PSI - Issue 22

Andrey Burov et al. / Procedia Structural Integrity 22 (2019) 243–250 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Song et al. (2018, 2019) have investigated the influence of TGO growth mode (uniform or non-uniform) and thermal loading waveform on stress evolution and cracking at the TC/TGO interface. It has been found that the interfacial roughness and TGO growth mode do not practically change the location of crack nucleation which always occurs at the middle region. However, non uniform TGO growth accelerates the onset and evolution of interfacial damage. Important is that with the non-uniform oxide growth, mixed mode cracks are more likely to be initiated whereas the uniform growth leads to initiation of tensile mode cracks. The TBC failures can be associated with the nucleation and evolution of cracks within the TC, and the delamination of TC/TGO and TGO/BC interfaces as Cen et al. (2019) have pointed out. What fracture mechanism will occur depends on the constituents properties, TGO thickness and interface morphology. The TGO/BC interface delamination primarily depends on the strain energy stored within the TGO while the low fracture strength and toughness of TC/TGO interface is mainly responsible for debonding between the TC and TGO layers. However, most studies related to modeling of the interface failure process have been performed assuming that debonding occurs either at the TC/TGO or TGO/BC interface. A notable exception is work of Ranjbar Far et al. (2012) which have used the CZM approach to investigate failure of a TBC system due to crack propagation along the TC/TGO and TGO/BC interfaces as well as within a lamellae-structured TC layer. They have shown a complicated interplay between failure mechanisms resulting in different crack development scenarios when a simultaneous separation of both interfaces is permitted. In the present work, finite element (FE) modeling is employed to study interfacial cracking behaviour in TBC on a single crystal Ni-based superalloy. The cohesive zone elements are implemented in the model to simulate debonding between the TC, TGO and BC layers. To evaluate the effect of the interface geometry on the residual stress state and interface cracking behaviour, two cases of the TGO profile are analysed: a regular sinusoidal undulation with constant thickness and an irregular (unevenly thicker) TGO layer with symmetrical penetration into TC and BC layers. 2. Materials and methods 2.1. Materials behavior The considered TBC system consists of four layers: the 2 mm thick substrate (ZhS32 superalloy), the 30 μm thick NiCoCrAlY-bond coat (BC), the 60 μm thick EB -PVD partially stabilized zirconia (ZrO 2 -7wt%Y 2 O 3 ) top coat (TC), and α Al 2 O 3 thermally grown oxide (TGO) of an average 7 μm thickness (Fig. 1a). Materials of all layers are treated as homogeneous and isotropic. It is assumed that the substrate, TC and TGO are viscous elastic materials. For the BC material exhibiting an elastic and viscous-plastic behavior, the elastic-ideal plastic law is adopted. The Norton power-law is employed to compute the creep strain rate: ̇ =  The temperature-dependent material data for the coefficient of thermal expansion  x 10 -6 /  C  , Young’s modulus E (GPa), Poisson’s ratio v and yield strength  s (MPa) collected from works of Cheng et al. (1998), Zhou and Hashida (2001), and Eliseev et al. (2008) are listed in Table 1. The values of B and n are also temperature-dependent as presented in Table 2.

Table 1. Temperature-dependent properties of the TBC constituents T,  C TC TGO Substrate

BC

E

v

E

v

E

v

E

v

 







 s

20

9.0 9.6

48 0.10 44 0.10

8.0 8.4 9.0 9.6

400 0.23 380 0.24 355 0.25 320 0.25

12.1 13.1 14.7 16.4

141 0.30 135 0.30 126 0.30

13.6 14.6 16.1 17.6

200 175 145 110

0.30 0.31 0.32 0.33

426 396 284 114

400 800

10.8 34 0.11 12.2 22 0.12

1100

84

0.30

Table 2. Temperature-dependent data for creep parameters TC TGO

Substrate

BC

T,  C

1100

1100

800  C

 900

 600

700

 850





B 1.8  10 -11 1.8  10 -8 7.3  10 -12 7.3  10 -8 1.28  10 -19 1.13  10 -13 6.54  10 -19 2.2  10 -12 2.5  10 -8 n 1 1 1 1 5 4.55 4.57 2.99 2.45

2.2. Finite element model A two-dimensional FE model is constructed by using the commercial package ANSYS (ANSYS, 2016). The model is designed to represent the coating configuration corresponding to that obtained with microstructure analysis on the TBC cross-