Closed-form solutions for 2-D axisymmetric modeling of thermal-stress in solid material induced by an annular long pulsed laser irradiation

In this paper, 2-D axisymmetric modeling of thermal-stress of solid material induced by an annular long pulsed laser was presented using closed-form solutions. Physical model of annular long pulsed laser irradiation was established and closed-form solutions of thermal-stress were obtained by analytical method based on thermo-elasticity theory. Thermal-stress of silicon material induced by an annular long pulsed laser was simulated. Results show that, when the silicon material is irradiated by an annular long pulsed laser, the thermal-stress on the surface of the material is the largest, and with the increase of the depth, the thermal-stress is gradually reduced. On the silicon surface, when the inside radius of the annular laser is fixed, the greater the outside radius, the larger region of the higher thermal-stress occupies. When the width between inside radius and outside radius of the annular laser is fixed, for the radial component of the thermal-stress, the smaller the irradiation center location, the greater the maximum value of stress; for the hoop and axial components, the difference of the maximum stress for different irradiation center location is not obvious. With the increase of the pulse width of annular long pulsed laser, the maximum value of the thermal-stress is also gradually increased.