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On sintering of tiny glass beads in oscillating diametric compressions

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Abstract

Sintering of tiny spherical glass beads induced by oscillating diametric compression at room temperature is considered. The amorphous glass beads are modeled as isotropic elasto-plastic solid with bilinear stress-strain constitutive relationship, which is implemented in a finite element code. The coupled thermal and mechanical response of the glass beads under cyclic compressions is investigated. Our numerical simulations show that the local temperatures and stresses near the contact points can significantly be raised during adiabatic compression cycles. The temperature rise is more pronounced for contact between two beads with different sizes or for contact with more neighboring beads. There exist temperature and stress gradients from the interiors toward the contact points. These findings provide a feasible explanation for the sintering found in recent triaxial compression experiments with tiny glass beads under room temperature and low pressure.

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Notes

  1. A similar phenomenon is reported in e.g. [12], in which colliding of two large steel balls with a thin sheet of material in between may “burn” or “melt” a hole on the sheet.

  2. Glass is in fact a rheological fluid in supercooled region.

  3. Single monotonic diametric compression is equally applicable with maximum compression displacement to trigger viscous flows of materials, leading to fracture of glass beads.

  4. Although stress-strain relations of glasses depend significantly on the constituting components, experimental studies suggest that Fig. 2a is representative, see e.g. [16–18].

  5. Spherical grains are assumed to distort into oblate spheroids with \(c=d>b\).

  6. The density and thermal conductivity are quoted from [3, 4], while the others are from [1, 2, 25] for conventional silica glasses. Since material properties depend significantly on sample size, e.g. [26–28], tiny glass beads may assume larger values in their properties, e.g. they are stronger in compression than their counterparts with normal size. Thus, numerical simulations with Table 1 deliver a conservative estimation on the stress and temperature fields.

  7. This is done to simplify the analysis, for the focus of the study is to examine if the temperature and stress near the contact points can be risen sufficiently to trigger sintering. More accurate estimations can be accomplished when empirical temperature-dependent formulations of glass properties are taken into account.

  8. In the compression, the dissipated energy in a single glass bead alters its temperature distribution. The temperature gradients on the bead boundary give rise to the convective heat transfer toward the interstitial air, and the conductive heat transfer among the neighboring beads in contact. These are lumped by prescribing the value of \(\mathbf {q}_s\). For the adiabatic case, all dissipated energy is confined within the bead, while half of the dissipated energy is taken into account in the thermo-mechanical response for the 50 % diathermal case.

  9. The “two-calabash” conjunction is numerically possible, and yet recognized in experiments.

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Acknowledgments

The authors are indebted to the Ministry of Science and Technology, Taiwan, for the financial support via the project NSC 102–2221–E–006–198. The authors also thank the editor and reviewers for their comments and suggestions which led to improvements.

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Authors and Affiliations

  1. Department of Civil Engineering, National Cheng Kung University, No.1, University Road, Tainan City, 701, Taiwan

    Chung Fang, Yung-Jung Lin & Yen-Hung Chen

  2. Institute of Geotechnical Engineering, University of Natural Resources and Life Sciences Vienna, Feistmantelstrasse 4, 1180, Vienna, Austria

    Wei Wu

  3. Laboratoire Génie Civil et Bâtiment, LGCB, LTDS, UMR 5513, ENTPE, Rue M. Audin, 69518, Vaulx en Velin Cedex, France

    Thiep Doanh

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  1. Chung Fang
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Correspondence to Chung Fang.

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The study was supported by the Ministry of Science and Technology, Taiwan, via the project NSC 102–2221–E–006–198. The results have not been presented elsewhere. All authors agree to the content of the paper, and authorize the corresponding author to be representative for all copyright and submission issues. The authors also declare that no competing interests exist.

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Fang, C., Wu, W., Lin, YJ. et al. On sintering of tiny glass beads in oscillating diametric compressions. Granular Matter 18, 73 (2016). https://doi.org/10.1007/s10035-016-0669-2

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