PSI - Issue 22

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

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

sections of turbine blade samples after the high temperature cyclic oxidation (Fig. 1). Two cases of the TGO profile shown in Fig. 1a are analysed: a regular sinusoidal undulation with constant thickness and an irregular TGO layer with symmetrical sinusoidal penetration into the TC and BC layers. A sine curve with wavelength of 50  m and amplitude of 10  m is used to reproduce the TC/TGO and TGO/BC interfaces. The finite element model includes about 25000 eight-node generalized plane strain elements with the mesh refinement near the interfaces. Symmetry and periodicity boundary conditions are imposed on opposite lateral edges while the nodes at bottom are fixed along the y-direction, as shown in Fig. 1b.

Fig. 1. TBC system on the study: (a) BSE SEM micrograph of cross section; (b) finite element model.

The thermal loading history corresponding to the operating conditions of gas turbine blades consists of three stages: heating at the rate of 0.5 °C/h followed by dwelling for 22 h at 1100 °C, and finally cooling down to room temperature in 0.5 h. No temperature gradient within the TBC system is assumed. The stresses developed during oxide growth is not taking into account since their level is negligible compared with the thermally induced stresses as pointed out by Li et al. (2017).

2.3. Modelling crack development

The bilinear cohesive zone material model based of framework of Alfano and Crisfield (2001) and implemented in ANSYS (ANSYS, 2015) is used to simulate the crack development along the TC/TGO and TGO/BC interfaces. The interfacial debonding is defined in terms of contact gap and tangential slip distance. In mixed-mode debonding the interface separation depends on both normal and tangential components of traction. The equations for the normal and the tangential contact stresses are written as:     1 1 n n n m t t t m K u d , K u d       Damage is initiated when the corresponding stress in the cohesive element reaches its critical value  max or  max . It is assumed that the cohesive elements do not experience any damage under pure compression. The non-dimensional effective separation parameter for the mixed-mode is defined as:

2

2

n u                t m n t u u u

The debonding (damage) parameter is given by:

0 0 d         1 m m m m d   

1

1 m         m 

d

d





m

m

1

and

  

      

  

c n

c

u

u

t

 

c n u u 

c u u 

n

t

t