Stress intensity factors for two-dimensional crack problems using constrained finite elements

1985 ◽  
Vol 28 (2) ◽  
pp. 55-68 ◽  
Author(s):  
G. Ogen ◽  
B. Schiff
Keyword(s):  
Stress Intensity ◽  
Finite Elements ◽  
Stress Intensity Factors ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Crack Problems

scholarly journals Stiffness Derivative Finite Element Technique to Determine Nodal Weight Functions With Singularity Elements

1983 ◽  
Author(s):  
George T. Sha
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Weight Functions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Crack Face ◽  
Crack Geometry ◽  
Crack Problems

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements. The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ(rs), is equivalent to loading the cracked body with remote loads, which produces σ(rs) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficient calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated. In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, (rs), from crack-tip has been successfully demonstrated by the following equation: h a , r s = A a √ r s + B a + C a √ r s + D a r s Coefficients A(a), B(a), C(a) and D(a), which are functions of crack length (a), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients A, B, C and D of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry, resulted in a total loss of accuracy of less than 1%.

Stress Intensity Factors for Unequal Longitudinal-Radial Cracks in Thick-Walled Cylinders

1991 ◽  
Vol 113 (1) ◽  
pp. 22-27 ◽  
Author(s):  
J. L. Desjardins ◽  
D. J. Burns ◽  
R. Bell ◽  
J. C. Thompson
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Finite Elements ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Radial Cracks ◽  
Good Agreement

Finite elements and two-dimensional photoelasticity have been used to analyze thick-walled cylinders which contain arrays of straight-fronted, longitudinal-radial cracks of unequal depth. The stress intensity factor K1 has been computed for the dominant crack and for some of the surrounding cracks. Cylinders with 2, 4, 6, 8, 16, 36 and 40 cracks have been considered. Good agreement has been obtained between the experimental and the numerical results and, for cylinders with 2 or 4 cracks, with previously published predictions. The results for all of the foregoing cases are used to develop simple, approximate techniques for estimating K1 for the dominant crack, when the total number of cracks is different from those that have been considered herein. Estimates of K1 obtained by these techniques agree well with corresponding finite element results.

Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Ratnesh Khandelwal ◽  
J. M. Chandra Kishen
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
The Other ◽  
Weight Functions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Analogy Method ◽  
Elastic Bodies ◽  
Crack Problems ◽  
Finite Crack

In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.

Improved crack analysis of two-dimensional functionally graded materials by enriched natural element method

2020 ◽  
Vol 234 (10) ◽  
pp. 2012-2023
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

The numerical calculation of stress intensity factors of two-dimensional functionally graded materials is introduced by an enriched Petrov–Galerkin natural element method (enriched PG-NEM). The overall trial displacement field is basically approximated in terms of Laplace interpolation functions and it is enriched by the near-tip asymptotic displacement field. The overall strain and stress fields which were approximated by PG-NEM were smoothened and enhanced by the patch recovery. The modified interaction integral [Formula: see text] is used to evaluate the stress intensity factors of functionally graded materials with the spatially varying elastic modulus. The validity of present method is justified through the evaluation of crack-tip stress distributions and the stress intensity factors of four numerical examples. It has been found that the proposed method effectively and successfully captures the near-tip stress singularity with a remarkably improved accuracy, even with the remarkably coarse grid, when compared with an extremely fine grid and the analytical and numerical reference solutions.

Stress Intensity Factors for Semi-Elliptical Surface Cracks With Flaw Aspect Ratio Beyond the ASME XI Limit

2009 ◽  
Author(s):  
Christian Malekian ◽  
Eric Wyart ◽  
Michael Savelsberg ◽  
Anne Teughels ◽  
Pierre-Eric Fouquet ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Finite Elements ◽  
Aspect Ratio ◽  
Stress Intensity Factors ◽  
Large Range ◽  
Crack Depth ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Flat Plates ◽  
Circular Shape

Most of the literature about fracture mechanics considers cracks having an elliptical shape with a flaw aspect ratio a/l lower or equal to 0.5 where ‘a’ is the crack depth and ‘l’ the total length of the crack. This is also case in the ASME XI Appendix A where Stress Intensity Factors KI formulations are given for a large range of crack depths and for a flaw aspect ratio a/l between 0 and 0.5. The limitation to 0.5 corresponds to a semi-circular shape for surface cracks and to a circular shape for subsurface cracks. This limitation does not seem to be inspired by a theoretical limitation nor by a computational limit. Moreover, it appears that limiting the ratio a/l to 0.5 may generate in some cases some unnecessary conservatism in flaw analysis. The present article specifically deals with the more unusual narrow cracks having a/l >0.5, in the case of surface cracks in infinite flat plates. Several Finite-Elements calculations are performed to compute KI for a large range of crack depths and for 4 typical load cases (uniform, linear, quadratic and cubic). The results can be presented with the same formalism as in the ASME XI Appendix A, such that the work can provide an extension of the ASME coefficients in table A-3320-1&2. By doing the study, one had the opportunity to compare the results obtained by two different Finite-Elements softwares (Systus and Ansys), each one with a different cracked mesh. In addition, a comparison has been made for some cases with results obtained by a XFEM approach (eXtended Finite-Element Method), where the crack does not need to be meshed in the same way as in classical Finite-Elements. The results indicate how the KI can be reduced when considering the real flaw aspect ratio instead of the conventional semi-circular flaw shape. They also show that, for specific theoretical stress distributions, it is not always possible to reduce the analysis of KI to only 2 points, namely the crack surface point and the crack deepest point. The crack growth evaluation of such unusual crack shape should still be investigated to verify whether simple rules can be established to estimate the evolution of the crack front.

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