scholarly journals Boundary Weight Functions for Cracks in Three-Dimensional Finite Bodies

1999 ◽  
Vol 15 (1) ◽  
pp. 17-26
Author(s):  
Chien-Ching Ma ◽  
I-Kuang Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Three Dimensional ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Arbitrary Loading

ABSTRACTAn efficient boundary weight function method for the determination of mode I stress intensity factors in a three-dimensional cracked body with arbitrary shape and subjected to arbitrary loading is presented in this study. The functional form of the boundary weight functions are successfully demonstrated by using the least squares fitting procedure. Explicit boundary weight functions are presented for through cracks in rectangular finite bodies. If the stress distribution of a cut out rectangular cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple integration. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the proposed boundary weight function method.

scholarly journals Calculation of Stress Intensity Factors for Elliptical Cracks in Finite Bodies by Using the Boundary Weight Function Method

1999 ◽  
Vol 121 (2) ◽  
pp. 181-187 ◽  
Author(s):  
C.-C. Ma ◽  
I-K. Shen
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Arbitrary Shape ◽  
Function Method ◽  
Weight Functions ◽  
Mode I ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Arbitrary Loading

In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.

scholarly journals Weight Functions and Stress Intensity Factors for Axial Cracks in Hollow Cylinders

1994 ◽  
Vol 116 (4) ◽  
pp. 423-430 ◽  
Author(s):  
C.-C. Ma ◽  
J.-I. Huang ◽  
C.-H. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Weight Functions ◽  
Intensity Factors ◽  
Arbitrary Loading ◽  
Hollow Cylinders

In this study, stress intensity factors for axial cracks in hollow cylinders subjected to mechanical and thermal loadings are determined by using the weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. The weight function may be thought of as Green’s function for the stress intensity factor of cracked bodies. Once the weight function for a cracked body is determined, the stress intensity factor for any arbitrary loading can be simply and efficiently evaluated through the integration of the product of the loading and weight function. A numerical method for the determination of weight functions relevant to cracked bodies with finite dimensions is used. Results for weight functions covering a wide range of hollow cylinder geometries are presented in functional or graphical form. The explicit crack face weight functions for applying mechanical loadings are obtained by using the least-squares fitting procedure. As a demonstration, some examples of special loading problems are solved by the weight function method, and the results are compared with available results in the published literature.

scholarly journals Weight Function Method for Stress Intensity Factors of Semi-Elliptical Surface Cracks on Functionally Graded Plates Subjected to Non-Uniform Stresses

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3155
Author(s):  
Kun-Pang Kou ◽  
Jin-Long Cao ◽  
Yang Yang ◽  
Chi-Chiu Lam
Keyword(s):  
Stress Intensity ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Functionally Graded ◽  
Weight Functions ◽  
Surface Cracks ◽  
Functionally Graded Plates ◽  
Intensity Factors ◽  
Weight Function Method

In this paper, a weight function method based on the first four terms of a Taylor’s series expansion is proposed to determine the stress intensity factors of functionally graded plates with semi-elliptical surface cracks. Cracked surfaces that are subjected to constant, linear, parabolic and cubic stress fields are considered. The weight functions for the surface, deepest and general points on the crack faces of long and deep cracked functionally graded plates are derived, which has never been done before in the literature. The accuracy of the method in this study is then validated by comparing the results with those of finite element modeling. The numerical results indicate that the derived weight functions are highly accurate and robust enough to predict the stress intensity factors for cracked functionally graded plates subjected to non-uniform stress distributions. The weight function method is therefore a time-saving technique and suitable for handling non-uniform stress fields.

Stress Intensity Factors and Weight Function for Internal Surface Faults in Cylindrical Vessels

2013 ◽  
Vol 705 ◽  
pp. 209-215
Author(s):  
Yan Ling Ni ◽  
Shang Tong Yang ◽  
Chun Qing Li
Keyword(s):  
Stress Intensity ◽  
Aspect Ratio ◽  
Weight Function ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Stress Singularity ◽  
Weight Functions ◽  
Intensity Factors ◽  
Weight Function Method ◽  
Aspect Ratios

Failure of cylindrical vessels can be caused by stress singularity at pitting corrosion induced cracks. Literature suggests that most of research focuses on how to determine stress intensity factors for surface cracks with low aspect ratios, i.e.,a/c1.0. Situation may well arise where the aspect ratio of cracks is larger than one. This paper attempts to propose a weight function method to determine stress intensity factors for high aspect ratio semi-elliptical cracks in cylindrical vessels. The weight functions are derived based on three dimensional finite element analysis. The proposed weight function method is verified numerically. It is found that the higher the aspect ratio of cracks the larger the stress intensity factors, and that the aspect ratio of cracks may alter the failure mode of cylindrical vessels.

Comparison of Different Methods for the Determination of Stress Intensity Factors of Cracks in Pipes With Stress Gradients

1984 ◽  
Vol 106 (2) ◽  
pp. 209-213 ◽  
Author(s):  
C. Mattheck ◽  
P. Morawietz ◽  
D. Munz ◽  
H. Stamm
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Weight Function ◽  
Excellent Agreement ◽  
Stress Intensity Factors ◽  
Function Method ◽  
Weight Functions ◽  
Intensity Factors ◽  
Stress Gradients

Stress intensity factors for long longitudinal and complete circumferential cracks under stress gradients were calculated using a weight function method. The weight functions were obtained by a method proposed by Petroski and Achenbach [3] and by a finite element fit procedure. Excellent agreement was obtained with finite element results of Labbens, et al. [7].

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