Computational model of cracking in circular heated disk
Keywords:
circular disk, temperature field, zone of weakened interparticle bonds, tractions in bonds, crackingAbstract
A computational model describing the cracking in the circular disk under the influence of thermal stresses is developed. It is assumed that the zone of cracking process is a finite length layer, containing the material with partially broken bonds between the individual structural elements. The bonds between the prefracture zone faces are modeled by the cohesive forces continuously applied to the faces and constraining its disclosure. The boundary problem for equilibrium of the heated disk weakened by rectilinear prefracture zone is reduced to a nonlinear singular integrodifferential equation with a Cauchy type kernel. The singular integrodifferential equation 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. It is assumed that the temperature field in the circular disk has an axial symmetry, and the elastic characteristics and the coefficient of linear thermal expansion of the material do not depend on temperature. The limit equilibrium analysis of the zone of weakened interparticle bonds is performed on the basis of criterion of limit traction of the bonds. Relations for determining the critical value of the heat effect intensity at which in the circular disk occurs cracking are obtained.
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