Evaluation of the ability of full-field displacement measurements to extract yield surface parameters

Abstract

We explore the ability of using volumetric three-dimensional (3D) full-field displacement measurements on a single specimen geometry to extract the parameters that describe an isotropic yield surface that depends on all three stress invariants. This is attempted via a numerical study (including specimen design) to investigate the sensitivity of a residual function constructed based on full-field displacement data to the constitutive model parameters. Overall, the sensitivity of the residual function to the parameters is low and this is expected to make the extraction of the parameters to be sensitive to measurement noise. Nonetheless, when the yield surface evolves self-similarly with plastic strain, the calculations show that the multi-axial yield strength can be predicted to a high level of accuracy. Remarkably, such predictions do not require a complex 3D specimen geometry but can also be made to the same level of fidelity using relatively simple notched plane stress or axisymmetric specimens. However, the ability to predict a non self-similarly evolving yield surface is much more limited for all types of specimens. Equally, if the wrong form of the constitutive model is assumed the magnitude of the residual function is shown not to be a good indicator of the poor choice of the constitutive model. We speculate that for the relatively low order constitutive models explored here, adding more displacements data (e.g. 3D data versus 2D data) results in minimal information gain. Rather, additional independent data such as elastic strain measurements might alleviate some of the issues associated with parameter extraction highlighted in the study.