On transition functions and nonlinearity measures in gradient coatings

Purpose: In this paper the influence of the shape of transition functions between the single layers of multilayer coating on the final internal stresses states in the coating was investigated. Additionally the degree of nonlinearity and asymmetry of postulated gradient layers was calculated. Design/methodology/approach: Physical and mathematical models of the layers were created basing on classical theory of elasto-plastic materials. Computer model of the object (coating + substrate) describing internal strains and stresses states in layers, after deposition process, was created using FEM method. Findings: New concepts of nonlinearity and asymmetry measurability of transition function were introduced. Using predefined measures the dependence between internal stresses fields in postulated class of gradient layers and values of nonlinearity and asymmetry were obtained. Research limitations/implications: There are an infinite number of possible measures of heterogeneity and nonlinearity of the transition layers. Also there are infinitely many functions with the same measures of asymmetry and nonlinearity, but different mathematical forms, thus a functions of the same measures value form a kind of class of abstraction. So it is convenient to consider specific representatives of the given class and expand the obtained results to remaining representatives which is laborious and ambiguous task. Practical implications: Proposed measures of gradient layers will become a significant components of the PC software in future, which will upgrade the designing process of hard, wear resistant coatings architecture. Originality/value: A class of monotonic and asymmetric transition functions, describing continuous physico-chemical material’s parameters changes in each layer of K-layered coating was created. Also a new measures of nonlinearity and asymmetry of transition function were introduced.