Solution for the stress and displacement fields in the vicinity of a V-notch of negative wedge angle in plane problems of elasticity

Seweryn, A.; Zwoliński, Janisław

doi:10.1016/0013-7944(93)90052-t

Cited by 19 publications

(7 citation statements)

References 3 publications

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“…It has been widely demonstrated that for notch angles ranging from 0 • to approximately 102.6 • corresponding to 0 < λ II < 1, Eq. (10) produces unbounded in-plane shear stresses at the notch tip (Williams 1952;Seweryn and Zwolinski 1993). Alternatively, a separate singular and admissible solution corresponding to the singular behaviour of the out-of-plane shear stresses can be obtained from the second component of Eq.…”

Section: First Order Plate Theory Predictionsmentioning

confidence: 99%

“…Whilst the singular power describes the asymptotic rate at which the stress distributions increase as the notch tip is approached, the magnitude of the singular stress distributions can be given by means of the notch stress intensity factors defined in the present paper according to (Seweryn and Zwolinski 1993):…”

Section: Computational Proceduresmentioning

confidence: 99%

“…In accordance with a remotely applied shear load, boundary displacements are applied to the outer radial edges of the finite element models corresponding to a far field two-dimensional plane stress distribution. The applied polar displacements (boundary conditions) corresponding to mode II plane stress solution, which is valid far from the notch tip, are given in a rearranged form by (Seweryn and Zwolinski 1993) …”

Section: Computational Proceduresmentioning

confidence: 99%

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Transverse singular effects in V-shaped notches stressed in mode II

et al. 2010

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The concept of a stress singularity is a cornerstone of modern fracture mechanics. A new mode of stress singularity, the out-of-plane singular mode or K (O) mode, was recently identified for V-shaped notches subjected to in-plane loading. This new mode is coupled with the shear mode and related to Poisson's effect. The previous studies based on the first order plate theory focused on the derivation of a characteristic equation describing the strength of this singularity and provide no information regarding the intensity, extent and relevance of this mode to practical problems. This paper aims to fill this gap. The approach utilises the 3D finite element method and a standard regression technique for characterisation of the notch singular modes. A comprehensive study of the influence of Poisson's ratio, plate thickness and notch opening angle on the value of the notch stress intensity factor associated with this mode is conducted for infinite plates. Additionally, to demonstrate the relevance of this new singular mode to practical problems an investigation of the out-of-plane mode and associated three-dimensional effects are presented for the case of a welded lap joint. Main areas of further research are also identified

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Section: First Order Plate Theory Predictionsmentioning

confidence: 99%

Section: Computational Proceduresmentioning

confidence: 99%

Section: Computational Proceduresmentioning

confidence: 99%

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Transverse singular effects in V-shaped notches stressed in mode II

et al. 2010

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“…Boundary displacements rather than stresses are applied to the outer radial edges of the finite element models corresponding to a far field two-dimensional plane stress distribution for a notch with opening angle a, as given by Seweryn and Zwolinski (1993).…”

Section: Out-of-plane Singularity (K O -Mode)mentioning

confidence: 99%

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Kotousov

2010

International Journal of Solids and Structures

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Keywords:Effect of plate thickness Plain problems of elasticity Stress singularity Asymptotic methods of fracture assessment Linear-elastic fracture mechanics Notch stress intensity factor a b s t r a c t Notched plates are often found in various applications ranging from microelectronic devices to largescale civil structures. Stress analysis of plate components wherein the loading is uniformly distributed over the thickness, parallel to the plane of the plate, is normally based on plane stress or plane strain assumptions. Three-dimensional effects, such as the influence of the plate thickness on stress components, are largely ignored or considered as negligible for all practical purposes.This paper summarizes recent theoretical and numerical studies and discusses some important features of the three-dimensional singular solutions for sharp notches obtained within linear elasticity. Taking into account dimensionless considerations, the relationships between the intensities of the singular stress states corresponding to the three-dimensional linear elastic solutions and the plate thickness are established. The obtained relationships have many intriguing implications for the failure assessment of notched plates made of sufficiently brittle material. For example, based on a similar argument to the one used in classical linear-elastic fracture mechanics, it can be shown that a sufficiently thick plate with a sharp re-entrant corner should have virtually zero strength when subjected to antisymmetric (or mixed mode) loading. The theoretical conclusions drawn in this paper have direct applications to fracture testing and fracture assessment of plate components, and they set new goals for further experimental studies.

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“…Notch SIF'sK V I andK V II introduced in (1) and (6), (7) are defined as follows (Cherepanov 1979;Seweryn and Zwolinski 1993) …”

Section: Stress Distribution In Elastic Domains With Notchesmentioning

confidence: 99%

Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches

Savruk

Kazberuk

2009

Int J Fract

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The survey of research on the problems of fracture mechanics of solids with V-shaped notches is discussed. The methods of solution of plane problems of the elasticity theory for domains with angular points on boundary contours are considered. Special attention is paid to the results of the research which authors obtained applying the unified approach to the solution of stress concentration problems in the neighborhood of the vertices of sharp and rounded V-notches. The solutions of elastostatics problems for domains with rounded V-shaped notches were obtained by singular integral equation method. Based on the relation between stress intensity factor at the sharp notch vertex and the stress concentration factor at the vertex of rounded V-notch (notch with straight edges and vertex rounded with circular arc), the stress intensity factors for V-notches in various domains were obtained. The presented examples include notch stress intensity factors for periodically placed notches in the edge of halfplane, diamond and lens-like holes in infinite plane. Through limit transition from the system of periodically placed diamond-shaped ovals to infinite doublesided notch, the stress concentration factors for rounded deep V-notch and the notch stress intensity factors for sharp notch were obtained. The comparison between calculated data and known solutions for the hyperbolic notch documents strong influence of the notch shape in the neighborhood of the rounded vertex on the stress concentration values for small vertex radii. The numerical results are presented not only in graphical form but also the numerous approximation formulas are given. Based on the solution of the nonlinear problem of rounded V-notch with plastic strip at the vertex, the new deformation fracture criterion is proposed. This criterion contains only standard strength parameters and it is intended to determine fracture toughness of the elements with rounded notches made of quasibrittle materials.

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Solution for the stress and displacement fields in the vicinity of a V-notch of negative wedge angle in plane problems of elasticity

Cited by 19 publications

References 3 publications

Transverse singular effects in V-shaped notches stressed in mode II

Transverse singular effects in V-shaped notches stressed in mode II

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches

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