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Estimation of Spatio-temporal Temperature Evolution During Laser Spot Melting Using In Situ Dynamic X-Ray Radiography

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Abstract

A novel approach to estimate the sub-surface temperature (and thermal gradient) distribution during melting/solidification and its time evolution using in situ dynamic synchrotron X-ray radiography data is proposed in this work. The proposed approach uses the Beer–Lambert’s law as a physical basis and is demonstrated using an in situ laser spot-melting experiment on Ti–6Al–4V alloy. This methodology also incorporates the recipe described previously by Gilbert and Deinert allowing for the extraction of a “radially-resolved” temperature distribution.

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Acknowledgments

This research was sponsored by the Department of the Navy, Office of Naval Research under ONR Award Number N00014-18-1-2794. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Office of Naval Research. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. This work was initiated as a part of the Ph.D. dissertation study (made available online in Aug 2022)[18] of R. R. Kamath under the supervision of Prof. H. Choo at the University of Tennessee Knoxville.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    Rakesh R. Kamath, Hahn Choo & Sudarsanam Suresh Babu

  2. X-ray Science Division, Argonne National Laboratory, Lemont, IL, 60439, USA

    Kamel Fezzaa

  3. Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    Sudarsanam Suresh Babu

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  1. Rakesh R. Kamath
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Correspondence to Rakesh R. Kamath or Sudarsanam Suresh Babu.

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Appendix

Appendix

1.1 Section A1

See Figure A1.

Fig. A1
figure 5

The median intensity of rows corresponding to Y = 10 (argon), 110, 210, 310, and 410 μm (bottom part of Ti-64 substrate), in Figure 1(a), as a function of image sequence number. Note that image sequence #1 corresponds to 0 μs (i.e., laser on) and image sequence #560 corresponds to 8000 μs (i.e., laser off). The figure shows that median intensity of all the rows increases with time. However, a basic thermal diffusion calculation tells us that for the given laser-on time frame (8 ms), the lower parts of the Ti-64 substrate (Y = 410 μm) should not experience any heating. This justifies the need for the time-series correction sub-step implemented as a part of the background correction in Step 1 of the workflow (Color figure online)

Full size image

1.2 Section A2

See Figure A2.

Fig. A2
figure 6

(a) Density vs. temperature data obtained from the literature.[28,29,30] The assumption made here during the calculation of the density of the solid and liquid mixture in the mushy zone is that the liquid fraction varies linearly with the temperature. This is shown as a plot of liquid fraction vs temperature in the mushy zone in (b) (Color figure online)

Full size image

1.2.1 Section A3: Contributors to Spatial Resolution of the Measurement

The raw imaging data obtained contained square pixel with dimensions of 2 μm each. However, the effective spatial resolution of the square pixels was determined to be about 4 μm and the contributors to the same have been discussed in detail below.

1.2.2 Smoothing Step

The median filtering operation, performed as a part of Step 1, assigns the running average of eight neighboring pixels to a given pixel. This effectively changes the spatial resolution from 2 μm (1 pixel) to about 4 μm (2 pixels).

1.2.3 Point Spread Function of the Detector

The detector used is a Photron SA-Z high-speed camera with 1024 × 1024 pixel resolution with each pixel being 20 μm in size. A Mitutoyo 10X Microscope objective (NA 0.28) is used to image the 100 μm thick LuAG:Ce scintillator crystal in the camera providing an effective pixel size of 2 μm for the measurement. The point spread function (PSF) of this detector was measured by scanning a knife edge (GaAs cleaved crystal) positioned against the scintillator. The scan steps (0.2 μm) were much smaller than the effective pixel size (2 μm). A Gaussian fit to the measured peak yield a 4 μm (FWHM) for the PSF.

1.2.4 Finite Size of X-Ray Source

Another contribution to the overall spatial resolution comes from the finite size of the X-ray source (282 μm FWHM). Given the source-sample distance (38 m) and the sample-detector distance (0.35 m), the projected horizontal source turns out to be 2.6 μm FWHM. Adding in quadrature the two contributions yields a 4.8 μm FWHM total detection resolution.

1.2.5 Sample Expansion Due to Heating by X-Ray Beam

The power of the beam incident on the 1 × 1 mm2 area (approximately equal to the FOV used in the study) at the sample location (38 m from the source) is about 17 W. For the sample size used (50 mm × 3 mm × 0.5 mm) this has seen to result only in the expansion of the about 2 to 4 μm during the 8 ms duration (without the laser source switched on). Also, it is reasonable to assume that the expansion in the perpendicular direction (along X-ray beam) should also be in a similar (2 to 4 μm) and doesn’t change the X-ray path length significantly enough contribute to the accuracy of the temperature measurement.

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Kamath, R.R., Choo, H., Fezzaa, K. et al. Estimation of Spatio-temporal Temperature Evolution During Laser Spot Melting Using In Situ Dynamic X-Ray Radiography. Metall Mater Trans A 55, 983–991 (2024). https://doi.org/10.1007/s11661-024-07307-w

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