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Crack propagation through a material interface
Náhlík, Luboš
This paper describes a study of the fatigue crack propagation through a material interface of two different elastic materials under assumptions of linear elastic fracture mechanics. Two procedures for estimation of threshold value for further crack propagation from bi-material interface to the second material are suggested. Special attention is devoted to crack perpendicularly oriented to the bi-material interface. The first one is based on modified Sih?s strain energy density concept and the second one on the size of area of the plastic zone in front of the crack tip. It is shown that the corresponding fatigue threshold value is strongly influenced by the existence of an interface between two materials. As a numerical example the procedures are in applied on body with protective layer. The calculation of the corresponding threshold values and comparison of both suggested procedures is performed. Both procedures make it possible to decide whether the crack will stop at the interface or will continue growing into the second material. The results generally contribute to a better understanding of the failure of structures with protective layers.
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Fracture process zone of concrete: analysis of aggregate-crack interaction
Keršner, Z. ; Náhlík, Luboš ; Knésl, Zdeněk
Concrete is modelled as a two-phase material. Behaviour of a crack with its tip on the interface between two different materials - hardened cement paste (matrix) and aggregate (particle) - is studied. In contrast to cracks in homogeneous materials the stress singularity for a crack terminating at the interface is of the type r -lambda, where the value of the stress singularity exponent, lambda, is in the interval 0 < lambda < 1. Than classical fracture mechanics theory and criterion cannot be applied. In the paper a new stability criterion is used to estimate the critical stress for the intersection of coarse aggregate particles.
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Formulation of the brittle failure conditions for composite bodies
Náhlík, Luboš ; Knésl, Zdeněk
A stability criterion based on generalized strain energy density factor for a crack terminating at the bi-material interface is suggested. The strain energy density distribution in the vicinity of the crack as well as the generalized stress intensity factors, and the crack propagation direction are calculated. The crack is oriented arbitrarily to the interface and both stress singularities around the crack tip are taken into account. The problem is solved by combination of analytical and numerical approaches. A numerical example of application of the proposed approach is presented.
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Critical stress for crack propagation in concrete
Náhlík, Luboš ; Knésl, Zdeněk
Concrete is modelled as a two-phase material. Behaviour of a crack with its tip on the interface between two different materials - hardened cement paste (matrix) and aggregate (particle) - is studied. In contrast to cracks in homogeneous materials the stress singularity for a crack terminating at the interface is of the type r -lambda, where the value of the stress singularity exponent, lambda, is in the interval 0 < lambda < 1. Than classical fracture mechanics theory and criterion cannot be applied. In the paper a new stability criterion is used to estimate the critical stress for the intersection of coarse aggregate particles.
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Analýza rozdělení napětí pro trhlinu s vrcholem na rozhraní dvou materiálů
Náhlík, Luboš
The problem of arbitrarily oriented crack terminating at the boundary of two bonded materials is studied from the point of view of linear elastic fracture mechanics. The nature of the stress singularity for the crack terminating at the interface is different from 1/ square root of r and thus current fracture mechanics criteria cannot be adopted. The values of stress singularity exponent for selected ratio of elasticity modulus of both applied materials in dependency on orientation of crack and interface are calculated.
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Determination of a crack propagation direction initiated at the bi-material interface
Náhlík, Luboš
The strain energy density distribution in the vicinity of a crack with its tip at the bi-material interface and the generalized strain energy factor is calculated. The crack orientated arbitrarily with respect to the interface and both cases of stress singularities around the crack tip, corresponding to normal and shear modes of loading, are taken into account. The problem is solved by a combination of analytical and numerical calculations. To estimate the crack propagation direction, the generalized strain energy criterion is used. A numerical example is presented.
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Estimation of the Critical Stress for Failure of a Protective Layer
Náhlík, Luboš
This contribution describes a study of the behaviour of a crack growing in a protective layer and penetrating through an interface into a substrate. Special attention is devoted to a crack touching the interface. Conditions for the stability of a crack terminating at the interface between two materials are analyzed. The problem is studied under the assumptions of linear-elastic fracture mechanics. A new tentative criterion of stability based on application of the strain energy density concept is formulated and applied to the problem. The suggested criterion is used to estimate the critical applied stress for the failure of a substrate caused by a crack growing through the protective layer. It is shown that the critical stress may strongly depend on the fracture toughness of the substrate and on the bi-material parameters.
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Influence of grain orientation on threshold values of short fatigue cracks
Náhlík, Luboš ; Knésl, Zdeněk
The influence of a grain boundary on the propagation of a fatigue crack is studied. To this aim the grain boundary is considered as an interface between two different materials with their elastic constants depending on the orientation of the adjacent grains. The main goal is to estimate the threshold value of a microstructurally short fatigue crack propagating through the grain boundary. The corresponding threshold values are calculated as a function of material parameters of grains. Corresponding modelling have been performed by combination of analytical and numerical approach. For numerical calculations the finite element system ANSYS has been used. The model describes only one of many aspects of short fatigue crack behaviour and the results obtained contribute to a better understanding of microstuctural aspects of short fatigue crack growth.
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Influence of material characteristics on the fatigue crack growth through bi-material interface
Náhlík, Luboš
This contribution describes a study of the behaviour of a fatigue crack growing in one material and penetrating through the bi-material interface into a second material. Dependence of the stress singularity exponent on Poisson's ratio of both materials is studied. The study especially aims to quantify the influence of the interface on the values of fatigue threshold. It is suggested that the controlling variable for the behaviour of a crack approaching to the interface is the size of the plastic zone existing near the tip of the crack. The results of the contribution makes it possible to decide whether the crack will stop at the interface or continue growing into the second material. The results contribute to a better understanding of the damage of composite materials.
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Estimation of the Critical Stress for Failure of a Protective Layer
Náhlík, Luboš ; Knésl, Zdeněk
This contribution describes a study of the behaviour of a crack growing in a protective layer and penetrating through an interface into a substrate. Special attention is devoted to a crack touching the interface. Conditions for the stability of a crack terminating at the interface between two materials are analyzed. The problem is studied under the assumptions of linear-elastic fracture mechanics. A new tentative criterion of stability based on application of the strain energy density concept is formulated and applied to the problem. The suggested criterion is used to estimate the critical applied stress for the failure of a substrate caused by a crack growing through the protective layer. It is shown that the critical stress may strongly depend on the fracture toughness of the substrate and on the bi-material parameters.
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