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In the latter case, the motion of the liquid surface is often fast and non-smooth, so mixing and heat transport are enhanced. The fraction of the energy of the laser beam absorbed by the substrate is a result of both the temperature-dependent absorptivity of the metal and the geometry of the liquid surface, typically ranging from 20вЂ“30% for mild melt pool surfaces to above 80% in the presence of a cavity generated by a keyhole 3.

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The motion of the fluid is largely driven by surface tension gradients induced by temperature gradients (the Marangoni effect), and the recoil-pressure from evaporating fluid particles on the free surface of the fluid. In contrast, in the liquid or melted region of the substrate, heat transport takes place through both heat conduction and convection, i.e., heat transported by the moving fluid particles. This boundary is diffusely located somewhere between the liquidus and solidus isotherms, and their evolution defines the solidification front speed. In the solid regions of the substrate, the temperature history is defined by heat conduction, the way heat can escape the substrate through its boundaries, and most importantly, the time-dependent shape of the melt pool boundary. The complex multi-physics of the problem raises the question of how well thermal histories in the substrate can be extracted from a computational model. Ignoring convective effects leads to results that are inconsistent with experiments, even for the mild melt pools here. Poor control of the laser beam leads to potentially multiple three-dimensional melt pool shapes compatible with the melt pool trace, and therefore to multiple potential thermal histories. We find that thermal histories appear to be reliably computed provided that (a) the power density distribution of the laser beam over the substrate is well characterized, and (b) convective heat transport effects are accounted for. To this end, we perform experiments in which one of two different laser beams moves with constant velocity and power over a substrate of 17-4PH SS or Ti-6Al-4V, with low enough power to avoid generating a keyhole. Here we examine the question of how reliable thermal histories computed from a model that reproduces the melt pool trace are. Since temperature measurements beneath the surface are difficult, estimates are obtained from computational thermo-mechanical models calibrated against traces left in the sample revealed after etching, such as the trace of the melt pool boundary. The study of microstructure evolution in additive manufacturing of metals would be aided by knowing the thermal history.

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