THREE-DIMENSIONAL J-INTEGRAL CALCULATIONS OF PART-THROUGH SURFACE CRACK PROBLEMS

The problem of a shallow shell containing a surface crack and subjected to general loading conditions is considered. It is shown that, as in the three-dimensional elasticity formulation, the mode I state can be separated whereas modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions. A shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell is then considered. Reissner’s transverse shear theory is used to formulate the problem by assuming that the shell is subjected to all five moment and stress resultants. The uncoupled antisymmetric problem is solved for cylindrical and toroidal shells having a surface crack in various orientations and the primary and the secondary stress intensity factors are given. The results show that, unlike the through crack problems, in surface cracks the effect of shell curvature on the stress intensity factors is relatively insignificant.

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Evaluation of the J Integral of a Surface Crack by the Three-dimensional Local Hybrid Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.321-323.28 ◽

2006 ◽

Vol 321-323 ◽

pp. 28-31

Author(s):

Kenji Machida ◽

Gaku Mizukami ◽

Hirohisa Oyama

Keyword(s):

Stress Field ◽

Relative Error ◽

Hybrid Method ◽

Surface Crack ◽

Three Dimensional ◽

High Accuracy ◽

Problem Analysis ◽

J Integral ◽

Uniform Load ◽

Bending Load

To evaluate the 3-D stress field inside a specimen from displacement data on the free surface obtained from the 2-D intelligent hybrid method, we developed the 3-D local hybrid method based on inverse problem analysis. In a previous study, when a uniform load was applied to a structure with a surface crack, it was demonstrated that the stress field was analyzed with high accuracy. In this study, the 3-D local hybrid method was applied to a structure with a surface crack subjected to bending load. However, a suitable solution was not able to be obtained on a bending problem. Therefore, another method was applied. The relative error between the J integral value of the whole model and the local model was compared, and accuracy was investigated. First, the variation of accuracy with width and thickness was examined. If thickness is increased, the relative error decreases as found in the uniform load case. Moreover, as width increases, the relative error decreases. However, even if width and thickness become large, accuracy does not necessarily become better. Therefore, the relative error was compared and a suitable hybrid size was examined.

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Application of the Three-Dimensional Local Hybrid Method to the Structure with a Surface Crack Subjected to Bending Load

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.345-346.469 ◽

2007 ◽

Vol 345-346 ◽

pp. 469-472 ◽

Cited By ~ 1

Author(s):

Kenji Machida ◽

Takanori Ueno

Keyword(s):

Free Surface ◽

Hybrid Method ◽

Surface Crack ◽

Three Dimensional ◽

High Accuracy ◽

Local Model ◽

J Integral ◽

Uniform Load ◽

Bending Load ◽

Model Size

We developed the 3-D local hybrid method to evaluate the 3-D stress field inside the specimen from displacement data on the free surface obtained from the 2-D intelligent hybrid method. When a uniform load was applied to the structure with a surface crack, high accuracy was already acquired in stress analyses. The 3-D local hybrid method was anew applied to a structure with a surface crack which is subjected to bending load. It is expected that the accuracy depends on local model size. In this study, the width, the thickness and the height of the local model were changed widely, and analyses were carried out. Then the size of the local model necessary for the analyses was examined. Assessment of analyses was performed by comparing J integral value of a whole model and a local model.

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