INVESTIGATIONS ON THE THERMAL BEHAVIOR AND ASSOCIATED THERMAL STRESSES OF THE FRACTIONAL HEAT CONDUCTION FOR SHORT PULSE LASER HEATING

For complex heat transfer process and related thermal stress in materials subjected to short pulse laser heating, the existing thermal stress theory based on Fourier law or Cattaneo-Vernotte relaxation equation combined with elastic theory has serious defects in describing its thermophysical process.In this paper, based on the fractional calculus theory, the fractional Cattaneo type heat conduction equation and the corresponding thermal stress equation with appropriate initial and boundary conditions are established for a semi-infinite space irradiated by non-Gaussian lase. The analytical solutions of the temperature field and the thermal stress field are obtained via Laplace transform method, and the thermophysical behaviors are illustrated. Firstly, the theoretical solution is verified, then the variations of temperature field and thermal stress field are studied under the fractional order p=0.5, and the influence of laser parameters on temperature and thermal stress field are also researched. Finally, the effects of fractional order parameters on temperature and thermal stress field are calculated. The calculation results show that the temperature and thermal stress fields described by the fractional Cattaneo type heat transfer equation and thermal stress equation have wave diffusion the characteristics. Compared with the classical Fourier heat transfer model and the standard Cattaneo type heat transfer model, the larger the fractional order is, the smaller the thermal wave velocity is, the more significant the thermal wave dynamics is. On the contrary, the larger the thermal wave velocity is, the stronger the thermal diffusivity is. The faster the laser heating and cooling rate is, the faster the temperature rises and falls, the faster the alternating change of compressive stress and tensile stress is, the smaller the temperature change amplitude is, and the variations of thermal stress amplitude is not obvious