Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing �mathematical� crack in an infinite plate and the respective Stress Intensity Factors

Abstract

This is the first part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. The motive of this first paper is to highlight some controversial issues, related to the unnatural overlapping of the lips of a �mathematical� crack in an infinite plate loaded by specific combinations of principal stresses at infinity (predicted by the classical solution of the respective first fundamental problem), and the closely associated issue of negative mode-I Stress Intensity Factor. The problem is confronted by superimposing to the first fundamental problem of Linear Elastic Fracture Mechanics for an infinite cracked plate (with stress-free crack lips) an �inverse� mixed fundamental problem. This superposition provides naturally acceptable stress and displacement fields, prohibiting overlapping of the lips (by means of contact stresses generated along the crack lips, which force the overlapped lips back to naturally accepted position) and, also, non-negative mode-I Stress Intensity Factors. The solutions of this first paper form the basis for the next two papers of the series, dealing with the respective problems in finite domains (recall, for example, the cracked Brazilian disc configuration) weakened by artificial notches (rather than �mathematical� cracks), by far more interesting for practical engineering applications.

Keywords

• linear elastic fracture mechanics
• �mathematical� cracks
• stress intensity factors
• stresses
• displacements and contact stresses
• overlapping crack lips
• complex potentials