МОДЕЛЮВАННЯ ПРОЦЕСІВ СТРУКТУРОУТВОРЕННЯ КОМПОЗИТІВ МЕТОДАМИ ТЕОРІЇ КАТАСТРОФ

Abstract

The paper examines the possibility to model the structure formation processes in binder materials using some methods of catastrophe theory. Events at the level of coexistence and interaction of macroscopic and microscopic phenomena are analyzed. The dynamics of transformations at this level of material organization is considered using the method of structural potential, similar to the thermodynamic one, with the possibility of its empirical identification based on the processing of microscopic images. The transition to the potential functions of the theory of catastrophes is carried out by means of geometric parameterization ‒ selection of areas of the volume occupied by material phases and areas associated with interface boundaries. The model of structure formation is presented as a phenomenon in stochastic gradient systems caused by the emergence of features of the structural potential and their transformation upon changing the controlling physicochemical parameters. The possibility of adapting the apparatus of phase diagrams of three-component systems to the considered tasks and its affinity with catastrophe theory models is shown. The structural-phase diagram is constructed by analogy to the Gibbs-Roseboom method on a triangle, while the coordinates are parts of components with different geometric structures ‒ cavities, continuous material at a given scale and interfaces with the surrounding transformed material. From the potential functions of the theory of catastrophes, those that correspond to the analyzed system are reasonably selected - umbilical functions, and in the simplified version ‒ potentials of one variable. A scheme for the study of materials using methods of structural potentials has been developed, which is based on the determination of mesoscopic scales for the material being studied, on the transition to the frequency characteristics of the image, then to the structural potential, which determines the range of structures realized in the material and, in the future, to the transition from structural potentials to physical properties.