The Relation Between Similarity Fields and Invariant Path Integrals in Nonlinear Fracture Mechanics

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The Relation Between Similarity Fields and Invariant Path Integrals in Nonlinear Fracture Mechanics Gustavo Gioia, University of Illinois at Urbana-Champaign Computational simulations indicate that the plastic-zone fields of growing cracks depend on the stress intensity factor K and the t-stress T through a single similarity variable, implying that we can ascertain the type of fracture (brittle or ductile) associated with any combination of K and T by performing experiments over a range of values of a single variable. Yet the origin of similiarity fields remains unknown. Here we will trace these similarity fields to the existence of invariant path integrals. We will relate the similarity variable to the crack-tip energy flux, viscosity, cohesion, and triaxiality. For several failure criteria, we will construct diagrams identifying the ductile, transitional, and brittle regions in K-T space. We will also study separable crack-tip similarity fields and establish their connection with critical phenomena. Last, we will study the case of stationary cracks, where the fields are not similarity ields but there exists an invariant path integral.