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Self‐similar crack patterns induced by spatial stress fluctuations
Author(s) -
Dyskin A. V.
Publication year - 2002
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1046/j.8756-758x.2002.00487.x
Subject(s) - brittleness , crack closure , stress (linguistics) , materials science , amplitude , mechanics , stress concentration , tension (geology) , perpendicular , radius , crack tip opening displacement , stress intensity factor , fracture mechanics , physics , composite material , geometry , mathematics , ultimate tensile strength , optics , linguistics , philosophy , computer security , computer science
A mechanism of the formation of multiscale self‐similar crack structures in brittle materials is proposed based on the action of spatial random stress fluctuations (random stress fields) with vanishing mathematical expectation. The presence of self‐equilibrating stress fluctuations is, in many cases, characteristic of heterogeneous brittle materials even in the absence of external loading. Some examples are given by residual stresses—stresses caused by phase transformations or internal microscopic heat sources. If the stress fluctuations are strong enough to cause cracking, the cracks will be originated in regions with and perpendicular to the highest local tension. As a legacy of this special location, additional local tractions opening the crack in its centre are developed even in self‐equilibrating stress fields. This mechanism is modelled by disklike cracks opened by a pair of concentrated forces applied at the centre. Two cases are considered: (i) the crack growth in the moving equilibrium conditions caused by the self‐equilibrating stress fluctuations of increasing amplitude; and (ii) the subcritical crack growth under the stress fluctuations of either sustained (creep) or oscillating (fatigue) amplitudes. As the cracks grow, the interaction between them leads to a separation of crack sizes. The effects of the interaction are modelled by the differential self‐consistent method that is shown to become asymptotically accurate as the ratio between the sizes of the interacting cracks increases. The interaction results in the crack distribution tending to a self‐similar one with the distribution function proportional to the inverse fourth power of the crack radius.