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posted on 13.05.2020 by Lingbin Meng

There has been increasing demand for 3D printed metals from aerospace & defense and automotive end-use industries, due to their low manufacturing cost, and reduction in lead times. Although the significant advancement in metal 3D printing promises to revolutionize industry, it is constrained by a widespread problem: the cracks and other defects in the metal 3D printed parts. In this work, two major causes of defects in the laser power bed fusion (L-PBF) process are focused: keyhole mode and spattering phenomena. Both defect sources are highly dependent to the processing parameters. Although extensive efforts have been made on experiments and computational models to improve the quality of printed parts, the high experimental costs and large computational intensity still limit their effect on the optimization of the processing parameters. In addition, the uncertainty in the design process further limits the accuracy of these models.

The aim of this thesis is to develop a probabilistic design framework for reliability-based design in the L-PBF process. The modeling framework spans physical models, machine learning models, and probabilistic models. First, the keyhole mode and spattering phenomena are simulated by physical models including computational fluid dynamics (CFD) and smoothed particle hydrodynamics (SPH) methods, respectively. Then, the data acquired by the physical models serve as the training data for machine learning models, which are used as surrogates to alleviate the high computational cost of physical models. Finally, the feasible design region is computed by probabilistic models such as Monte Carlo simulation (MCS) and the first order reliability method (FORM). The feasible design region can be used assessing a satisfactory reliability not lower than the specified reliability level.

The developed Gaussian process (GP) based machine learning model is capable of predicting the remelted depth of single tracks, as a function of combined laser power and laser scan speed in the L-PBF process. The GP model is trained by both simulation and experimental data from the literature. The mean absolute prediction error magnified by the GP model is only 0.6 μm for a powder bed with layer thickness of 30 μm, suggesting the adequacy of the GP model. Then, the process design maps of two metals, 316L and 17-4 PH stainless steel, are developed using the trained model. The normalized enthalpy criterion of identifying keyhole mode is evaluated for both stainless steels. For 316L, the result suggests that the criterion should be related to the powder layer thickness. For 17-4 PH, the criterion should be revised to .

Moreover, a new and efficient probabilistic method for the reliability analysis is developed in this work. It provides a solution to address quality inconsistency due to uncertainty in the L-PBF process. The method determines a feasible region of the design space for given design requirements at specified reliability levels. If a design point falls into the feasible region, the design requirement will be satisfied with a probability higher or equal to the specified reliability. Since the problem involves the inverse reliability analysis that requires calling the direct reliability analysis repeatedly, directly using MCS is computationally intractable, especially for a high reliability requirement. In this work, a new algorithm is developed to integrate MCS and FORM. The algorithm finds the initial feasible region quickly by FORM and then updates it with higher accuracy by MCS. The method is applied to several case studies, where the normalized enthalpy criterion is used as a design requirement. The feasible regions of the normalized enthalpy criterion are obtained as contours with respect to the laser power and laser scan speed at different reliability levels, accounting for uncertainty in seven processing and material parameters. The results show that the proposed method dramatically alleviates the computational cost while maintaining high accuracy. This work provides a guidance for the process design with required reliability.

The developed SPH model is used to simulate the spattering phenomenon in the L-PBF process, to overcome the limitation of commercial CFD packages, including their incapability of phase change and particle sticking phenomena, which are however commonly seen in the spattering process. The SPH model is capable to couple heat transfer, particle motion and phase change. The sticking phenomenon observed in the experiment is successfully reproduced by the SPH model using a similar scenario.

In summary, the modeling framework developed in this thesis can serve as a comprehensive tool for reliability-based design in the L-PBF process. The work is helpful for applying machine learning models in the additive manufacturing field.


Degree Type

Doctor of Philosophy


Mechanical Engineering

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Jing Zhang

Advisor/Supervisor/Committee co-chair

Benxin Wu

Additional Committee Member 2

Xiaoping Du

Additional Committee Member 3

Shengfeng Yang

Additional Committee Member 4

Mohammad Al Hasan



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