3次元き裂に対する全体的Jスカラーの二, 三の適用

抄録

In a previous paper J-integrals of a three-dimensional crack embedded in a linear or nonliner elastic material were discussed. J-integrals of three-dimensional cracks proposed so far were classified into three categories; local J vector, local J scalar and global J vector. A new parameter, global J scalar, was also proposed which was defined by using a kind of crack extension vector. The characteristics and the interrelation of these four J-integrals were discussed. It was shown that the global J scalar plays a very important role in the understanding of J-integral of three-dimensional cracks.
In this paper some applications of the global J scalar were made. The results obtained are as follows:
(1) Rice's J-integral and Knowles-Sternberg's M- and L-integrals were derived from the global J scalar as its special cases. The global J scalar is a generalized form of J-, M- and L-integrals. Some extensions of M- and L-integrals were made by using the global J scalar.
(2) As one of the simplest applications of J-integral of three-dimensional cracks, two expressions of J-integral at the tip of an axi-symmetric crack were obtained by using the local J-vector and the global J-vector. Many expressions, including these two expressions, were also derived using the global J scalar.
(3) An application of the global J scalar to an arbitrary three-dimensional crack was presented. An economical method to determine the distribution of value of J-integral along the crack front was proposed.