A Non-local Damage Model for Brittle Fracture in Metallic Structures with Stress Concentrators

Abstract

This work is devoted to the development of the constitutive relations for the description of the defect evolution near the stress concentrators. A structural sensitive parameter is introduced as an averaging of the symmetrical tensor characterizing unit defect with the Boltzmann-Gibbs distribution function. Constitutive equation for structural parameter was derived under an assumption of the local thermodynamic equilibrium. The application of the developed approach is illustrated by the numerical simulation of a nonlocal fracture process occurring in a Grade-2 titanium specimen with a stress concentrator under uniaxial tension condition. Nonlocal character of the fracture near the stress concentrator was shown and physical explanation of the critical distance theory as a length of a dissipative structure growing in blow-up mode kinetics in the defect ensemble was proposed.