Limiting state of an elastoplastic orthotropic plate with a periodic system of collinear cracks

Bogdanova, O. S.

doi:10.1007/s10778-007-0052-4

Cited by 8 publications

(8 citation statements)

References 9 publications

(11 reference statements)

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“…Numerous studies regarding this subject were done in the literature [18][19][20][21][22][23]. Analytic solutions for stress distribution and crack interaction for a composite material containing two collinear cracks can be found in the works [24][25][26][27][28][29]. The problem of three collinear crack interaction, elastic fields distribution and crack propagation using the integral equations method were studied in [30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of three equal collinear cracks in an orthotropic solid

et al. 2015

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We consider a homogeneous elastic, orthotropic solid containing three equal collinear cracks, loaded in tension by symmetrically distributed normal stresses. Following Guz's representation theorem and solving Riemann-Hilbert problems we determine the expressions of the complex potentials. Using the asymptotic analysis, we obtain the asymptotic values of the incremental stress and displacement fields. We determine the tangential stresses near the crack tips. Using the maximum tangential stress criterion and numerical computations we study the interaction problem for a Graphite-epoxy fiber reinforced composite material.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling of three equal collinear cracks in an orthotropic solid

et al. 2015

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“…In the present paper, on the basis of the general solution obtained in [1,9] and the Hoffman strength criterion [2], we investigate the influence of the anisotropy of the material (the differences between moduli of elasticity along axes of orthotropy and between the ultimate tensile strength and ultimate compressive strength) on the limit state of a thin orthotropic plate weakened by a periodic system of collinear cracks under conditions of biaxial external loading.…”

Section: Introductionmentioning

confidence: 99%

Influence of the anisotropy of the material on the limit state of an orthotropic plate weakened by a periodic system of collinear cracks

Bogdanova¹

2012

J Math Sci

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539.375On the basis of a modified Dugdale model, we investigate the influence of the anisotropy of the material, in particular, differences between the ultimate tensile strength and ultimate compressive strength, on the limit state of an orthotropic plate weakened by a periodic system of periodic collinear cracks under biaxial external loading. As a strength criterion, the Hoffman strength criterion is considered. Strength diagrams of an orthotropic plate with a crack for different strength and crack resistance parameters are obtained.

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“…An extensive review of relevant studies can be found in [3]. The limit state of an orthotropic plate with periodic cracks is analyzed in [12,13]. The stress-strain state of spherical shells with an eccentric circular hole and prestressed shells was studied in [14,18].…”

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confidence: 99%

“…( )are continuous functions, which can be expressed in terms of the regular parts of the kernels K ij 0 of (5) and the functions h i .In accordance with(12), the functions R x j ( )are represented as…”

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Limit equilibrium of a transversely isotropic spherical shell with two surface cracks

2009

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An analog of the d c -model is used to reduce the limit-equilibrium problem for a transversely isotropic spherical shell with surface cracks to a system of integral equations. An algorithm for numerical solution of this system is proposed Keywords: transversely isotropic spherical shell, surface crack, plastic strains, integral equations, crack opening displacement Introduction. When loaded, a solid with cracks undergoes plastic deformation at their tips. Since the classical solution of elastoplastic problems for cracked bodies involves severe difficulties (because two systems of equations, one in the elastic domain and the other in the plastic domain have to be solved simultaneously, with the boundary between these domain being unknown), simplified models that agree with experimental data take on special significance. For example, the d c -model [7,15] and its analogs [4,17] can effectively be applied to thin plates and shells whose fracture is preceded by the development of large plastic zones. This was demonstrated experimentally in [11] for plates and in [2, 10] for large-scale specimens such as welded joints of structural steels with low and medium strength. The satisfactory agreement of theoretical and experimental data was also observed when the shape of plastic zones in specimens differed from that in the d c -model. An analog of this model was used to study the stress state and limit equilibrium of cylindrical [16] and isotropic spherical shells with part-through cracks [4,5]. An extensive review of relevant studies can be found in [3]. The limit state of an orthotropic plate with periodic cracks is analyzed in [12,13]. The stress-strain state of spherical shells with an eccentric circular hole and prestressed shells was studied in [14,18]. The stress intensity factor for an orthotropic cylindrical shell of medium thickness with an internal surface crack was determined in [9].The present paper uses an analog of the d c -model and the refined Timoshenko-type theory of shells [3] to analyze the limit equilibrium of a transversely isotropic elastoplastic spherical shell weakened by two surface cracks.1. Let us consider a shell with two identical surface cracks arranged along a straight (in plan) line. The length and depth of the cracks are denoted by 2 0 l and 2d, the distance between their centers by 2l d . We choose a coordinate system XOY so that the OX-axis is aligned with the crack line and the origin is at the middle of the segment 2l d . The stress-strain state of the shell is symmetric about the lines X = 0and Y = 0. The external loads, crack length, and the behavior of the material are supposed to be such that the plastic zones originating at the crack front would develop as narrow strips on the crack continuation all the way throughout the thickness of the shell. Denote the length of the plastic zones near the internal (neighboring) tips by l p and near the external tips by l p . In accordance with [4], assuming that tensile stresses act near the crack tips, we model the plastic zones by the disco...

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Limiting state of an elastoplastic orthotropic plate with a periodic system of collinear cracks

Cited by 8 publications

References 9 publications

Mathematical modeling of three equal collinear cracks in an orthotropic solid

Mathematical modeling of three equal collinear cracks in an orthotropic solid

Influence of the anisotropy of the material on the limit state of an orthotropic plate weakened by a periodic system of collinear cracks

Limit equilibrium of a transversely isotropic spherical shell with two surface cracks

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