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Data-informed uncertainty quantification for laser-based powder bed fusion additive manufacturing

Mihaela Chiappetta, Chiara Piazzola, Lorenzo Tamellini, Alessandro Reali, Ferdinando Auricchio, Massimo Carraturo

TL;DR

This study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark, and employs a multi-fidelity surrogate modeling technique, specifically the multi-index stochastic collocation method.

Abstract

We present an efficient approach to quantify the uncertainties associated with the numerical simulations of the laser-based powder bed fusion of metals processes. Our study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark proposed by the National Institute of Standards and Technology (NIST). The proposed approach consists of a forward uncertainty quantification analysis of the residual strains of the cantilever beam given the uncertainty in some of the parameters of the numerical simulation, namely the powder convection coefficient and the activation temperature. The uncertainty on such parameters is modelled by a data-informed probability density function obtained by a Bayesian inversion procedure, based on the displacement experimental data provided by NIST. To overcome the computational challenges of both the Bayesian inversion and the forward uncertainty quantification analysis we employ a multi-fidelity surrogate modelling technique, specifically the multi-index stochastic collocation method. The proposed approach allows us to achieve a 33\% reduction in the uncertainties on the prediction of residual strains compared with what we would get basing the forward UQ analysis on a-priori ranges for the uncertain parameters, and in particular the mode of the probability density function of such quantities (i.e., its ``most likely value'', roughly speaking) results to be in good agreement with the experimental data provided by NIST, even though only displacement data were used for the Bayesian inversion procedure.

Data-informed uncertainty quantification for laser-based powder bed fusion additive manufacturing

TL;DR

This study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark, and employs a multi-fidelity surrogate modeling technique, specifically the multi-index stochastic collocation method.

Abstract

We present an efficient approach to quantify the uncertainties associated with the numerical simulations of the laser-based powder bed fusion of metals processes. Our study focuses on a thermomechanical model of an Inconel 625 cantilever beam, based on the AMBench2018-01 benchmark proposed by the National Institute of Standards and Technology (NIST). The proposed approach consists of a forward uncertainty quantification analysis of the residual strains of the cantilever beam given the uncertainty in some of the parameters of the numerical simulation, namely the powder convection coefficient and the activation temperature. The uncertainty on such parameters is modelled by a data-informed probability density function obtained by a Bayesian inversion procedure, based on the displacement experimental data provided by NIST. To overcome the computational challenges of both the Bayesian inversion and the forward uncertainty quantification analysis we employ a multi-fidelity surrogate modelling technique, specifically the multi-index stochastic collocation method. The proposed approach allows us to achieve a 33\% reduction in the uncertainties on the prediction of residual strains compared with what we would get basing the forward UQ analysis on a-priori ranges for the uncertain parameters, and in particular the mode of the probability density function of such quantities (i.e., its ``most likely value'', roughly speaking) results to be in good agreement with the experimental data provided by NIST, even though only displacement data were used for the Bayesian inversion procedure.
Paper Structure (22 sections, 22 equations, 15 figures, 7 tables)

This paper contains 22 sections, 22 equations, 15 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Governing equations
  3. Thermal problem
  4. Mechanical problem
  5. Experimental setup
  6. Numerical simulations
  7. Meshing strategy
  8. Material properties
  9. Printing process
  10. Uncertainty quantification workflow and surrogate modelling approach
  11. Uncertainty quantification framework
  12. Multi-fidelity MISC surrogate model
  13. Results of the UQ workflow
  14. Bayesian inverse UQ analysis
  15. Uncertain parameters and available data
  16. ...and 7 more sections

Figures (15)

  • Figure 1: AMBench2018-01 benchmark for the experiment performed by the NIST NISTlevine2020outcomes.
  • Figure 2: Meshing strategy for the part-scale PBF-LB/M thermomechanical model of the Inconel 625 cantilever beam: $(a)$ coarse mesh, $(b)$ fine mesh.
  • Figure 3: Temperature dependent properties of Inconel 625 extrapolated from Ansys2021-R2: bilinear isotropic plastic hardening model with temperature dependent yielding behaviour.
  • Figure 4: PBF-LB/M numerical model of the cantilever beam 75 mm long, 12 mm high and 5 mm wide with a build platform measuring 85 mm long, 12 mm high and 20 mm wide. Points marked in purple are the locations $\mathbf{x}_{k,meas}, k=1,\ldots,5$ used during the Bayesian inverse UQ analysis; the (blue) dotted line marks the locations where we predict residual strains using data-informed forward UQ analysis.
  • Figure 5: Displacements at the 11 ridges at the top of the cantilever beam provided by the NIST NIST.
  • ...and 10 more figures