On the Interaction of Inclusions with Migrating Grain Boundaries

  • M. F. Ashby
  • J. Lewis
Part of the Sagamore Army Materials Research Conference Proceedings book series (SAMC, volume 14)


The interaction energy of a grain boundary with a precipitate particle or inclusion of a second phase is considered in detail. When the nature of the inclusion is considered, two regimes emerge: (a) the grain boundary may enter and pass through certain coherent inclusions, leaving them coherent; (b) more commonly, the grain boundary may envelop and bypass the inclusion, causing one which was coherent to lose coherency. The maximum pinning force exerted by an inclusion or particle on a boundary depends on its nature.

A simple differential equation describes the equilibrium of a segment of boundary which is pushed between particles. Numerical integration gives the shape of the boundary. These shapes are complicated by having double curvature, and depend on the nature and spacing of the inclusions. However, certain characteristics of the shape depend only on the pressure, or driving force, acting on the boundary tending to make it migrate. This means that the local pressure on a grain boundary can be measured by measuring its shape, much as the local stress in a crystal can be calculated from the local curvature of a dislocation.


Full Line Boundary Energy Precipitate Particle Equilibrium Shape Critical Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ashby, M. F. and Palmer, I. G., “The Dragging of Solid Particles Through Metals by Grain Boundaries,” Acta Met., 15 (1967), 420.CrossRefGoogle Scholar
  2. 2.
    Koch, E. F. and Aust, K. T., “The Movement of Solid Particles in a Solid,” Acta Met., 15 (1967), 405.CrossRefGoogle Scholar
  3. 3.
    Ashby, M. F. and Centamore, R. M. A., “The Dragging of Small Oxide Particles by Migrating Grain Boundaries in Copper,” Acta Met., 16 (1968), 1863.CrossRefGoogle Scholar
  4. 4.
    Zener, C., quoted by C. S. Smith, “Grains, Phases, and Interfaces: An Interpretation of Microstructure,” Trans. AIME, 175 (1948), 15.Google Scholar
  5. 5.
    McLean, D., Grain Boundaries in Metals, Oxford Univ. Press (1957).Google Scholar
  6. 6.
    Gladman, T., “On the Theory of the Effect of Precipitate Particles on Grain Growth in Metals,” Proc. Roy. Soc, A294 (1966), 298.Google Scholar

Copyright information

© Syracuse University Press Syracuse, New York 1968

Authors and Affiliations

  • M. F. Ashby
    • 1
  • J. Lewis
    • 1
  1. 1.Harvard UniversityCambridgeUSA

Personalised recommendations