scholarly journals Hybrid Analytical and MLS-Based NMM for the Determination of Generalized Stress Intensity Factors

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Feng Liu ◽  
Hong Zheng ◽  
Xiuli Du
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Intensity Factors ◽  
Problem Domain ◽  
Extended Finite Element ◽  
Generalized Stress Intensity Factors ◽  
Cover Systems ◽  
Integral Procedure ◽  
Numerical Manifold

The numerical manifold method (NMM) is characterized by its two cover systems, the mathematical cover and the physical cover. In the standard NMM, the mathematical cover is required to cover the whole problem domain. In this study, however, around each crack tip we specify a small domain on which the displacement is taken as the truncated Williams’ displacement series. And accordingly all such small domains are not covered by the mathematical cover that only covers the rest of the problem domain. Meanwhile, the mathematical cover is constructed by designating all supports of the scattered nodes arising in the moving least squares interpolation as the mathematical patches. In this way, any physical patch contains no crack tip and can be approximated by polynomials. As a result, no blending element issue exists as in the extended finite element method and NMM. In addition to high precision, the proposed procedure is especially suitable for the situation where a crack tip is very close to other cracks, a case difficult to treat by the interaction integral procedure that is commonly used in the extraction of the stress intensity factors of mixed mode cracks.

scholarly journals Dynamic Mixed Mode I-II Crack Kinking Under Oblique Stress Wave Loading in Brittle Solids

1990 ◽  
Vol 57 (1) ◽  
pp. 117-127 ◽  
Author(s):  
Chien-Ching Ma
Keyword(s):  
Stress Intensity ◽  
Stress Wave ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Elastic Solid ◽  
Perturbation Parameter ◽  
Intensity Factors ◽  
Linear Superposition ◽  
Dynamic Stress Intensity Factors ◽  
Brittle Solids

The dynamic stress intensity factors of an initially stationary semi-infinite crack in an unbounded linear elastic solid which kinks at some time tf after the arrival of a stress wave is obtained as a function of kinking crack tip velocity v, kinking angle δ, incident stress wave angle α, time t, and the delay time tf. A perturbation method, using the kinking angle δ as the perturbation parameter, is used. The method relies on solving simple problems which can be used with linear superposition to solve the problem of a kinked crack. The solutions can be compared with numerical results and other approximate results for the case of tf = 0 and give excellent agreement for a large range of kinking angles. The elastodynamic stress intensity factors of the kinking crack tip are used to compute the corresponding fluxes of energy into the propagating crack-tip, and these results are discussed in terms of an assumed fracture criterion.

scholarly journals A Numerical Evaluation of SIFs of 2-D Functionally Graded Materials by Enriched Natural Element Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3581 ◽  
Author(s):  
Jin-Rae Cho
Keyword(s):  
Stress Intensity ◽  
Functionally Graded Materials ◽  
Displacement Field ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Functionally Graded ◽  
Intensity Factors ◽  
Graded Materials ◽  
Natural Element Method ◽  
Natural Element

This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.

Crack tip stress intensity factors for a crack emanating from a semi-infinite notch with application to the avoidance of fatigue in complete contacts

2008 ◽  
Vol 223 (4) ◽  
pp. 789-794 ◽  
Author(s):  
A G Philipps ◽  
S Karuppanan ◽  
N Banerjee ◽  
D A Hills
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Crack Development ◽  
Short Crack ◽  
Length Scale ◽  
Intensity Factors ◽  
Reference Length ◽  
Complete Contact ◽  
Crack Tip Stress

Crack tip stress intensity factors are found for the problem of a short crack adjacent to the apex of a notch, and lying perpendicular to one of the notch faces. Loading is represented by the two Williams eigensolutions, the ratio between which provides a reference length scale and permits a comprehensive display of the solution. The results are applied to the problem of a crack starting from the edge of a notionally adhered complete contact, and conditions for the avoidance of crack development are found.

An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures

1987 ◽  
Vol 22 (4) ◽  
pp. 203-207 ◽  
Author(s):  
M H Aliabadi ◽  
D P Rooke ◽  
D J Cartwright
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Boundary Element ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Stress Fields ◽  
Element Formulation ◽  
Intensity Factors ◽  
Singular Stress ◽  
Singular Stress Field

In order to compute stress intensity factors accurately, the standard boundary element method is modified to take explicit account of the singularity in the stresses at a crack-tip. The known expansion terms of the crack tip displacement and stress fields are subtracted to remove the numerical difficulties associated with the representation of a singular stress field at the crack-tip. Hence the accuracy of calculation is much improved, without appreciably increasing the amount of computation involved. Furthermore, the stress intensity factor is directly obtained as a part of a solution and no extrapolations are required. The improved formulation is applied to a configuration, which is representative of a part of the wing in a civil transport aeroplane. This configuration consists of a pair of circular cut-outs (supply ports) near to which smaller holes exist; these small holes are particularly susceptible to cracking.

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