Residual stress indentation model based on material equivalence

A novel residual stress indentation model for conical indentation loading is proposed to describe the relationship between the residual stress, material constitutive parameters, load, and displacement for materials with a uniaxial constitutive relationship that obeys Hollomon’s power law (H-law). The novel model was established based on the principle that the equivalent material without residual stress corresponds to the original material with residual stress, conical indentation theoretical model based on energy density equivalence, and an assumed power-law relationship between the dimensionless residual stress and relative difference of the yield stresses of the equivalent material and original material. Sixty imaginary H-law materials with ten equibiaxial and ten uniaxial residual stresses were investigated by Finite Element Analysis (FEA). The residual stresses predicted by the novel model from the indentation load–displacement curves simulated for the imaginary materials are in close agreement with those applied by the FEA. Finally, indentation tests for Cr12MoV steel, 45 steel, and 6061-T6511 aluminum alloy were carried out on their specimens without residual stress and their bending specimens with equibiaxial and uniaxial residual stresses. The residual stresses predicted by the novel model according to the indentation load–displacement test curves are in good agreement with those applied by the tests.