Tensile crack-tip fields in elastic-ideally plastic hexagonal crystals and layered materials

Abstract

Crack tip stress and deformation fields for tensile loaded ideally plastic crystals, as described by Rice [ Mech. Mater. 6, 317 (1987)], have been applied to hexagonal crystals and hexagonal layered solids. The specific case of ( 01 10 ) cracks growing in the [ 2 110 ] direction is considered for hexagonal layered solids, like Pyrolytic graphite (PG) and Carbon ribbon to understand why certain crack orientation and growth directions show unusual fracture toughness values. For the growing crack case, despite the same crack orientation in the two materials, two different types of stress fields are observed, as the orientation of the weakest slip planes with respect to the crack plane is different for the two cases. Furthermore, only one type of elastic sector is present for PG. This is in contrast to the cases of cracks growing in f.c.c. and b.c.c. crystals, wherein two kinds of elastic sectors were present. Surprisingly for (0001) cracks growing in the ( 2 110 ) direction in hcp crystals of Zn and Ti no kinematically permissible solutions were found.