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Conical indentation methods to determine residual stress are proposed by examining the finite element solutions based on the incremental plasticity theory. We first note that hardness depends on the magnitude and sign of residual stress and material properties and can change by up to 20% over a specific range of elastic tensile and compressive residual stress, although some prior indentation studies reported that hardness is hardly affected by residual stress. By analyzing the characteristics of conical indentation, we then select some normalized indentation parameters, which are free from the effect of indenter tip rounding. Adopting dimensional analysis, we present practical conical indentation methods for the evaluation of elastic/plastic equi- and nonequi-biaxial residual stresses. The validity of developed approaches is confirmed by applying them to the experimental evaluation of four-point bending stress.

In this study, we obtain true stress-strain (SS) curves for a sheet specimen under consideration of local necking and material anisotropy. We first extract the SS curve up to the diffuse necking point from the tensile test load-displacement data. The curve's part after the onset of diffuse necking is extrapolated by the weighted-average method proposed by Ling [Y. Ling, AMP J. Technol. 5, 37-48 (1996)]. Initiation of local necking is predicted by means of the minor-to-major strain ratio in the specimen's center. We propose a criterion to determine the strain ratio at the onset of local necking and the major strain corresponding to the strain ratio at local necking. We complete the true SS curve by cutting off the SS curve at the major strains corresponding to the local necking or apparent fracture point. Finally, the effects of material anisotropy on SS curves are discussed.

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