Inverse identification of constitutive parameters with instrumented indentation test considering the normalized loading and unloading P-h curves

Abstract

The feature of instrumented indentation test (IIT) makes it suitable for the characterization of local constitutive behavior in a small volume of solids. In the present study, the relationship between the shape of the normalized loading P-h curve and the indenter tip rounding radius, and the influences of the constitutive parameters of a Ludwik-type isotropic hardening model on the shape and the initial slope of the normalized unloading P-h curve were investigated by theoretical analysis and sophisticated numerical sensitivity analysis. From the analytical results, a two-stage analytical approach that can inversely identify multiconstitutive parameters simultaneously was proposed. In the first stage, by considering the least-square distance between the experimental and the simulated normalized loading P-h curves (g(h/hmax)) as the objective and C1 in the tip area function as the input variable, the tip rounding was identified by a single-objective optimization procedure. With the optimal tip rounding, a multiobjective optimization procedure was then performed to identify the constitutive parameters of the target materials. The initial slope of the normalized unloading P-h curve (ΔS’(P/Pmax-h/hmax)), absolute value of the differences between the simulated and the experimental maximum load (ΔPmax), initial slope of the unloading P-h curve (ΔS), and contact hardness (ΔH) were set as objectives, while all the material parameters except the Poisson's ratio (v) were considered as input variables. Results of the numerical verification with a set of arbitrarily selected constitutive parameters and the experimental verification on Ti-18 (a near-β high-strength titanium alloy) fit fairly well with uniaxial tensile parameters. With regard to T40, the identified true stress-true plastic strain curve is about 20% higher than the uniaxial tensile curve. One possible explanation is the occurrence of the strength differential and anisotropy effects during the plastic deformation process of α-phase titanium. It is worthy to be noticed that the present study may propose a new way to calibrate the tip area function directly on the target material without any standard indentation sample and improve the quality of the identification of the material constitutive parameters by IIT.