On the Crack Extension in Plates Under Plane Loading and Transverse Shear

1963 ◽  
Vol 85 (4) ◽  
pp. 519-525 ◽  
Author(s):  
F. Erdogan ◽  
G. C. Sih
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Extension ◽  
Brittle Materials ◽  
Crack Tip ◽  
Intensity Factors ◽  
Plane Shear ◽  
Tearing Modes ◽  
Symmetric Plane ◽  
General Plane

The crack extension in a large plate subjected to general plane loading is examined theoretically and experimentally. It is found that under skew-symmetric plane loading of brittle materials the “sliding” or the crack extension in its own plane does not take place, instead crack grows in the direction approximately 70 deg from the plane of the crack. This is very nearly the direction perpendicular to the maximum tangential stress at the crack tip, which is 70.5 deg. The hypothesis that the crack will grow in the direction perpendicular to the largest tension at the crack tip seems to be verified also by cracked plates under combined tension and shear. In spite of the fact that “sliding” and “tearing” modes of crack extension do not take place in brittle materials it is shown that one can still talk about critical stress intensity factors in plane shear and transverse bending of plates. It is also shown that, in general plane loading, the fracture criterion in terms of stress intensity factors is an ellipse.

An Efficient and Accurate Numerical Method of Stress Intensity Factors Calculation of a Branched Crack

2005 ◽  
Vol 72 (3) ◽  
pp. 330-340 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Extension ◽  
Crack Tip ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Displacement Discontinuity Method ◽  
Intensity Factors ◽  
Constant Displacement ◽  
The Right

Based on the analytical solution of Crouch to the problem of a constant discontinuity in displacement over a finite line segment in an infinite elastic solid, in the present paper, the crack-tip displacement discontinuity elements, which can be classified as the left and the right crack-tip elements, are presented to model the singularity of stress near a crack tip. Furthermore, the crack-tip elements together with the constant displacement discontinuity elements presented by Crouch and Starfied are used to develop a numerical approach for calculating the stress intensity factors (SIFs) of general plane cracks. In the boundary element implementation, the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The method is called the hybrid displacement discontinuity method (HDDM). Numerical examples are given and compared with the available solutions. It can be found that the numerical approach is simple, yet very accurate for calculating the SIFs of branched cracks. As a new example, cracks emanating from a rhombus hole in an infinite plate under biaxial loads are taken into consideration. The numerical results indicate the efficiency of the present numerical approach and can reveal the effect of the biaxial load on the SIFs. In addition, the hybrid displacement discontinuity method together with the maximum circumferential stress criterion (Erdogan and Sih) becomes a very effective numerical approach for simulating the fatigue crack propagation process in plane elastic bodies under mixed-mode conditions. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the HDDM. Crack propagation is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented.

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.

Propose of Simplified Stress Intensity Factor Equation for SCC Extension of the Pipe Welds

2008 ◽  
Author(s):  
Mayumi Ochi ◽  
Kiminobu Hojo ◽  
Itaru Muroya ◽  
Kazuo Ogawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Crack Extension ◽  
Crack Depth ◽  
Alloy 600 ◽  
Intensity Factors ◽  
Axial Crack ◽  
Extension Analysis

Alloy 600 weld joints have potential for primary water stress corrosion cracks (PWSCC). At the present time it has been understood that PWSCC generates and propagates in the Alloy 600 base metal and the Alloy 600 weld metal and there has been no observation of cracking the stainless and the low alloy steel. For the life time evaluation of the pipes or components the crack extension analysis is required. To perform the axial crack extension analysis the stress intensity database or estimation equation corresponding to the extension crack shape is needed. From the PWSCC extension nature mentioned above, stress intensity factors of the conventional handbooks are not suitable because most of them assume a semi-elliptical crack and the maximum aspect ratio crack depth/crack half length is one (The evaluation in this paper had been performed before API 579-1/ASME FFS was published). Normally, with the advance of crack extension in the thickness direction at the weld joint, the crack aspect ratio exceeds one and the K-value of the conventional handbook can not be applied. Even if those equations are applied, the result would be overestimated. In this paper, considering characteristics of PWSCC’s extension behavior in the welding material, the axial crack was modeled in the FE model as a rectangular shape and the stress intensity factors at the deepest point were calculated with change of crack depth. From the database of the stress intensity factors, the simplified equation of stress intensity factor with parameter of radius/thickness and thickness/weld width was proposed.

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