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The most dangerous flaw orientation in brittle materials and structures

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Abstract

In the present paper a sheet of material is considered. It is loaded by uniaxial tensile stress and contains a random distribution of flaw orientations, with the flaws thought of as flat pre-cracks of comparable length, and with all crack planes being oriented perpendicular to the faces of the sheet. Intuition suggests that the most likely flaw to initiate fracture, which will be termed the “most dangerous defect”, lies orthogonally to the major load axis. The purpose of the present paper is to show that such an assumption is incorrect. Neither the most dangerous defect nor the first increments of crack growth will be oriented perpendicularly to the stress direction (nor will they be co-planar with the orientation of the most critical flaw).

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Notes

  1. The process of cracking in continuum bodies reveals three well defined phases: loading without crack growth, stable crack growth, and unstable crack growth. If crack elongation is totally prevented the safety factor is measured against the load that allows the stable crack growth propagation phase to begin. Such a transition point is termed onset of crack propagation, whereas loading without crack growth happens in the safe equilibrium domain.

  2. Let \(t\) represent any variable which monotonically increases in physical time and merely orders events; the mechanical phenomena to study are time-independent. The global incremental quasi-static fracture propagation problem at time \(t\) depends on the geometry at time \(t\) as well as on the actions that drive the problem itself, as external loads, self equilibrated stresses due to diffusion of species, thermal loads, fatigue, environment changes.

  3. In Eq. (1.4), \(E\) is Young modulus and \(\nu \) Poisson’s coefficient.

  4. The dependence is only on \(\omega \), since the “condition” has made \(\theta \) a function of \(\omega \).

  5. Equivalently, it is the one for which the flaw leaves the state of safe equilibrium for the first time in the loading process \(\kappa (t)\).

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  1. DICATAM, Università di Brescia, via Branze 43, 25123 , Brescia, Italy

    A. Salvadori & A. Giacomini

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  1. A. Salvadori
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  2. A. Giacomini
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Correspondence to A. Salvadori.

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Salvadori, A., Giacomini, A. The most dangerous flaw orientation in brittle materials and structures. Int J Fract 183, 19–28 (2013). https://doi.org/10.1007/s10704-013-9872-x

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