The Early Research Of Dislocation Distribution Function For Propagation Crack

Dislocation distribution function of modeâ…¢propagation crack, modeâ…¢interface propagation crack and axially symmetric propagation crack are studied in this paper. By utilizing the methods of the theory of complex variable functions and self-similar functions, discussed problems with different boundary conditions can be transformed into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. By application of self-similar functions, those dissimilar types of crack extension problems are solved, moreover, analytical solutions of dislocation distribution function can be obtained.Dynamic propagation problems of modeâ…¢crack are mostly investigated in chapter 2. Crack propagation problems under the influence of the edges of the crack subjected to homogenous loads, the origin of the coordinates subjected to concentrated increasing loads, the central zone of the edges of the crack subjected to homogenous loads, the certain point of the edges of the crack subjected to moving unit step loads, the origin of the coordinates subjected to moving increasing loads Px m, the edges of the crack subjected to instantaneous impulse loads, the edges of the crack subjected to moving concentrated variable loads, the origin of the coordinates subjected to point loads, the edges of the crack subjected to a constant moving concentrated loads and the origin of the coordinates subjected to instantaneously moving impulse loads are studied respectively, and the analytical solutions of dislocation distribution function have been obtained.Dynamic extension problems of modeâ…¢interface crack between dissimilar composite materials are mainly discussed in chapter 3. Interface crack propagation problems under the influence of the central zone of the crack subjected to homogenous loads, the edges of the crack subjected to homogenous loads, the edges of the crack subjected to moving concentrated variable loads Px/ t and the origin of the coordinates subjected to point loads are studied separately, and analytical solutions of dislocation distribution functioncan also be attained. When the two materials have the same coefficient of materials, the solution of each of the above problems will be transformed into relevant solution...