Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Dilatant shear bands in solidifying metals

Nature volume 445, pages 70–73 (2007)Cite this article

Abstract

Compacted granular materials expand in response to shear1, and can exhibit different behaviour from that of the solids, liquids and gases of which they are composed. Application of the physics of granular materials has increased the understanding of avalanches2, geological faults3,4, flow in hoppers and silos5, and soil mechanics6,7. During the equiaxed solidification of metallic alloys, there exists a range of solid fractions where the microstructure consists of a geometrically crowded disordered assembly of crystals saturated with liquid. It is therefore natural to ask if such a microstructure deforms as a granular material and what relevance this might have to solidification processing. Here we show that partially solidified alloys can exhibit the characteristics of a cohesionless granular material, including Reynolds’ dilatancy1 and strain localization in dilatant shear bands 7–18 mean crystals wide. We show that this behaviour is important in defect formation during high pressure die casting of Al and Mg alloys, a global industry that contributes over $7.3 billion to the USA’s economy alone8 and is used in the manufacture of products that include mobile-phone covers and steering wheels. More broadly, these findings highlight the potential to apply the principles and modelling approaches developed in granular mechanics to the field of solidification processing, and also indicate the possible benefits that might be gained from exploring and exploiting further synergies between these fields.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Vane rheometry of partially solidified Mg-9Al-0.7Zn.
Figure 2: Al-7Si-0.3Mg with globular morphology deformed in a direct shear cell.
Figure 3: Shear band thickness ( w ) and particle size in the shear band ( dsb).
Figure 4: Defect bands in high pressure die castings.

Similar content being viewed by others

References

  1. Reynolds, O. On the dilatancy of media composed of rigid particles in contact. Phil. Mag. 20, 469–481 (1885)

    Article  Google Scholar 

  2. Daerr, A. & Douady, S. Two types of avalanche behaviour in granular media. Nature 399, 241–243 (1999)

    Article  ADS  CAS  Google Scholar 

  3. Marone, C. & Kilgore, B. Scaling of the critical slip distance for seismic faulting with shear strain in fault zones. Nature 362, 618–621 (1993)

    Article  ADS  Google Scholar 

  4. Scott, D. Seismicity and stress rotation in a granular model of the brittle crust. Nature 381, 592–595 (1996)

    Article  ADS  CAS  Google Scholar 

  5. Duran, J. Sands, Powders and Grains: An Introduction to the Physics of Granular Materials (Springer, New York, 2000)

    Book  Google Scholar 

  6. Vardoulakis, I. Deformation of water saturated sand: II. Effect of pore water flow and shear banding. Geotechnique 46, 457–472 (1996)

    Article  Google Scholar 

  7. Desrues, J. & Viggiani, G. Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28, 279–321 (2004)

    Article  Google Scholar 

  8. Shaping America’s future. 〈http://www.diecasting.org/information/dc_shape.htm〉 (2005)

  9. Kurz, W. & Fisher, D. J. Fundamentals of Solidification (Trans Tech Publications, Zurich, Switzerland, 1998)

    Book  Google Scholar 

  10. Martin, C. L., Kumar, P. & Brown, S. Constitutive modeling and characterization of the flow behavior of semisolid metal alloy slurries. 2. Structural evolution under shear deformation. Acta Metall. Mater. 42, 3603–3614 (1994)

    Article  CAS  Google Scholar 

  11. Rappaz, M., Jacot, A. & Boettinger, W. J. Last-stage solidification of alloys: Theoretical model of dendrite-arm and grain coalescence. Metall. Mater. Trans. A 34, 467–479 (2003)

    Article  Google Scholar 

  12. Flemings, M. C. Behavior of metal alloys in the semisolid state. Metall. Trans. A 22, 957–976 (1991)

    Article  Google Scholar 

  13. Dahle, A. K. & Arnberg, L. Development of strength in solidifying aluminium alloys. Acta Mater. 45, 547–559 (1997)

    Article  CAS  Google Scholar 

  14. Metz, S. A. & Flemings, M. C. Hot tearing in cast metals. AFS Trans. 77, 329–334 (1969)

    CAS  Google Scholar 

  15. Arnberg, L., Chai, G. & Bäckerud, L. Determination of dendritic coherency in solidifying melts by rheological measurements. Mater. Sci. Eng. A 173, 101–103 (1993)

    Article  Google Scholar 

  16. Stangeland, A., Mo, A., Nielsen, Ø., Eskin, D. G. & M’Hamdi, M. Development of thermal strain in the coherent mushy zone during solidification of aluminium alloys. Metall. Mater. Trans. A 35, 2903–2915 (2004)

    Article  Google Scholar 

  17. Martin, C. L., Favier, D. & Suéry, M. Viscoplastic behaviour of porous metallic materials saturated with liquid. Part I: constitutive equations. Int. J. Plast. 13, 215–235 (1997)

    Article  CAS  Google Scholar 

  18. Sumitomo, T., StJohn, D. H. & Steinberg, T. The shear behaviour of partially solidified Al-Si- Cu alloys. Mater. Sci. Eng. A 289, 18–29 (2000)

    Article  Google Scholar 

  19. Martin, C. L., Braccini, M. & Suéry, M. Rheological behavior of the mushy zone at small strains. Mater. Sci. Eng. A 325, 292–301 (2002)

    Article  Google Scholar 

  20. Terzaghi, K. Theoretical Soil Mechanics (Wiley & Sons, New York, 1943)

    Book  Google Scholar 

  21. Eskin, D. G., Suyitno & Katgerman, L. Mechanical properties in the semi-solid state and hot tearing of aluminium alloys. Prog. Mater. Sci. 49, 629–711 (2004)

    Article  CAS  Google Scholar 

  22. Roscoe, K. H. The influence of strains in soil mechanics. Geotechnique 20, 129–170 (1970)

    Article  Google Scholar 

  23. Stephens, D. J. & Bridgwater, J. The mixing and segregation of cohesionless particulate materials. 1. Failure zone formation. Powder Technol. 21, 17–28 (1978)

    Article  CAS  Google Scholar 

  24. Muir Wood, D. Some observations of volumetric instabilities in soils. Int. J. Solids Struct. 39, 3429–3449 (2002)

    Article  Google Scholar 

  25. Oda, M. & Kazama, H. Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Geotechnique 48, 465–481 (1998)

    Article  Google Scholar 

  26. Wong, R. C. K. Shear deformation of locked sand in triaxial compression. Geotech. Test. J. 23, 158–170 (2000)

    Article  Google Scholar 

  27. Mühlhaus, H. B. & Vardoulakis, I. The thickness of shear bands in granular materials. Geotechnique 37, 271–283 (1987)

    Article  Google Scholar 

  28. Nemat-Nasser, S. & Okada, N. Radiographic and microscopic observation of shear bands in granular materials. Geotechnique 51, 753–765 (2001)

    Article  Google Scholar 

  29. Alshibli, K. A. & Sture, S. Sand shear band thickness measurements by digital imaging techniques. J. Comput. Civ. Eng. 13, 103–109 (1999)

    Article  Google Scholar 

  30. Bridgwater, J. On the width of failure zones. Geotechnique 30, 533–536 (1980)

    Article  Google Scholar 

Download references

Acknowledgements

We thank C. J. Davidson for help recording the volumetric strain, H. Wang for providing a direct shear cell sample, Hydro Aluminium for providing the HPDC samples, and H. I. Laukli for discussions on defect bands in HPDC. This work was supported by the CAST CRC.

Author information

Authors and Affiliations

  1. The CAST CRC, Materials Engineering, The University of Queensland, Queensland, 4072, Brisbane, Australia

    C. M. Gourlay & A. K. Dahle

  2. The Australian Research Council CoE for design in light metals, Materials Engineering, The University of Queensland, Queensland, 4072, Brisbane, Australia

    A. K. Dahle

Authors
  1. C. M. Gourlay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Dahle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to C. M. Gourlay or A. K. Dahle.

Ethics declarations

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Figures 1-20 with legends, Supplementary Tables 1-5, and Supplementary Notes. This file provides an expanded methods section, additional micrographs in support of our findings and a discussion of changes in crystal size and shape during post-deformation solidification. (PDF 3921 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gourlay, C., Dahle, A. Dilatant shear bands in solidifying metals. Nature 445, 70–73 (2007). https://doi.org/10.1038/nature05426

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature05426

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing