Thermal analysis of the arc welding process: Part II. effect of variation of thermophysical properties with temperature
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CTION Part I,[1] an analytical solution for the temperature rise distribution in arc welding of short workpieces is developed based on the moving heat source theory (Jaeger[2] and Carlsaw and Jaeger[3]) and the pioneering work of Rosenthal[4] to predict the transient thermal response. The arc beam is considered as a moving plane (disc) heat source with a pseudo-Gaussian distribution of heat intensity based on the work of Goldak et al.[5] It is a general solution (for both transient and quasi-steady state) in that it can determine the temperature rise distribution in and around the arc beam heat source as well as the width and depth of the melt pool (MP) and the heat-affected zone (HAZ) in welding short lengths where quasi-steady state conditions may not have been established. The analytical model developed can determine the time required for reaching quasi-steady state and
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R. KOMANDURI, Regents Professor, and Z.B. HOU, Visiting Professor, are with the Mechanical & Aerospace Engineering Department, Oklahoma State University, Stillwater, OK 74078. Manuscript submitted June 5, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS B
solve the equation for the temperature distribution—be it transient, or quasi-steady state. It can also calculate the temperature on the surface as well as with respect to depth at all points including those very close to the heat source. The analysis presented is exact and the solution can be obtained quickly and in an inexpensive way compared to numerical techniques, such as finite element method (FEM) or finite difference method (FDM). The analysis also facilitates in the optimization of the process parameters for good welding practice. In the thermal analysis of welding, one of the advantages of the numerical methods, such as the FDM or the FEM, over the analytical techniques is the ability to account for the variable thermal properties with temperature. However, only simple functions of the variation of thermal properties with temperature, such as linear variation over a certain temperature range, can be considered. In the analytical technique, however, only constant values of the thermal properties, namely, the thermal conductivity, , specific heat, c, and thermal diffusivity, a, can be used due to the complexity involved in solving the partial differential equation of heat VOLUME 32B, JUNE 2001—483
(a)
above this temperature followed by a constant thermal conductivity up to 3000 ⬚C. This is due to a change in phase from the solid state to the liquid state. The specific heat, on the other hand, increases almost linearly from room temperature (25 ⬚C) to ⬇500 ⬚C reaching a constant value and maintaining it up to very high temperatures. If we consider the thermophysical properties over the temperature range of room temperature (25 ⬚C) to 1300 ⬚C, they cannot be described by a simple linear relationship. If, however, one were to consider the temperature range from ⬇400 ⬚C to 1300 ⬚C, since the specific heat is constant over this range, they can be expressed by simple linear relationships
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