Finite element modelling strategy for determining directivity of thermoelastically generated laser ultrasound

Laser ultrasound (LU) is a contactless and couplant-free remote non-destructive (NDE) technique, which uses lasers for ultrasonic generation and detection rather than conventional piezoelectric transducers. For a transducer, an important characteristic is the directivity, the angle-dependent amplitude of the ultrasonic waves generated in the material. In the non-destructive thermoelastic regime, LU source has been widely modelled as a surface force dipole. However, the directivity of LU in more complex material, where there is an increasing demand for NDE, such as carbon fibre reinforced plastic (CFRP), is yet to be understood. In the current paper, a finite element (FE) modelling methodology to obtain the directivity of LU in complex material is presented. The method is applied to a conductive isotropic material (aluminium, Al) for validation against an existing analytical solution and then applied to a heterogeneous anisotropic material (carbon-fibre reinforced plastic, CFRP). To get the directivity of a specific wave mode, the signal for that mode needs to be resolved in time from other modes at all angles. This is challenging for shear (S) waves in a small model domain due to the head wave, so a technique for suppressing the head wave is shown. The multi-physics model solves for thermal expansion, which models the laser source as a surface heat flux for the Al case, and a buried heat source for the CFRP case, according to where the energy is deposited in the material. The same ultrasound generation pattern can be obtained by using a suitable pure elastodynamic loading, which is shown to be a surface force dipole as per the validation case for Al, and a buried quadrupole for the CFRP case. The modelled directivities are scaled and fitted to experimental measurements using maximum likelihood, and the goodness of fit is discussed. For the Al case, the S wave is preferred over the longitudinal (L) wave for inspection due to greater signal amplitude. For the CFRP case, the quasi-longitudinal (qL) wave in CFRP shows a maximum amplitude directly below the source, and has a greater amplitude than the quasi-shear (qS) wave, suggesting a better choice for inspection.