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Journal ArticleDOI

A crack perpendicular to an elastic half-plane

01 May 1970-International Journal of Engineering Science (Pergamon)-Vol. 8, Iss: 5, pp 351-362
TL;DR: An exact solution for an elastic half-plane containing a crack perpendicular to the free surface, when the faces of the crack are subjected to a particular, but rather general, distribution of pressure is given in this paper.
About: This article is published in International Journal of Engineering Science.The article was published on 1970-05-01. It has received 78 citations till now. The article focuses on the topics: Crack tip opening displacement & Crack closure.
Citations
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Journal ArticleDOI
TL;DR: In this article, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments.
Abstract: SUMMARY Tool-rock interaction processes can be classified as indentation or cutting depending on the direction of motion of the tool with respect to the rock surface. The modes of failure induced in the rock by an indenting or a cutting tool can be ductile and/or brittle. The ductile mode is associated with the development of a damage zone, whereas the brittle mode involves the growth of macrocracks. This is the first part of a series of two papers concerned with an analysis of the cutting and the indentation processes based on using the discrete element method. In this paper, numerical simulations of the cutting process are conducted to reproduce the transition from a ductile to a brittle failure mode with increasing depth of cut, which is observed in experiments. The numerical results provide evidence that the critical depth of cut d * controlling the failure mode transition is related to the characteristic length l = (KIc ∕ σc)2 with KIc denoting the material toughness and σc its unconfined compressive strength. The nature of frictional contact between the cutter face and the rock in the ductile failure mode is also examined. It is shown that the inclination of the total cutting force is controlled by a multi-directional flow mechanism ahead of the cutter that is related to the formation of a wedge of failed material, intermittently adhering to the cutter. As a result, the inclination of the total cutting force varies with the rake angle of the cutter and cannot be considered an intrinsic measure of the interfacial friction between the cutter and the rock. Copyright © 2012 John Wiley & Sons, Ltd.

243 citations

Book ChapterDOI
01 Jan 1973
TL;DR: The alternating method as discussed by the authors combines analytical results with the numerical calculations to solve the crack problem in a free edge or surface, where the crack intersects a free surface and requires special attention.
Abstract: Over the past decade, numerous analytical solutions of crack problems have appeared in the open literature [1]. A great number of these solutions are concerned with idealized crack geometries in plane or axisymmetric elasticity. However, only a few problems involving the interaction of cracks with neighboring boundaries have been solved satisfactorily. In situations where the crack intersects a free edge or surface, the method of solution becomes much more difficult and requires special attention. The advent of computers has no doubt facilitated the numerical computation of stress distributions around cracks. Without them, many of the tedious calculations would not be attempted. The alternating method is one which intimately combines analytical results with the numerical calculations.

151 citations


Cites background or result from "A crack perpendicular to an elastic..."

  • ...The latest by Stallybrass [18] obtains the stress intensity factors for stress on the crack varying as a power of distance from the edge....

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  • ...where C0, C , •••, CIQ are arbitrary constants, then the stress intensity factor is [18]...

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  • ...(5) Polynomial stress [18] If the form of the stress in Figure A-l is not linear, but is given by %' = -<*<, I C (x/a) y u n=0 r -72-...

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  • ...1 Source Irwin [3,10] Bueckner [11] Koiter [13,14] W i g g l e s w o r t h [16] Lachenbruch [4] S ta l l yb rass [18] Sneddon [19] Append ix Va/a 1 1 1 1 1 1 1 1 ....

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  • ...The result for linearly varying pressure agrees with that of Stallybrass [18]....

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Journal ArticleDOI
TL;DR: In this article, a method of deriving weight functions for cracks subjected to mode I loading is discussed, where the general weight function expression and its characteristic properties are used as the complementary information necessary for the determination of the unknown weight function parameters.

114 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the failure mechanisms induced by a wedge-shaped tool indenting normally against a rock surface using the discrete element method (DEM) to explore the conditions controlling the transition from a ductile to a brittle mode of failure.
Abstract: SUMMARY The failure mechanisms induced by a wedge-shaped tool indenting normally against a rock surface are investigated using the discrete element method (DEM). The main focus of this study is to explore the conditions controlling the transition from a ductile to a brittle mode of failure. The development of a damage zone and the initiation and propagation of a brittle fracture is well captured by the DEM simulations. The numerical results support the conjecture that initiation of brittle fractures is governed by a scaled flaw length Λ, a ratio between the flaw size λ and the characteristic length (where KIc is the toughness and σc the uniaxial compressive strength). The size of the damage zone agrees well with analytical predictions based on the cavity expansion model. The effects of a far-field confining stress and the existence of a relief surface near the indenter are also examined.Copyright © 2012 John Wiley & Sons, Ltd.

74 citations


Cites background from "A crack perpendicular to an elastic..."

  • ...With the additional assumption that the length of the initial flaw is small compared with the size of the plastic zone, that is, h, the stress intensity factor KI at the flaw tip can be approximated by the expression for an edge crack subjected to linearly distributed normal stress in a semi-infinite medium [15]....

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Journal ArticleDOI
TL;DR: In this article, a method for determining the behavior of the solution to a hypersingular integral equation near the end-points of the interval of integration is presented. But the method uses the Mellin transform.
Abstract: We consider one-dimensional hypersingular integral equations over finite intervals; the integral must be interpreted as a finite-part integral. Such equations arise naturally in various physical situations, involving thin rigid bodies or cracks; examples are given. A method is developed for determining the behaviour of the solution to a hypersingular integral equation near the end-points of the interval of integration. The method uses the Mellin transform. Several examples are worked out in detail.

67 citations


Cites background from "A crack perpendicular to an elastic..."

  • ...4) The corresponding boundary-value problem can be solved exactly; see, for example, Stallybrass (1970) who gives a solution for v(s) = with /? > — 1....

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  • ...Pressurized edge-crack in a half-plane Set d = 0 in (2.12) to give L(s,t) = — 1 / {s + + V2st/ (5 + 1)\ (3.4) The corresponding boundary-value problem can be solved exactly; see, for example, Stallybrass (1970) who gives a solution for v(s) = with /?...

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References
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Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of determining the stresses and displacements in a semi-infinite elastic plate which contains a thin notch perpendicular to its edge, and is in a state of plane strain or generalized plane stress under the action of given loads.
Abstract: The problem considered here is the determination of the stresses and displacements in a semi-infinite elastic plate which contains a thin notch perpendicular to its edge, and is in a state of plane strain or generalized plane stress under the action of given loads. The axes of x and y are taken along the infinite edge and along the notch, and the scale is chosen so that the depth of the notch is unity (Fig. 1).

78 citations