The stress-strain state and duration to fracture of ring plates under creep conditions

Abstract

The stress-strain state of axisymmetrically loaded ring plates is investigated at any time before the beginning of fracture using the Rabotnov kinetic creep theory, which describes all three stages of creep. The time of onset of fracture is the time at which at any point of the plate the damage parameter reaches a critical value equal to unity (damage parameter is equal to zero for the undamaged material). The calculation of stress-strain state is carried out in two ways, and then the results are compared. In the first case, the solution of the unsteady-state creep problem taking into account damage accumulation is based on the solution of the steady-state creep problem. For simplicity, the von Mises criterion in constitutive equations is linearized, which is equivalent to using the Tresca-Saint-Venant criterion. In order to obtain a solution to the unsteady-state creep problem, it is necessary to multiply the known solution of the steady-state creep problem by some functions of coordinates and time. These functions can be found from the corresponding system of equations. The second technique is based on a finite element method, and the constitutive equations include the von Mises criterion. In the ANSYS program, a custom UserСreep procedure is activated for modeling damage accumulation. Dependences of the time of onset of fracture on the value of a bending moment applied to the contour of the inner hole of a ring plate are plotted. Diagrams obtained by two methods show that the use of the Tresca-Saint-Venant criterion provides a lower estimate for the time of onset of fracture.