Modeling of thermal stresses in elastic multilayer coating systems

Abstract

The performance and reliability of multilayer coating systems are strongly influenced by thermal stresses. The present study develops an alternative analytical model to predict the thermal stresses in elastic multilayer coating systems. An exact closed-form solution is obtained which is independent of the number of coating layers. In addition, with the definition of the coordinate system, the closed-form solution is concisely formulated. Specific results are calculated for thermal stresses in HfO2/SiO2 multilayer optical coatings, and a finite element analysis is performed to confirm the analytical results. The two results agree fairly well with each other. Also, when the thicknesses of the coating layers are much less than the substrate thickness, the approximate solution is obtained based on the exact closed-form solution, and its accuracy is examined.

Design of Comb Crack Resistant Milling Inserts: A Comparison of Stresses, Crack Propagation, and Deformation Behavior between Ti(C,N)/α-Al2O3 and Zr(C,N)/α-Al2O3 CVD Coatings

“…For the stress evaluation in the Ti(C,N) and Zr(C,N) layers, an average value of the DEC for TiC/TiN and ZrC/ZrN was used, respectively. Residual theoretical and thermal stresses were calculated for each layer using Equation (2), assuming a plane-state of residual stress [22]:…”

Thermal residual stresses in silicon thin film solar cells under operational cyclic thermal loading: A finite element analysis

“…Therefore, it is concluded that the Stoney stress model is merely valid for very small thickness ratios. Moreover, as mentioned in the introduction section, the Timoshenko and Gao et al models have been developed based on the beam bending theory using the strain continuity at the interfaces of the layers (Gao et al, 2015;Timoshenko, 1925). Also, the results of the Timoshenko and Gao et al models are the same at both thickness ratios given in Fig.…”

“…The width of the thin film-substrate composite is equal to 10 mm. Therefore, it is clear that the problem is multi-scale in nature (nano-sized film versus micro scale substrate with millimeter value for width of the composite) and hence Table 1 Biaxial stress relations in the thin film according to some analytical models (Gao et al, 2015;Stoney, 1909;Suhir, 1988;Timoshenko, 1925).…”

“…This model preserves the strain continuity at the interface of the two metal layers. Next, Kim et al (2000Kim et al ( , 1999 and Gao et al (2015) multilayers coating systems and compared their results with numerical solutions. While these models only consider the normal stresses, the 2D model proposed by Suhir (1988) captures the shear stress component in addition to the normal ones at the layer interfaces.…”

In Situ Investigations on Stress and Microstructure Evolution in Polycrystalline Ti(C,N)/α-Al2O3 CVD Coatings under Thermal Cycling Loads

“…Hkl A comparison of the experimentally obtained residual stress values (σ ) and the theoretical values (σ th ) was made. Since the magnitude of the total coating thickness is of micrometers (~9 µm) compared to the bulk size (5000 µm), it can be assumed that the coating is in a plane-state of residual stress and that the theoretical stress value of each single layer can be assumed to be independent of each other in the multilayer [22]. Hence, the magnitude of the thermal residual stress depends on the elastic modulus of the coating, the CTE of the layers and substrate, as well as the temperature variation.…”