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.

Complex Stress Intensity Factors in Bent Plates With Cracks

1982 ◽  
Vol 49 (1) ◽  
pp. 87-96 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Stress ◽  
Intensity Factors ◽  
Simple Method ◽  
Cracked Plates ◽  
Crack Tips ◽  
Asymmetric Bending ◽  
Bent Plates

The experimental method of caustics was applied to the study of asymmetric bending of isotropic cracked plates and to the determination of the complex stress intensity factors (S.I.F’s) at the crack tips. It was shown that the method of reflected caustics is convenient for detecting and evaluating both KI and KII stress intensity factors. Based on the singular approximation of the elastic solution around the crack tip, the theory of formation of the caustics was developed and related to the evaluation of both components of stress intensity factors. It was also shown that the generalized method of caustics, known as the method of pseudocaustics, is a potential and simple method for determining S.I.F’s in cracked plates submitted to bending. Experimental evidence with specimens made either of optically inert materials, such as plexiglass, or of any opaque material like steel, and elastically loaded, has corroborated the theoretical results.

Stress-Intensity Factors and Complex Path-Independent Integrals

1980 ◽  
Vol 47 (2) ◽  
pp. 342-346 ◽  
Author(s):  
P. S. Theocaris ◽  
N. I. Ioakimidis
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Analysis ◽  
Complex Stress ◽  
Complex Potentials ◽  
Intensity Factors ◽  
Antiplane Elasticity ◽  
Elasticity Problems ◽  
Crack Tips

Path-independent integrals about crack tips may be used to estimate stress-intensity factors at crack tips in plane and antiplane elasticity problems. In this paper a new class of such integrals is established by using complex stress functions and the trivial application of the Cauchy theorem of complex analysis. Both the simple Westergaard complex potentials of plane and antiplane elasticity and the more general Muskhelishvili complex potentials will be used for the construction of appropriate path-independent integrals. Two applications of these integrals to the theoretical determination of stress-intensity factors at crack tips are presented. An optical method for the experimental determination of stress-intensity factors at crack tips, based on the use of appropriate complex path-independent integrals, is also proposed.

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

scholarly journals Interaction between line cracks in an orthotropic layer

2002 ◽  
Vol 29 (1) ◽  
pp. 31-42 ◽  
Author(s):  
Subir Das
Keyword(s):  
Fourier Transform ◽  
Stress Intensity ◽  
Finite Thickness ◽  
Intensity Factors ◽  
Orthotropic Layer ◽  
Finite Hilbert Transform ◽  
Crack Tips ◽  
The Fourier Transform ◽  
Analytical Expressions ◽  
Elastostatic Problem

We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic layer of finite thickness2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips are obtained for largeh. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the layer.

Weight Functions for an External Longitudinal Semi-Elliptical Surface Crack in a Thick-Walled Cylinder

1997 ◽  
Vol 119 (1) ◽  
pp. 74-82 ◽  
Author(s):  
A. Kiciak ◽  
G. Glinka ◽  
D. J. Burns
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Reference Stress ◽  
Pressurized Cylinder ◽  
Walled Cylinder

Mode I weight functions were derived for the deepest and surface points of an external radial-longitudinal semi-elliptical surface crack in a thick-walled cylinder with the ratio of the internal radius to wall thickness, Ri/t = 1.0. Coefficients of a general weight function were found using the method of two reference stress intensity factors for two independent stress distributions, and from properties of weight functions. Stress intensity factors calculated using the weight functions were compared to the finite element data for several different stress distributions and to the boundary element method results for the Lame´ hoop stress in an internally pressurized cylinder. A comparison to the ASME Pressure Vessel Code method for deriving stress intensity factors was also made. The derived weight functions enable simple calculations of stress intensity factors for complex stress distributions.

Acousto-elastic measurement of stress and stress intensity factors around crack tips

Ultrasonics ◽  
1983 ◽  
Vol 21 (2) ◽  
pp. 57-64 ◽  
Author(s):  
A.V. Clark ◽  
R.B. Mignogna ◽  
R.J. Sanford
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Intensity Factors ◽  
Crack Tips
Sign in / Sign up

Export Citation Format

Share Document