Stress intensity factors for a semiinfinite crack with branches

Savruk, M. P.; Rytsar, R. B.

doi:10.1007/bf02539126

Cited by 2 publications

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“…Further, we find the lengths and angles of orientation of the slip bands by the method of successive approximations. For given parameters In and an, n = 1, 3, we arrive at a two-dimensional problem of the theory of elasticity for a plane with semiinfinite branched crack [3]. In each approximation, we solve the following system of three singular integral equations by the method of mechanical quadratures [3,4]: Tie -rn…”

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confidence: 99%

“…Beyond these surfaces, the body is supposed to be elastic [ 1,2]. However, within the framework of this model, it is mathematically difficult to describe the onset of plastic deformation (small-scale yield) for a crack of finite length [3][4][5][6][7]. In the present work, by using the method of singular integral equations, we develop a general approach to the solution of the problem of propagation of slip bands near a semiinfinite crack of mixed type (mode I + II) under the conditions of plane stressed state or plane deformation.…”

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Propagation of plasticity bands from the tip of a semiinfinite crack of mixed type

Savruk¹,

Rytsar²

1997

Mater Sci

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539.375 In the framework of the model of plasticity bands, we analyze an elastoplastic fracture-mechanics problem of propagating plasticity bands near the tip of a semiinfinite crack of mixed type. It is assumed that, under the conditions of plane stressed state, plastic strains near the tip of a semiinfinite crack are localized along three plasticity bands (L I , L 2, L 3 ) and, under the conditions of plane deformation, they are localized along two bands (L 1, L 2). One of these bands (L 3 ) is simulated by a line of discontinuity of normal and tangential displacements. The remaining two bands (L I, L 2) are simulated by the lines of discontinuity of tangential displacements. Their lengths and orientations are determined in the process of numerical solution of the problem by the method of singular integral equations. We also present the values of crack tip opening displacements.In the vicinity of crack tips, materials always undergo plastic deformation. To analyze plasticity zones, it is customary to use the model of plasticity bands regarded as surfaces of discontinuities of displacements satisfying the conditions of plasticity. Beyond these surfaces, the body is supposed to be elastic [ 1,2]. However, within the framework of this model, it is mathematically difficult to describe the onset of plastic deformation (small-scale yield) for a crack of finite length [3][4][5][6][7]. In the present work, by using the method of singular integral equations, we develop a general approach to the solution of the problem of propagation of slip bands near a semiinfinite crack of mixed type (mode I + II) under the conditions of plane stressed state or plane deformation. We determine crack tip opening displacements and the lengths of plasticity bands under general loading. For some cases, we also present approximate formulas in the explicit form. The solution of this problem can be regarded as the asymptotics of the corresponding solution of the problem of propagation of plasticity zones near the tip of a crack of finite length under the conditions of small-scale yield.Plastic deformation near the crack tip in the case of small-scale yield was studied by using various approaches [8][9][10][11]. Most often, these investigations deal with tensile cracks for which the plasticity zone is symmetric about the crack line [8,9]. The problems of propagation of the plasticity zone near the tip of a semiinfinite crack of mixed type in a homogeneous body [10] and along the interface of rigid and elastic materials [11] were studied only under the assumption that the crack tip serves as the origin of a single slip band (simulated by a jump of tangential displacements). In [5,6], the parameters of nonlinear fracture mechanics are evaluated for a crack of mixed type. Plane Stressed StateConsider a semiinfinite crack L 0 with plasticity bands in an infinite plate. We assume that three bands (L 1 , L 2, L 3 ) of different lengths and orientations originate from the tip of this crack (Fig. 1). The crack L 0 is directed along the Ox-axis (x...

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confidence: 99%