Elena N. Vilchevskaya

Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations

We develop an approach to studying the influence of stresses and strains on the kinetics of chemical reaction fronts based on the expression of the chemical affinity tensor that determines the configurational force acting at the transformation front. For a chemical reaction between diffusive gaseous and deformable solid constituents we formulate a kinetic equation in a form of the dependence of the reaction front velocity on the normal component of the chemical affinity tensor that in turn depends on stresses. We describe a locking effect—blocking the reaction by stresses at the reaction front and define the forbidden stresses or strains at which the chemical reaction cannot go. We develop a finite-element model to describe how stresses affect a chemical reaction front propagation. To demonstrate how the model works we consider a chemical front propagation in a plate with a groove assuming that the solid constituents are linear elastic. Comparing the front propagation in the vicinity of the groove top and at the bottom of the plate far from the groove we study how the stress concentrations, internal stresses and external loading, material and reaction parameters affect the reaction.

On Kinetics of Chemical Reaction Fronts in Elastic Solids

A chemical reaction front where an oxidation reaction is localized is considered as an internal surface dividing two solid deformable constituents. The reaction is sustained and controlled by the diffusion of the gas constituent through the oxide layer. The transformation strains produced by the chemical reaction lead to internal stresses which in turn affect the chemical reactions front kinetics. Analitical solution of axially-symmetric mechano-chemistry problems in a case of small strain approach are obtained. We examine how stress state affects the reaction front kinetics and demonstrate reaction locking effects due to internal stresses. We also study how the reaction rate depends on the chemical reaction front curvature.

Time Derivatives in Material and Spatial Description—What Are the Differences and Why Do They Concern Us?

This paper has many, albeit mostly didactic objectives. It is an attempt toward clarification of several concepts of continuum theory which can lead and have led to confusion. In a way the paper also creates a bridge between the lingo of the solid mechanics and the fluid mechanics communities. More specifically, an attempt will be made, first, to explain and to interpret the subtleties and the relations between the so-called material and spatial description of continuum fields. Second, the concept of time derivatives in material and spatial description will be investigated meticulously. In particular, it will be explained why and how the so-called material and total time derivatives differ and under which circumstances they turn out to be the same. To that end, material and total time derivatives will be defined separately and evaluated in context with local fields as well as during their use in integral formulations, i.e., when applied to balance equations. As a special example the mass balance is considered for closed as well as open bodies. In the same context the concept of a “moving observation point” will be introduced leading to a generalization of the usual material derivative. When the total time derivative is introduced the distinction between the purely mathematical notion of a coordinate system and the intrinsically physics-based concept of a frame of reference will gain particular importance.

Description of Thermal and Micro-Structural Processes in Generalized Continua: Zhilin’s Method and its Modifications

The method of description of thermal and micro-structural processes, developed by P.A.Zhilin is discussed. The main idea of the method consists of trans- formation of the energy balance equation to a special form called the reduced equation of energy balance. This form is obtained by separation of the stress tensors into elastic and dissipative components and introduction of quantities characterizing the physical processes associated with neglected degrees of freedom. As a result the energy bal- ance equation is divided into two or more parts, one of them is the reduced equation of energy balance, and the rest have a sense of heat conduction equation, diffusion equation, equation of structural transformations, etc. We discuss the applicability of this method to generalized continua, in particular, to media with rotational degrees of freedom and media with microstructure. Comparative analysis of various modifi- cations of Zhilins method, differed in the way of temperature, entropy and chemical potential introduction, is carried out.

Critical Radius in the Effect of Transformation Toughening of Zirconia Doped Ceramics and Cermets

Possible increase in fracture toughness of ceramics can be derived from stress induced martensite transformation from tetragonal to monoclinic polymorph of ZrO2 particles embedded into a bulk ceramic material. The incidence of transformations depends on zirconia particle size: too small particles remain overstabilized and do not experience transformation while too large particle may spontaneously transform at the technological stage of cooling. The critical particle size is, therefore, of primary concern for toughening of intrinsically brittle materials. We give a brief review of the previous results obtained. Then basing on the Gibbs energy expression and taking into account interface surface energy as well as thermal stresses, external loading and elastic interaction of the inclusions we estimate the proper range of particle sizes needed for considerable increase in fracture toughness. We specify general results obtained for the case of yttria stabilized ZrO2 particles in Al2O3- and WC-based ceramics.

Micropolar theory with production of rotational inertia: A farewell to material description

This paper takes a new look at micropolar media. Initially the necessary theoretical framework for a micropolar continuum is presented. To this end the standard macroscopic equations for mass, linear and angular momentum are complemented by a recently proposed kinetic equation for the moment of inertia tensor containing a production term. The main purpose of this paper is to study possible forms of this production term and its effects. For this reason two examples are investigated. In the first example we study a continuum of hollow particles subjected to an external pressure and gravity, such that the number of particles does not change. In the second example a continuous stream of matter through a crusher is considered so that the total number of particles will change. In context with these examples it will also become clear that the traditional Lagrangian way of describing the motion of solids is no longer adequate and should be superseded by an Eulerian approach.

On phase transitions in a domain of material inhomogeneity. II. Interaction of a crack with an inclusion experiencing a phase transition

We pose and study the problem on the interaction between a crack and an inclusion experiencing a phase transition of martensite type. We develop an algorithm for determining the inclusion phase state, which is numerically implemented with the finite element method. This procedure is used to study the inclusion phase transitions in the crack-induced field including the effects of the interaction between the crack and the inclusion. The detailed strain fields are calculated depending on the relative position of the crack and the inclusion, the external field, and the material parameters. It is shown that, for sufficient residual strains arising in the inclusion because of the crack, the inclusion material experiences a phase transition, which, in turn, can change the character of the subsequent crack propagation. We demonstrate that a stress-independent intrinsic phase transition, which can be caused, for example, by a change in the temperature, can also affect the crack propagation path. We also show that the influence of the phase transition induced field on the crack propagation path can be suppressed by the external field.

Micropolar Theory with Production of Rotational Inertia: A Rational Mechanics Approach

The aim of this paper is a review on recently found new aspects in the theory of micropolar media. For this purpose the necessary theoretical framework for a micropolar continuum is initially presented. Here the standard macroscopic equations for mass, linear and angular momentum, and energy are extended in two ways. First, the aspect of coupling linear and angular rotational kinetic energies is emphasized. Second, the equations are complemented by a recently proposed kinetic equation for the moment of inertia tensors containing a production term. We then continue to explore the possibilities of this new term for the case of micropolar media encountering a change of moment of inertia during a thermomechanical process. Particular emphasis is put on the general form of the production of moment of inertia for a transversally isotropic medium and its potential to describe, for example, structural changes from a transversally isotropic state to an isotropic one. In order to be able to comprehend and to study the influence of the various material parameters the production term is interpreted mesoscopically and various other examples are solved in closed form. Moreover, in context with the presented example problems it will also become clear that the traditional Lagrangian way of describing the motion of solids might sometimes no longer be adequate and must then be replaced by a Eulerian approach.

Modeling Stress-Affected Chemical Reactions in Solids–A Rational Mechanics Approach

In materials science the inluence of mechanical stresses on chemical reactions in solids is typically introduced empirically as part of diffusion or reaction coefficients by means of an Arrhenius ansatz. However, more recently an alternative approach based on rational mechanics was proposed, where the stresses affect the chemical process at the reaction front by a driving force given by the normal component of the chemical affinity tensor, which is composed of the chemical potential (or Eshelby) tensors characteristic of the reaction. In this paper the repercussions from both types of models will be investigated and compared to each other. As a specific example the process of silicon oxidation will be considered. However, the proposed alternative method could also be applied to other binary reactions in solids accompanied by eigenstrain formation. Moreover, an attempt is made to introduce the effect of all stress components on bulk diffusion in a logical fashion leading to a tensorial expression of the diffusion coefficient. Several model calculations are performed, mostly in explicit closed form, so that the effect of the various involved parameters can easily be studied.

Micropolar theory from the viewpoint of mesoscopic and mixture theories

This paper takes a nontraditional look at micropolar media. It emphasizes the idea that it may become necessary to abandon the concept of material particles if one wishes to describe micropolar matter in which structural changes or chemical reactions occur. Based on recent results presented by Ivanova and Vilchevskaya (2016) we will proceed as follows. First we shall summarize the theory required for handling such situations in terms of a single macroscopic continuum. Mne of its main features are new balance equations for the local tensors of inertia containing production terms. The new balances and in particular the productions will then be interpreted mesoscopically by taking the inner structure of micropolar matter into account. As an alternative way of understanding the new relations we shall also attempt to use the concepts of the theory of mixtures. However, we shall see by example that this line of reasoning has its limitations: A binary mixture of electrically charged species subjected to gravity will segregate. Hence it is impossible to use a single continuum for modeling this kind of motion. However, in this context it will also become clear that the traditional Lagrangian way of describing motion of structurally transforming materials is no longer adequate and should be superseded by the Eulerian approach.