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.

Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part II: Stretching finite strips weakened by single edge parabolically-shaped notches

“…In spite of this skepticism, it was highlighted in ref. [1] that the solutions of LEFM, if properly adjusted, can provide interesting results, also, for actual structures. In this context, an attempt is described here to relief the suffocating assumptions of 'mathematical' discontinuities and 'infinite' media, by considering a uniaxially stretched plane strip of finite dimensions weakened by a notch of parabolic shape.…”

“…his is the second part of a short three-paper series, the aim of which is to revisit some classical concepts of Linear Elastic Fracture Mechanics (LEFM). In the first paper of the series [1] some controversial issues were discussed, related to: (i) the unnatural overlapping of the lips of 'mathematical' cracks in 'infinite plates' (a phenomenon that is predicted by the solution of the respective first fundamental problem of LEFM, in case it is formalistically applied), and, (ii) the closely associated issue of negative mode-I Stress Intensity Factors (SIFs). It could be counterargumented of course T that concepts like 'infinite plate' and 'mathematical' cracks are of limited applicability in practical engineering problems (where neither the size of actual structural members is infinite nor the discontinuities are 'mathematical' cuts with singular point tips).…”