A unified theory for brittle and ductile shear mode fracture 
 
Authors:  Luca Cimbaro 
 
Institution:  Department of Physics, Imperial College London, London, UK 
 
Abstract:  A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the IrwinOrowan formula. For purely ductile solids, the theory makes direct contact with the BilbyCottrellSwinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the PeachKoehler force overcomes it. A dislocationfree zone separates the plastic zone from and the tip of the crack. The dislocationfree zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocationfree zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocationfree zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture. 
 
Keywords:  Mechanical properties fracture toughness cracks Griffith's theory BilbyCottrellSwinden model dislocationfree zone 

