Alternative methods to determine the elastoplastic properties of sintered hydroxyapatite from nanoindentation testing

Abstract

• The direct and inverse FE-models for nanoindentation tests are done. • A semi-empirical method is presented to calculate the hardening parameters of HA. • We examine the effect of sintering temperature on the mechanical properties. • An algorithm for the inverse technique is used to obtain elastoplastic material model. This study introduces alternative methods to determine the elastoplastic properties of bovine-derived Hydroxyapatite (HA) porous bone graft through a set of nanoindentation tests with a Berkovich indenter. Generally, experimental data obtained from nanoindentation tests are force displacement, hardness and elastic modulus. However, to determine plastic properties such as strength coefficient and work hardening exponent of bovine HA, analytical or inverse finite element models are required. In this paper, the effect of sintering temperature on these properties of HA is studied for the range of 1000–1400 °C. The direct and inverse Finite Element (FE) simulation models for nanoindentation tests were written in MSC, MARC ® software. A special algorithm for the inverse technique was developed to infer the most suitable elastoplastic material model for HA. A semi-empirical method was adapted to calculate the elastoplastic material properties of HA. The numerical results of harder hydroxyapatite showed better agreement with the experiments while the work hardening exponent, or n -value, and strength coefficient k of hard HA were found to be 0.23 and 8.05 GPa respectively. A comparison between the experimental and predicted load–displacement curves showed that the proposed inverse technique is effective in predicting the elastoplastic material properties from the nanoindentation test with error below 4% at maximum load.