Singular elastic solutions in corners and cracks with spring boundary conditions with varying spring stiffness are studied. First, a novel analytic procedure is developed for the antiplane strain case. Then, some general observations obtained are checked for the plane strain case by using a FEM code. Finally, applications of these observations in a suitable computational implementation of the Coupled Criterion of Finite Fracture Mechanics are discussed.
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Themes: Finite Fracture Mechanics: Theoretical Aspects, Numerical Procedures, and Experimental Applications
FEM IMPLEMENTATION OF THE COUPLED CRITERION BASED ON MINIMIZATION OF THE TOTAL ENERGY SUBJECTED TO A STRESS CONDITION TO PREDICT MIXED MODE CRACK ONSET AND GROWTH
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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MODELING HYDRAULIC FRACTURE INITIATION OF A NOTCH-FREE WELLBORE IN ANISOTROPIC ROCKS
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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V-NOTCHED COMPONENTS UNDER TORSIONAL FATIGUE LOADING [Keynote]
Finite Fracture Mechanics (FFM) is applied to assess the brittle or quasi-brittle failure initiation at sharp V-notches under torsional loading. By assuming that failure is shear stress governed, the approach is developed in the fatigue framework. The analysis includes a discussion on the calibration of the material properties, and the comparison with experimental data available in the literature.
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MULTIPLE DELAMINATIONS PREDICTION ON ILTS SPECIMENS BY AN ABAQUS IMPLEMENTATION OF THE COUPLED CRITERION OF FFM AND LEBIM [Keynote]
Inter-Laminar Tensile Strength (ILTS) test uses L-shaped composite coupons with laminas having different orientations. To model multiple delaminations that occur in ILTS specimens a quite general formulation of the Coupled Criterion of Finite Fracture Mechanics (CCFFM) with the Linear Elastic-perfectly Brittle Interface Model (LEBIM) is applied.
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