Abstract
In this work, we introduce an analytical expression for approximating the transient melting radius during powder melting in Selective Laser Melting (SLM) assumed with a stationary laser heat source. The purpose of this work is to evaluate the suggested analytical approach in determining the melt pool geometry during laser processing, by considering heat transfer and phase change effects. This will allow for the rendering of the first findings on the way to a quasi-real time calculation of the melt pool during laser melting, which will contribute significantly to the process design and control, especially when new powders are applied. Initially, we consider the heat transfer process associated with a point heat source, releasing a continuous and constant power (in a semi-infinite powder bed. On the point of the heat source the temperature is infinite, and the material starts to melt spherically outwards, creating an interface that separates the solid from the molten material; we assume different properties between the two phases. Unlike the cases of the cartesian and cylindrical coordinates, (in a cartesian coordinate the heat source is over a plane, i.e., W/m2, and in cylindrical along a line, i.e., W/m), where the melting process is proportional to the square root of time, in spherical coordinates the melting stops at a finite radius, i.e., a maximum radius, which depends only on the heat source, the conductivity of the solid and the difference between the far-field temperature and the melting temperature of the material. Here we should also point out that to achieve continuous melting in spherical coordinates the power of the source must increase with the square root of the time. The obtained analytical expression for the maximum melting radius and the approximate expression for its dependence on the time compare well with the numerical results obtained by a finite element analysis.
Highlights
Melting due to a heat source is very significant in thermal manufacturing processes such as Selective Laser Melting (SLM) [1,2,3,4,5,6] and Selective Laser Sintering (SLS) [7,8], spot welding, torch welding [9,10,11], and arc welding [12], to name a few
After a cooling down to an ambient temperature due to a non-linear interaction of thermal, elastic and plastic stresses and the phase change, rest stresses are formed in the solid structure, so called residual stresses [17,18]
In particular in the case of SLM processes, a residual stresses formation is of great importance since residual stresses are dominated by the actual process parameters [19]
Summary
Melting due to a heat source is very significant in thermal manufacturing processes such as Selective Laser Melting (SLM) [1,2,3,4,5,6] and Selective Laser Sintering (SLS) [7,8], spot welding, torch welding [9,10,11], and arc welding [12], to name a few. Analytical expressions for the phase change process can be obtained in one-dimensional cartesian coordinates in the case of the solidification of a supercooled liquid, and the melting or solidification in a half-space with a constant temperature along the boundary [28]. Paterson [26], who considered the problems of phase change in cylindrical and spherical coordinates, and was able to obtain an analytical solution in spherical coordinates only under the assumption that the power of the heat source increases with the square root of time; this solution is of less practical importance. We consider the problem of phase change in spherical coordinates assuming a continuous but constant heat source at a single point. This is justified because at a steady-state the terms related to convection must be zero, and the system of Equations (1)–(7) would be applicable
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