IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

A Theory of Brittle Fracture Based upon an Extension of Continuum Mechanics to the Nano-Scale

  • March 25, 2009
  • 3 p.m.
  • Sumwalt 102

Abstract

A theory of fracture of brittle materials is presented that is formulated with a continuum theory incorporating nano-scale effects in the vicinity of fracture surfaces. These nano-scale effects account for changes in the bulk behavior of material near in interfacial regions due to long range intermolecular forces from adjoining phases. These effects are incorporated into the theory by two mechanisms: a mutual force correction to the balance of linear momentum and idealizing a material interface (fracture surface in this case) as a dividing surface (in the sense of Gibbs) endowed with excess properties such as surface tension, surface internal energy and free energy, surface entropy, surface mass and momentum. It is shown that for special classes of constitutive assumptions concerning the dependence of surface tension (of fracture surfaces) upon curvature, that the crack tip singular stresses and strains of classical brittle fracture theories do not occur. More specifically, the theory predicts bounded crack tip stress and a cusp-shaped crack tip profile. This necessitates a new notion of energy release rate and a new approach to developing a fracture criterion, which is also discussed.

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