Necessary corrections of the mathematical foundation of fracture mechanics

Tom van der Put

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Abstract

It is shown, that the applied fracture mechanics textbook boundary value problem solution is identical to the sum of the transformed exact solutions of pure normal stress loading alone, and of pure shear stress loading alone, although these two solutions exclude each other and cannot apply at the same time. This delivers, already since the fifties, a wrong, incompatible, equilibrium system with incorrect transformed field stresses, which does not represent linear elastic fracture mechanics. As correction, the right exact limit analysis solution is given, which also provides the derivation of “mixed I-II-mode” fracture criterion, which is shown to be precisely verified by empirical research. It further is shown that the postulated stress function is based on a stress transformation from elliptical coordinates to confocal polar coordinates. However that transformation applies for lower order distances to the singularity and therefore don’t give the right result on the applied macro scale. The discussion of a necessary limit analysis approach for failure, provides the proof of a necessary linear elastic analysis up to initial yield. Linear elastic stress and displacement terms represent the none vanishing, first order terms of virtual work behavior, of any non-linear stress division. This has consequences for non-linear fracture mechanics, which is shown, to be necessarily replaced by the linear approach of limit analysis. As example, the critical stress intensity is given of a test series with different initial crack lengths, which, in terms of nonlinear fracture mechanics, was subject to undeterminable failure behavior by large scale yielding.
Original languageEnglish
Number of pages32
Journal International Journal of Fracture and Damage Mechanics
Publication statusAccepted/In press - 2020

Keywords

  • Fracture mechanics
  • Notch fracture boundary value analysis
  • fracture limit analysis

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