JEC COMPOSITES MAGAZINE - Issue #75 - August/September 2012 - 51

Tab. 2: Overview of the results of the evolutionary optimization algorithm

True values Optimization Increment Optimized values space [GPa] Dc [GPa] [GPa] [GPa] C11 C12 C13
Fig. 5: Critical bulk wave angles for the UD carbon/epoxy composite corresponding to (a) the minimum bounds of the optimization space and (b) the maximum bounds of the optimization space

Relative difference [%]
0.13 8.79 8.79 0.50 0.46 0.50 0.54 0.83 0.56

173.73 4.95 4.95 13.87 6.47 13.87 3.70 7.19 7.19

100-200 1-10 1-10 5-15 1-10 5-15 1-10 1-10 1-10

0.5 0.01 0.01 0.1 0.01 0.1 0.01 0.01 0.01

173.5 4.52 4.52 13.8 6.44 13.8 3.68 7.25 7.15

C22 C23 C33 C44 C55 C66

Fig. 6: Critical bulk wave angles corresponding to the optimized elasticity parameters Cij (a) and deviation ∆θ between the critical bulk wave angles of the true elasticity constants and the optimized constants (b)

Extensions of the polar scan principle
Backscatter polar scan During a polar scan experiment, a small amount of acoustic energy is non-specularly back-reflected to the emitting transducer, even at a large incident angle θ [4]. Analysis of the corresponding TOFD value indicates that the backscattered signal corresponds to an ‘echo’ coming from the surface of the targeted material. A schematic of the backscatter polar scan Fig. 7: Schematic of the principle of non-specularly principle is shown in backscattered ultrasound Fig. 7. The recorded backscatter patterns do not reflect the anisotropic nature of the investigated material at all (see Fig. 8). Furthermore, the patterns are highly dependent on the employed acoustic frequency f, which strongly suggests that the exact origin has to be found in some kind of diffraction process. To this end, the surface state of the material was microscopically investigated. Fig. 8b shows that the surface is characterized by a microscopic texture, where several symmetry directions can be identified (indicated by the yellow arrows). The origin of this surface profile should be attributed to the autoclave manufacturing process, where a peel ply was used. By constructing the normals on the symmetry directions, the axes of enhanced backs-

Cij is evaluated. Once a predefined fitness value is obtained, the procedure ends and thus the optimized set of Cij is obtained. The critical bulk wave angles associated to the optimized Cij are shown in Fig. 6a. Because of the excellent agreement with the true critical bulk wave angles, the difference Δθ between the two sets of curves is plotted in Fig. 6b. Note that the differences Δθ are in the range [0° - 0.5°]. An overview of the optimization results is presented in Table 2. The last column shows the relative error between the true and the optimized Cij. The results are very promising: except for C12 and C13, the optimized values are within 1% of their original values. The ‘large’ deviation of the parameters C12 and C13 can be attributed to the fact that these parameters are rather ill-conditioned. To improve the accuracy of C12 and C13, the predefined fitness value has to be adapted, which drastically deteriorates the computational efficiency of the optimization algorithm. A second possibility to refine the optimization of C12 and C13 consists in performing a second polar scan where a different material symmetry plane is considered (e.g. the X-Z plane). Compared to conventional testing techniques, the present results are very competitive, especially when considering that several material parameters are practically impossible to measure with conventional test methods. Hence, it can be concluded that the implemented optimization algorithm is very robust and leads to accurate results. Current research involves the application of the present optimization procedure to a real polar scan experiment.

No75 August - September 2012 /

jec composites magazine 51

JEC COMPOSITES MAGAZINE - Issue #75 - August/September 2012

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #75 - August/September 2012