Determination of gradient residual stress for elastoplastic materials by nanoindentation

Residual stress is an important manufacture factor affecting the working life of components and structures. In this paper, a dimensionless method is proposed to determine the residual stress profile by using the nanoindentation technique. An exponential function is formulated in a generalized form to describe the residual stress profile in the elastoplastic substrate material. A finite element (FE) model is created to simulate the entire process including the loading stage with the indenter penetrating into the substrate up to the maximum depth and also the subsequent unloading stage. For elastoplastic substrate materials following the power-law constitutive model, a wide range of FE predictions are made by considering various gradient residual stresses of interest. The results show that the applied load–penetration depth curve is highly consistent with the variation of gradient residual stress. Based on FE simulations, dimensionless functions considering the residual stress is derived for both the applied load and the total work done. Thereafter, a reverse algorithm is proposed to elegantly predict the gradient residual stress in elastoplastic materials. With several work examples, the proposed reverse algorithm is confirmed to be excellent for determining residual stresses by comparing the existing experimental results. More importantly, the proposed reverse algorithm can effectively determine the type and trend of gradient residual stresses, which helps to guide the optimization of manufacturing process for critical components and structures.