Journal
INTERNATIONAL JOURNAL OF FRACTURE
Volume 166, Issue 1-2, Pages 179-201Publisher
SPRINGER
DOI: 10.1007/s10704-010-9523-4
Keywords
Notch; Re-entrant corner; Wedge; Microstructure; Micro-mechanics; Dipolar gradient elasticity; Toupin-Mindlin theory; Asymptotics; Knein-Williams technique
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Funding
- NTU Athens [65/1695]
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In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain- gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant c is introduced, in addition to the standard Lam, constants (lambda, mu). The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics.
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