Strain field analysis in nanoindentation test of gradient coatings

Purpose: In the paper strain distributions within TiAlN/TiN gradient coatings in nanoindentation test were analysed. The main goal was to examine the influence of the type of a gradient layer on strain distributions in the area of the indenter/coating. Design/methodology/approach: For physical modelling purposes Cr, TiN and TiAlN layers were treated as a continuous medium. Basing on this simplification for the mathematical description of the strain states in the coating a classical theory of stiffness was used. Gradient layers were modelled using the conception of transition function which describe continuous physico-chemical material parameters changes in each layer in the multilayer coating. The computer analysis of the strain fields in the coating after deposition process was done vie FEM method. Findings: For a chosen types of gradient coatings the strain distributions in the coating under external loads (nanoindentation test) were calculated. Using created examples of transition functions, the influence of the shape of the function on strain isolines in the area of the indenter/coating was examined. Research limitations/implications: The main simplification which was done during creation of the mathematical model was an assumption that the coating and the substrate are continuous media. This assumption causes that some physical effects occurring during experimental nanoindentation test can not be properly described in a computer model. Also there are numerous mathematical models of contact, so obtained numerical results (strain distributions) strongly depend of the postulated contact model. Practical implications: For a practical implications of the obtained results one should include a mathematical description of the strain states in the nanoindentation test of gradient coatings. The stress and strain fields analysis is extremely important in respect of fracture analysis. It should be also emphasis, that proposed mathematical description of gradient layer using transition function conception is an easy way to represent physical and chemical properties of gradient coating in computer models. The advantage of such a description of gradient layers can be used for example in polyoptimization process of multilayer gradient coatings. Originality/value: The main value of the paper is the comparison study of strain distribution in nanoindentation test of three different gradient coatings represented be three types of transition functions: (a) step function, (b) linear function and (c) modified non symmetrical sigmoidal function.