Effects of residual stress on the hardness of elastoplastic material under spherical indentation

Residual stress can strongly affect the mechanical behaviors of engineering components. In this work, the authors revisit the role of equi-biaxial residual stress in the spherical indentation of elastoplastic solids by the finite element method. When specified residual stress remains in the body, the material hardness and the corresponding indentation depth at the inception of fully plastic deformation are examined for the first time. It is found that the hardness is remarkably dependent on the value of residual stress, especially for materials with a relatively small ratio of modulus to yield strength. Based on the dimensional analysis as well as numerical calculations, explicit expressions of the hardness and the critical indentation depth are generalized with respect to residual stress, indentation modulus, and yield strength. These results can be employed in the analysis and determination of residual stress by spherical indentation tests.