PSI - Issue 22

2

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

Andrey Burov et al. / Procedia Structural Integrity 22 (2019) 243–250

244

Nomenclature ̇

equivalent creep strain rate (s -1 ) von Mises equivalent stress (MPa) creep pre-factor (s -1 MPa -n ) power law creep exponent

 B n

damage parameter in mixed-mode debonding normal and tangential stress (MPa), respectively

d m

 n ,  t

 max ,  max

maximum normal and tangential stress (MPa) contact elements can bear, respectively

u n , u t c n n u ,u t t u ,u n t K ,K n t G ,G cn ct G ,G c

contact gap and tangential slip distance (  m)

contact gap at  max and completion of debonding, respectively tangential slip distance at  max and completion of debonding, respectively normal and tangential contact stiffness (MPa/m), respectively

normal and tangential fracture energies (J/m

2 ), respectively

normal and tangential critical fracture energies, respectively

Finite element simulation is a valuable tool in studying the stress state and failure of TBCs as it provides insights into the influence of interface morphology, service conditions and properties of constituents on the TBC behavior. Computational studies carried out by Ranjbar-Far et al. (2010) have revealed that upon cooling of a TBC system from a stress-free state down to ambient temperature, the mismatch between the thermal expansion coefficients of components and the interface asperity cause stresses normal to the interfaces. Stresses are largest at the maximum convex (peak) or minimum concave (valley) region of the interface profile. The stresses are tensile in the peak and compressive in the valley if the oxide layer is thin or absent. The TGO growth increases the stress level while the stresses turn to be tensile in valley regions and compressive at the peaks. The maximum tensile stresses in the TBC layer are shifted from the peak to the middle of asperity flank. Also, the tensile and the compressive stresses become progressively larger as the asperity amplitude is increased. Similar results have been reported by Białas (2008) and Moridi (2014). Besides the thermal mismatch, interface asperity and TGO growth, the residual stress state is governed by a set of other factors such as non-homogenous temperature distribution, relaxation via plastic or creep deformation, thermal load waveform and interface delamination. It should be mentioned, the computed stress state and fracture pattern strongly depend on simulation parameters and materials used for a particular TBC system. A comprehensive review on critical issues in modelling the stress and failure evolution in TBC systems has been presented by Baker and Seiler (2017). A sinusoidal approximation of interface geometry with a constant TGO thickness is generally used to model a periodic unit of TBC. However, as stressed by Gupta et al. (2015), the real interface is very nonhomogeneous consisting of regions with convex or concave asperities of different amplitude and wavelength as well as uneven TGO thickness. The use an idealized geometry may therefore underestimate the stress state as it has been demonstrated by Baker and Seiler (2017). In our previous work (Fedorova et al. 2018), it has been shown that the TGO shape has a significant impact on the residual stress state in both the TC/TGO and TGO/BC interfaces. In the case of the unevenly thicker TGO, the compressive stresses in the TGO layer near the peak of the TC/TGO interface are almost three times higher than the stresses developed at the same location in the TBC system with the even TGO layer. A similar, although less pronounced, effect is observed in the peak region of the TGO/BC interface. The level of compressive stresses implies a higher possibility of TBC failure at the TC/TGO interface than at the boundary between the TGO and BC layers. In a similar way, Che et al. (2009) have shown that the uneven TGO leads to 200% increase in the out-of-plane stresses and 60% decrease in maximum tensile stresses along the TGO/TC interface. Chen et al. (2018) have also demonstrated a remarkable influence of inhomogeneous TGO thickness on residual stresses along the TC/TGO and TGO/BC interfaces. Although the stress analysis of TBCs performed without considering the interfacial fracture can forecast the location and conditions favorable for crack onset or growth, it lacks to predict its propagation and reflect the stress redistribution induced by the debonding process. These limitations are overcome by using new computational methods based on fracture mechanics, such as extended finite element method, virtual crack closured technique, and cohesive zone model. Application of these methods in studying the crack propagation behavior of TBCs has been described in detail by Wang et al. (2016). The cohesive zone model (CZM) based on a softening relationship between traction and separation has been widely employed to reproduce the fracture process at the TC/TGO and TGO/BC interfaces. The CZM is well suited for simulating the initiation as well as propagation of interfacial cracks. Cen et al. (2019) have analyzed normal and tangential stresses at the TC/TGO and TGO/BC interfaces to investigate the interfacial delamination. Results obtained with the CZM approach have shown that the delamination at TGO/BC interface on cooling is started with crack nucleation near the peak position followed by its development along the interface. The crack is finally arrested before entering the valley due to compressive stress region. The interaction between the TGO/BC debonding and a possible evolution of cracks within the TC layer is observed as the former leads to an increase in the tensile stresses in the TC. However, the delamination of the TGO/TC interface has not been considered in this study as the authors have concluded a low probability of its occurrence.