Crack paths in three-dimensional elastic solids. i: two-term expansion of the stress intensity factors—application to crack path stability in hydraulic fracturing

✍ Scribed by Jean-Baptiste Leblond

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 465 KB
• Volume: 36
• Category: Article
• ISSN: 0020-7683
• DOI: 10.1016/s0020-7683(97)00276-x

✦ Synopsis

The aim of this work is to lay theoretical foundations for the prediction of crack paths within the theory of quasistatic LEFM under the most general hypotheses] arbitrary three!dimensional geometry\ arbitrary loading[ This objective requires to derive the expression of the stress intensity factors along the crack front after an arbitrary in_nitesimal propagation[ Only the _rst two terms of their expansion in powers of the crack extension length d\ proportional to d 9 0 and d 0:1 \ are considered in this paper[ Fully general formulae for these terms are obtained by combining arguments of dimensional analysis "scale changes# and regularity properties "continuity\ di}erentiability# of the stresses at a _xed\ given point with respect to d for d 9 derived from the BuecknerÐRice weight function theory[ This notably allows to extend the CotterellÐRice criterion for stable rectilinear propagation of a mode I crack under plane strain conditions to the three! dimensional case[ As an application\ a penny!shaped crack induced by hydraulic fracturing is considered[ Conclusions concerning the in~uence of the orientation and depth of such a crack upon the stability of its coplanar propagation seem to be compatible with experimental evidence[