Laser thermoelastic generation in metals above the melt threshold

An approach is presented for calculating thermoelastic generation of ultrasound in a metal plate exposed to nanosecond pulsed laser heating, sufficient to cause melting but not ablation. Detailed consideration is given to the spatial and temporal profiles of the laser pulse, penetration of the laser beam into the sample, the appearance and subsequent growth and then contraction of the melt pool, and the time dependent thermal conduction in the melt and surrounding solid throughout. The excitation of the ultrasound takes place during and shortly after the laser pulse and occurs predominantly within the thermal diffusion length of a micron or so beneath the surface. It is shown how, because of this, the output of the thermal simulations can be expressed as axially symmetric transient radial and normal surface force distributions. The epicentral displacement response to these force distributions is obtained by two methods, the one based on the elastodynamic Green's functions for plate geometry determined by the Cagniard generalized ray method and the other using a finite element numerical method. The two approaches are in very close agreement. Numerical simulations are reported on the epicentral displacement response of a 3.12 mm thick tungsten plate irradiated with a 4 ns pulsed laser beam with Gaussian spatial profile, at intensities below and above the melt threshold.