Inspection of ratcheting models for pathological error sensitivity and overparametrization

Abstract

Accurate analysis of plastic strain accumulation under stress-controlled cyclic loading is vital for numerous engineering applications. Typically, models of plastic ratcheting are calibrated against available experimental data. Since actual experiments are not exactly accurate, one should check the identification protocols for pathological dependencies on experimental errors. In this paper, a step-by-step algorithm is presented to estimate the sensitivities of identified material parameters. As a part of the sensitivity analysis method, a new mechanics-based metric in the space of material parameters is proposed especially for ratcheting-related applications. The sensitivity of material parameters to experimental errors is estimated, based on this metric. Moreover, a relation between pathological error sensitivity and overparametrization is established. This relation gives rise to a new criterion of overparametrization. The advantages of the new overparametrization criterion are exposed and its plausibility is checked by alternative criteria, like the consideration of correlation matrices and validation of identified parameters on “unseen” data. For demonstration purposes, the accumulation of irreversible strain in the titanium alloy VT6 (Russian analog of Ti-6Al-4V) is analysed. Three types of phenomenological models of plastic ratcheting are considered. They are the Armstrong-Frederick model as well as the first and the second Ohno-Wang models. Based on real data, a new rule of isotropic hardening is proposed for greater accuracy of simulation. The ability of the sensitivity analysis to determine reliable and unreliable parameters is demonstrated.