Resonant ultrasound spectroscopy for crystalline samples containing initial strain

Abstract

Resonant ultrasound spectroscopy (RUS) is a mature and robust technique for the nondestructive characterization of the elastic properties of solids capable of providing the elastic constants of anisotropic crystalline solids. The traditional method is based on assuming that the solid is linear elastic and, therefore, obeys a linearized Hookean constitutive relationship (Hooke’s law). In this article, an alternative constitutive law is provided that allows for an initial strain or prestrain to be present stemming from residual stress. Then, the constitutive relationship is integrated into the RUS framework. The model is demonstrated using a realistic prestrain field obtained by simulating shot-peening processing of a polycrystalline Cu sample. The sensitivity of the resonances to the developed prestrain is established and discussed. This work allows researchers to consider the influence of initial strain or residual stress in their samples and the potential influence on accurate elastic constant estimates. The model also supports the potential of RUS for the nondestructive characterization of prestrain in materials.