PSI - Issue 17

J.P. Pascon et al. / Procedia Structural Integrity 17 (2019) 411–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Following the work of Benz and Sander (2015), a node release scheme has been adopted instead of determining the actual crack growth rate. At the beginning of the analysis, all the nodes ahead of the circle corresponding to the initial crack length in the right drawing of Figure 3 are restricted along the vertical direction. For both load ratios ( R = 0 and R = -1), 11 loading cycles have been used and, at the end of each cycle, four nodes whose spacing is 0.05 mm are released (from the right to the left) in terms of the vertical displacement, that is, the crack length increases 0.2 mm along each cycle. In the present work, no crack closure was modelled and the distribution of stresses and strains are determined directly from the numerical approximation. 3. Results and discussion The elastic and plastic material coefficients, determined from the experimental data, are given in Table 1. The maximum values of equivalent stress and equivalent plastic strain for both load ratios adopted in the numerical simulations and considering three distinct crack lengths are given in Table 2. These results correspond to the first unreleased node at each crack tip, on the surface of the specimen. Comparing the load ratios, the maximum values provided in Table 2 show that there is no significant variation in terms of the equivalent stress ( σ eq ), but there are considerable differences in the equivalent plastic strain ( κ ). In fact, the compressive phase in the specimen under the negative load ratio ( R = -1) also contributes to increase the equivalent plastic strain, which means that the level of yielding becomes higher even when the specimen is compressed. It is worthy to mention that no contact between the cracked surfaces have been observed and, thus, no compression occurs along these surfaces. Table 1. Material coefficients determined from the experimental data for aluminum alloy 6005-T6. Hooke’s law Swift isotropic hardening E (GPa) ν K (MPa)  0 n  k 0 (MPa) 66 0.33 408.02 0.00103309 0.0678 256.1

Table 2. Maximum values of equivalent stress and equivalent plastic strain determined from the numerical model.

R = 0

R = -1

2a (mm)

F (kN)

κ

κ

 eq (MPa)

 eq (MPa)

20.5

321.44 213.50

0.00812 0.00837

321.44 213.50 344.00 204.37 328.19 255.42 353.82 251.64 335.24 292.03 361.43 293.14

0.00812 0.00837 0.02251 0.02261 0.02841 0.02841 0.02949 0.03003 0.03726 0.03726 0.03781 0.03922

0

11

-20.5

- -

- -

0

20.5

326.70 254.60

0.01125 0.01196

0

13

-20.5

- -

- -

0

20.5

332.88 291.36

0.01493 0.01570

0

15

-20.5

- -

- -

0

It is worth discussing the results shown in Table 2 in the light of the fatigue crack growth data presented in the previous paper by Torres et al. (2017) and reproduced in Figure 4. It is clear from this figure that under R = -1 loading the crack grows faster than under R = 0 as the length increases. Although the peak load is the same for both cases, and  eq is quite similar, the much higher κ values calculated for R = -1 can be related to a larger cumulative damage and, therefore, a higher crack growth rate under the same ΔK + (i.e., the same positive part of the cyclic loading). In other words, the negative load ratio increases the damage accumulation at the crack tip.