Discrete and continuum studies of some fundamental issues in brittle fracture mechanics

Abstract

This thesis addresses four fundamental, yet unresolved, issues in brittle fracture mechanics: (a) the validity of linear elasticity in the crack-tip region, (b) crack growth direction under mixed-mode loading, (c) the nature and impact of cohesive stresses, (d) the effect of crack-face friction on the crack growth criterion in Griffith’s model for compressive failure. It is a well known fact that, according to classical elasticity, the stress in the near-tip region of the crack is singular, which has led to a debate over the validity of linear elasticity in this region. The strain, stress and elastic strain energy of a cracked silicon crystal in the crack-tip region is calculated, according to atomistic simulations, and compared to the classical elasticity solution. The classical continuum solution is found to have the ability to match the atomistic stresses and strains, very close to the crack tip. Multiple criteria have been proposed, inconsistent among themselves, to predict the direction of crack growth under mixed-mode loading, with no consensus as to which one is the most accurate. A new lattice spring model that simulates an isotropic elastic material is developed. A pre-cracked model is taken, and the crack is allowed to grow under the influence of mixed-mode loading, to calculate the direction of crack growth. The growth direction matches several well-known criteria in different ranges of loading. The theory of cohesive stresses has been used widely, specially in numerical simulations. However, there has been no concerted effort to explain the nature of this force, and its influence on stresses and deformations around crack. A clearer insight into the origins and impact of cohesive stress in cracks will lay down a solid foundation for its correct application in numerical simulations. An analytical method based on complex potentials has been employed to find the variation of crack aperture and stress in the crack plane in the presence of a cohesive stress. Friction has been incorporated into the Griffith crack theory for compressive loading for a long time. However, it has always been considered to be acting at its maximum value, and not as an inequality. In the present work, the latter treatment is made, in which the crack faces have variable slip-stick regions. Using this more accurate model for crack face friction, the condition for crack growth at the crack tip is re-visited.