抄録
Extension of Rice's J-integral to three-dimensional crack problems is one of the most important but not fully-developed issues in the field of elastic-plastic fracture mechanics. This paper deals with theoretical considerations on J-integral of three-dimensional cracks by using continuum mechanics. The following five assumptions were used in this study. (i) The behavior of the material is linear or nonlinear elastic. (ii) Infinitesimal deformation theory can be applied. (iii) There is no body force acting on the body. (iv) There is no traction on crack surface. (v) The crack surface and the crack front are smooth.
The results obtained are as follows:
(1) J-integrals of three-dimensional cracks proposed so far can be classified into three categories; local J vector Jlocal, local J scalar Jlocal and global J vector Jglobal. Global J scalar Jglobal(m) was proposed using a vector m which is defined in the body and may be interpreted as a kind of crack extension vector. Jglobal(m) is independent of integration surface.
(2) Local J vector Jlocal is perpendicular to the crack front.
(3) Relations between the four J-integrals, Jlocal, Jlocal, Jglobal and Jglobal(m) were discussed. Jglobal is equal to the line integral of Jlocal along crack front. Jglobal(m) is given by the line integral of inner product of Jlocal and m along crack front.
(4) Global J scalar Jglobal(m) represents the potential energy release rate when the crack extension vector is given by m on the crack front.
(5) Global J scalar Jglobal(m) can be obtained from load-displacement record of a body containing three-dimensional crack.
(6) Representations of J-integrals for curvilinear coordinates were obtained.
