A constitutive model independent analytical method in determining the tensile properties from incremental spherical indentation tests (ISITs)

Abstract

In this study, an analytical method based on the simplified expanding cavity model, the equivalent energy principle, and the differential approach was proposed to determine the stress-strain relationship (constitutive behavior) of materials from incremental spherical indentation tests (ISITs). Apart from the load-depth curve obtained from the load cell and displacement sensor, respectively, one measurement of the plastic zone radius rp after the indentation test through digital image correlation (DIC) method was also used to determine the proportional limit σ0. The analytical derivation of this method has a clear physical meaning and does not depend on any specific constitutive models, and thus can be used on a large variety of materials and can be considered as a substitute for destructive uniaxial tensile tests. Experiments were conducted on four materials, 15CrMoR, TC21, SA508, and SA533. Two different models, which took the characteristics of the derived stress-strain data points into consideration, were used to describe the constitutive behavior of the four experimental materials. Experimental results proved that ISITs provided almost identical Young's modulus E (with a maximum error of less than 3%), stress-strain curves, proof strength Rp0.2 (with a maximum error of -5.9% when the strain threshold εth = 0.6%), and tensile strength RT (with a maximum error of -6.7% when εth = 0.6%) as their tensile counterparts. Furthermore, the stress-strain data points derived with the method proposed in this study could even characterize the yield plateau in the stress-strain curves of 15CrMoR, SA508, and SA533.