneath the ball has been developed. The algorithms uses experimental load–indentation data as well as the multiaxial stress and strain parameters obtained from 2D axisymmetric elastic-plastic finite element simulations. The stress and strain multiaxial parameters are functions of applied load, material yield stress and strain hardening exponents. The algorithm is iterative in nature and uses suitable initial guess values for material yield stress and strain hardening exponents and it converges very quickly. This method can be applied to determine the material stress–strain curve for a wide range of equivalent plastic strain, yield stress as well as plastic strain hardening exponent of the engineering materials. The data points of load vs. indentation depth as obtained directly from the ball indentation tests can be used in the new algorithm without the need for conducting unloading during the test. To illustrate the new scheme, two case studies have been presented where the results from the proposed new method have been compared with those of the existing method in literature and tensile test data to check the accuracy.