Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

Abstract

UDC 539.375 I. M. Lavit and Nguyen Viet TrungThe thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data.Introduction. In strength analysis, structural members used in power and chemical engineering can be treated as thick-walled cylinders subjected to internal pressure and a nonuniform temperature field. Under quasistatic loading, fracture of a cylinder is a results of radial crack propagation from the inner surface. The length of the segment of steady crack growth is comparable to the thickness of the cylinder; therefore, the strength of the cylinder should be analyzed using the fracture mechanics concepts. In addition, it is necessary to take into account the possibility of plastic deformation.The computational scheme of the problem is given in Fig. 1. A cylinder of inner radius R 1 and outer radius R 2 is in a plane strain state. It is assumed that the material of the cylinder is homogeneous, isotropic, and perfectly plastic and that its strain is small. In elastic deformation, the behavior of the material obeys Hooke's law, and in plastic deformation, it obeys the Prandtl-Reuss relations and the Mises yield condition. The yield point σ Y depends on temperature. The cylinder is weakened by a radial crack of length a. The interior of the cylinder and the crack cavity are acted upon by pressure p. The cylinder is heated nonuniformly. By virtue of the quasistatic formulation of the problem, the temperature field can be considered axisymmetric.The problem of elastic deformation of a cracked cylinder was first solved by Bowie and Freese [1] using the Kolosov-Muskhelishvili method with a conformal mapping of a circular ring onto the cross section of the cracked cylinder combined with a collocation method. Only the action of external pressure was considered. Shannon [2] solved the problem of the action of internal pressure using a finite-element method. In this case, unlike in the case considered in [1], pressure was also applied to the crack faces. Andrasis and Parker [3][4][5] improved the method proposed in [1] and solved a linear fracture mechanics problem for a cylinder containing a varied number of identical cracks equidistant from each and subjected to external and internal pressures, and also in the presence of a selfbalanced field of residual stresses. Pu and Hussain [6] solved the same problem using the finite-element method. The elastoplastic deformation of cracked cylinders have also been studied. Sumpter [7] solved an elastoplastic problem for a cylinder subjected to internal pressure using the finite-element method, and Tan an...

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