International audienceIn this work, a formulation is developed within the phase field method for mod-eling interactions between interfacial damage and bulk brittle cracking in complex microstructures. The method is dedicated to voxel-based models of highly complex microstructures, as obtained from X-ray microtomography images. A smoothed displacement jump approximation is introduced by means of level-set functions to overcome the issue of pixelized interfaces in voxel-based models. A simple technique is proposed to construct the level-set function in that case. Compared to recent work aiming at modeling cohesive cracks within the phase field method, our framework differs in several points: the formulation is such that interfaces are not initially damaged; no additional variables are required to describe the discontinuities at the interface and fatigue cracks can be modeled. The technique allows interaction between bulk and interface cracks, e.g. nucleation from interfaces and propagation within the matrix, and for arbitrary geometries and interactions between cracks. Several benchmarks are presented to validate the model. The technique is illustrated through numerical examples involving complex microcracking in X-ray CT image-based models of concrete microstructures

International audienceThe phase field method is a versatile simulation framework for studying initiation and propagation of complex crack networks without dependence to the finite element mesh. In this paper, we discuss the influence of parameters in the method and provide experimental validations of crack initiation and propagation in plaster specimens. More specifically, we show by theoretical and experimental analyses that the regularization length should be interpreted as a material parameter, and identified experimentally as it. Qualitative and quantitative comparisons between numerical predictions and experimental data are provided. We show that the phase field method can predict accurately crack initiation and propagation in plaster specimens in compression with respect to experiments, when the material parameters, including the characteristic length are identified by other simple experimental tests

A new multi-phase-field method is developed for modeling the fracture of polycrystals at the microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals.

Anisotropy is inherent to crystalline materials (among others) due to the symmetry of the atomic lattice. However, failure anisotropy is questioning the foundations of brittle failure as the equivalence between the principle of local symmetry and the maximum energy release rate criterion is no longer valid. Many experimental observations have been reported in the literature but anisotropic failure is thus still an open path for fundamental research. The aim of the paper is to propose a phase field model that could reproduce (energetically) non-free anisotropic crack bifurcation within a framework allowing for robust and fast numerical simulations. After the model and its finite element implementation have been detailed, its ability to capture the thought phenomenon is illustrated through several examples.

Keywords:Micro cracking Quasi-brittle Heterogeneous material Phase-field method Gradient damage model Voxel-based models In situ testing X-ray microtomography Digital volume correlation a b s t r a c tWe provide the first direct comparisons, to our knowledge, of complex 3D micro cracking initiation and propagation in heterogeneous quasi-brittle materials modelled by the phase field numerical method and observed in X-ray microtomography images recorded during in situ mechanical testing. Some material parameters of the damage model, including the process zone (internal) length, are identified by an inverse approach combining experimental data and 3D simulations. A new technique is developed to study the micro cracking at a finer scale by prescribing the local displacements measured by digital volume correlation over the boundary of a small sub-volume inside the sample during the numerical simulations. The comparisons, performed on several samples of lightweight plaster and concrete, show a remarkable quantitative agreement between the 3D crack morphology obtained by the model and by the experiments, without any a priori knowledge about the location of the initiation of the cracks in the numerical model. The results indicate that the crack paths can be predicted in a fully deterministic way in spite of the highly random geometry of the microstructure and the brittle nature of its constituents.

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This paper presents an image subtraction technique based on digital volume correlation to detect and extract the complex network of microcracks that progressively developed in a lightweight concrete sample submitted in situ to uniaxial compression and imaged by X‐ray computed tomography. From local digital volume correlation measurements, performed only on positions with sufficient image contrast, the mechanical transformation is estimated at all voxels within the whole sample using an adjusted interpolation procedure that computes an affine approximation of the local transformation. The deformed image (containing cracks) is thus transformed back to the same frame as the reference image (without cracks) to compute the difference between both images, taking into account possible brightness and contrast adjustments. The resulting subtracted image reveals the path of cracks, which is clearly visible without the underlying heterogeneous microstructure of the concrete. The detection accuracy is here estimated to one tenth of a voxel, allowing early‐age cracks to be detected while they would barely have been noticed on the X‐ray computed tomography images. Segmentation of the crack network is also made much easier. To overcome a low signal‐to‐noise ratio for the tiniest cracks, a Hessian‐based filter is used to extract the complex crack network. The cracks can be directly located in the microstructure segmented in the reference image and compared for all loading steps to characterise their initiation and propagation.