Experiments and numerical simulations studied the mechanics of two interacting colinear and offset cracks. Quasi-static experiments were carried out on acrylic sheets to determine the crack growth direction in the specimens with double parallel cracks or a single crack. The Finite Element Method (FEM) was adopted to calculate stress intensity factors at the crack tips. The interaction and influence of crack growth and direction of propagation with various geometries of cracks and their positions were discussed. This interaction is observed through a change in the propagation directions of crack tips. As the cracks grow, the SIF at the crack tip continuously increases. When the cracks are very close, SIF sharply increases for the colinear case. Crack growth behavior is observed, and the stress intensity factor is calculated at each step of crack growth for both cracks. The interaction effect on the crack path during propagation in simulation is predicted by the Maximum Tangential Stress (MTS) criterion. Some experiments are conducted to validate the analysis results. Comparisons are also made with experiments conducted under this study.
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Themes: Finite Fracture Mechanics: Theoretical Aspects, Numerical Procedures, and Experimental Applications
THE THEORY OF CRITICAL DISTANCES TO MODEL THE STATIC STRENGTH OF ADDITIVELY MANUFACTURED CONCRETE/POLYMERS CONTAINING MANUFACTURING DEFECTS/VOIDS [Keynote]
The present paper deals with the use of the Theory of Critical Distances to model the detrimental effect of manufacturing defects and voids in 3D-printed concrete/polymers subjected to static loading. The validity and robustness of the proposed approach is assessed against a large number of experimental results that were generated by testing 3D-printed specimens of both concrete and polylactide (PLA) containing manufacturing defects/voids. The sound agreement between experiments and predictive model makes it evident that the Theory of Critical Distances is not only a reliable design approach, but also a powerful tool suitable for guiding and informing effectively the additive manufacturing process.
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SINGULAR ELASTIC SOLUTIONS IN CORNERS AND CRACKS WITH SPRING BOUNDARY CONDITIONS WITH VARYING STIFFNESS [Keynote]
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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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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STUDY OF INTRA- AND INTER-LAMINAR DAMAGE INTERACTIONS IN LAMINATED COMPOSITES USING FINITE FRACTURE MECHANICS
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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3D FINITE FRACTURE MECHANICS UNDER MODE I LOADING: THE FLAT ELLIPTICAL CRACK [Keynote]
In recent years, the Finite Fracture Mechanics approach, originally proposed by Leguillon in 2002, has been applied successfully to several material and geometrical configurations. However, up to now, most of the applications were restricted to two-dimensional geometries. In the present paper, we provide an insight to a simple yet challenging three-dimensional case, namely the flat elliptical crack. Results are provided in analytical form.
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ON THE DIFFICULTY OF IMPLEMENTING THE COUPLED CRITERION TO PREDICT GLASS FRACTURE [Keynote]
Glass is an extremely brittle material that behaves almost perfectly linear elastic until it fractures. The linear-elastic fracture mechanics (LEFM) approach described by Griffith’s energy criterion is typically used to explain failure from a pre-existing crack like defect. However, LEFM reaches its limits in explaining failure processes at general stress concentration points and implementing the Coupled Criterion (CC) to take over is a tricky task. This mainly because it requires the knowledge of the tensile strength of the material which is a parameter not easy to characterize in glass. It is in general defined through a statistical law and relies strongly with surface flaws. The general aim of this work is to give an overview of the current understanding of glass tensile strength.
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