PSI - Issue 42

A. Kostina et al. / Procedia Structural Integrity 42 (2022) 425–432 A. Kostina / Structural Integrity Procedia 00 (2019) 000–000

430

6

Table 3. Material parameters for stress-strain calculation. Material K, Pa G, Pa C 0 , Pa C 1 , Pa

C 2 , Pa

γ 1

γ 2

σ ys0 , Pa 690 10 6 307 10 6

Ti-5Al-2V

0.8 10 11 0.32 10 11 9 10 9

9.4 10 9

6 10 9

5 2

2 1

Grade 2

0.7 10 11 0.3 10 11

7.5 10 10 9.8 10 10 5 10 10

Table 4. Material parameters for stored energy calculation. Material a , Pa n τ p , s σ 1 , Pa

m 1

Ti-5Al-2V

5 10 6 5 10 6

0.8

3 3

690 10 6 0.009 307 10 6 0.024

Grade 2

0.83

5. Results and discussion Figures 2-3 show values of plastic work, dissipated and stored energies per loading cycle against crack length for the considered titanium alloys obtained numerically for two different loading values. It can be seen that in all cases dissipated energy is larger than stored in the considered crack length diapason and rises with the increase in crack length. Comparison of the results for 8.5 kN and 9.5 kN presented in Fig. 2 demonstrates that higher loading of Ti 5Al-2V induces more pronounced non-linearity in dependence of plastic work and dissipated energy on crack length while for smaller loading a linear dependence between crack lengths of 10 and 17 mm was obtained. Also, higher loading provides a twofold increase in values of plastic work, dissipated and stored energy. a b

Fig. 2. Energy balance vs crack length for Ti-5Al-2V obtained with the maximum force equal to: (a) 8.5 kN; (b) 9.5kN.

As regards to the Grade-2 titanium alloy, all curves presented in Fig. 3 have noticeable non-linear character. Values of plastic work, dissipated and stored energy are one order of magnitude higher than the ones obtained for Ti 5Al-2V titanium alloy. This is because the value of yield stress for Grade-2 titanium alloy is lower than for Ti-5Al 2V titanium alloy (Table 3). Increase in maximum loading force from 7.5 kN to 8 kN for Ti-5Al-2V induces increase in magnitudes of energy balance components by 39% for the largest from the considered crack lengths as shown in Fig.3. a b

Fig. 3. Energy balance vs crack length for Grade-2 obtained with the maximum force equal to: (a) 7.5 kN; (b) 8kN.