Duality of singularities of multiscale damage localization and crack advance: length variety in Theory of Critical Distances

Oleg Naimark

doi:10.3221/igf-esis.49.27

Abstract

The existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered as the physical basis for the interpretation of the Theory of Critical Distances. The free energy metastability of solid with defects and corresponding free energy release explain the conception of the Finite Fracture Mechanics in the presence of the finite amplitude energy barrier. The variety of crack paths is analyzed as duality of inherently linked two types of singularities related to the singularity of multiscale damage kinetics under crack nucleation and singularity of stress field at the crack tip as the classical framework of fracture mechanics. The singularity of multiscale damage kinetics is a natural precursor of crack nucleation that could provide in some cases the totally independent scenario of fracture from the stress singularity at the crack tips. The influence of two singularities with the nature of intermediate asymptotical solutions for stress at the crack tip and damage localization kinetics over the set of spatial scales represents two attractors, which provides the variety of crack paths for corresponding loading conditions.

Highlights

Nonlinear aspects of multiscale damage evolution in the presence of stress concentration, cracks and notches are the subject of intensive experimental and theoretical studies in the problem of damage-failure transition for quasi-static, fatigue and dynamic statements, which generally are inherently linked
The existence of two singularities related to the stress field at the crack tip and blow-up kinetics of damage localization is considered as the physical basis for the interpretation of the Theory of Critical Distances
The free energy metastability of solid with defects and corresponding free energy release explain the conception of the Finite Fracture Mechanics in the presence of the finite amplitude energy barrier

Summary

Introduction

Nonlinear aspects of multiscale damage evolution in the presence of stress concentration, cracks and notches are the subject of intensive experimental and theoretical studies in the problem of damage-failure transition for quasi-static, fatigue and dynamic statements, which generally are inherently linked. The influence of two singularities with the nature of intermediate asymptotical solutions for stress at the crack tip and damage localization kinetics over the set of spatial scales represents two attractors, which provides the variety of crack paths for corresponding loading conditions.

Results

Conclusion