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A mathematical model of transformation plasticity in zirconium oxide ceramics

Klyuev A.V., Trussov P.V.

#### Abstract:

Ceramics based on zirconium dioxide is widely used for production of components for gas turbines, cutting tools, devices for electronics, and equipment for sports. We propose to subdivide mathematical models for such materials into two groups: (1) structural models; (2) models where the transformation of isolated phase is accounted for. The latter group includes the models of `interphase boundaries’, which help us to study the equilibrium of interphase boundaries. Analysis of both groups of mathematical models can clarify significantly the physics of the plasticity of transformation. Our goal is to develop a mathematical model for description of deformation of ceramics based on zirconium dioxide and to determine the basic relationships for such kind of materials. In order to develop the model on a macrolevel, we use the theory of nonequilibrium thermodynamics and estimate the unknown constants in equations using the structural models. A criterion of transformation of structural element is formulated using the concept of equilibrium thermodynamics. It is proven that the approach applied satisfies the hypothesis of local equilibrium of a nonequilibrium system, which can be described by a representative volume of structural model.

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