Depth-sensing instrumented indentation with dual sharp indenters: stability analysis and corresponding regularization schemes Original Research Article

In this paper, the stability of the reverse dual indenter algorithms proposed by Chollacoop et al. [Acta Mater. 51 (2003) 3713] to determine the plastic properties of materials has been explored further by using the mathematical theory of inverse problems. To identify the representative stress σεr, an explicit form of the condition number has been derived which can be used directly to examine ill-conditioned or ill-posed cases in the inverse problem. Corresponding regularization schemes have been proposed to produce stable results. To determine the plastic properties of materials according to the identified representative stress, the sensitivity matrix properties have been varied to achieve more accurate results. Two methods have been suggested, i.e., introduction of prior knowledge of the model space using the well-known Tikhonov regularization scheme, and systematic investigation of the influence of the tip apex angles on the accuracy of the identified plastic properties. Guidelines for selecting the tip apex angles have also been presented.