Stress Distribution Near Internal Crack Tips for Longitudinal Shear Problems

1965 ◽  
Vol 32 (1) ◽  
pp. 51-58 ◽  
Author(s):  
G. C. Sih
Keyword(s):  
Stress Distribution ◽  
Stress Singularity ◽  
Crack Tip ◽  
Longitudinal Shear ◽  
Complex Stress ◽  
Internal Crack ◽  
Vertex Angle ◽  
Crack Tips ◽  
Bending Problems ◽  
Half Power

A method is developed for finding the stress distribution in a cracked body under longitudinal shear and applied to solve a number of problems. Stress solutions are obtained in closed form and discussed in connection with the Griffith-Irwin theory of fracture. The results indicate that current fracture-mechanics theories may be applied directly to longitudinal shear problems. More specifically, the character of the stress distribution near the vertex of a sector cylinder in shear is examined. The inverse half-power law of the stress singularity at a crack tip may be verified by taking a vertex angle of 2π. In addition, crack-tip, stress-intensity factors are defined and evaluated from a complex stress function in a manner similar to those previously given for extension and plate-bending problems. Results of such studies clarified the behavior of branched cracks and other crack systems of interest.

An Arc-Shaped Debonding Crack Opened by Internal Pressure

1998 ◽  
Vol 14 (2) ◽  
pp. 83-89
Author(s):  
Ru-Min Chao
Keyword(s):  
Internal Pressure ◽  
Crack Opening ◽  
Stress Singularity ◽  
Crack Tip ◽  
Singular Integral Equations ◽  
Contact Length ◽  
Infinite Matrix ◽  
Closed Crack ◽  
Opening Displacement ◽  
Crack Tips

AbstractIn this paper, the problem of a debonding crack at the interface between a circular fiber and an infinite matrix opened by internal pressure is discussed. We concentrated on the effect of contact near the crack tips within the content of linear elastic fracture mechanics. The Muskhelishvili complex variable method is used in this analysis. The frictionless contact crack tip condition is adopted in this study in order to avoid the oscillatory stress singularity at the crack tip as shown in the classical solution. By using the crack opening displacement gradient as the primary variable, the problem is then reduced to two coupled singular integral equations, and the final discretization of the equations employs the method given by Erdogan and Gupta (1972). The comprehensive numerical results of stress fields and the mode II SIF at the closed crack tip will be given in the paper. It is also found from the numerical evidences that the contact length at the crack tip is independent of one of the Dundurs parameters, α.

Stress Distribution in a Nonhomogeneous Elastic Plane With Cracks

1963 ◽  
Vol 30 (2) ◽  
pp. 232-236 ◽  
Author(s):  
Fazil Erdogan
Keyword(s):  
Stress Intensity ◽  
Stress State ◽  
Stress Singularity ◽  
Complex Stress ◽  
Elastic Plane ◽  
Stress Singularities ◽  
Intensity Factors ◽  
Line Segments ◽  
Straight Line ◽  
Crack Tips

The problem of two semi-infinite elastic planes with different elastic properties bonded to each other along a finite number of straight-line segments and subjected to loads at infinity is formulated and the solution of the problem is reduced to the evaluation of ordinary integrals. The solutions for the cases with one and two bonding segments are given. For the general case, the stress state near the crack tips is analyzed and it is shown that the stress singularity is in the form of r−1/2, r being the distance from the crack tip. Finally, the stress-intensity factors, which are used in the fracture mechanics and which can be taken as the measure of the strength of stress singularities, are expressed in terms of the complex stress function.

Strip Yield Analysis of Plastic Zone Coalescence for Collinear Edge Crack and Internal Crack in a Semi-Infinite Sheet

1999 ◽  
Vol 122 (1) ◽  
pp. 86-89 ◽  
Author(s):  
Toshihiko Nishimura
Keyword(s):  
Plastic Zone ◽  
Integral Equations ◽  
Edge Crack ◽  
Stress Singularity ◽  
Crack Tip ◽  
Internal Crack ◽  
Crack Face ◽  
Plastic Zones ◽  
Crack Tip Opening ◽  
Remote Stress

The coalescence conditions of plastic zones are calculated for an edge crack and an internal crack in a semi-infinite sheet. The cracks and their plastic zones are treated as a fictitious crack, and integral equations are formulated on equilibrium of surface traction, no stress singularity at the crack tip, and zero crack face displacement at the coalesced point of plastic zones. The integral equations are iteratively solved, and critical values of remote stress, plastic zone sizes, and crack tip opening displacements are determined. Numerical results for an edge crack and an internal crack due to remote stress are presented. [S0094-9930(00)00301-2]

A mode III crack at the interface between two nonlinear materials

1990 ◽  
Vol 429 (1876) ◽  
pp. 247-257 ◽  
Keyword(s):  
Power Law ◽  
Stress Singularity ◽  
Crack Tip ◽  
Longitudinal Shear ◽  
Homogeneous Material ◽  
Stress Singularities ◽  
Mode Iii ◽  
Nonlinear Materials ◽  
Mode Iii Crack

The stress singularity at the tip of a crack at the interface between two different power-law materials under mode III loading (longitudinal shear) is considered. By considering expansions at the crack tip in each region, and matching across the interface ahead of the crack, it is found that the stress singularities are the same in each material, and correspond to that for a crack in a homogeneous material with hardening exponent equal to the maximum of the hardening exponents of the two materials. The displacements near the crack tip are found to be of different orders in the two materials, and it is shown that all the crack tip energy is concentrated in the material with the largest hardening exponent. The results are illustrated by means of an example involving a displacement loaded bimaterial strip.

Blunting of a Plane Strain Crack Tip Into a Shape With Vertices

1977 ◽  
Vol 99 (4) ◽  
pp. 290-297 ◽  
Author(s):  
Robert M. McMeeking
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Crack Tip ◽  
The Body ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Crack Tips ◽  
Stress And Deformation ◽  
Material Points ◽  
Growth Of Voids

When monotonically increasing tensile opening loads are applied to a cracked, plane strain, elastic-plastic body, the crack tip will blunt until fracture occurs. At least within the rigid-plastic model for nonhardening material, the shape of the blunted tip is not unique. The blunted tip shape may have two or more sharp corners, or be smoothly curved. When the shape involves corners, the opening is predominantly accommodated by shearing of the material at the corners. This shearing transports material from the interior of the body onto the crack surface. In contrast, the smoothly blunted crack tip involves no such transfer of material points from the interior. However, the smoothly blunted crack, which was originally sharp, involves infinite strains on the crack tip surface. The crack with corners on the tip has large but finite strains on the crack tip surface. The stress and deformation field in front of a crack with two corners and with three corners on the tip, as calculated using the slip line method, is presented for the nonhardening, fully plastic, deeply cracked, double edge-notched thick panel. As in the case of the smoothly blunted crack tip, the elevated stress between the crack tips cannot be maintained very close to the crack tip, due to a lack of constraint. The stress distribution in the case of the crack tip with vertices on it differs from that of the smoothly blunted crack tip case. In particular, immediately in front of the crack tip with three corners, the stress is higher than that immediately in front of the smoothly blunted crack tip. An approximation for a power law hardening material indicates that the maximum stresses near the blunted crack tip is much the same for a crack with vertices on the tip as for a smoothly blunted crack tip. The details of the stress distribution, though, will depend on the mechanism by which the crack blunts. These results for stress and strain and some calculations of the growth of voids near the crack tips indicate the same fracture process could lead to different fracture toughnesses, depending on the type of mechanism by which the crack blunts.

Strip Yield Analysis for Multiple Cracked Sheet With Riveted Stiffeners

1993 ◽  
Vol 115 (4) ◽  
pp. 398-403 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Plastic Zone ◽  
Stress Singularity ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tips ◽  
Fictitious Crack ◽  
Crack Tip Opening

An elasto-plastic analysis is conducted based upon a strip yield model for analyzing multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown fictitious surface tractions and fastener forces, Fredholm integral equations are formulated from the equilibrium condition along multiple cracks in the sheet. In addition compatibility equations of displacements are formulated among the sheet, fasteners and stiffeners. Based upon no stress singularity at the fictitious crack tips, these equations are iteratively solved as a single system of equations. Then the unknown fictitious surface tractions, fastener forces, and plastic zone sizes ahead of the crack tips are determined. The crack tip opening displacements for a multiple cracked sheet with riveted stiffeners are determined from the derived fictitious surface tractions and plastic zone sizes. Four example calculations and predictions are presented.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

Comparison of Strip Yield and Net Section Plasticity Models for a Bar in Bending With a Single Edge Crack

2017 ◽  
Author(s):  
Wolf Reinhardt ◽  
Don Metzger
Keyword(s):  
Edge Crack ◽  
Large Scale ◽  
Stress Singularity ◽  
Crack Tip ◽  
Small Scale ◽  
Single Edge ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tip Plasticity ◽  
Stress And Deformation

The strip yield model is widely used to describe crack tip plasticity in front of a crack. In the strip yield model the stress in the plastic zone is considered as known, and stress and deformation fields can be obtained from elastic solutions using the condition that the crack tip stress singularity vanishes. The strip yield model is generally regarded to be valid to describe small scale plasticity at a crack tip. The present paper examines the behavior of the strip yield model at the transition to large-scale plasticity and its relationship to net section plasticity descriptions. A bar in bending with a single edge crack is used as an illustrative example to derive solutions and compare with one-sided and two-sided plasticity solutions.

scholarly journals A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

2020 ◽  
Vol 25 (1) ◽  
pp. 92-105
Author(s):  
Pradeep Mohan ◽  
R. Ramesh Kumar
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Power Series ◽  
Orthotropic Shell ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Power Series Solution ◽  
Element Analysis ◽  
Full Field ◽  
Analytical Technique

AbstractThe intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

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