PSI - Issue 18

Plekhov O. et al. / Procedia Structural Integrity 18 (2019) 711–718 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

717

7

state and energy balance simulation:

,

0.003    ,

8 1 3 10    ,

8 1 10 a  ,

6 2 625 10    ,

,

5

10

0.003

2 a 

p  

0.85 n  , 1   . To illustrate the algorithm we estimate a lifetime of Ti-1Al-1Mn compact tension specimen (CT-specimen) subjected to the cyclic loading with stress the ratio 0.1 R  . Four values of a force magnitude has been chosen: 1 2500 F N  , 2 3500 F N  , 3 4300 F N  , 4 5000 F N  . For every considered force magnitude a critical crack length was obtained with the use of (13). Polynomial function f for the considered specimen has the form:   2 3 4 1.5 2 ' (0.886 4.64 ' 13.32( ') 14.72( ') 5.6( ') ) (1 ') f f f f f f f        , (14) 0.07 k  , 0.004 m  ,



 



3

2

' 8 10  

/ 4 10  . The critical crack lengths for considered force amplitudes are 1 20 c a  mm, 4 13 c a  mm. The value of 3 mm was chosen as the first approximation for the initial 



f

a



where

c

2 17 c a  mm,

3 15 c a  mm,

crack length for every considered force magnitudes. To calculate the functions ( ) l a for every force magnitude we estimate J-integral values and values of the stored energy per cycle should be obtained. Fig. 3a shows dependence of the J-integral values upon the crack length for the considered force magnitudes. We can note that J-integral values increase with the rise of the force magnitude. Fig. 3b depicts stored energy values per cycle in semi-log scale. (a) (b) x 10 4 10 -1

5

F=2500N F=3500N F=4300N F=5000N

F=2500N F=3500N F=4300N F=5000N

4

10 -2

3

10 -3

2

J, N/m

10 -4 dE s /dN, J/cycle

1

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 10 -5

a, m

a, m

Fig. 3. (a) J-integral values versus crack length for the applied force magnitudes; (b) The stored energy values per cycle versus crack length for the applied force magnitudes.

(a)

(b)

10 -3

5000

F=2500N F=3500N F=4300N F=5000N

4500

10 -4

4000

10 -5

F a , N

3500

da/dN, m/cycle

10 -6

3000

10 -7

0

0.005

0.01

0.015

0.02

2500

0

0.5

1

1.5

2

2.5

a, m

N, cycles

x 10 4

Fig. 4. (a) Fatigue crack growth rate versus crack length for the applied force magnitudes; (b) Applied force magnitudes versus number of cycles to fracture.