HEAT-CONDUCTION IN HIGH-SPEED LASER-WELDING

The three-dimensional, time-dependent temperature distribution in a moving solid of finite thickness due to a laser beam with a Gaussian power distribution on its surface is investigated. The effects due to latent heat and the keyhole are neglected. The model is determined by Peclet number Pe = r0U/2-kappa, a non-dimensional melting temperature THETA-m = lambda-r0-pi-3/2(T(m) - T0)/P and a non-dimensional thickness zeta-0 = h/r0 (where r0 is the focal radius, h the thickness of the specimen, U the speed of travel, P the laser power, kappa the thermal diffusivity, lambda the thermal conductivity and T(m) and T0 the melting and ambient temperatures respectively.) An upper limit for the time needed to establish the steady state is 0.1 s in the case of iron for all travel speeds. Accounting for the effects due to the finite thickness of the specimen is essential for the thin metal sheets used in high-speed laser welding. Asymptotic solutions for high Pe are provided. The resulting weld pool for high Pe are long, narrow and shallow; the weld pool may be approximated by a cylinder. For a given value of the power, the weld pool length depends only slightly on Pe, and consequently a simple approximate formula for the dependence on laser power P is possible and is presented here. The depth and width of the weld pool decease significantly with increasing Pe and THETA-m. A comparison of weld pool width and depth to experiments is found to be in reasonable agreement. The length and depth of the weld pool are not sensitive to small changes of the focal radius, whereas the width is. It was discovered that the temperature distribution on the surface of the specimen parallel to the x axis has two maxima for Pe greater-than-or-equal-to 10, resulting in isotherms with two maxima.