New expanding cavity model for conical indentation and its application to determine an intrinsic length scale of polymeric materials

Abstract

New expanding spherical cavity model (ECM) for conical indentation is proposed. For polymeric materials description, the model incorporates isotropic non-monotonic strain-hardening. For capturing the indentation size effect (ISE), the model incorporates the strain gradient dependence in yield strength based on lower-order strain gradient plasticity assumptions. Specifically, the forward gradient of the equivalent (accumulated) plastic strain is utilized as a non-local part of the yield strength. To predict the indentation depth-dependent hardness based on the proposed model, it is sufficient to numerically integrate one nonlinear ODE of the first order, and then calculate the definite integral. For the local plasticity model, the hardness is obtained as an analytical expression that differs from known ECMs. The hardness estimate obtained numerically using the proposed model is compared with the experimental ISE data for polycarbonate (PC) and polymethyl methacrylate (PMMA). For the local plasticity model, the formula obtained in the study is compared with the experimental data on the hardness of preliminary workhardened materials. In both cases, the model shows good agreement with the experimental data. Fitting the experimental data on ISE, we found that intrinsic length scale of PMMA should be near 3 micron and near 9 micron for PC.