EXPLICIT FORMULATIONS OF THE J-INTEGRAL CONSIDERING HIGHER-ORDER SINGULAR TERMS IN EIGENFUNCTION EXPANSION FORMS - PART I - ANALYTICAL TREATMENTS

Authors
Citation
Yh. Chen et N. Hasebe, EXPLICIT FORMULATIONS OF THE J-INTEGRAL CONSIDERING HIGHER-ORDER SINGULAR TERMS IN EIGENFUNCTION EXPANSION FORMS - PART I - ANALYTICAL TREATMENTS, International journal of fracture, 85(1), 1997, pp. 11-34
Citations number
25
Language
INGLESE
art.tipo
Article
ISSN journal
0376-9429
Volume
85
Issue
1
Year of publication
1997
Pages
11 - 34
Database
ISI
SICI code
0376-9429(1997)85:1<11:EFOTJC>2.0.ZU;2-F
Abstract
A semi-infinite crack with a nonlinear zone around the crack tip is st udied in detail in the following four cases: (i) antiplane shear defor mation, (ii) plane deformation, (iii) plane anisotropic deformation wi th purely imaginary characteristic roots, and (iv) interface between d issimilar solids, respectively. The complete Williams eigenfunction ex pansion forms including both positive and negative powers of a distanc e from the crack tip in each of the four cases are considered, which c ould be used to describe the elastic state in an annulus around the no nlinear zone. Explicit formulations of the path independent J-integral are presented by utilizing the differential property and the so-calle d pseudo-orthogonal property of the complete Williams expansion forms in each of the four cases. It is shown that the complete Williams expa nsion forms in every case mentioned above have two kinds of contributi ons to the J-integral. The first one is similar to the traditional one arising from the well-known r(-1/2) singularity (or r(-1/2+i epsilon) singularity for the interface crack). The second one is a summation i nduced from the interaction of higher order singular terms and nonsing ular terms of the expansion forms. Although the coefficients of the co mplete Williams expansion forms-in each of the four cases should be de termined not only by the prescribed outer boundary conditions but by s ome specific material model for the nonlinear zone surrounding the cra ck tip, once they are determined by whatever method, the J-integral co uld be calculated by using the formulations derived in this paper with out any difficulties. It is found also that the elastic T-term acting parallel to the crack plane has no direct interaction with the higher order singular terms such that has no direct effect to the J-integral, although the presence of the T-term will dramatically affect the size of the nonlinear zone and in this way affect the coefficients of the higher order singular terms and in turn the values of the J-integral. The present results in the four cases support the conclusion derived b y Hui and Ruina (1995) that the nonsingular terms and the higher order singular terms in the complete Williams expansion forms are of equal importance. Thus, in order to improve and to confirm the small scale y ielding description, not only the nonsingular terms, but also the high er order singular terms should be determined for a given crack configu ration, body geometry, loading conditions and the prescribed material model in the nonlinear zone.