PSI - Issue 2_A

Ido Simon et al. / Procedia Structural Integrity 2 (2016) 205–212

211

I. Simon et al. / Structural Integrity Procedia 00 (2016) 000–000

7

da dN

mm cycle

da dN

5 . 7

= 7 . 1 × 10 − 13 ∆ K I

10 -2

R 2 = 0 . 894

FTG-4-02 (R d FTG-4-03 (R d FTG-4-04 (R d FTG-4-05 (R d

= 0.10)

10 -3

= 0.33)

= 0.50)

= 0.75)

10 -4

10 -5

10 -6

∆ K I ( N / m)

10 -7

1

10

100

Fig. 5: Delamination propagation rate da / dN versus ∆ K I given in eq. (8) and the resulting master curve.

In Fig. 5, the resulting plot of da / dN versus ∆ K I is shown. It may be observed in Fig. 5 that all four curves nearly collapse into one master curve which is una ff ected by the di ff erence in R P . The constants used to achieve this master curve were A = 670 N / m and ∆ G Ie f f thr = 24 N / m. The first was taken from the value of the G R -curve in eq. (4) at ∆ a = 5 mm, as may be seen in Fig. 4a. The second constant value ∆ G Ie f f thr was chosen as that value for which eq. (7) results in a best fit of the experimental data. The cons tants D and m are calculated by fitting a power law using Microsoft Excel. The fitted power law is given by

da dN =

7 . 1 × 10 − 13 ∆ K

I

5 . 7

(12)

.

4. Conclusions

Mode I constant amplitude fatigue tests were conducted for four di ff erent displacements ratios R d using DCB specimens. The displacement cyclic ratios applied were R d = 0.1, 0.33, 0.5 and 0.75. When plotting the delamination propagation rate da / dN versus di ff erent functions of G I , the fatigue curve behavior changes. For example, when da / dN is plotted versus G Imax as in Fig. 4a, an asymptotic value of G R is reached for high values of da / dN and the di ff erent displacement ratios R d . Meanwhile, when da / dN is plotted versus ∆ G Ie f f as in Fig. 4b, all four curves approach a common threshold. With this in mind, a modification to the for mulation given in Jones et al. (2014a) was made. The result of this modified formulation is a master curve una ff ected by changes of the load ratio (see Fig. 5). Furthermore, the power of the master curve, m = 5.7, is much smaller as compared to the power of each of the fatigue curves as shown in Table 3. Note that eq. (7) is a function of √ G and thus in order to compare the power of eq. (12) to the power of each of the other fatigue curves presented in Table 3, one should use m = 2 . 85. Using the master curve in eq. (12) and the load ratio values, all other fatigue curves may be back calculated regardless of the function used for plotting da / dN . The ability to predict the delamination propagation rate da / dN for any given load ratio R P is required in order to anticipate the behavior of the composite laminate under more realistic fatigue tests. This is a result of the fact that it is unlikely that constant amplitude tests will be conducted at all load ratios possible. That, and the fact that in those more realistic fatigue tests, which are derived from a load spectrum of a real structure, the load ratio may change after several cycles, resulting in a large number of load ratios.