Fracture of non-uniformly heated annular disk
Keywords:
non-uniformly heated annular disk, crack with bonds between the faces, prefracture zone, cohesive forcesAbstract
A fracture model for non-uniformly heated annular disk, based on consideration of fracture process zone near the crack tip was proposed. The fracture zone (end zone) is a finite length layer, which is part of the rectilinear crack, and in which bonds between individual structural elements is partially broken. The bonds between the crack faces in the end zone are modeled by continuous application to crack surface the cohesive forces constraining crack disclosure. The boundary problem for equilibrium of the disk weakened by rectilinear crack with bonds between faces, under the action of heat stress and forces in bonds, is reduced to a nonlinear singular integrodifferential equation with a Cauchy type kernel. The singular integrodifferential equation using an algebraization procedure is reduced to a system of nonlinear algebraic equations which is solved by the method of successive approximations, and an iterative algorithm similar to Il’yushin elastic solutions method. The limit equilibrium condition for crack with end zones in the annular non-uniformly heated disk is formulated taking into account the criterion of limit bonds stretching. The dependence of limit intensity of thermal effect on the annular disc from the crack length are obtained; forces in bonds between the crack faces in the end zone are found.
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