PSI - Issue 13

R.R. Yarullin et al. / Procedia Structural Integrity 13 (2018) 902–907 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

4

905

Crack front positions

a, mm

c, mm a/c

1- initial 2- middle

2.0

2.0

1.0

3.5

7.0

0.5

3- final

4.8

12.0

0.4

a)

b)

c)

Fig. 3. Details of the crack initiation zone (a, b) and corner surface crack sizes (c).

In general three FE models with different crack front positions, namely: initial, middle and final, were analyzed for room and elevated temperature conditions. In order to perform numerical calculations, the main mechanical properties determined by testing and listed in Table 1 were used. The typical equivalent stress distributions for compressor disk’s submodel with initial quarter-circular crack are presented in Fig. 4c.

a) c) Fig. 4. FE mesh (a, b) and equivalent stress distributions (c) for the compressor disk with quarter-elliptical crack. b)

4. Elastic and elastic-plastic fracture resistance parameters 4.1. Constraint parameters

In order to use the numerical data, it is necessary to calculate the fracture resistance parameter distributions along the corner surface crack tip. Moreover, the stress-strain state analysis of the compressor disk with corner cracks must be carried out taking into account both in-plane and out-of-plane constraint effects. Shlyannikov et al. (2015 2016b) showed that different traditional approaches, which can successfully describe the in-plane constraint, are inaccurate for describing 3D surface cracks. Yarullin and Ishtyryakov (2016) analyzed constraint parameters as a function of cyclic tension loading and temperatures conditions. Therefore, the numerical calculations used in this study include an analysis for the elastic constraint parameter in the form of the non-singular T Z – factor, as well as the elastic-plastic constraint parameters in the form of the local stress triaxiality h and I n -factor for the specified combinations of crack sizes and temperature conditions. All parameters are determined at the crack tip distance range of r/a=0.0025-0.01 where the numerical solution provides a stabilized result. To compare parameter distributions along the corner surface crack tip, it is convenient to introduce dimensionless coordinates in the following form:   0 0 0 0 0 0 , , , sin , cos , sin , cos , sin , cos                           c c i i i i i c c c c y x y x y x (1)

       

1

 

 

  0,1

(2)

, 2 2  

R

X Y R



0 x x X x x i 

y y Y y y i i 

,

,

i

0

i

i

i

2

c

c

0

0