Assessing and ensuring parameter identifiability for a physically-based strain hardening model for twinning-induced plasticity

• New method for assessing identifiability of parameters in constitutive models.
• Application to a physically-based model for TWIP steel.
• Two-step method ensuring identifiability of all model parameters.

Physically-based strain hardening models have become important ingredients in metal forming simulations over the last years, since they allow for the modeling of multi-stage forming processes based on the evolution of physically meaningful internal variables. Although these models are physically-based, there are still many fitting parameters involved which have to be identified from experiments. As a matter of fact, for each physical effect that is included in the model, a separate equation with new fitting parameters is introduced, such that physically-based models tend to contain a large number of fitting parameters. Parameter estimation is often based on the macroscopic response of a specimen which is tested in compression, tension or shear at various strain rates and temperatures. It is not guaranteed that this macroscopic information suffices to estimate parameters in model equations that describe (sub-) microscopic phenomena, since the effect of one parameter on the course of strain hardening can be compensated by other parameters. Since such parameter correlations are hard to detect from the model equations alone, the parameter estimation process may be ill-conditioned, i.e. numerous parameter sets can be found for such models that deliver almost the same minimum value of the error function in the parameter identification process. Given that parameter estimation involves a series of costly experiments, methods are needed that allow for analyzing the identifiability of the model parameters before costly experiments are performed. In this paper, an approach is presented that analyzes model parameter dependencies and quantifies the identifiability of the model parameters. The model considered in this study calculates the flow stress based on the evolution of three dislocation densities and the evolution of deformation twins. The analysis shows that correlations between the model parameters exist and that it is not possible to determine all model parameters based on an experimental set of flow curves in a single curve fitting procedure. An adapted fitting strategy is presented in which fitting is performed step-wise so that in each fitting step, only identifiable parameters are estimated, allowing for successful parameter identification.