Analytical Solution for the Circular Orifice Problem with Four-Cracks

2015 ◽  
Vol 778 ◽  
pp. 10-17
Author(s):  
Lu Guan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Complex Analysis ◽  
Exact Analytical Solution ◽  
Plane Elasticity ◽  
Crack Problems ◽  
Circular Orifice ◽  
Plane Elasticity Problem

Using the method of complex analysis, the paper investigates the plane elasticity problem of circular orifices with four-cracks through conformal mapping, and provides an exact analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated circular orifices with three-cracks, symmetrical four-cracks, asymmetrical collinear double-cracks, and symmetrical collinear double-cracks; as well as the crack problems of asymmetrical cross-shaped cracks, symmetrical cross-shaped cracks, and T-shaped cracks.

An Exact Analytical Solution for Star-Shaped Cracks

2015 ◽  
Vol 1094 ◽  
pp. 458-463 ◽  
Author(s):  
Zhu Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Analytical Solution ◽  
Complex Analysis ◽  
Exact Analytical Solution ◽  
Plane Elasticity ◽  
Type I ◽  
Griffith Crack ◽  
Shaped Crack ◽  
Plane Elasticity Problem

Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.

A Stress Analysis of the Circular Orifice Problem for 2k Periodic Radial Cracks

2015 ◽  
Vol 744-746 ◽  
pp. 1611-1617
Author(s):  
Lu Guan
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Conformal Mapping ◽  
Stress Analysis ◽  
Complex Analysis ◽  
Crack Tip ◽  
Circular Orifice ◽  
Radial Cracks

Using the method of complex analysis, the study investigates the circular orifice problem for 2k periodic radial cracks through constructing conformal mapping, and provides an analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated the circular orifice problems of cross-shaped cracks, symmetrical eight-cracks, single cracks, symmetrical double-cracks, and symmetrical four-cracks.

Analytical Solution of the Star-Shaped Crack in One-Dimensional Hexagonal Quasicrystals

2013 ◽  
Vol 838-841 ◽  
pp. 2254-2261
Author(s):  
Lu Guan ◽  
Zhu Chen
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Conformal Mapping ◽  
Complex Analysis ◽  
Crack Tip ◽  
One Dimensional ◽  
Shaped Crack ◽  
Shear Problem

With the use of complex analysis, and by introducing adequate conformal mapping, the anti-shear problem of the star-shaped crack in One-dimensional Hexagonal Quasicrystals was studied. An analytical solution to the crack tip stress intensity factor is found.

Computation of Stress Intensity Factor for Multiple Cracks Using Singular Finite Element

2011 ◽  
Vol 214 ◽  
pp. 75-79 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail ◽  
A. Zulkifli
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Crack Width ◽  
Width Ratio ◽  
Multiple Cracks ◽  
Two Dimensional ◽  
Interval Ratio

The simplification of two dimensional approaches in singular finite elements has promoted the method to be used in the formulation of stress intensity factor (SIF) of multiple cracks in finite body. The effect of shielding and amplification are considered in defining the SIF. As been observed, the current available analytical approximations are more restricted to several assumptions. The more accurate and less restricted method has motivated this study. This paper presents the investigation of singular finite elements applied in two dimensional finite element models subjected to different crack-width ratio and cracks interval ratio. The newly finite element formulations are resulted with good agreement with theoretical statement compared to analytical solution. The weak points of presented analytical solution are discussed regards to the influence of crack width ratio and cracks interval ratio.

scholarly journals Stress Intensity Factor for Interface Cracks in Bimaterials Using Complex Variable Meshless Manifold Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfen Gao ◽  
Gaofeng Wei
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Complex Variable ◽  
Interfacial Crack ◽  
Dissimilar Materials ◽  
Complex Stress ◽  
Interface Cracks ◽  
Interfacial Cracks ◽  
Crack Problems

This paper describes the application of the complex variable meshless manifold method (CVMMM) to stress intensity factor analyses of structures containing interface cracks between dissimilar materials. A discontinuous function and the near-tip asymptotic displacement functions are added to the CVMMM approximation using the framework of complex variable moving least-squares (CVMLS) approximation. This enables the domain to be modeled by CVMMM without explicitly meshing the crack surfaces. The enriched crack-tip functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The complex stress intensity factors for bimaterial interfacial cracks were numerically evaluated using the method. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized.

Structure of Near-Tip Stress Field and Variation of Stress Intensity Factor for a Crack in a Transversely Graded Material

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Sarveshwar C. Wadgaonkar ◽  
Venkitanarayanan Parameswaran
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Modulus ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Elastic Properties ◽  
Crack Front ◽  
Homogeneous Material ◽  
Graded Materials ◽  
Crack Problems

The existing studies on the behavior of cracks in continuously graded materials assume the elastic properties to vary in the plane of the crack. In the case of a plate graded along the thickness and having a crack in its plane, the elastic properties will vary along the crack front. The present study aims at investigating the effect of elastic gradients along the crack front on the structure of the near-tip stress fields in such transversely graded materials. The first four terms in the expansion of the stress field are obtained by the eigenfunction expansion approach (Hartranft and Sih, 1969, “The Use of Eigen Function Expansion in the General Solution of Three Dimensional Crack Problems,” J. Math. Mech., 19(2), pp. 123–138) assuming an exponential variation of the elastic modulus. The results of this part of the study indicated that for an opening mode crack, the angular structure of the first three terms in the stress field expansion corresponding to r(−1∕2), r0, and r1∕2 are identical to that given by Williams’s solution for homogeneous material (Williams, 1957, “On the Stress Distribution at the Base of a Stationary Crack,” ASME J. Appl. Mech., 24, pp. 109–114). Transversely graded plates having exponential gradation of elastic modulus were prepared, and the stress intensity factor (SIF) on the compliant and stiffer face of the material was determined using strain gauges for an edge crack subjected to pure bending. The experimental results indicated that the SIF can vary as much as two times across the thickness for the gradation and loading considered in this study.

An Analytical Solution for Dynamic Stress Intensity, Kd, under Impact Loading

2010 ◽  
Vol 452-453 ◽  
pp. 413-416
Author(s):  
A. Malekzadeh ◽  
Saeid Hadidi-Moud
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Impact Loading ◽  
Dynamic Stress ◽  
Research Work ◽  
Dynamic Stress Intensity Factor ◽  
Experimental Studies ◽  
Critical Stress Intensity Factor

Characterisation of failure of components subjected to impact fatigue has received much interest in recent years. Critical stress intensity factor, i.e. fracture toughness, is a characteristic parameter for fracture conditions. Evaluation of this parameter is therefore of primary importance in the study of structures containing cracks. Due to its significance numerous research work have been carried out to provide dynamic stress intensity descriptions under cyclic, impulse and impact loading conditions. These methods are mainly based on numerical analyses and / or experimental techniques led to a range of approximate models. This paper firstly provides a review of fatigue failure due to impact loading and explains the principles of impact mechanics concepts including impact loading, stress wave equation and resulting stress distributions. Then, based on available experimental studies on developing and propagating cracks under impact loading, suggests a simple model leading to an approximate analytical solution for determination of dynamic stress intensity factor, kd under high strain rate loading. Calculated values based on the suggested solution compare well with the experimental data.

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