The new process called L-SIP (outer surface irradiated Laser Stress Improvement Process) is developed to improve the tensile residual stress of the inner surface near the butt welded joints of pipes in the compression stress. The temperature gradient occurs in the thickness of pipes in heating the outer surface rapidly by laser beam. By the thermal expansion difference between the inner surface and the outer surface, the compression stress occurs near the inner surface of pipes.
In this paper, the theoretical equation for the temperature distributions of pipes heated by moving rectangular Gauss distribution heat source on the outer surface is derived. The temperature histories of pipes calculated by theoretical equation agree well with FEM analysis results. According to the theoretical equation, the controlling parameters of temperature distributions and histories are q/2ay, vh, ax/h and ay/h, where q is total heat input, ay is heat source length in the axial direction, ax is Gaussian radius of heat source in the hoop direction, v is moving velocity, and h is thickness of the pipe. The essential variables for L-SIP, which are defined on the basis of the measured temperature histories on the outer surface of the pipe, are Tmax, F0=kτ0/h2, vh, WQ and LQ, where Tmax is maximum temperature on the monitor point of the outer surface, k is thermal diffusivity coefficient, τ0 is the temperature rise time from 100°C to maximum temperature on the monitor point of the outer surface, WQ is τ0×v, and LQ is the uniform temperature length in the axial direction. It is verified that the essential variables for L-SIP match the controlling parameters by the theoretical equation.