A numerical procedure predicting crack onset and growth in a mixed mode in brittle materials is developed using the Coupled Criterion of Finite Fracture Mechanics (CCFFM), which assumes crack advances by finite steps and requires both stress and energy conditions are fulfilled. The Principle of Minimum Total Energy subjected to a Stress Condition (PMTE-SC) is implemented by a load-stepping algorithm, minimising the total energy change due to a crack advance allowed by the stress criterion. A simple implementation of PMTE-SC in FEM code Abaqus considers cracks geometrically modelled as topological discontinuities in the FEM mesh, with cracks introduced explicitly during the discretisation of the domain, the crack faces coinciding with the element edges. Several numerical examples are solved for mixed-mode crack onset and propagation.
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In this study, we address hydraulic fracture initiation from a notch-free wellbore subjected to compressive in-situ stresses, where the wellbore is situated in an anisotropic host rock with transversely isotropic properties. To capture the three unknown parameters, i.e. the initial crack length, orientation, and the fluid pressure at initiation in anisotropic formations, we extend the mixed criterion proposed for isotropic rock formations in the literature. The mixed criterion requires that both stress and energy conditions at the initiation point are met. To do so, we calculate the fracture energy through the displacement discontinuity method (DDM), where the kernel matrix appropriate to the geometry of the problem (i.e. an infinite plane with a circular hole) is adopted for a transversely isotropic formation. To evaluate the reliability of our formulation at any degree of material anisotropy, the crack emanating from the wellbore is simulated by the finite element method, and consequently the energy dissipated between the cracked and crack-free states is measured. While the two methods are in agreement, the results unravel the systematics of how the competition between the material anisotropy and the differential in-situ stresses determines the initiation parameters.
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Composite laminates are widely used in aerospace industry overall for their mass-to-performance ratio. In this context, the storage of cryogenic propellant is subject to numerous studies, in which the composite must ensure a sealing function. However, the permeability is strongly related to the damage state of the laminate and heterogeneities at micro and meso scales make their damage behavior hard to predict. Among all damage mechanisms, transverse cracks and microdelamination are particularly interesting. Indeed, their coalescence through the laminate thickness is likely to generate leakage paths. Experimental observations often show that the transverse cracking bifurcates either in microdelamination at ply interfaces or in additional transverse cracks in adjacent plies. The Finite Fracture Mechanics (FFM) demonstrated its relevance in the prediction of crack propagation but it relies on a presupposed path. In this context, two scenarios, microdelamination at transverse crack tips and transverse cracking in adjacent plies are studied with FFM in order to identify the preferred mechanism regarding some material properties (limit strength, energy release rate…) and geometrical parameters (thickness, orientation…). In addition to the cracking scenario and morphology, FFM will also provide information on cracking rates with the aim of predicting the overall damage state of the laminate.
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