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

Abstract

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 predictions of the cavity expansion model for the material hardness, for different indentation depths and speeds, are compared against the available experimental results for OFHC copper, for strain rates varying from 10 −4 s −1 to 10 8 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 analyses 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 analyses show 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.

Size effects on the plastic shock formation in steady-state cavity expansion in porous ductile materials

“…see Aboulkhair et al [1] and Heidari et al [25]), so that the range of void volume fractions investigated in this work can be representative of actual metallic materials. Moreover, the range of values investigated for the dimensionless length scale parameter 0 ≤ l /a ≤ 0.002 is similar to that considered by dos Santos et al [41]. The critical dimensionless velocity increases with the normalized length scale, bringing out that size effects hinder the emergence of plastic shocks.…”

“…The extension of the hypervelocity cavity expansion model of Cohen and Durban [9] to size-dependent materials developed by dos Santos et al [41] has been used to determine the effect of size, induced by plastic strain gradient, on the formation of plastic shocks in porous materials. In particular, we have shown that the critical cavity expansion velocity for which plastic shocks emerge increases with the length scale parameter that controls the effect of size, and decreases with the material porosity, with the influence of porosity decreasing as the effect of size increases.…”

“…The constitutive framework is the same used in the recent paper of dos Santos et al [41]. The rate of deformation tensor is considered to be the sum of an elastic part, d e , and a plastic part, d p :…”

“…Moreover, Cleja-Tigoiu et al [8] developed a rate-dependent cavity model to address hypervelocity penetration in porous concrete structures. Recently, the model of Cohen and Durban [9] has been extended by dos Santos et al [41] in an effort to account for plastic strain gradient induced size effects on the dynamic micro-indentation of porous materials. As a subsequent study, this work uses the formulation of dos Santos et al [41] to elucidate the effects of size and material porosity on the formation of plastic shocks emerging during hypervelocity cavitation of porous solids.…”

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

“…These models are attractive in that they often provide closed-form relationships between hardness (the load on the indenter measured in the experiment) and the plastic and elastic parameters of the material. The ECMs based on various material models are proposed [Durban and Masri, 2008;Gao et al, 2006;Gao, 2006a,b;dos Santos et al, 2021]. It is widely accepted that cone indentation models are also suitable for Vickers and Berkovich indenters if the cone half-angle is 70.3   .…”