On the velocity of a moving phase boundary in solids (original) (raw)

A general relationship between the driving force and the velocity of a moving phase boundary in thermoelastic solids is established on the basis of non-equilibrium jump relations at the discontinuity. The non-equilibrium jump relations are formulated in terms of contact quantities and local equilibrium fields. The contact quantities are introduced following ideas of the thermodynamics of discrete systems. It is shown that under certain simplifications the derived relationship can be reduced to a known kinetic relation.

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On the thermodynamic conditions at moving phase-transition fronts in thermoelastic solids

Journal of Non-Equilibrium Thermodynamics, 2000

The main goal of the paper is to establish possible thermodynamic conditions at a phase boundary to describe a propagation of phase-transition fronts in crystalline solids. Classical equilibrium conditions are not valid in the case of fast propagation of sharp phase interfaces through the material during a stress-induced martensitic phase transformation. We propose to extend the equilibrium conditions to the non-equilibrium case in the framework of the thermodynamics of discrete systems. To provide the description of non-equilibrium states, the thermodynamic state space includes so-called contact quantities in addition to usual local equilibrium variables.

Thermomechanics of Moving Phase Boundaries in Solids

2005

A common problem in crack tip or phase-transition front propagation is the determination of the velocity of the irreversible motion of the singularity set. A supplementary constitutive assumption is needed for this determination. A typical solution is the introduction of a kinetic relation between the velocity and the driving force acting on the singularity set. Any kind of such kinetic relation determines entropy production at the singularity set. This means that a direct assumption about the entropy production can be equivalently employed. The entropy production supposes a non-equilibrium description of the process. The corresponding non-equilibrium description is developed in the case of phase-transition front propagation. The nonequilibrium jump relations at the phase boundary followed by a simple hypothesis about entropy production at the front provide a good agreement with experimental observations and theoretical predictions. The same approach can be applied to the problem of crack propagation.

Moving singularities in thermoelastic solids

International Journal of Fracture, 2007

The solution of the evolution problem of a discontinuity requires the formulation of a kinetic law of the progress relating the driving force and the velocity of the singularity. In the case of a crack, the energy-release rate can be computed (in quasi-statics and in the absence of thermal and intrinsic dissipations) by means of the celebrated Jintegral of fracture that is known to be path-independent and, therefore, provides a very convenient estimation of the driving force once the field solution is known. However, the velocity at the crack tip remains undetermined. A similar situation holds for a displacive phase-transition front propagation. The driving force acting on the phase boundary can be determined, but not the velocity of the displacive phasetransition front.

Stress-induced phase-transition front propagation in thermoelastic solids

European Journal of Mechanics - A/Solids, 2005

A simplest possible mathematical model of martensitic phase transition front propagation is considered in the paper. Martensite and austenite phases are treated as isotropic linear thermoelastic materials. The phase transition front is viewed as an ideal mathematical discontinuity surface. Only one variant of martensite is involved. The problem remains nonlinear even in this simplified description that supposes a numerical solution. A non-equilibrium description of the process is provided by means of non-equilibrium jump relations at the moving phase boundary, which are formulated in terms of contact quantities. The same contact quantities are used in the construction of a finite-volume numerical scheme. The additional constitutive information is introduced by a certain assumption about the entropy production at the phase boundary. Results of numerical simulations show that the proposed approach allows us to capture experimental observations while corresponding to theoretical predictions in spite of the idealization of the process.

Thermodynamical description of running discontinuities

Kluwer Academic Publishers eBooks, 2006

Determination of the evolution of a system is studied through the definition of functionals presented here in the case of non linear dynamics. After a short account of the necessary notions for the description of the motion and of the mechanical interactions, the paper is devoted to the Hamiltonian functional of the system. The evolution of discontinuities along moving surfaces generally generates an entropy production which is a linear function of the speed of the moving interface. The thermodynamical force accompanying this motion is an energy release rate, the expression of which is related to the gradient of Hamiltonian of the system. The canonical equations of shock waves and moving discontinuities are established for any continuum. This provides a useful way of establishing constitutive laws for moving interfaces.

The Riemann problem for thermoelastic materials with phase change

Journal of Differential Equations, 2004

We consider the Riemann problem for a system of conservation laws related to a phase transition problem. The system is nonisentropic and we treat the case where the latent heat is not zero. We study the cases where the initial data are given in the same phase and in the different phases. The role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion. We confine our attention to the case where the speeds of phase boundaries are close to zero. This is one interesting case in physics. We discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the Riemann problem.

On impact induced propagating phase boundaries. Thermal effects

Eds. WK Nowacki, Han Zhao, Proceedings of the 10th …, 2007

Abstract: This paper investigates dynamic aspects of solid-solid phase transitions when thermal effects are taken into account. We consider an explicit one-dimensional non-monotone thermo-elastic model able to describe some aspects of the thermomechanical response ...

Boundary integral equations of dynamics problems for multi-connected thermoelastic semi-plane with a free boundary

International Journal of Computational Methods and Experimental Measurements

The dynamics of multi-connected thermoelastic semiplane with the non-stationary power source and thermal effects by using of a model of coupled thermoelasticity is investigated. Green's tensor in the space of the Laplace transforms in time describes the displacements of medium under the effect of the impulse concentrated power and thermal sources. The generalized solution of the problem of the dynamics of thermoelastic semiplane with the free boundary under the effect of arbitrary mass forces and thermal sources in 2D-case is built.

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