Analytical modeling and analysis of fracture of functionally graded coatings
Coating and Surface Technology
Theoretical Chemistry: Molecules, Materials, Surfaces
Final Report Abstract
A theoretical model for functionally graded coatings on a homogeneous substrate (FGC/H) with pre-existing multiple cracks in the FGC was formulated with respect to possible application to thermal barrier coatings and to real materials. In this regard thermal loads (a heat flux and one cycle of cooling by ΔT) and mechanical loads are considered. The mathematical description of the model is based on the concept of singular integral equations. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The thermo-mechanical properties of an FGC are continuous functions of the thickness coordinate. The thermo-elastic problem for FGC/H structures was investigated as well as the problem with taking into account plasticity by using Dugdale-Barenblatt model, where the plastic zones are located near the crack tips. This model allows to use elasticity theory and to keep similar constitutive equations as in thermo-elastic problem. The model takes into account different crack models, namely, the thermal isolated and partially thermal permeable cracks in the thermal problem, cracks with closure and with plastic zones in the thermo-elastic problem. Two kinds of solutions of the singular integral equations were obtained, a numerical solution based on the Chebyshev polynomials for a general case, and an approximate analytical solution for a special case when one crack is much larger than others. The presented model allows to examine different crack patterns, which are reported in the literature, by carrying out numerical experiments and calculating stress intensity factors (SIFs), fracture angles (a deviation of cracks from the initial direction of propagation), critical loads, when this propagation starts, as well as crack tip opening displacements (CTODs). The problems with taking crack closure effects into account and accounting for plasticity are more complicated and need to solve some additional non-linear equations. Consequently the model with plasticity is still under construction. The analysis of the results show, that for thermo-elastic problems with accounting for the thermal residual stresses, the contribution of these stresses due to sudden cooling by ΔT is much greater than the residual stresses obtained from the thermal problems for FGC/H under a heat flux. In the case of a heat flux the maximum contribution to residual stresses gives the thermo-isolated cracks. Considering the partially thermal permeable cracks, which reflect the more practical case, because of the thermal conductivity of a gas inside the cracks, leads to a decrease of thermal residual stresses. The fully permeable cracks show no residual stresses at all. The developed model combines fracture mechanics and material models (FGCs) for thermomechanical loads for FGC/H structures. This theoretical investigation, applied to real material combinations, e.g. zirconia/nickel or zirconia/steel, shows some peculiarities of the problem (e.g. the influence of material gradations on the mutual crack interactions with respect to the fracture characteristics) and shows the directions of further investigations of FGC/H structures. In addition, the proposed model (of functional gradation) in combination with a detailed parametric analysis can help to optimize (e.g. in terms of SIFs and CTODs) the gradation of FGCs (i.e. material parameters) and their structure (i.e. geometrical parameters) in order to improve the fracture resistance of FGC/H systems.
Publications
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Thermal fracture of a functionally graded/homogeneous bimaterial with a system of cracks, Theor. Appl. Fract. Mech., 55 (2011), 148-157
V. Petrova, S. Schmauder
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Mathematical modelling and thermal stress intensity factors evaluation for an interface crack in the presence of a system of cracks in functionally graded/ homogeneous bimaterials, Comp. Mater. Sci. 52 (2012), 171-177
V. Petrova, S. Schmauder
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Crack closure effects in thermal fracture of functionally graded/homogeneous bimaterials with systems of cracks, Z. Angew. Math. Mech. (ZAMM) 95 (10) (2015), 1027-1036
V. Petrova, S. Schmauder
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Modeling of edge cracks interaction, Frattura ed Integrita Strutturale 10(36) (2016), 8-26
V. Petrova, S. Schmauder, A. Shashkin
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Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction, Physical Mesomechanics 20(3) (2017), 241-249
V. Petrova, S. Schmauder
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Fracture of functionally graded thermal barrier coating on a homogeneous substrate: Models, methods, analysis, Journal of Physics: Conference Series 973(1) (2018), 012017
V. Petrova, S. Schmauder
