The heating rate influence on the dynamics of sample destruction

Abstract

We consider a mathematical model of the dynamics of the initial stage of destruction of a homogeneous sample under the influence of heating. For the mathematical description of the process we apply recently proposed mathematical model of a non-equilibrium phase transitions formulated in terms of the Cahn-Hillard theory of spinodal decomposition. The mathematical model is one-dimensional in spatial variables. The mathematical model is an initial boundary value problem for a system of four nonlinear partial differential equations of the fourth order. The mathematical model is formulated for the given variables. Using the specified mathematical model, the influence of the heating rate of the left end of the sample on the dynamics of the initial stage of sample destruction was studied. A modified finite difference method of the second order of accuracy is used as one of the numerical methods. The description and analysis of examples of the obtained numerical results are carried out. The obtained results of numerical studied of the mathematical model demonstrate a nonlocal character of the process. The directions of further investigations of the initial stage of homogeneous samples and structures destruction are discussed.

Keywords

• destruction of a homogeneous sample
• critical processes
• external action
• heating
• mathematical model
• theory of spinodal decomposition
• numerical experiments