An Infinite Sequence of Collinear Cracks Subjected to Concentrated Loads

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xiangqiao Yan ◽  
Yintao Wei
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Infinite Sequence ◽  
Numerical Approach ◽  
High Accuracy ◽  
Concentrated Loads ◽  
Intensity Factors ◽  
Collinear Cracks ◽  
Numerical Examples ◽  
Very High

A numerical approach to an infinite sequence of collinear cracks is presented in this paper. Numerical examples are included to illustrate the accuracy of the numerical approach. Specifically, an infinite sequence of collinear cracks subjected to concentrated loads is analyzed using the numerical approach. Many numerical results of the stress intensity factors (SIFs) are given. In addition, an experiential formula to calculate the SIFs of the infinite sequence of collinear cracks is presented. Numerical examples show that the experiential formula has very high accuracy.

Stress Intensity Factors of Multiple Cracked Sheet With Riveted Stiffeners

1991 ◽  
Vol 113 (3) ◽  
pp. 280-284 ◽  
Author(s):  
T. Nishimura
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Fredholm Integral Equations ◽  
Multiple Cracks ◽  
Basic Solution ◽  
Intensity Factors ◽  
Single Crack ◽  
Numerical Examples ◽  
Unknown Density

A new method is proposed for analyzing the stress intensity factors of multiple cracks in a sheet reinforced with riveted stiffeners. Using the basic solution of a single crack and taking unknown density of surface tractions and fastener forces, Fredholm integral equations and compatibility equations of displacements among the sheet, fasteners, and stiffeners are formulated. After solving the unknown density, the stress intensity factors of multiple cracks in the sheet are determined. Some numerical examples are analyzed.

An Efficient and Accurate Numerical Method of Stress Intensity Factors Calculation of a Branched Crack

2005 ◽  
Vol 72 (3) ◽  
pp. 330-340 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Extension ◽  
Crack Tip ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Displacement Discontinuity Method ◽  
Intensity Factors ◽  
Constant Displacement ◽  
The Right

Based on the analytical solution of Crouch to the problem of a constant discontinuity in displacement over a finite line segment in an infinite elastic solid, in the present paper, the crack-tip displacement discontinuity elements, which can be classified as the left and the right crack-tip elements, are presented to model the singularity of stress near a crack tip. Furthermore, the crack-tip elements together with the constant displacement discontinuity elements presented by Crouch and Starfied are used to develop a numerical approach for calculating the stress intensity factors (SIFs) of general plane cracks. In the boundary element implementation, the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called the hybrid displacement discontinuity method (HDDM). Numerical examples are given and compared with the available solutions. It can be found that the numerical approach is simple, yet very accurate for calculating the SIFs of branched cracks. As a new example, cracks emanating from a rhombus hole in an infinite plate under biaxial loads are taken into consideration. The numerical results indicate the efficiency of the present numerical approach and can reveal the effect of the biaxial load on the SIFs. In addition, the hybrid displacement discontinuity method together with the maximum circumferential stress criterion (Erdogan and Sih) becomes a very effective numerical approach for simulating the fatigue crack propagation process in plane elastic bodies under mixed-mode conditions. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the HDDM. Crack propagation is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented.

scholarly journals Thermoelastic Analysis for Two Collinear Cracks in an Orthotropic Solid Disturbed by Antisymmetrical Linear Heat Flow

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Bing Wu ◽  
Jun-gao Zhu ◽  
Daren Peng ◽  
Rhys Jones ◽  
Shi-hu Gao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Heat Flow ◽  
Intensity Factor ◽  
Thermal Resistance ◽  
Integral Equations ◽  
Stress Intensity Factors ◽  
Mode Ii ◽  
Intensity Factors ◽  
Collinear Cracks

The problem of two collinear cracks in an orthotropic solid under antisymmetrical linear heat flow is investigated. It is assumed that there exists thermal resistance to heat conduction through the crack region. Applying the Fourier transform, the thermal coupling partial differential equations are transformed to dual integral equations and then to singular integral equations. The crack-tip thermoelastic fields including the jumps of temperature and elastic displacements on the cracks and the mode II stress intensity factors are obtained explicitly. Numerical results show the effects of the geometries of the cracks and the dimensionless thermal resistance on the temperature change and the mode II stress intensity factors. Also, FEM solutions for the stress intensity factor K are used to compare with the solutions obtained using the method. It is revealed that the friction in closed crack surface region should be considered in analyzing the stress intensity factor K.

Stress intensity factors in elastic plates with re-entrant corners asymmetrically loaded

1980 ◽  
Vol 15 (4) ◽  
pp. 195-200 ◽  
Author(s):  
P S Theocaris ◽  
J Prassianakis
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
High Accuracy ◽  
Complex Stress ◽  
Theoretical Solution ◽  
Polar Coordinates ◽  
Elastic Plates ◽  
Intensity Factors ◽  
Asymmetric Stress ◽  
Stress States

The method of reflected caustics was extended to evaluate the complex stress intensity factors at the roots of re-entrant corners in elastic plates under generalized plane-stress conditions. The plates were considered loaded under a general mode of loading creating asymmetric stress states at the corners and, thus, engendering complex stress intensity factors at these zones. For the evaluation of the complex stress intensity factors the coordinates of at least two points on the caustics are necessary whose polar coordinates on the respective initial curves on the specimen are defined in advance. These experimental data must be introduced into a system of six equations, four of which are linear and the remaining two non-linear. The solution of this system yields the components of the complex stress intensity factors with a high accuracy, independently of the form and shape of the caustics developed around the roots of the corners. This high accuracy was achieved among others by the fact that two terms in the asymptotic expansion of Muskhelishvili's complex stress function Φ(z) are taken into consideration for the evaluation of stress intensity factors. The method was applied first to a symmetric notch whose theoretical solution is known, so that the accuracy of the method could be checked, and afterwards to an asymmetrically loaded notch whose theoretical solution does not exist. For this case a recurrent procedure was applied for checking the accuracy of the experimental results.

ANALYSIS OF GENERALIZED STRESS INTENSITY FACTORS OF V-SHAPED NOTCH PROBLEMS BY FEM

2013 ◽  
Vol 10 (06) ◽  
pp. 1350068 ◽  
Author(s):  
XUE-CHENG PING ◽  
MENG-CHENG CHEN ◽  
NAO-AKI NODA ◽  
YI-HUA XIAO
Keyword(s):  
Finite Element Method ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Present Method ◽  
Analytical Form ◽  
Intensity Factors ◽  
Numerical Examples ◽  
Elastic Bodies ◽  
Generalized Stress Intensity Factors ◽  
Refined Meshes

This paper deals with a-finite element method (FEM) based on a V-shaped notch corner tip stresses to solve generalized stress intensity factors (GSIFs) in 2D elastic bodies. The method does not need extremely refined meshes and special elements accounting for the analytical form of singularities around the V-shaped notch corner tip. The generalized stress intensity factors of the V-shaped notch problems are evaluated from the ratios of FEM stress values at the notch corner tip for a given problem and a reference one. Several numerical examples show that present method is effective and applicable to dealing with the V-shaped notch problems.

scholarly journals Internal and Edge Cracks in a Plate of Finite Width Under Bending

1983 ◽  
Vol 50 (3) ◽  
pp. 621-629 ◽  
Author(s):  
H. Boduroglu ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Internal Crack ◽  
Finite Width ◽  
Free Boundaries ◽  
Intensity Factors ◽  
Collinear Cracks ◽  
Shear Theory ◽  
Title Problem ◽  
Edge Cracks

In this paper the title problem is studied by using Reissner’s transverse shear theory. The main purpose of the paper is to investigate the effect of stress-free boundaries on the stress intensity factors in plates under bending. Among the results found particularly interesting are those relating to the limiting cases of the crack geometries. The numerical results are given for a single internal crack, two collinear cracks, and two edge cracks. Also studied is the effect of Poisson’s ratio on the stress intensity factors.

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