Plastic deformation ahead of a plane stress tensile crack growing in an elastic-perfectly-plastic solid

Guo, Quanxin; Li, Kerong

doi:10.1016/0013-7944(87)90209-8

Cited by 17 publications

(13 citation statements)

References 4 publications

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“…The method has been used for an antiplane crack before [Achenbach and Li 1984;Guo and Li 1987;Yi 1992]. The elasticplastic solutions obtained in those references are the same as those given by Hult and McClintock near the crack line, but any such solution is still inadequate and is still confined by the small-scale yielding assumptions.…”

Section: Statement Of the Hult-mcclintock Solutionmentioning

confidence: 72%

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Revisiting the Hult–McClintock closed-form solution for mode III cracks

2010

J. Mech. Mater. Struct.

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The well-known closed-form solution given by Hult and McClintock for an antiplane crack in an elasticperfectly plastic material is reconsidered using the crack line analysis method. A precise elastic-plastic solution near the crack line region, different from Hult and McClintock's, is deduced by matching the general solution of the plastic field with that of the exact elastic field. It is verified from the deduction that the Hult-McClintock elastic-plastic solution is inadequate for many purposes.

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Section: Statement Of the Hult-mcclintock Solutionmentioning

confidence: 72%

“…Here we have taken into account that τ x z and w are antisymmetric, while τ yz and λ are symmetric with respect to θ = 0. (In [Guo and Li 1987;Yi 1992] the corresponding expressions in rectangular coordinates are considered.) Figure 2.…”

Section: Introduction To the Crack Line Analysis Methodmentioning

confidence: 99%

Revisiting the Hult–McClintock closed-form solution for mode III cracks

2010

J. Mech. Mater. Struct.

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“…(3a) and (3b) into the equilibrium equation (1) and the yield criterion equation (2) and collecting the terms of the same order y yield…”

Section: Fig 2 Crack Surface Regionmentioning

confidence: 99%

“…In other words, the solutions satisfying Eqs. (1) and (2), which are hard to determine, are countless. Fortunately, the crack line analysis method has specific merits in mathematics, i.e., the problem of solving partial differential equations can be transformed to the problem of solving ordinary differential equations, through which the general solution of the plastic stresses near the crack line region can be obtained effectively [4,[8][9] .…”

Section: Introductionmentioning

confidence: 98%

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Elastic-plastic analysis of antiplane crack near crack surface region

et al. 2010

Appl. Math. Mech.-Engl. Ed.

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The elastic-plastic stress distribution and the elastic-plastic boundary configuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by considering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.

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The more precise crack line analyses for antiplane quasistatically propagating crack

1992

Int J Fract

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Achenbach and Dunayevsky [1], and Guo and Li [2] investigated the near crack line fields of stress and deformation for an antiplane growing crack in an elastic perfectly-plastic material. In both [1] and [2], the elastic dominant terms (K-dominated terms) of the stress and deformation fields have been used to match with the plastic fields at the elastic plastic boundary. In this paper, the K-dominated terms have not been adopted but the precise elastic solutions for cracked bodies have been used as the elastic fields outside the crack-tip plastic region. Thus the solutions of this paper are more reasonable than the solutions of [1] and [2] for an antiplane quasistatically growing crack in an elastic perfectly-plastic material.For the typical mode III crack in an infinite body as shown in Fig. 1, the precise elastic solutions have been obtained by using Westergaard's complex stress function. Linear elastic fracture mechanics is generally concerned with the dominant terms of the stresses and displacements near the crack tip. The author, however, is more interested in the stresses and deformations near the crack line.Expanding Westergaard's precise elastic stresses and displacement in a power series of the angle 0 to the crack line, we have x r r -a r(a+r) ] -L j0 + 0(0) 3 x= "#r(2a + r) 2 x [ ( 2a2r + a 3 L21 ---4 -x"-~lr(2a +r)(a + r ) -~2-~+~-~2Ju j+o~t~ ) "C .r a+r ] W =--d'~lr(2a + r ~ ~a + r 0+0(03) (la) (ib) (2)where G is the elastic shear modulus.Equations (la,b) and (2) are valid near the crack line from r----> 0 to r--->~.In the plastic region, by the basic equations (the equilibrium equations, the Int Journ of Fracture 55 (1992)

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Plastic deformation ahead of a plane stress tensile crack growing in an elastic-perfectly-plastic solid

Cited by 17 publications

References 4 publications

Revisiting the Hult–McClintock closed-form solution for mode III cracks

Revisiting the Hult–McClintock closed-form solution for mode III cracks

Elastic-plastic analysis of antiplane crack near crack surface region

The more precise crack line analyses for antiplane quasistatically propagating crack

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