Formulation of constitutive relations based on indentation test

Abstract

Extensive finite element analyses are performed to simulate instrumented indentation of elasto-plastic materials obeying power law strain-hardening with conical and pyramidal indenters. The relationships between the characteristics of the load-indentation curve and the material properties are examined. The non-uniqueness of material properties extracted from the results of a single indenter is analytically and numerically demonstrated. A reverse analysis algorithm based on results from dual indenters which yield unique material properties is presented. Artificial neural network and least squares support vector machines models which enable the direct mapping of the characteristics of indentation load-displacement curves to the elasto-plastic material properties are proposed. A series of C0 solid, axisymmetric and plane strain/stress finite elements for materials with strain gradient effects is established. The formulation is based on conventional mechanism-based strain gradient plasticity theory and the numerical results incorporating these elements agree well with those of nanoindentation experiments performed on Al7075 and copper.