PSI - Issue 61

Mehmet N. Balci et al. / Procedia Structural Integrity 61 (2024) 331–339 Balci and Yalcin / Structural Integrity Procedia 00 (2019) 000 – 000

335

5

I K and

II K are found as:

tip R   + 2 1

tip R   + 2 1









( ) ( v v v v − − − E C D B

)

( ) ( u u u u − − − E C D B

)

4

,

K

=

4

.

K

=

(17)

I

II

tip

tip





The normalized SIFs at the tip of the crack are provided as (Li et al., 2020):

K

K

*

.

K

=

*

II

,

K

(18)

=

I

(

)

II

(

)

I

a T T    −

a T T    −

0

i

i

0

i

i

where i sc = for Case-A and i s = for Case-B crack configurations. The total strain energy release rate ( ) ( ) ( ) 2 2 2 1 , T I II G E K K  = − + based on the SIFs obtained in DCT. Note that in order to avoid material mismatch for the interface crack, bond coating material is ceramics for Case-A and it is K 3 alloy for the Case-B. While calculating the energy release rate, J- integral method were also employed in ANSYS (2016) and results are presented together. The relative magnitude of mode II with respect to mode-I SIF is expressed as phase angle, which is ( ) 1 tan II I K K  − = (Ping-wei et al., 2015). 4. Numerical results Numerical results are obtained for different values of crack length and elastic modulus ratio of materials with respect to increasing thermal shock time. Thermal shock can be either cold or hot and crack configuration is changing according to the cases. Case-A indicates crack at surface coating interface and Case-B shows crack at the bond coating interface. In simulations, the following material properties are utilized (Ping-wei et al., 2015). The surface coating is ZrO 2 +8%w.t. Y 2 O 3 and the substrate material is K 3 alloy. In addition, Ping-wei et al. (2015) used bond coating material as intermetallic alloy NiCoCrAlY. However, in this study, bond coat material is assumed as ceramic for Case-A and it is assumed as K 3 alloy for the Case-B in order to avoid mismatch within material properties. Utilization of dissimilar solids at different sides of interface crack leads to oscillatory singularity rather than square root singularity. Due to this fact, SIFs have a complex form and Dundur’s parameters should be used in direct interface analysis. However, in this study, material properties are same and continuous between the crack faces (Dundurs, 1969; Hutchinson and Suo, 1991; Fan et al., 2014). It is assumed that materials remain linearly elastic for the range of temperature considered. In presenting results, stress intensity factors (SIFs), total energy release rate and phase angle are provided with respect to shock time varying from 0s to 8s. Firstly, computational SIF results based on DCT are compared with those obtained SIFs using related commands available in ANSYS (2016) software for identical material (K 3 alloy) used for surface coating, bond coating and the substrate for Case-A configuration and half-length of crack 1 . a mm =  denotes the percent difference between results. Table 2 shows that SIFs calculated based on DCT are in a good agreement with those found from ANSYS (2016). Fig. 3 shows normalized mode I and mode II SIFs, total energy release rate based on DCT and J- integral, and the phase angle for materials provided in Table 1 under the effect of cold thermal shock. Table 1. Utilized material parameters for the coating substrate system (Ping-wei et al., 2015). Materials ( ) k W m C  ( ) 3 kg m  ( ) kg°C c J ( ) GPa E  ( ) 6 10 1 C  −  Ceramic coating (sc) 1.5 6037 500 53 0.25 7.2 Substrate (s) 28.1 7750 361 200 0.32 15.5 As the crack length is increased, total energy release rate is increased. In each case, it reaches a stable level after some time. Phase angle shows that either the crack-tip field is shear dominant or not. For instance, 45 o   means , II I K K  45 o  = indicates II I K K = and 45 o   implies . II I K K  As shock time is increased, phase angle reaches around 90 degrees and gradually decreases especially for larger crack length cases.