A weighted residual method for elastic-plastic analysis near a crack tip and the calculation of the plastic stress intensity factors

1991 ◽  
Vol 12 (12) ◽  
pp. 1123-1134
Author(s):  
Zhang Ning-sheng ◽  
Zhao Xue-ren ◽  
Hsueh Dah-wei
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Tip ◽  
Intensity Factors ◽  
Weighted Residual Method ◽  
Residual Method ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Plastic Stress

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.

Mode III Stress Intensity Factors of Surface Crack in Round Bars

2011 ◽  
Vol 214 ◽  
pp. 192-196 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Mode Iii ◽  
Element Analysis ◽  
Proposed Model

This study presents a numerical investigation on the stress intensity factors (SIF), K of surface cracks in round bars that were obtained under pure torsion loadings or mode III. ANSYS finite element analysis (FEA) was used to determine the SIFs along the crack front of surface cracks embedded in the solid circular bars. 20-node isoparametric singular elements were used around the crack tip by shifting the mid-side node ¼-position close to a crack tip. Different crack aspect ratio, a/b were used ranging between 0.0 to 1.2 and relative crack depth, a/D were ranged between 0.1 to 0.6. Mode I SIF, KI obtained under bending moment was used to validate the proposed model and it was assumed this proposed model validated for analyzing mode III problems. It was found that, the mode II SIF, FII and mode III SIF, FIII were dependent on the crack geometries and the sites of crack growth were also dependent on a/b and a/D.

High-Speed Frictional Heating of an Elastic Medium With a Near-Surface Horizontal Line Crack

1993 ◽  
Vol 115 (1) ◽  
pp. 56-60 ◽  
Author(s):  
T. Y. Chen ◽  
Frederick D. Ju
Keyword(s):  
Temperature Field ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
High Speed ◽  
Frictional Heating ◽  
Crack Tip ◽  
Horizontal Line ◽  
Intensity Factors ◽  
Near Surface ◽  
Line Crack

This paper studies the effect of high-speed frictional heating over the surface of an elastic material, which has a near surface horizontal line crack. The frictional heating is represented by a high-speed moving heat source, since the mechanical loading effect is much smaller than the thermal effect in the resulting stress field. Finite difference methods are employed to compute the temperature field and the displacement field, taking into consideration the characteristic singularity at the crack tip. The temperature field solutions are first computed, using the method of heat balance. The thermo-mechanical solutions follow with particular interest in the vicinity of the line crack as represented by the stress intensity factors at the crack tip. It was found that both the open mode and the shear mode occur, as a result of the excitation of the moving thermal load. The paper also presents effects on the stress intensity factors from varying the thermal and the mechanical properties of the medium, and the location of the line crack from the wear surface. The depth at which the maximum thermal stress occurs is an exponential function of the Peclet number, as in the cases when there is no defect in the wear material and when there is a near surface cavity. Albeit, the “critical depth” reduces with increasing Peclet number and severity of the defect.

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