PSI - Issue 17

D. Camas et al. / Procedia Structural Integrity 17 (2019) 894–899 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

897

4

The minimum element size in the direction of the crack propagation and through the thickness was determined following the conclusions obtained in a previous study in which the effect of the mesh size in PICC results was analysed (Camas et al. (2018)). Fig. 2 shows the mesh considered for this work. In this kind of analysis, the material model considered is another key issue. The elasto-plastic behavior of the material has been modelled as the corresponding one to the Al-2024-T351 aluminum alloy. This material shows a weak hardening and its main parameters are E =73.5GPa, σ y =425MPa, K’ =685MPa and n’=0.073. Instead of the monotonic stress-strain curve, in this analysis the cyclic stress-strain curve has been considered. This approach implies that in a numerical load cycle, many actual cycles are considered. A three-linear stress-strain curve with isotropic hardening law has been employed to model the material behaviour. Four different cases have been considered ranging from 1 to 8 load cycles from the moment in which the last set of nodes is released. For all the cases considered, the crack has grown applying one load cycle between node releases, a constant amplitude load has been applied in terms of stress intensity factor K =25MPa·m 1/2 and a stress ratio of R=0.3 was considered. Previous plastic wake developed is 0.4 times r pD . The crack advance was simulated in the numerical model by deleting the boundary conditions and releasing the nodes. The minimum element size was 90 times smaller than r pD , which fits with the recommendations by Camas et al. (2018).

(a)

(b)

Fig. 2. (a) Three-dimensional finite element model; (b) mesh around the crack front.

3. Results

In this section, the results for each number of loading cycles are presented. Data are taken during the last loading unloading cycle. Data are collected at the first, second, fourth and eighth cycle and the evolution of the results is studied.

Ͳ Ͳ Ǥ Ǥ Ͳ ͷ ͳ ͳ Ǥ Ǥ Ͳ ͷ ʹǤͲ ͲǤͲͲͲ ͲǤͲͲͷ ͲǤͲͳͲ ͲǤͲͳͷ ͲǤͲʹͲ (a)

Ǧ Ǧ ͵ ʹ ǡ ǡ Ͳ Ͳ Ͳ Ͳ Ǧ Ͳ ͳǡ ǡͲ Ͳ Ͳ Ͳ ͳ ʹ ǡ ǡ Ͳ Ͳ Ͳ Ͳ ͵ǡͲͲ ͶǡͲͲ ͲǡͲʹͲ ͲǡͲ͵Ͳ ͲǡͲͶͲ ͲǡͲͷͲ ͲǡͲ͸Ͳ ͲǡͲ͹Ͳ Ǧ Ǧ ͵ ʹ Ǥ Ǥ Ͳ Ͳ Ǧͳ Ͳ Ǥ Ǥ Ͳ Ͳ ͳ ʹ Ǥ Ǥ Ͳ Ͳ ͵ Ͷ Ǥ Ǥ Ͳ Ͳ ͲǤͲʹ σ › / σ ›‹‡Ž† (b)

σ › / σ ›‹‡Ž†

ͲǤͲͶ

ͲǤͲ͸

Ǧ Ǧ ʹ ͳ Ǥ Ǥ Ͳ ͷ Ǧ Ǧ ͳ Ͳ Ǥ Ǥ Ͳ ͷ

σ › / σ ›‹‡Ž†

ε

ε

ˆ‹”•– …›…Ž‡•

Žƒ•– …›…Ž‡•

Fig. 3. Stress-strain loops during loading cycles after releasing the last set of nodes (a) at the surface and (b) in the mid-plane.