Multivariate Calibration and Experimental Validation of a 3D Finite Element Thermal Model for Laser Powder Bed Fusion Metal Additive Manufacturing

  • Mohamad Mahmoudi
  • Gustavo Tapia
  • Kubra Karayagiz
  • Brian Franco
  • Ji Ma
  • Raymundo Arroyave
  • Ibrahim Karaman
  • Alaa ElwanyEmail author
Technical Article


Metal additive manufacturing (AM) typically suffers from high degrees of variability in the properties/performance of the fabricated parts, particularly due to the lack of understanding and control over the physical mechanisms that govern microstructure formation during fabrication. This paper directly addresses an important problem in metal AM: the determination of the thermal history of the deposited material. Any attempts to link process to microstructure in AM would need to consider the thermal history of the material. In situ monitoring only provides partial information and simulations may be necessary to have a comprehensive understanding of the thermo-physical conditions to which the deposited material is subjected. We address this in the present work through linking thermal models to experiments via a computationally efficient surrogate modeling approach based on multivariate Gaussian processes (MVGPs). The MVGPs are then used to calibrate the free parameters of the multi-physics models against experiments, sidestepping the use of prohibitively expensive Monte Carlo-based calibration. This framework thus makes it possible to efficiently evaluate the impact of varying process parameter inputs on the characteristics of the melt pool during AM. We demonstrate the framework on the calibration of a thermal model for laser powder bed fusion AM of Ti-6Al-4V against experiments carried out over a wide window in the process parameter space. While this work deals with problems related to AM, its applicability is wider as the proposed framework could potentially be used in many other ICME-based problems where it is essential to link expensive computational materials science models to available experimental data.

Graphical Abstract

Two-stage multi-variate statistical calibration of the finite element thermal model


Metal additive manufacturing Powder bed fusion Ti-6-Al-4V Finite element thermal models Uncertainty quantification 



R.A. also acknowledges the support of NSF through the NSF Research Traineeship (NRT) program under Grant No. NSF-DGE-1545403, “NRT-DESE: Data-Enabled Discovery and Design of Energy Materials (D3EM).” R.A. and I.K. also acknowledge the partial support from NSF through Grant No. NSF-CMMI-1534534.

Funding Information

This work was supported by an Early Stage Innovations grant from NASA’s Space Technology Research Grants Program, Grant No. NNX15AD71G. Portions of this research were conducted with High Performance Research Computing resources provided by the Texas A&M University (


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Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  • Mohamad Mahmoudi
    • 1
  • Gustavo Tapia
    • 1
  • Kubra Karayagiz
    • 2
  • Brian Franco
    • 2
  • Ji Ma
    • 2
  • Raymundo Arroyave
    • 2
  • Ibrahim Karaman
    • 2
  • Alaa Elwany
    • 1
    Email author
  1. 1.Department of Industrial & Systems EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Materials Science & EngineeringTexas A&M UniversityCollege StationUSA

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