Reverse Analysis of Surface Strain in Elasto-Plastic Materials by Nanoindentation

In this study, nanoindentation technology is utilized to investigate the in situ mechanical behavior of small-sized packaging materials. Rather than the ideal cases with unprestressed materials which have been intensively studies, this paper focuses on the effect of surface stress by prestressing the materials to be indented by a Berkovich indenter. The loading process until the maximum penetration depth is simulated by finite element (FE) models. With elastoplastic materials as described by a power-law model, extensive FE predictions are performed with the wide ranges of Young's modulus, yield strength and hardening exponent with and without pre-strain. FE results show that with different prestress values, the applied load-penetration depth responses vary in a highly consistent manner. The residual indentation profiles are found to be closely related with the stress state due to the pre-strain values. On the basis of FE simulations, a dimensionless function is therefore derived and a reverse algorithm is proposed to estimate the constitutive parameters and also the surface stress of elastoplastic materials. With one of the most commercialized lead-free solder materials in electronic packaging structures, the proposed reverse algorithm is utilized to estimate the residual stress based on the nanoindentation response of solder samples with different annealing conditions.