The combined effect of size, inertia and porosity on the indentation response of ductile materials

Herein, we present a self-similar cavity expansion model that follows from the work of Cohen and Durban (2013b) to analyze the dynamic indentation response of elasto-plastic porous materials while accounting for the plastic strain gradient induced size effect. The incorporation of the plastic strain gradient induced size effect in the dynamic cavity expansion model for elasto-plastic porous materials is the key novelty of our model. The material hardness predicted using the cavity expansion model for a wide range of indentation depths and speeds is compared against the available experimental results for OFHC copper, for strain rates varying from 10−4 s−1 to 108 s−1. We note that despite several simplifying assumptions, the predictions of our cavity expansion model show a reasonable agreement with the experimentally measured material hardness over a wide range of indentation depths and speeds. In addition, we have also carried out parametric analysis to elucidate the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process. In particular, our parametric analysis shows that there exists a critical value of the indentation speed beyond which the contribution of inertial effect becomes extremely important and the material hardness increases rapidly. While the influence of the initial porosity on the material hardness is found to increase with increasing indentation speed and decrease with increasing size effect.TdS wishes to acknowledge the support of FAPERGS, Fundação de Amparo ã Pesquisa do Estado do Rio Grande do Sul, grant agreement 19/2551 − 0001054 − 0. JAR-M acknowledges the financial support obtained from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme. Project PURPOSE, grant agreement 758056