Distributed dislocation technique for cracks based on non-singular dislocations in nonlocal elasticity of Helmholtz type

• Published in: Engineering fracture mechanics 2015-03, Vol.136, p.79-95
• Main Authors: Mousavi, S. Mahmoud, Lazar, Markus
• Format: Article
• Language: English
• Subjects: Cracks; Dislocation density; Dislocation mobility; Dislocations; Fracture mechanics; Integral equations; Materials Engineering; Materialteknik; Mathematical models; Nonlocal elasticity; Stress concentration; Stresses
• ISSN: 0013-7944; 1873-7315; 1873-7315
• DOI: 10.1016/j.engfracmech.2015.01.015

•Distributed dislocation technique is employed for cracks within nonlocal elasticity of Helmholtz type.•Non-singular nonlocal dislocation stresses lead to non-singular nonlocal stress fields for cracks of modes I, II and III.•The results fulfill the equilibrium, boundary and incompatibility conditions of a plane weakened by a crack.•Non-singular crack stresses are zero at or near the crack tip and possess a maximum value near the crack tip. In the present paper, the distributed dislocation technique is extended for crack problems within Eringen’s theory of nonlocal elasticity of Helmholtz type. Employing distributed dislocation technique, non-singular stresses of cracks of modes I, II and III are obtained using the non-singular stresses of climb edge, glide edge and screw dislocations and dislocation density functions which are solutions of the non-singular integral equations of distributed dislocation technique. The cracks are modeled by a continuous distribution of straight dislocations. The nonlocal elasticity solutions of crack problems do not contain a stress singularity. We found that the non-singular crack stresses are zero at the crack tip or near the crack tip.