Weight function for an elliptic crack in an infinite medium. I. Normal loading
Citations
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Cites methods from "Weight function for an elliptic cra..."
...The authors of [10] proposed an original method of integral equations for solving an integral-differential equation, which relates the displacement field to the load acting on the crack surface....
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Cites background from "Weight function for an elliptic cra..."
...In the text to follow we determine a necessary condition for the zone to remain circular during sliding and a relation between its radius a and the applied shear load T. For further convenience, a traditional polar coordinate system (p, ~o) is introduced in the plane z = 0. The stress intensity factors entering criterion of propagation (2) and calculated on the boundary of the circular zone are as follows (Borodachev, 1982, Saha and Roy, ......
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References
923 citations
"Weight function for an elliptic cra..." refers background or methods in this paper
...Rice (1972) independently showed that weight functions could be determined by differentiating known elastic displacement field solutions with respect to crack length....
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...Foundations of the three dimensional weight function theory were given independently by Rice (1972) in the Appendix of that publication and by Bueckner (1973) in a review....
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876 citations
"Weight function for an elliptic cra..." refers background in this paper
...The concept was first introduced by Bueckner (1970) for two-dimensional cracked bodies....
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832 citations
"Weight function for an elliptic cra..." refers background or methods in this paper
...Now using the following relations (see Gradshteyn and Ryzhik, 1980 )...
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...Here it may be noted that the only contributing term in the weight function is W 0 0 . All other terms contribute zero either due to the orthogonal property of sine and cosine functions, or due to orthogonality of Jacobi’s polynomials or due to the relation ( Gradshteyn and Ryzhik, 1980 )...
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...respect to between 0 and 1, one obtains after making use of the orthogonality property (see Gradshteyn and Ryzhik, 1980 ):...
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