Continuous and discrete methods based on X-ray computed-tomography to model the fragmentation process in brittle solids over a wide range of strain-rates - application to three brittle materials

Abstract

In the present work, two methods, named “continuous” and “discrete”, are proposed to model the fragmentation process in brittle solids. Both methods rely on a preliminary analysis of the existing flaws population in scanned samples with X-ray micro-Computed Tomography (microCT). By converting the size of defects into critical stresses, the density of critical defects versus the applied stress level is deduced and used as an input of both a continuum and a discrete method. To do so, the concept of critical defects obscuration is implemented. Introduced in the DFH (Denoual-Forquin-Hild) micromechanics model, this concept consists in describing how cracks propagating from triggered flaws prevent neighbouring flaws from being activated. This obscuration phenomenon is implemented in the present work by using the flaws population determined via microCT analysis as an input. In the continuous method, the differential equation of the obscuration probability provided in the DFH model is integrated. In the discrete method, a cubic sub-volume of the scanned volume is considered and the growth of obscuration volumes is numerically simulated considering the real location of each critical defect and their stress of activation. Both methods provide predictions for the material dynamic strength and final cracking density according to the applied strain-rate. These two methods are applied to three types of brittle materials: an Ultra-High Performance Concrete (UHPC), a porous polycrystalline ice and a silicon carbide with spherical “fuse-flaws”. Finally, the obtained predictions are compared to the closed-form solution of the DFH model, which is based on a Weibull distribution of the critical flaws identified from bending tests. Whereas the three approaches match very well at low strain-rates, the continuous and discrete methods diverge from the DFH closed-form solution at high strain-rates, due to the activation of smaller and more numerous defects that could not be activated in the quasi-static bending tests.