PSI - Issue 13

P.N.B. Reis et al. / Procedia Structural Integrity 13 (2018) 1999–2004 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

2002

4

It is possible to observe that the maximum bending stress increases from 55.9 MPa at 4.25×10 -6 s -1 to 85.5 MPa at 4.25×10 -2 s -1 , which represents an increase about 53%. As suggested by McKown and Cantwell (2007), a linear model fits the data according the equation = 96. 16 + 6. 71 × ̇ with a correlation coefficient (R) of 0.953. In this equation,  is the maximum flexural stress and ̇ the logarithm of strain rate. In terms of modulus, this parameter increases from 2.21 GPa at 4.25×10 -6 s -1 to 2.99 GPa at 4.25×10 -2 s -1 , which represents an increase of 35.3%. According to Brandt and Fridley (2003), this is explained by the viscoelastic nature of both reinforcing tapes and matrix, where increasing the rate-of-load decreases the effect of viscous flow of the material and, consequently, the flexural modulus increases. Similarly, the relationship between the logarithm of strain rate ( ̇ ) and flexural modulus (E) can be well described by the equation = 3. 3 + 0. 17 × ̇ with a correlation coefficient (R) of 0.877. Both maximum bending stress and flexural modulus increase with the increase of the strain rate, but the slope of the curves shows that the flexural strength is much more sensitive to the strain rate than the flexural modulus. This tendency agrees with the study developed by Mckown and Cantwell (2007). Finally, the strain-rate effect on the strain at maximum bending stress shows that strain decreases with the increasing of the strain rate, which is in good agreement with the studies developed by Mckown and Cantwell (2007). In terms of mathematical formulation, the strain at maximum bending stress (  ) is expressed by the equation = 5 . 57 - 0 . 05 × ̇ with a correlation coefficient (R) of 0.807. In terms of stress relaxation, a fixed strain was applied and the stress recorded in function of time. As reported previously, the strain values used were 0.64%, 1.41% and 2.71%. From these tests, the stress was plotted versus time and the data are shown in Fig. 3 in terms of average curves.

Fig. 3. Stress relaxation curves.

A decreasing of the stress can be observed, but this tend becomes more pronounced with the increase of the strain at which the experiment is performed. For a constant strain of 2.71%, which corresponds to 58 MPa, the stress decreases continually during the time analysed (3 h) to the level of 36.8 MPa. Relatively to the initial stress, it decreases about 26.2% after 1200 s and 36.9% after 10800 s. On the other hand, for 0.64% (19 MPa) the decrease is around 21.2% and 32.5%, respectively. Maxwell model was tried to fit the data obtained from the stress relaxation tests, but the results indicated that it is not good enough to predict the stress relaxation time. Therefore, the Kohlrausch-Williams-Watts (KWW) function was considered (Hutchinson et al ., 1999), and Fig. 4 compares the experimental results against the theoretical ones obtained with the KWW model. The comparison is stablished for a strain correspondent to 50 % of the maximum bending stress, but it is representative of all conditions analysed. KWW model fits the data successfully, as proven in Table 1, and all parameters of the KWW model are shown in Table 1.