Solving problems of thermoviscoelastoplastic and continuous fracture of prismatic bodies

Abstract

A procedure of solving problems of thermoviscoelastoplasticity and continuous fracture of prismatic bodies based on the semianalytic finite-element method is developed and implemented Keywords: thermoviscoelastoplasticity, continuous fracture, semi-analytic finite-element method, prismatic body, spatial problemsIntroduction. The thermoviscoelastoplastic deformation of three-dimensional bodies has to be considered in a great many applied problems [16][17][18][19][20], which should be solved numerically. The finite-element method (FEM) is widely used in scientific and engineering numerical simulation and applied to constantly expanding range of objects and processes. Despite the high efficiency of modern computers, it is of importance to develop modifications of the FEM to be applied to a wide class of objects with specific shape, which makes it possible to optimize the structure of the governing equations and to develop efficient algorithms for solving systems of FEM equations. One of such modifications of the FEM is the semianalytic finite-element method (SFEM), which is currently used to solve a wide range of problems. For example, the application of the SFEM to elastic, elastoplastic, creep, contact, and fracture problems is discussed in [1, 2, 14, 15, etc.].One of the applications of the problem considered here is determining the life of critical elements of power equipment such as turbine blades. Methods for solving spatial creep problems are described in [4, 7, 12, etc.]. In [4,12], the creep of a blade was modeled regardless of its damage. Moreover, these and other studies disregard the facts that a continuous fracture zone may occur and develop and that a crack may form.A method for modeling creep and continuous fracture zones in prismatic bodies was developed in [15]. This method was then used to determine the life of a gas turbine blade taking into account continuous fracture. It was shown that a continuous fracture zone is a stress concentrator with instantaneous plastic strains around. Moreover, blades operate in a stationary inhomogeneous temperature field, which induces thermal strains. These factors give rise to additional stress components, which were neglected in [15]. In [1], it was demonstrated that insignificant changes in the stress-strain state (SSS) have a significant effect on the creep life.To improve the efficiency of the problem-solving method, it is necessary to use finite elements that would allow us to obtain exact solutions based on finite-element models of minimum dimension and efficient algorithms for iterative solution of systems of SFEM equations.Thus, the objective of the present paper is to develop an efficient procedure based on the SFEM for solving problems of thermoviscoelastoplasticity and continuous fracture for prismatic bodies, including derivation of governing equations for new finite elements that account for the variation of the metric tensor in the cross section, to develop efficient algorithms for iterative solution of systems of SFEM equations, and to analyze the i...