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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Themes: Finite Fracture Mechanics: Theoretical Aspects, Numerical Procedures, and Experimental Applications
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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MODELING OF GLASS MATRIX COMPOSITES BY THE COUPLED CRITERION AND THE MATCHED ASYMPTOTICS APPROACH. THE ROLE OF A SINGLE PLATELET.
The fracture toughness of glass can be increased by introducing a second constituent with high modulus, strength and/or ductility. Among others, a very attractive solution for industrial proposes is the borosilicate glass/Al2O3 platelet composite. Hence, in this work different toughening mechanisms in this composite are analysed from the point of view of the Coupled Criterion, together with the Matched Asymptotics approach.
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ON-LINE TOOL FOR ANALYSIS OF SINGULAR STRESSES AND DISPLACEMENTS IN ANISOTROPIC MULTI-MATERIAL CORNERS
A Python code based on a semianalytic procedure for the analysis of singular stress and displacement fields in anisotropic multi-material corners in generalized plane strain is developed. Open and closed (periodic) multi-material corners formed by isotropic, transversely isotropic or anisotropic materials with perfectly bonded interfaces or in frictionless or frictional sliding contact are considered. Many kinds of boundary conditions as free, clamped, displacement allowed or not in any given direction, and frictionless or frictional sliding contact are covered. This computational tool may help researchers who need to know the singularity exponents and the singular eigenfunctions for stresses and displacements for a corner, e.g., to improve or check their numerical results by FEM, or to verify their analytic formulas of eigenequations developed for specific stress singularity problems. With the aim of sharing this useful tool, it has been made available on research group website, where the user can introduce the corner problem parameters and the corner singularity problem is solved by a high-performance computing server.
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ON FFM/PFM FAILURE CRITERIA FOR METALS UNDERGOING SSY – NEW INSIGHTS AT V-NOTCHED TIPS [Keynote]
Structures made of steel alloys may fracture at V-notch tips at which a small plastic zone usually evolves. Failure criteria for predicting fracture loads for such quasi-brittle alloys, as a function of the V-notch opening angle are very scarce and have not been validated, to the best of our knowledge, by a set of experimental observations. Neither the FFM coupled criterion (FFMCC) for brittle fracture, nor two phase-field models (the classical AT1 for brittle materials and a ductile version) could predict the increase of the crack nucleation force observed in the four-point bend (4PB) experiments performed on AISI 4340 specimens as the opening angle increased. Extension of the FFMCC to account for the small plastic zone and further 4PB experiments on a new steel alloy (H13) are being considered to improve the failure criterion.
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CRACK DEFLECTION AT CURVED INTERFACES. A FINITE FRACTURE MECHANICS ANALYSIS [Keynote]
Curved weak interfaces present promising advantages to be implemented as crack arrestors in structures designed under the tolerant-design principles. Among other advantages, they neither add extra weight nor affect significantly to the global stiffness of the structural element, in contrast with other crack arrestors. To be employed as crack arrestor, it is key that the interface can deviate the crack. If the crack penetrates across the interface, the effect of the weak interface as crack arrestor is canceled. In view of this, this work studies how to set the interface parameters to promote the crack deviation along the interface. In particular, following the dimensional analysis of the problem, the effect of three significant dimensionless parameters is studied: interface to bulk fracture toughness, interface to bulk tensile strength and the interface curvature radius normalized with the material characteristic length. The study is carried out using the Coupled Criterion of the Finite Fracture Mechanics.
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FINITE FRACTURE MECHANICS VERSUS PHASE FIELD: A CASE STUDY ON THE CRACK ONSET FROM CIRCULAR HOLES UNDER BIAXIAL LOADING CONDITIONS
The phenomenon of brittle crack onset stemming from a circular hole embodied in a biaxially loaded infinite plate is herein investigated. Three different approaches are used to determine the biaxial safety domains: Finite Fracture Mechanics, Cohesive Zone Model and Phase Field. In particular, the original formulation of Finite Fracture Mechanics (FFM) proves to be consistently more optimistic than its averaged-stress variant (FFM-avg); likewise, both agree in predicting the existence of a region in the loading space where failure is governed by the energy condition. Besides, failure predictions according to Dugdale’s Cohesive Zone Model (CZM) prove to be fairly close to those by FFM, whereas the differences between CZM and FFM-avg result more noticeable. Lastly, the Phase Field model of fracture is implemented paying special attention to the choice of the energy decomposition, being herein implemented two relevant options: No-Decomposition and No-Tension decomposition. In particular, the latter showcases reasonable agreement with FFM (and CZM), thus rendering it a solid contender for its use in applications in which combined tension-compression stress states appear, such as in the dynamic failure of brittle materials.
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MECHANICS OF THE INTERACTION OF TWO PARALLEL, SIMULTANEOUSLY GROWING CRACKS USING LEFM
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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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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