Hole Crack Problems in Infinite Plate Subjected to Uniform Internal Pressure

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Xiangqiao Yan ◽  
Baoliang Liu
Keyword(s):  
Internal Pressure ◽  
Crack Problem ◽  
Infinite Plate ◽  
Elliptical Hole ◽  
Displacement Discontinuity ◽  
Intensity Factors ◽  
Center Crack ◽  
Crack Problems ◽  
Amplifying Effect ◽  
Hole Geometry

This brief deals with crack(s) emanating from a hole in infinite plate subjected to uniform internal pressure. Such a crack problem is called a hole crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, three hole crack problems (an elliptical hole crack problem, a rhombus hole crack problem, and a triangle hole crack problem) in infinite plate subjected to uniform internal pressure are analyzed in detail. By changing hole geometry form and hole geometry parameters and by comparing the stress intensity factors (SIFs) of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack(s) emanating from the hole. The shielding and amplifying effects are varied with hole geometry form and hole geometry parameters.

Hole Crack Problems in Infinite Elastic Plate in Tension

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xiangqiao Yan ◽  
Baoliang Liu
Keyword(s):  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
Infinite Plate ◽  
Elliptical Hole ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Center Crack ◽  
Crack Problems ◽  
Hole Geometry

This paper deals with crack(s) emanating from a hole in infinite elastic plate in tension. Such a crack problem is called a hole crack problem for short. By extending Buckner’s principle suited for a crack to a hole crack problem in infinite plate in tension, here, the original problem (the hole crack problem in infinite plate in tension) is divided into a homogeneous problem (the one without hole crack) subjected to remote loads and a hole crack problem in an unloaded body with applied tractions on the surfaces of the hole and crack. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of a hybrid displacement discontinuity (a boundary element method) proposed recently by Yan. Numerical examples are included to illustrate that the numerical approach is very simple and effective for analyzing the hole crack problem in infinite plate in tension. By using the proposed approach, three hole crack problems (i.e., a pair of cracks emanating from an elliptical hole, a pair of cracks emanating from a rhombus hole, and a crack emanating from a triangular hole in infinite plate in tension) are analyzed in detail. By changing the hole geometry form and the hole geometry parameters and by comparing the SIFs of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and the hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack(s) emanating from the hole. The shielding and amplifying effects varied with the hole geometry form and the hole geometry parameters.

An Effective Numerical Approach for Multiple Void-Crack Interaction

2005 ◽  
Vol 73 (4) ◽  
pp. 525-535 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
General System ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Crack Problems ◽  
Element Method

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

Corner Crack at the Bore of a Rotating Disk

1976 ◽  
Vol 98 (4) ◽  
pp. 465-470 ◽  
Author(s):  
A. S. Kobayashi ◽  
N. Polvanich ◽  
A. F. Emery ◽  
W. J. Love
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Plate ◽  
Rotating Disk ◽  
Single Edge ◽  
Intensity Factors ◽  
Corner Crack ◽  
Aspect Ratios ◽  
Crack Problems ◽  
Corner Cracks

Stress intensity factors of corner cracks at the bore of a rotating disk are estimated from the stress intensity factor of a quarter-elliptical crack in a quarter infinite solid and pressurized by the hoop stress. Curvature effect of the bore is incorporated through a curvature correction factor derived from the stress intensity factors of a single edge-cracked bore in a large plate and a single edge-cracked semi-infinite plate. Stress intensity factors for quarter-elliptical cracks with crack aspect ratios of b/a = 0.2, 0.4, and 0.98 at crack depths of b/Ri = 0.1, 0.3 and 1.0 in a rotating disk with R0/Ri = 8 are determined. Application of the developed procedure to corner crack problems at a through-bolt hole is indicated.

An Empirical Formula for Stress Intensity Factors of Double Edge Half-Circular-Hole Cracks in a Rectangular Sheet in Tension

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Stress Intensity ◽  
Boundary Element Method ◽  
Circular Hole ◽  
Stress Intensity Factors ◽  
Empirical Formula ◽  
Crack Problem ◽  
Displacement Discontinuity ◽  
Displacement Discontinuity Method ◽  
Intensity Factors ◽  
Double Edge

This note deals with the stress intensity factors (SIFs) for double edge half-circular-hole cracks in a rectangular sheet in tension by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is simple, yet accurate for evaluating the SIFs of the crack problem.

A Surface Crack in Shells Under Mixed-Mode Loading Conditions

1988 ◽  
Vol 55 (4) ◽  
pp. 795-804 ◽  
Author(s):  
P. F. Joseph ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Mixed Mode ◽  
Shallow Shell ◽  
Crack Problem ◽  
Three Dimensional ◽  
Loading Conditions ◽  
Intensity Factors ◽  
Crack Problems

The problem of a shallow shell containing a surface crack and subjected to general loading conditions is considered. It is shown that, as in the three-dimensional elasticity formulation, the mode I state can be separated whereas modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions. A shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell is then considered. Reissner’s transverse shear theory is used to formulate the problem by assuming that the shell is subjected to all five moment and stress resultants. The uncoupled antisymmetric problem is solved for cylindrical and toroidal shells having a surface crack in various orientations and the primary and the secondary stress intensity factors are given. The results show that, unlike the through crack problems, in surface cracks the effect of shell curvature on the stress intensity factors is relatively insignificant.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Analysis of Multiple Rigid-Line Inclusions for Application to Bio-Materials

2007 ◽  
Author(s):  
Pawan S. Pingle ◽  
Larissa Gorbatikh ◽  
James A. Sherwood
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Building Blocks ◽  
Duality Principle ◽  
Inclusion Problem ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Aspect Ratios ◽  
Rigid Line

Hard biological materials such as nacre and enamel employ strong interactions between building blocks (mineral crystals) to achieve superior mechanical properties. The interactions are especially profound if building blocks have high aspect ratios and their bulk properties differ from properties of the matrix by several orders of magnitude. In the present work, a method is proposed to study interactions between multiple rigid-line inclusions with the goal to predict stress intensity factors. Rigid-line inclusions provide a good approximation of building blocks in hard biomaterials as they possess the above properties. The approach is based on the analytical method of analysis of multiple interacting cracks (Kachanov, 1987) and the duality existing between solutions for cracks and rigid-line inclusions (Ni and Nasser, 1996). Kachanov’s method is an approximate method that focuses on physical effects produced by crack interactions on stress intensity factors and material effective elastic properties. It is based on the superposition technique and the assumption that only average tractions on individual cracks contribute to the interaction effect. The duality principle states that displacement vector field for cracks and stress vector-potential field for anticracks are each other’s dual, in the sense that solution to the crack problem with prescribed tractions provides solution to the corresponding dual inclusion problem with prescribed displacement gradients. The latter allows us to modify the method for multiple cracks (that is based on approximation of tractions) into the method for multiple rigid-line inclusions (that is based on approximation of displacement gradients). This paper presents an analytical derivation of the proposed method and is applied to the special case of two collinear inclusions.

The Axisymmetric Crack Problem in a Nonhomogeneous Medium

1993 ◽  
Vol 60 (2) ◽  
pp. 406-413 ◽  
Author(s):  
M. Ozturk ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Shear Modulus ◽  
Mixed Mode ◽  
Crack Opening ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Nonhomogeneous Medium ◽  
Intensity Factors ◽  
Simple Simulation ◽  
Graded Properties

In this paper, the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by μ = μ0eαz. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed-mode problem and is formualated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a function of the nonhomogeneity parameter a for various loading conditions. Also given are some sample results showing the crack opening displacements.

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