The Investigation On The Radial Climb Somigliana Ring Dislocation And Its Applications In The Indentation Fracture

Dislocations and dislocation loops play important roles in determining such mechanical properties of material as deformation, fatigue and toughness. At the micro-size level, the mechanical properties of the material are different from those for the bulk case. The mechanism of the deformation and the failure mode will change, and the size effects based on the geometrically necessary dislocations as well as the deformation-misfit of the film-substrate system must be considered. These problems make the traditional phenomenological methods invalid and require the further investigation on the physical singularity like dislocation.The project is concerned with the toughness in the indentation/scratch test. We first find the solutions of a single radial climb Somigliana ring dislocation. Secondly, we compare two methods to form a single radial climb Somigliana ring dislocation, and obtain the more general physical picture. Finally, we tackle with the interaction of a single radial Somigliana ring dislocation with the interface, and obtain the solutions of the initial surface crack in the indentation/scratch test by virtue of simulating the crack with the dislocation pileup.The main contents include:(1) Apply the radial cut to form a radial climb Somigliana ring dislocation, obtain the exact solutions of the problem, and compare the solutions with those of an axial glide Somogliana ring dislocation given by Korsunsky. (2) On the basis of the exact solutions, determine the interaction of a single radial climb Somigliana ring dislocation with the interface.(3) Simulate the initial indentation crack by using the dislocation pileup, present the fracture model, explain the mechanism of the initial surface crack, and predict the crack sizes in agreement with the experimental observation.The conclusion shows that, on the one hand, the representations of two kinds of Somigliana ring dislocations can be reduced to one physical singularity; and on the other hand the Green functions of the axial failure configuration can be obtained by tackling with the physical singularity. Finally, the indentation initial fracture problem is treated based on the solutions of the radial climb Somigliana ring dislocation. The numerical results are in agreement with the experimental phenomena, and this indicates the feasibility of the model.