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.