Closed-Form Solutions for the Mode ii Crack tip Plastic Zone Shape

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K II and non-singular T-stresses T x and T y parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0 • to 90 • . A compressive T y increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T x decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T x = T y ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.

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“…which is in agreement with that derived by Jing et al (2003), except for a 1/2 factor dropped there.…”

Section: Effects Of the T-stresses On The Effective Stresssupporting

confidence: 93%

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

Liu

Lee

2009

Int J Fract

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“…Jing and Khraishi [27,28] derived analytical solutions for crack tip plastic zone shape using the Von Mises and Tresca yield criteria and closed-form solutions for mode II crack tip plastic zone shape. Not only do these works talk about the plastic zone shape In the SIF calculations, the number of modified solid elements is 12 at the crack tip, and the circumference of the crack tip is divided into 12 equal parts, each with an angle of 30 • .…”

Section: Theoretical Shape Of Plastic Zonementioning

confidence: 99%

“…Jing and Khraishi [27,28] derived analytical solutions for crack tip plastic zone shape using the Von Mises and Tresca yield criteria and closed-form solutions for mode II crack tip plastic zone shape. Not only do these works talk about the plastic zone shape that the current paper discusses but they also talk about criteria for the path of crack extension.…”

Section: Theoretical Shape Of Plastic Zonementioning

confidence: 99%

Fracture Mechanical Analysis of Thin-Walled Cylindrical Shells with Cracks

Yue

2021

Metals

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The fracture mechanical behaviour of thin-walled structures with cracks is highly significant for structural strength design, safety and reliability analysis, and defect evaluation. In this study, the effects of various factors on the fracture parameters, crack initiation angles and plastic zones of thin-walled cylindrical shells with cracks are investigated. First, based on the J-integral and displacement extrapolation methods, the stress intensity factors of thin-walled cylindrical shells with circumferential cracks and compound cracks are studied using linear elastic fracture mechanics, respectively. Second, based on the theory of maximum circumferential tensile stress of compound cracks, the number of singular elements at a crack tip is varied to determine the node of the element corresponding to the maximum circumferential tensile stress, and the initiation angle for a compound crack is predicted. Third, based on the J-integral theory, the size of the plastic zone and J-integral of a thin-walled cylindrical shell with a circumferential crack are analysed, using elastic-plastic fracture mechanics. The results show that the stress in front of a crack tip does not increase after reaching the yield strength and enters the stage of plastic development, and the predicted initiation angle of an oblique crack mainly depends on its original inclination angle. The conclusions have theoretical and engineering significance for the selection of the fracture criteria and determination of the failure modes of thin-walled structures with cracks.

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“…Then, the distribution pattern of the plastic zone at the crack tip in pure Mode II cracks was gradually explored. For example, Peihua (Jing et al, 2003) investigated the evolution of the crack tip plastic zone under different criteria, and proposed that the distribution of the crack tip plastic zone has a complex dependence on Poisson's ratio under plane strain. As the research in this field continues to advance, important breakthroughs have also been made in the plastic zone distribution of composite cracks (Sousa et al, 2013;Huang, 2023).…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the stress field and plastic zone at the tip of a closed crack

Wu,

Wang,

Peng

2024

Front. Earth Sci.

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The investigation of stress field and plastic zone distribution at the closed crack tip provides a fundamental basis for failure analysis and life prediction of geotechnical materials. Closed crack is a common crack in geotechnical materials. Studying the distribution of stress field and plastic zone at the tip of closed crack can provide theoretical basis for stability evaluation of geotechnical structures. In this study, we employ the superposition principle to obtain complex function solutions for the stress field and displacement field at the crack tip. Furthermore, we analyze the plastic zone distribution at the crack tip based on the Mohr Coulombs criterion. We investigate how factors such as crack angle, confining pressure, and material properties influence the stress field, displacement field, plastic zone size, and crack propagation direction. Our results demonstrate that this method effectively characterizes the distribution of stress field and displacement field at closed crack tips. Moreover, we elucidate that wing cracks are primarily formed due to tension-shear coupling effects. The solutions for the stress field and displacement field at the crack tip are obtained using the superposition principle. The distribution of the plastic zone at the crack tip is analyzed based on the M-C (Mohr-Coulomb) criterion. Subsequently, an analysis is conducted to investigate the influence of crack angle, confining pressure, and material properties on stress field, displacement field, plastic zone, and crack propagation direction. Lower crack angles and higher confining pressures effectively suppress slip between crack surfaces by reducing tension-shear coupling effects and inhibiting wing foil crack development. The results further indicate that the rock cohesion and internal friction angle exert negligible influence on the stress field, displacement field, plastic zone shape at the crack tip, as well as the growth direction of new cracks. The results demonstrate the effective representation of stress field and displacement field at the closed crack tip using this method. The stress distribution at the crack tip reveals that the tension-shear coupling effect primarily contributes to wing crack formation. Lower crack angles and higher confining pressures effectively suppress surface slip, reduce tension-shear coupling effects, and inhibit wing crack propagation. Furthermore, material properties do not influence the crack propagation angle, stress field, or displacement field.

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Closed-Form Solutions for the Mode ii Crack tip Plastic Zone Shape

Cited by 20 publications

References 3 publications

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces

Fracture Mechanical Analysis of Thin-Walled Cylindrical Shells with Cracks

Analytical solution of the stress field and plastic zone at the tip of a closed crack

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