Prediction of Extreme Value Areal Parameters in Laser Powder Bed Fusion of Nickel Superalloy 625

Important to the success of additive manufacturing (AM) is the ability to inspect and qualify parts. The research community is pushing to identify correlations between part function and surface topography, yet little guidance specific to AM surface measurement exists. Thus, development of inspection methods for surface finish are required. In laser powder bed fusion (LPBF) AM, parts are built through a complex process with many variables, and the length scales of interest on the surface cover a wide range. Full characterization of the surface is time consuming and costly as high resolution in surface measurements decreases field-of-view (FoV), requiring stitching multiple FoVs to cover large areas. Statistical methods exist to estimate the maximum value based on a sample of FoVs, but are not yet commonplace in AM surface measurement. The goal of this work is to understand the use of these statistical methods in the estimation of maximum area valley depth ( $Sv$ ) of a surface, an extreme value parameter, for which researchers have already found relationship to fatigue life. This work also investigates the effect of microscope objective, measurement region size, and nesting index of areal filters on $Sv$ . A large (i.e., greater than 40 mm × 40 mm) planar LPBF surface is fabricated in nickel superalloy 625 and measured using a focus variation microscope with a $10\times$ objective and again with a $20\times$ objective. Results show that there is little difference in the maximum value of $Sv$ between the two objectives, but the nesting index does have some effect. Results also show that a Type 1 Generalized Extreme Value, or Gumbel, distribution can be used to accurately estimate the maximum value of $Sv$ for a surface from a small set of measurements, providing a framework for users to develop inspection routines that balance measurement time and accuracy of estimation.