Quantitative Evaluation of the Development of Stress and Strain Fields using Digital Image Correlation and Finite Element Methods

Abstract

In order to predict the nonuniform deformation behavior of engineering materials, both the evaluation and modeling of the strain field are very important. Recently, accurate and contactless measurement of the strain field was performed using digital image correlation (DIC). Evaluation of the stress field is also required to model the nonuniform deformation behavior of the material. In this study, the stress and strain fields are evaluated by coupling the DIC and the finite element methods (FEM). The local strain can be decomposed into elastic and inelastic parts, based on the stress equilibrium around the displacement-measurement points. The local stress tensor can then be obtained by introducing the elastic strain components into a generalized Hooke’s law. The large deformation theory, based on the updated Lagrange method, is also introduced to evaluate the local true stress and true strain tensors for large strain range. The stress and strain fields for pure copper specimens that had two different shapes, namely, specimens NU and U, were evaluated during tensile tests. The cross-section of specimen NU continually changes whereas it is constant for specimen U. Furthermore, two specimens with different crystal grain size were used to investigate the effect of the microscopic heterogeneity. The local true stress ̶true strain relationship spanned regions in the proximity of the global response, while the relationship for specimens NU and U were almost similar. The effect of the microscopic heterogeneity on the macroscopic nonuniform deformation was investigated using the evaluated stress and strain fields. In larger-grain specimens, the evaluated stress gradient was lower than that estimated using the strain gradient since the hardening rate spatially distributed owing to the microscopic heterogeneity.