JEC COMPOSITES MAGAZINE - Issue #75 - August/September 2012 - 49

acoustical energy to the composite sample. The recordings shown in this report are performed by means of broadband shock wave transducers (f = 1-15 MHz) which are piezo-electrically driven (Krautkramer). The robot can also be equipped with the GYMNA330 apparatus, producing a high-intensity, small-banded acoustic beam (f = 1-3 MHz) which closely resembles a plane wave. In order to reduce the number of ultrasonic transducers, the experiments were performed in double-through transmission by means of an acoustic mirror. In addition to the obvious economic reasons, double-through transmission recording has the advantage that the acoustic pulse interacts twice with the sample under investigation. Hence, the acoustic pulse ‘feels’ the elasticity constants of the investigated material twice, and consequently results in more defined and more detailed patterns in the polar scan. By Fig. 2: Experimental setup of the ultrasonic polar scan, using the 5-channel USIP40 for data acquisition appropriately time-gating the acoustic signal, the maximum amplitude and time-of-flight-diffracpendent solutions. These correspond to the wave vector k of the tion (TOFD) value can be recorded correctly. In this study, the 3 bulk waves of the material, i.e. a longitudinally polarized presincidence angle θ is varied from -65° to +65°, while the polar sure wave (L), a horizontally polarized shear wave (SH) and a angle φ ranges from 0° to 180°. The angular step at which an vertically polarized shear wave (SV) [1]. Taking into account acoustic pulse is fired at the sample, and consequently recorded, Snell-Descartes’ law for external borne sound, one arrives at the is fixed at 0.5°. Hence, one polar scan experiment involves concept of critical angles. Physically, a critical angle denotes the around 100,000 independent measurements. Three devices incident angle θ at which a bulk wave is refracted parallel to the are available to collect the large amount of data: the OMNISliquid-solid interface. It is precisely the generation of such a criCAN for phased array applications, the Gen5i oscilloscope for tical wave phenomenon which leads to the dark rings in a polar more ‘exotic’ measurements and a 5-channel USIP40 portable scan [2]. The computed critical bulk wave angles for a UD grabox. The results shown in this paper were all recorded using phite/epoxy composite and a carbon fabric/PPS laminate are the USIP40 apparatus. Routines were programmed in both shown in Fig. 3a-b. Note the (partial) absence of the vertically MATLAB and MAPLE to further post-process the recorded polarized shear wave (SV), simply due to the fact that its assodata. The automation of the mechanical setup in combination ciated phase velocity cph is smaller than the longitudinal phase with the dedicated data (post-)processing units limits the total velocity in water. According to Snell-Descartes’ law, this would experimental time to approximately 20 minutes. The mechanilead to an imaginary refractive angle, which has, for the present cal symmetry of the material can be exploited to further reduce application, no physical meaning. The elasticity constants used the experimental time. However, caution is required since a for the numerical calculations in this paper were determined by composite material rarely exhibits perfect symmetry in reality. the research team and are listed in Table 1.

Results and discussion

Demanding appropriate continuity relations to account for the Polar scan and forward modelling liquid-solid and the solid-liquid interface, the numerical analyThe propagation of bulk waves in solid materials is described by sis can be further extended to the computation of the reflection the elastic constants Cij and density ρ of the material. For full or transmission coefficient when applying an impinging plane anisotropy, there are 36 independent elasticity Tab. 1: Material constants of the UD graphite/epoxy (65% fibre volume fraction) and carbon constants Cij. This number reduces drastically fabric/PPS laminate used for the forward numerical computations for materials with higher symmetry: transverse isotropy, respectively orthotropy, is completely E22 E33 G12 G13 G23 r E11 v12 v13 v23 described by 5, respectively 9, independent Cij. [MPa] [MPa] [MPa] [Kg/m3] [GPa] [GPa] [GPa] Solving the Christoffel equation for non-trivial solutions, a sixth degree polynomial is obtained. 1614 UD 154.13 14.79 14.79 0.17 0.17 0.30 7480 7480 3370 A symmetry higher than or equal to monoclinic symmetry (which is the case for both transverse fabric 56.49 56.41 10.53 0.08 0.41 0.41 4280 3048 3045 1750 isotropy and orthotropy) leads to three indeNo75 August - September 2012 /

jec composites magazine 49

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

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