Journal Article10.1007/BF00035493
Strain-energy-density factor applied to mixed mode crack problems
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TL;DR: In this paper, the authors investigated the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position, and showed that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor.
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Abstract: This paper deals with the general problem of crack extension in a combined stress field where a crack can grow in any arbitrary direction with reference to its original position. In a situation, when both of the stress-intensity factors,k
1,k
2 are present along the crack front, the crack may spread in any direction in a plane normal to the crack edge depending on the loading conditions. Preliminary results indicate that the direction of crack growth and fracture toughness for the mixed problem of Mode I and Mode II are governed by the critical value of the strain-energy-density factor,S
cr. The basic assumption is that crack initiation occurs when the interior minimum ofS reaches a critical value designatedS
cr. The strain-energy-density factorS represents the strength of the elastic energy field in the vicinity of the crack tip which is singular of the order of 1/r where the radial distancer is measured from the crack front. In the special case of Mode I crack extensionS
cr is related tok
1c alone asS
cr = (κ − 1)k
1
2
/8μ. In general,S takes the quadratic forma
1 1
k
1 + 2a
1 2
k
1
k
2 +a
2 2
k
2 whose critical value is assumed to be a material constant. The analytical predictions are in good agreement with experimental data on the problem of an inclined crack in plexiglass and aluminum alloy specimens. The result of this investigation provides a convenient procedure for determining the critical crack size that a structure will tolerate under mixed mode conditions for a given applied stress.
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Citations
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