Methods for material parameter estimation : global and local approach

Abstract: The rapid development of computing technology has made powerful tools, such as finite element codes, available for more and more companies. The use of simulation tools, predictive engineering, is a prerequisite today in product development. To describe the material deformation a variety of constitutive models, based both on physical foundations and empirical considerations, are available. Common for all models is that they contain material parameters, which have to be estimated by utilising experimental methods. Despite the advanced numerical tools, the most common method to characterise materials in industry today is to use standard tensile tests. Those tests have a major drawback. When the loading is no longer homogenous, and plastic instability has initiated, the stress-strain relationship is no longer valid. The aim for this work is to investigate methods for parameter estimation in material models. The test material used is hot-rolled cold-forming steel. A further aim is to yield stress-strain curves more appropriate for large deformations compared to a standard tensile test. The main features are the use of experiments, finite element analysis (FEA) and inverse modelling combined. The parameter estimation is formulated as an inverse problem and an objective function, describing the residual error between experimental data and data from a FEA of the experiment, is formulated as a least-square functional. The objective function is minimised by an optimisation algorithm yielding a vector of best fit, or estimated, material parameters. Two approaches are investigated. One global, where experimental data from a forming experiment is used. Data is in the form of tool force and displacement, hence global data. This is in contrast with a local approach where in-plane full-field measurements of displacements on a flat specimen (hence, local data), subjected to a tensile test, are collected through the whole deformation history until fracture. The measurements are made with digital speckle photography (DSP). Parameters are estimated for a total of three different material models, assuming isotropic material properties and yield surface according to von Mises. Results from the global approach show significant difference in the stress-strain curves and a force response with optimised models compared to an extrapolated tensile test curve. In the local approach the DSP-technique provided measurements, where the maximum equivalent plastic strain in a specimen was approximately 0.8. The true stress-strain curves based on the estimated parameters are validated in the low strain region by comparison with curves from standard tension tests.