Finite element simulation of residual stress of double-ceramic-layer La2Zr2O7/8YSZ thermal barrier coatings using birth and death element technique
Highlights
► Double-ceramic-layer 8YSZ/La2Zr2O7 TBCs. ► Birth and death element technique. ► The failure mode strongly depend on the residual stress. ► Computational Micro-Mechanics.
Introduction
As important ceramic coating materials, thermal barrier coatings (TBCs) play an important role in reducing the service temperature of high temperature components and protecting the high temperature components (superalloy) against the wear, corrosion and erosion at high temperature. They are often considered to be used in the aircraft and the turbine blades [1], [2], [3], [4], [5]. The 8 wt.% yttria stabilized zirconia (8YSZ) has been used in the industry due to its low thermal conductivity, high thermal expansion coefficient which is near to the superalloy and bond-coat MCrAlY (where MNi and/or Co) for a long time. During those years, researchers have focused on the investigation of 8YSZ TBCs from the aspects of feedstock preparation, coating preparation and the characterization of the basic mechanical properties, such as residual stress, thermal insulation behavior, thermal shock resistance, oxidation resistance and failure at high temperature [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. As the operation temperature of the hot components is becoming higher and higher, and the demand to the TBCs is becoming urgently and which is strongly depend on the selection of the material of the TBCs not only being confined at the increase of the holding time of the high temperature. Based on the facts, in the past decades, the zirconate (aluminate)-based TBCs which are considered to be the candidate materials for the future were developed and investigated [19], [20], [21]. Previous research including the following aspects: preparation and characterization of the thermal barrier oxide bulk materials [22], [23], fabrication and characterization of the zirconate-based TBCs [24], [25]. But the latter research is relatively less. Especially, the failure mode and mechanism about the zirconate-based TBCs has nearly not been investigated so far.
There are many methods to evaluate and estimate the residual stress of the coating including the experimental means X-ray diffraction, micro-Raman techniques, micro displacement laser transducer, high-precision incremental-step hole-drilling method, Modified Layer Removal Method [26], [27], [28], [29], [30], [31], [32], [33], and the finite element method [34], [35], [36], [37], [38] (including the mathematical calculation [39], [40]). Many researchers have investigated the residual stress without considering the deposition process of the plasma sprayed coating using elastic–plastic finite element method [41], [42], [43], [44]. Especially, the residual stress of the multilayer or gradient coating are calculated by finite element method [45], [46], [47], [48], but still the coating seem to be finished in one time which is not consistent with the preparation process of the actual coating. Zhang et al. [49] has investigated the residual stress and further predicted the thermal residual stresses in elastic multilayer coating systems due to differential thermal contraction based on the balance of force and moment. A closed-form solution was obtained which is independent of the number of coating layers.
As the TBCs are composed of multilayer materials including the metallic layer and ceramic layer, the residual stress can be induced inevitable in the coating system due to the mismatch between the metal and ceramic layer. Residual stress is a very important factor which can affect the failure mode of the TBCs fabricated by atmospheric plasma spray (APS). The residual stress can promote the crack initiation, grown and propagation in the TBCs. The research of residual stress is becoming a hot topic because that the failure mode and life prediction of TBCs are often based on the residual stress. In this paper, the residual stress of the DCL LZ/8YSZ TBCs has been investigated by the finite element simulation using birth and death element technique. The authors will try to fill the gap of these relevant investigations.
Section snippets
Finite element procedure
Usually, the residual stress is often composed of the following parts:
- (i)
The quenching stress, when the coating was sprayed on to the cooler substrate and the quenching stress can be induced in the ceramic coating. Quenching stress was generated due to rapid contraction of the sprayed splats as which were rapidly cooled from processing temperature (usually assumed to be melting point) to substrate temperate. Analytically, the magnitude of tensile quenching stress can be estimated from:
Results and discussion
In this section, the simulation results about the stress during the thermal spraying and the cooling process have been extracted from the ANSYS visualization and analyzed systematically. Residual stress components resulting from the finite element analysis were obtained in the following directions: (1) radial stress corresponding to stress value along the radial direction (σxx); (2) axial stress component that refers to stress profile through the thickness of coatings (σyy) and (3) shear stress
Conclusions
In this paper, the residual stress of DCL LZ/8YSZ TBCs has been calculated using birth and death element based on the actual thermal spray process, and the residual stress of the single ceramic layer 8YSZ has also been calculated and compared systematically, some important result can be summarized as follows:
- (1)
The stress always increases with the increase of the spraying time (or increasing the deposition layers) in the process of thermal spraying. The maximum tensile radial stress increase
Acknowledgment
This work was supported by program of excellent team at Harbin Institute of Technology. The authors would also like to thank the High Speed Computational Center of Harbin Institute of Technology (HIT) for providing software support and simulation platform and would also thank Prof. Dongyang Li (University of Alberta, Edmonton, Alberta, Canada) for useful discussion about the finite element simulation.
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