PSI - Issue 51

Hugo Vidinha et al. / Procedia Structural Integrity 51 (2023) 9–16 H. Vidinha et al./ Structural Integrity Procedia 00 (2019) 000–000

15 7

38000

28000

1000N 3000N 6000N Load

18000

ε 11 (µm/m)

8000

-2000

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Fig. 5. Linear strain �� of the 12 plies of the tested samples in same z-axis position at different loading levels (z-axis represents the through-the thickness direction; 0 and 12 represent the plies at the surface). through-the-thickness direction) for three loading levels. It can be verified that the plies with the reinforcement aligned with the force direction are notably more deformed than the others (i.e. plies 1, 5, 7, and 11) which indicates that the load is mainly transferred by those plies. Furthermore, all plies with the same reinforcement orientation present approximately the same stain level. A comparison between the typical experimental failure patterns and the numerical predictions is displayed in Fig. 6. Fig. 6(a) shows the final fracture of the specimen near the geometric discontinuity, while Fig. 6(b) exhibits the damage progression simulated numerically. It is clear from the Fig. 11 that the two failure patterns are quite similar. The first damage footprints start to appear around the hole in two diametrically opposite sites but with an asymmetrical shape, which is substantiated by both the DIC observations, see Fig. 2, and by the numerical simulation. Then, the failure develops in a band normal to the loading direction, running through the laminate along the width direction until the specimen can no longer bear the applied load. Ply

(a)

(b)

Fig. 6. Comparison of damage progression: (a) experimental failure; (b) IFF failure pattern progression predicted by the FE model.

5. Conclusions This paper presented the implementation of a progressive failure model for 3D simulation of FRP laminates using the finite element method. The initial failure was predicted using Puck’s failure theory and the damage development was modelled by means of the Element Weakening Method. Then, the proposed numerical approach was validated from monotonic tensile tests and DIC measurements. The following conclusions can be drawn: (i) From the experimental observations, an asymmetrical strain field was verified, presumably due to the lamina sequence. The implemented progressive damage model accurately predicted the strain-field distributions; (ii) The failure load was predicted with an error of 5.1%, while the displacement at the failure was predicted with an error of about 13%; (iii) Regarding the damage initiation and propagation, both the fibre and the matrix damage initiate at the hole borderline; (iv) Both the matrix and the fibre damage are directly influenced by the direction of the reinforcement with respect to the force direction;