A Direct Numerical Method for Stress and Stress-Intensity Factor in Arbitrary, Cracked, Elastic Bars Under Torsion and Longitudinal Shear

1970 ◽  
Vol 37 (4) ◽  
pp. 971-976 ◽  
Author(s):  
J. Tirosh
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Method ◽  
Crack Tip ◽  
Numerical Differentiation ◽  
Longitudinal Shear ◽  
Integral Approach ◽  
Comparative Efficiency ◽  
Local Determination

A numerical method is proposed for a direct local determination of stresses in a general twisted and sheared cracked bar. Conceptually, the method employs the integral approach of the potential theory but is modified to yield the stress components without numerical differentiation or interpolation from a potential function. A general expression for the stress-intensity factor at the crack tip is formulated. It checks favorably with the corresponding theoretical solutions. Computer running time and storage requirements for typical problems indicate the comparative efficiency of the method in addition to its relatively high accuracy near the crack tip.

Crack Tip Stress Analysis of the Steam Generator Dissimilar Steel Welded Joint under Residual Stress Field

2019 ◽  
Vol 795 ◽  
pp. 451-457
Author(s):  
Bao Yin Zhu ◽  
Xian Xi Xia ◽  
He Zheng ◽  
Guo Dong Zhang
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Numerical Method ◽  
Steam Generator ◽  
Welded Joint ◽  
Crack Tip ◽  
Residual Stress Field

An typical mode of a structural integrity failure in dissimilar steel welded joints. This paper aims at studying crack tip stress of a steam generator dissimilar welded joint under residual stress field with the method of interaction integral and XFEM. Firstly, the corresponding weak form is obtained where the initial stress field is involved, which is the key step for the XFEM. Then, the interaction integral is applying to calculate the stress intensity factor. In addition, two simple benchmark problems are simulated in order to verify the precision of this numerical method. Finally, this numerical method is applying to calculate the crack tip SIF of the addressed problem. This study finds that the stress intensity factor increases firstly then decreases with the deepening of the crack. The main preponderance of this method concerns avoiding mesh update by take advantage of XFEM when simulating crack propagation, which could avoid double counting. In addition, our obtained results will contribute to the safe assessment of the nuclear power plant steam generator.

PARAMETER AND INTERACTION STUDY OF EDGE CRACK PROBLEM USING MESHFREE METHOD

2012 ◽  
Vol 03 (04) ◽  
pp. 1250016 ◽  
Author(s):  
KAMAL SHARMA ◽  
VIVEK BHASIN ◽  
I. V. SINGH ◽  
B. K. MISHRA ◽  
K. K. VAZE
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Edge Crack ◽  
Crack Problem ◽  
Crack Tip ◽  
Integral Approach ◽  
Enrichment Technique ◽  
Crack Problems ◽  
Edge Crack Problem

In this work, element free Galerkin method (EFGM) has been used to obtain the solution of edge crack problem under mechanical loads as it provides a versatile technique to model static as well as moving crack problems without any requirement of remeshing. At first, some techniques are presented for enriching the EFG approximations near the crack tip such as extrinsic and intrinsic enrichment. Extrinsic enrichment involves the addition of solution form to the trial function, whereas the EFG basis is expanded to include few terms from crack tip solution in intrinsic enrichment. Apart from enrichment techniques, four basic techniques of smoothing meshless approximations near nonconvex boundaries are also presented such as diffraction, transparency, see through and wedge model. These techniques are then used for the parameteric analysis of an edge crack problem under mode-1 loading and results obtained using different approaches are compared with each other as well as with exact solution. Among these techniques, the extrinsic PU enrichment technique was found to be more accurate as compared to other approaches. Extrinsic PU enrichment technique has also been used for the analysis of a shear edge crack problem. In all these techniques, the value of mode-1 stress intensity factor and mode-2 stress intensity factor has been evaluated by interaction integral approach. Effect of crack orientation is also studied for different cases.

A new type of cracks adding to Griffith–Irwin cracks

2019 ◽  
Vol 485 (2) ◽  
pp. 162-165
Author(s):  
V. A. Babeshko ◽  
O. M. Babeshko ◽  
O. V. Evdokimova
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Stress Concentrations ◽  
New Type

The distinctions in the description of the conditions of cracking of materials are revealed. For Griffith–Irwin cracks, fracture is determined by the magnitude of the stress-intensity factor at the crack tip; in the case of the new type of cracks, fracture occurs due to an increase in the stress concentrations up to singular concentrations.

scholarly journals Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Bing Yang ◽  
Zhanjiang Wei ◽  
Zhen Liao ◽  
Shuwei Zhou ◽  
Shoune Xiao ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plastic Zone ◽  
Relative Error ◽  
Crack Tip ◽  
Image Correlation ◽  
Preconditioned Conjugate Gradient ◽  
Loading Process ◽  
Tip Position

AbstractIn the digital image correlation research of fatigue crack growth rate, the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor, thereby affecting the life prediction. This paper proposes a Gauss-Newton iteration method for solving the crack tip position. The conventional linear fitting method provides an iterative initial solution for this method, and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix. A noise-added artificial displacement field is used to verify the feasibility of the method, which shows that all parameters can be solved with satisfactory results. The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result, and the relative error between the two is only − 0.621%; The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip, and the maximum relative error with the test plastic zone area is − 11.29%. The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%. The crack tip coordinates, stress intensity factors, and plastic zone contour changes in the loading and unloading phases are explored. The results show that the crack tip change during the loading process is faster than the change during the unloading process; the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process; under the same load, the theoretical plastic zone during the unloading process is higher than that during the loading process.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

Plastic Stress Intensity Factors for Small Scale Yielding in Antiplane Shear by Caustics

1982 ◽  
Vol 49 (4) ◽  
pp. 754-760 ◽  
Author(s):  
P. S. Theocaris ◽  
C. I. Razem
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Tip ◽  
Antiplane Shear ◽  
Elastic Behavior ◽  
Small Scale ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
Plastic Stress

The KIII-stress intensity factor in an edge-cracked plate submitted to antiplane shear may be evaluated by the reflected caustic created around the crack tip, provided that a purely elastic behavior exists at the crack tip [1]. For a work-hardening, elastic-plastic material, when stresses at the vicinity of the crack tip exceed the yield limit of the material, the new shape of caustic differs substantially from the corresponding shape of the elastic solution. In this paper the shape and size of the caustics created at the tip of the crack, when small-scale yielding is established in the vicinity of the crack tip, were studied, based on a closed-form solution introduced by Rice [2]. The plastic stress intensity factor may be evaluated from the dimensions of the plastic caustic. Experimental evidence with cracked plates made of opaque materials, like steel, corroborated the results of the theory.

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