The production of metal parts via laser powder bed fusion additive manufacturing is growing exponentially. However, the transition of this technology from production of prototypes to production of critical parts is hindered by a lack of confidence in the quality of the part. Confidence can be established via a fundamental understanding of the physics of the process. It is generally accepted that this understanding will be increasingly achieved through modeling and simulation. However, there are significant physics, computational, and materials challenges stemming from the broad range of length and time scales and temperature ranges associated with the process. In this paper, we review the current state of the art and describe the challenges that need to be met to achieve the desired fundamental understanding of the physics of the process.

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