Some remarks on elastic crack-tip stress fields
TL;DR: In this paper, it was shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factors for any other symmetric load system whatsoever on the same body may be directly determined.
About: This article is published in International Journal of Solids and Structures.The article was published on 1972-06-01 and is currently open access. It has received 923 citations till now. The article focuses on the topics: Stress intensity factor & Stress field.
Summary (1 min read)
INTRODUCTION
- CONSIDER a two-dimensional linear elastic body containing a straight crack under conditions of plane strain or of generalized plane stress.
- Of course, the 1 and 2 systems may represent any arbitrarily chosen load systems and thus it is being shown that if a solution for the displacement field and stress intensity factor is known for any particular load system} then this information is sufficient to determine the stress intensity factor for any other load system whatsoever.
- The authors therefore conclude that for any symmetrical load system leading to stress intensity factor K and displacement field u, the function (the derivativ~ being taken at fixed values of the applied loads) is a universal function for a cracked body of any given geometry and composition, regardless of the detailed way in which the body is loaded.
AN EXAMPLE
- All problems of symmetrical loading may be reduced, by superposition of a solution for a crack-free body under the same loads, to a similar problem of prescribed normal tractions along the crack.
- Hence it would seem advisable that, to the extent possible, displacements of the crack surfaces [or better the weight function hy(x, ±O, I)J as well as stress intensity factors be reported when crack problems are solved.
- Bueckner [1J, for example, shows how his previous solution for the edge-cracked half-plane in tension may be employed to obtain the weight function for that case.
- The inaccuracy of-such methods near the tip would then be irrelevant.
- This procedure seems, in fact, to be closely related to that proposed by Barone and Robinson [6J for numerical determination of coefficients ill eigenfunction expansions of stress fields about corner singUlarities.
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TL;DR: In this article, a necessary criterion for brittle fracture in crystals is established, in terms of the spontaneous emission of dislocations from an atomically sharp cleavage crack, and the stability of a sharp crack against emission of a blunting dislocation for a number of crystals and crystal types in two dimensions and the energy to form a stable loop of dislocation from the crack tip in three dimensions.
Abstract: A necessary criterion for brittle fracture in crystals is established, in terms of the spontaneous emission of dislocations from an atomically sharp cleavage crack. We have calculated the stability of a sharp crack against emission of a blunting dislocation for a number of crystals and crystal types in two dimensions and the energy to form a stable loop of dislocation from the crack tip in three dimensions. We find that contrary to previous expectations, an atomically sharp cleavage crack is stable in a wide range of crystal types, but that in the face centred cubic metals investigated, blunting reactions occur spontaneously. Of the body centred metals investigated, iron is an intermediate case between the brittle and ductile cases, and the ionic and covalent crystals investigated are all stable against dislocation emission. Qualitatively, we find that crystals whose dislocations have wide cores, and small values of the parameter μb/γ (μb/γ⋦7·5 to 10) are ductile while crystals with narrow cores ...
1,413 citations
TL;DR: In this article, it is shown that the initial zone, prior to crack growth, provides no change in stress intensity. As the crack grows, the zone associated with a positive transformation strain induces a stress-intensity reduction that rises to a maximum level after some crack propagation.
Abstract: Particles which undergo a stress-induced martensitic transformation are known to toughen certain brittle materials. The enhanced toughness can be considered to originate from the residual strain fields which develop following transformation and tend to limit the crack opening. The increased toughness can estimated from the crack-tip stress-intensity change induced by the transformation of a volume of material near the crack tip. It is found that the initial zone, prior to crackgrowth, provides no change in stress intensity. As the crack grows, the zone (associated with a positive transformation strain) induces a stress-intensity reduction that rises to a maximum level after some crack propagation. The influence of particle-size distribution on the stress-intensity reduction is also discussed.
958 citations
TL;DR: In this paper, the authors review the principal mechanical properties of multi-principal element alloys with emphasis on the face-centered cubic systems, such as the CrCoNi-based alloys, and suggest their favorable mechanical properties and ease of processing by conventional means suggest extensive utilization in many future structural applications.
567 citations
TL;DR: In this paper, the authors investigate the interplay and the competition between these processes, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.
Abstract: Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media under pre-existing compressive stresses as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including the flow of viscous fluid, creation of solid surfaces, and leak-off of fracturing fluid. The interplay and the competition between these processes lead to multiple length scales and timescales in the system, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.
377 citations
TL;DR: In this paper, a simple representation for the crack-face displacement is employed to compute a weight function solely from stress intensity factors for a reference loading configuration, and the weight function for a corner crack in an LMFBR hexagonal sub-assembly duct is constructed from stress-intensity-factor results for the uniformly over-pressurized case.
307 citations
References
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TL;DR: In this paper, the general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach and stress intensity factors, which permit concise representation of the conditions for crack extension, are defined and evaluated directly from stress functions.
Abstract: The general equations for crack-tip stress fields in anisotropic bodies are derived making use of a complex variable approach. The stress-intensity-factors, which permit concise representation of the conditions for crack extension, are defined and are evaluated directly from stress functions. Some individual boundary value problem solutions are given in closed form and discussed with reference to their companion solutions for isotropic bodies.
1,098 citations
Journal Article•
TL;DR: In this paper, a state of plane strain in a notched or cracked elastic domain under the action of boundary tractions is considered, and the stress intensity factor K at a root of a notch can be re presented in the form of a weighted average of the tractions.
876 citations
TL;DR: In this paper, an elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads was used to calculate the stress intensity for bending loads.
Abstract: Elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads
485 citations
Journal Article•
266 citations
01 Mar 1971
TL;DR: In this paper, a numerical method for determining stresses near corners and cracks in two-dimensional elastic bodies is presented based on an integral equation formulation which uses the character of the displacements near such irregular boundary points.
Abstract: : A numerical method for determining stresses near corners and cracks in two-dimensional elastic bodies is presented. The method is based on an integral equation formulation which uses the character of the displacements near such irregular boundary points. Kernels for the integral equations at points along smooth portions of the boundary are obtained from the solutions to concentrated force problems in the usual manner. The most significant part of the study consists of the development of convenient new kernels for the integral equations written at the irregular boundary points. Suitable numerical techniques are used to convert the set of integral equations to a set of linear algebraic equations which involve the boundary values as unknowns. Accurate results are obtained for three sample problems using a relatively small number of simultaneous equations. Moreover, the results are stable with respect to the number and distribution of boundary points. (Author)
4 citations