Thermoelastic wave induced by pulsed laser heating

In this work, a generalized solution for the thermoelastic plane wave in a semi-infinite solid induced by pulsed laser heating is developed. The solution takes into account the non-Fourier effect in heat conduction and the coupling effect between temperature and strain rate, which play significant roles in ultrashort pulsed laser heating. Based on this solution, calculations are conducted to study stress waves induced by nano-, pico-, and femtosecond laser pulses. It is found that with the same maximum surface temperature increase, a shorter pulsed laser induces a much stronger stress wave. The non-Fourier effect causes a higher surface temperature increase, but a weaker stress wave. Also, for the first time, it is found that a second stress wave is formed and propagates with the same speed as the thermal wave. The surface displacement accompanying thermal expansion shows a substantial time delay to the femtosecond laser pulse. On the contrary, surface displacement and heating occur simultaneously in nanoand picosecond laser heating. In femtosecond laser heating, results show that the coupling effect strongly attenuates the stress wave and extends the duration of the stress wave. This may explain the minimal damage in ultrashort laser materials processing. PACS: 62.30.+d; 46.40.Cd; 44.10.+i Excitation of thermoelastic waves by a pulsed laser in solid is of great interest due to extensive applications of pulsed laser technologies in material processing and nondestructive detecting and characterization. When a solid is illuminated with a laser pulse, absorption of the laser pulse results in a localized temperature increase, which in turn causes thermal expansion and generates a thermoelastic wave in the solid. In ultrashort pulsed laser heating, two effects become important. One is the non-Fourier effect in heat conduction which is a modification of the Fourier heat conduction theory to account for the effect ∗Corresponding author. of mean free time (thermal relaxation time) in the energy carrier’s collision process. Consideration of the nonFourier effect also eliminates the paradox of the infinite heat propagation speed [1, 2]. The other is dissipation of the stress wave due to coupling between temperature and strain rate, which causes transform of mechanical energy associated with the stress wave to thermal energy of the material. Many theoretical studies have been conducted to investigate thermoelastic waves. Since numerical techniques, such as the finite element method, do not have sufficient resolution for the thermoelastic wave generated in pulsed laser heating, most work is to search for analytical solutions. Due to the complexity of the generation of thermoelastic waves, various simplifications were used. The simplest approach is to solve thermoelastic wave problems without considering the non-Fourier effect and the coupling effect between temperature and strain rate [3–5]. Welsh et al. [6] solved the two-dimensional thermal stress in a half-space induced by a focused Gaussian beam in the near-surface region. Stress wave propagation and heat conduction in the solid were neglected in his solution. A large amount of work has been devoted to solving thermoelastic wave problems with the consideration of the coupling effect between temperature and strain rate. Stress waves in a half-space induced by variations of surface strain, temperature, or stress were studied by Boley and Tolins [7], and Chandrasekharaiah and Srinath [8]. Mozina and Dovc [9] attempted to use the Laplace transform to solve the thermoelastic stress wave induced by volumetric heating. Due to the difficulty in finding analytical Green’s functions, only the solution for locations far from the surface was obtained. Research also has been conducted to solve thermoelastic wave problems with the consideration of the non-Fourier effect, but without considering the coupling effect between temperature and strain rate. Kao [10] was the first to investigate the non-Fourier effect on the thermoelastic wave in a half-space. McDonald [11] studied the importance of thermal diffusion on the generation of thermoelastic waves in