PSI - Issue 22

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

247

5

To ensure that the ratio of contact gaps is the same as the ratio of tangential slips the tangential contact stiffness value is appropriately scaling as follows:

c max n c max t u u       

K

K

 

t

n

Under the mixed-mode debonding, both normal and tangential contact stresses contribute to the total fracture energy. A power law based energy criterion is used to define the bonding completion:

2

2

n ct G G G G               t cn

1

The normal and tangential fracture energies are computed as:

n t t G du , G du       n n t

The following data reported by Białas (2008) and Kim et al. (2007) are used to simulate interfacial debonding:  max = 50 MPa,  max = 25 MPa, cn G = 10 J/m 2 , ct G = 30 J/m 2 for the TC/TGO interface;  max = 200 MPa,  max = 100 MPa, cn G = 20 J/m 2 , ct G = 60 J/m 2 for the TGO/BC interface. 3. Result and discussion 3.1. Residual stress state without considering the interfacial debonding The simulation of the residual stresses developed in the TBC upon cooling without considering the interfacial debonding is done by switching off the cohesive option in contact elements. An attention is paid for regions with maximal stresses at the interfaces as responsible for the crack initiation. As Cen et al. (2019) have pointed out, in the crack initiation analysis it is more correct to consider the interfacial normal and tangential stresses than the out-of-plane stresses in the TC and BC layers since the former provide the driving force for interface damage. The distributions of the normal and tangential stresses along the TC/TGO and TGO/BC interfaces for the studied variants of periodical unit are shown in Fig. 2. The units of stresses hereinafter are MPa. As shown on the graph in Fig 2a, for the regular TGO shape the potential crack initiation sites are located at the peak of the TGO/BC interface, and at the valley and middle of the TC/TGO interface, where the corresponding normal and tangential stresses are well above the critical values. In the case of the irregular TGO, the stresses at the TC/TGO and TGO/BC interfaces exhibit a similar distribution pattern as shown in Fig. 2b (the sign of tangential stresses should not be considered). However, the maximum normal stresses located at the TGO/BC interfacial peak do not exceed 200 MPa implying there is no the initiation of mode I debonding at this location. Also, the debonding due to tangential contact stresses is most likely to occur at the middle of the TC/TGO and TGO/BC interfaces. We don’t discuss whether the debonding cracks will be further arrested due to existence of compressive stresses since the damage evolution will inevitably result in the stress redistribution.

Fig 2. Normal and tangential stresses along the interfaces: (a) for the regular and (b) irregular TGO profiles.