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Mathematics and Mechanics of Solids
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An Alternative Form of Propagation Criterion for Two Collinear Cracks under Compression

Zheming Zhu

Department of Engineering Mechanics, Sichuan University, Chengdu, Sichuan, 610065, China

Under compression, cracks extend, branch and coalesce. These fracturing processes have received much attention recently. In this paper, an attempt is made to find the analytical solution of stress intensity factors for the special case of cracks situated along a straight line, and to set up a fracture criterion. Under compression, cracks close and the crack surface friction can resist crack surface sliding. Considering crack surface friction, a set of complex stress functions is proposed for the special case of cracks situated along a straight line. The analytical solution is formulated, and for the case of only two collinear cracks inside an infinite plate, the exact analytical solution of stress intensity factor is presented. Finally, an alternative form of crack propagation criterion for two collinear cracks under compression is developed, which is expressed in terms of principal stresses. For the case of materials without pre-existing macrocracks, this new propagation criterion becomes the well known Coulomb—Mohr criterion.

Key Words: stress intensity factor • crack propagation criterion • crack surface friction • fracture toughness

This version was published on November 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 8, 727-746 (2009)
DOI: 10.1177/1081286508090043
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