Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test

Abstract

Abstract

The Effect of Residual Stresses on Stress–Strain Curves Obtained via Profilometry‐Based Inverse Finite Element Method Indentation Plastometry

“…The most relevant of these for current purposes are those involving relatively large spherical indenters. [ 28,30,32–35 ] These include the work of Peng et al, [ 32,35 ] who showed that changes in experimental load–displacement plots induced by imposing “residual” stresses via externally applied loads were consistent with FEM predictions. Of course, load–displacement plots cannot be used to infer anisotropic residual stress states, as they provide no directional information.…”

“…Furthermore, they assumed that the “residual” stress in the centre of their cruciform samples (where the indentation was conducted) was equal to the applied load over the sectional area of the “arm”: as shown below, this is an inaccurate assumption. Other relevant work includes that of Zhang et al, [ 30,34 ] who explored the effect of using different constitutive laws for plasticity and confirmed that the changes induced in the load–displacement plot by the presence of residual stresses can be significant. Finally, Wang et al [ 33 ] proposed a method for extracting both the plasticity parameters and the residual stress characteristics, using multiple indent depths.…”

“…The ill‐defined nature of hardness means that such approaches do not really have any potential in terms of experimental measurement of residual stresses. However, a number of others [ 23–35 ] have focused on monitoring how indenter penetration is affected by residual stresses. These investigations have all concerned metals, although similar procedures have been applied to polymers.…”

Evaluation of Non-Equibiaxial Residual Stresses in Metallic Materials via Instrumented Spherical Indentation

“…(3) substituting the above-obtained parameters into Equations (14) and (16) to calculate the equibiaxial and shear stress part; (4) identifying the direction of the maximum principal residual stress from the direction of the major axis of residual indentation imprint and calculating the principal residual stresses according to the definition of the equibiaxial and shear stress parts. Generally, the sample's plastic properties could be identified using spherical indentation methods [36][37][38][39][40][41][42] or uniaxial tensile tests. The relative change in loading curvature could be obtained by fitting the load-depth curves of stressed and unstressed samples with Equation (2).…”

“…Since the plastic parameters (i.e., yield strain, ε y , and strain-hardening exponent, n) of the tested materials are also involved in the established correlations, to calculate residual stresses, these plastic parameters must be known a priori. Fortunately, either uniaxial tensile/compressive tests or spherical indentation tests [36][37][38][39][40][41][42] could be utilized to determine the plastic parameters. Patel et al [39] established a protocol to obtain the uniaxial stress-strain curve directly from the spherical indentation stress-strain curve by introducing a scaling factor.…”