Speaker: Tsvetanka Sendova (IMA)
Title: A Theory of Fracture Based Upon Extension of Continuum Mechanics to the Nanoscale
Abstract: I will present the analysis of several fracture models based on a new approach to modeling brittle fracture. Integral transform methods are used to reduce the problem to a Cauchy singular, linear integro-differential equation. We show that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition, given by the jump momentum balance, leads to a sharp crack opening profile at the crack tip, in contrast to the classical theory of brittle fracture. However, such a model still predicts singular crack tip stress. For this reason we study a modified model, where the surface excess property is responsive to the curvature of the fracture surfaces. We show that curvature-dependent surface tension, together with boundary conditions in the form of the jump momentum balance, leads to bounded stresses and a cusp-like opening profile at the crack tip. Finally, I will discuss two possible fracture criteria, in the context of the new theory. The first one is an energy based fracture criterion. Due to the fact that the proposed modeling approach allows us to fully resolve the stress in a neighborhood of the crack tip, without the customary singularity, a second fracture criterion, based on crack tip stress, is possible.