Determination of the unit cell geometry in fibre-reinforced polymer sheets using guided acoustic waves

Woven fibre-reinforced polymers are used in a variety of application, especially where a low mass to stiffness ratio is required. Of paramount importance for the tailored mechanical properties these composite materials exhibit is the type and geometry of the fibre weave. Especially continuous fibre-reinforced thermoplastic composites are fabricated as laminates and subsequently exposed to forming processes which alter the geometry of the fibres unit cell and thus the local mechanical properties of the material. An approach utilising broadband ultrasonic waves is proposed to non-destructively determine the geometry of the unit cell of the weave. The dispersive behaviour of woven fibre-reinforced sheets is described in accordance with the Flouquet-Bloch theorem as a phononic crystal. In order to develop a model for a description of these periodically structured waveguides, the smallest repeating unit of the wave is modelled with periodic boundary conditions. The resulting dispersion diagram exhibits similarities to that of a homogeneous plate, but additionally displays a periodicity in the wavenumber regime, which correspond with the size of the unit cell. Experimental studies of the dispersive behaviour of acoustic waves in woven fibre-reinforced samples also show a periodicity in the wavenumber regime, enabling a measurement procedure of the unit cell geometry.