On the probabilistic prediction for extreme geometrical defects induced by laser-based powder bed fusion

Compared to traditional subtractive manufacturing processes, powder bed fusion (PBF) shows promise for making complex metal parts with design freedom, short development time, and environmental sustainability. However, there is a consensus within the additive manufacturing (AM) community that the random geometrical defects (e.g., porosity, lack-of-fusion) produced in PBF processes pose a great challenge to fabricating load-bearing parts, particularly under dynamic loading conditions. Therefore, it is imperative to quantify defect sizes and distributions to predict the critical, life-limiting defect size that significantly reduces fatigue life. This paper presents a comprehensive analysis of the defects induced by selective laser melting to quantify their sizes and statistical distributions. Then four cumulative distribution functions (i.e., Weibull, Gamma, Gumbel, and Lognormal CDFs) are leveraged and compared to predict the maximum defect size based on the principle of statistics of extremes. Both the peak over threshold (POT) approach and the block maxima (BM) approach are used for these predictions. The results show that the BM approach-based predictions for all CDFs to be much larger than the measured maxima while the POT approach-based predictions have less deviation. The Weibull and Gamma CDFs were best correlated to the data, measured by Pearson's R correlation coefficient, while the Gumbel and Lognormal CDFs were also well correlated.