Alexander B. Freidin

On the chemical affinity tensor for chemical reactions in deformable materials

The mass, momentum, and energy balance equations are written out for a chemical reaction localized on the reaction front in an open “deformable body-gaseous component” system to derive the entropy production equation, which naturally allows one to obtain a formula for the chemical affinity tensor. This tensor determines both the chemical equilibrium and the transformation front kinetics. The locking effect, i.e., the effect of blocking the reaction by the stresses on the front, is discussed, and the conditions on the phase interface and on the chemical reaction front are compared.

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.

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.

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.

Forbidden Strains and Stresses in Mechanochemistry of Chemical Reaction Fronts

The influence of stresses and strains on a chemical reaction rate and a chemical reaction front velocity is studied basing on the concept of the chemical affinity tensor. The notion of forbidden zones formed by strains or stresses at which the reaction cannot go is discussed. Examples of forbidden zones are constructed.

On transient layers as new phase domains in composite materials

A model describing the development of transient layers as new phase domains in compositematerials is constructed under the assumption that the transient layers around (nano)particles are layers of the matrix material changed by the phase transformation and increase the effective volume of inclusions which become compound and consist of the nucleus (original particle) and the shell (transient layer of the new phase). As a result, the inclusion volume fraction increases, which, in turn, increases the particle influence efficiency. An example of spherical particles is used to consider the new phase development around an isolated particle and then, in the effective field approximation, around interacting particles in the composite material. The dependence of the compound inclusion radius on the external (averaged) strain is obtained for isotropic phases. Stability of the interphase boundaries depending on the parameters of the original inclusion material and the matrix phase materials is studied. The energy variations and the stress redistribution owing to the development of the new phase domains are considered in detail. It is shown that, in the case of an isolated inclusion, the development of a new phase may lead to a local energy decrease near the inclusions and, as a consequence, to a decrease in the stress concentration. At the same time, the formation of transient layers due to the phase transformation can result in an increase in the bulk modulus of elasticity as the effective shear modulus decreases.