Physics:Grain Boundary Sliding

From HandWiki

Grain Boundary Sliding (GBS) is a material deformation mechanism where grains slide against each other. This occurs in polycrystalline material under external stress at high homologous temperature (above ~0.4[1]) and low strain rate and is intertwined with creep. Homologous temperature describes the operating temperature relative to the melting temperature of the material. There are mainly two types of grain boundary sliding: Rachinger sliding,[2] and Lifshitz sliding.[3] Grain boundary sliding usually occurs as a combination of both types of sliding. Boundary shape often determines the rate and extent of grain boundary sliding.[4] Many people have developed estimations for the contribution of grain boundary sliding to the total strain experienced by various groups of materials, such as metals, ceramics, and geological materials. Grain boundary sliding contributes a significant amount of strain, especially for fine grain materials and high temperatures.[5] It has been shown that Lifshitz grain boundary sliding contributes about 50-60% of strain in Nabarro-Herring diffusion creep.[6] This mechanism is the primary cause of ceramic failure at high temperatures due to the formation of glassy phases at their grain boundaries.[7] File:GBsliding.tif

Rachinger Sliding

Rachinger sliding is purely elastic; the grains retain most of their original shape.[6]The internal stress will build up as grains slide until the stress balances out with the external applied stress. For example, when a uniaxial tensile stress is applied on a sample, grains move to accommodate the elongation and the number of grains along the direction of applied stress increases.

Lifshitz Sliding

Lifshitz sliding only occurs with Nabarro-Herring and Coble creep.[6] The sliding motion is accommodated by the diffusion of vacancies from induced stresses and the grain shape changes during the process. For example, when a uniaxial tensile stress is applied, diffusion will occur within grains and the grain will elongate in the same direction as the applied stress. There will not be an increase in number of grains along the direction of applied stress.

Accommodation Mechanisms

When polycrystalline grains slide relative to each other, there must be simultaneous mechanisms that allow for this sliding to occur without the overlapping of grains (which would be physically impossible).[9] Various accommodation mechanisms have been proposed to account for this issue.

  • Dislocation movement: Dislocations can move through the material by processes such as climb and glide to allow for compatibility[10]
  • Elastic distortion: When the sliding distance is small, the grains can deform elastically (and sometimes recoverably) to allow for compatibility[4]
  • Diffusional accommodation: Using diffusional creep mechanisms, the material can diffuse along grain boundaries or through grains to allow for compatibility[4]

Deformation rate from Grain Boundary Sliding

Generally speaking, the minimum creep rate for diffusion can be expressed as:[11][6]

[math]\displaystyle{ \dot{\epsilon}_s=\frac{ADGb}{kT}\left(\frac{b}{d}\right)^p\left(\frac{\sigma}{G}\right)^n }[/math]

Where the terms are defined as follows:

  • [math]\displaystyle{ \dot{\epsilon}_s }[/math]= minimum creep rate
  • [math]\displaystyle{ A }[/math]= constant
  • [math]\displaystyle{ D }[/math]= diffusion coefficient
  • [math]\displaystyle{ b }[/math]= Burgers vector
  • [math]\displaystyle{ k }[/math]= Boltzmann constant
  • [math]\displaystyle{ T }[/math]= temperature
  • [math]\displaystyle{ d }[/math]= mean grain size
  • [math]\displaystyle{ \sigma }[/math]= stress
  • [math]\displaystyle{ G }[/math]= shear modulus
  • [math]\displaystyle{ p,n }[/math]= exponents that depend on the creep mechanism


In the case where this minimum creep rate is controlled by grain boundary sliding, the exponents become [math]\displaystyle{ p=1 }[/math], [math]\displaystyle{ n=2 }[/math], and the diffusion coefficient [math]\displaystyle{ D }[/math] becomes [math]\displaystyle{ D_L }[/math] (the lattice diffusion coefficient).[11][6] Thus, the minimum creep rate becomes:

[math]\displaystyle{ \dot{\epsilon}_s=\frac{AD_LGb}{kT}\left(\frac{b}{d}\right)\left(\frac{\sigma}{G}\right)^2 }[/math]

Experimental Evidence for Grain Boundary Sliding

File:Grainboundarysliding marker.tif Grain boundary scattering has been observed experimentally using various microscopy techniques. It was first observed in NaCl and MgO bicrystals in 1962 by Adams and Murray.[12] By scratching the surface of their samples with a marker line, they were able to observe an offset of that line at the grain boundary as a result of adjacent grains sliding with respect to each other. Subsequently this was observed in other systems as well including in Zn-Al alloys using electron microscopy,[13] and octachloropropane using in situ techniques.[9]

Nanomaterials

Nano-crystalline materials, or nanomaterials, have fine grains which helps suppress lattice creep. This is beneficial for relatively low temperature operations as it impedes dislocations motion or diffusion due to high volume fraction of grain boundaries. However, fine grains are undesirable at high temperature due to the increased probability of grain boundary sliding.[14]

Prevention

Grain shape plays a large role in determining the sliding rate and extent. Thus, by controlling the grain size and shape, the amount of grain boundary sliding can be limited. Generally, materials with coarser grains are preferred, as the material will have less grain boundaries. Ideally, single crystals will completely suppress this mechanism as the sample will not have any grain boundaries.

Another method is to reinforce grain boundaries by adding precipitates. Small precipitates located at grain boundaries can pin grain boundaries and prevent grains from sliding against each other. However, not all precipitates are desirable at boundaries. Large precipitates may have the opposite effect on grain boundary pinning as it allows more gaps or vacancies between grains to accommodate the precipitates, which reduces the pinning effect.

Application - Tungsten Filaments

The operation temperature for tungsten filaments used in incandescent lightbulbs is around 2000K to 3200K which is near the melting point of tungsten (Tm = 3695K).[15] As lightbulbs are expected to operate for long periods of time at a homologous temperature up to 0.8, understanding and preventing creep mechanism is crucial to extending their life expectancy.

Researchers found that the predominate mechanism for failure in these tungsten filaments was grain boundary sliding accommodated by diffusional creep.[16] This is because tungsten filaments, being as thin as they are, typically consist of only a handful of elongated grains. In fact there is usually less than one grain boundary per turn in a tungsten coil.[16] This elongated grain structure is generally called a bamboo structure, as the grains look similar to the internodes of bamboo stalks. During operation, the tungsten wire is stressed under the load of its own weight and because of the diffusion that can occur at high temperatures, grains begin to rotate and slide. This stress, because of variations in the filament, causes the filament to sag nonuniformly, which ultimately introduces further torque on the filament.[16] It is this sagging that inevitably results in a rupture of the filament, rendering the incandescent lightbulb useless. The typical lifetime for these single coil filaments is approximately 440 hours.[16]

To combat this grain boundary sliding, researchers began to dope the tungsten filament with aluminum, silicon and most importantly potassium. This composite material (AKS tungsten) is unique as it is composed of potassium and tungsten, which are non-alloying.[17] This feature of potassium results in nanosized bubbles of either liquid or gaseous potassium being distributed throughout the filament after proper manufacturing.[17] These bubbles interact with all defects in the filament pinning dislocations and most importantly grain boundaries. Pinning these grain boundaries, even at high temperatures, drastically reduces grain boundary sliding. This reduction in grain boundary sliding earned these filaments the title of "non-sag filaments" as they would no longer bow under their own weight.[17] Thus, this initially counter-intuitive approach to strengthening tungsten filaments began to be widely used in almost every incandescent lightbulb to greatly increase their lifetime.

References

  1. ↑ Bell, R.L., Langdon, T.G. An investigation of grain-boundary sliding during creep. J Mater Sci 2, 313–323 (1967). https://doi.org/10.1007/BF00572414
  2. ↑ W. A. Rachinger, J. Inst. Metals 81 (1952-1953) 33.
  3. ↑ I. M. Lifshitz, Soviet Phys. JETP 17 (1963) 909.
  4. ↑ 4.0 4.1 4.2 Raj, R., Ashby, M.F. On grain boundary sliding and diffusional creep. MT 2, 1113–1127 (1971). https://doi.org/10.1007/BF02664244
  5. ↑ Bell, R.L., Langdon, T.G. An investigation of grain-boundary sliding during creep. J Mater Sci 2, 313–323 (1967). https://doi.org/10.1007/BF00572414
  6. ↑ 6.0 6.1 6.2 6.3 6.4 Langdon, T.G. Grain boundary sliding revisited: Developments in sliding over four decades. J Mater Sci 41, 597–609 (2006). https://doi.org/10.1007/s10853-006-6476-0
  7. ↑ Joachim Rösler, Harald Harders, Martin Bäker, Mechanical Behaviour of Engineering Materials, Springer-Verlag Berlin Heidelberg, 2007, p 396. ISBN:978-3-540-73446-8
  8. ↑ Courtney, Thomas H. (2000). Mechanical behavior of materials (2 ed.). Boston: McGraw Hill. ISBN 0-07-028594-2. OCLC 41932585. https://www.worldcat.org/oclc/41932585. 
  9. ↑ 9.0 9.1 "Grain boundary sliding and development of grain boundary openings in experimentally deformed octachloropropane" (in en). Journal of Structural Geology 16 (3): 403–418. 1994-03-01. doi:10.1016/0191-8141(94)90044-2. ISSN 0191-8141. https://www.sciencedirect.com/science/article/abs/pii/0191814194900442. 
  10. ↑ Gifkins, R. C. (August 1976). "Grain-boundary sliding and its accommodation during creep and superplasticity". Metallurgical Transactions A 7 (8): 1225–1232. doi:10.1007/bf02656607. ISSN 0360-2133. http://dx.doi.org/10.1007/bf02656607. 
  11. ↑ 11.0 11.1 Yang, Hong; Gavras, Sarkis; Dieringa, Hajo (2021), "Creep Characteristics of Metal Matrix Composites" (in en), Reference Module in Materials Science and Materials Engineering (Elsevier): pp. B9780128035818118223, doi:10.1016/b978-0-12-803581-8.11822-3, ISBN 978-0-12-803581-8, https://linkinghub.elsevier.com/retrieve/pii/B9780128035818118223, retrieved 2021-05-11 
  12. ↑ Adams, M. A.; Murray, G. T. (June 1962). "Direct Observations of Grain‐Boundary Sliding in Bi‐Crystals of Sodium Chloride and Magnesia". Journal of Applied Physics 33 (6): 2126–2131. doi:10.1063/1.1728908. ISSN 0021-8979. http://dx.doi.org/10.1063/1.1728908. 
  13. ↑ Naziri, H.; Pearce, R.; Brown, M.Henderson; Hale, K.F. (April 1975). "Microstructural-mechanism relationship in the zinc/ aluminium eutectoid superplastic alloy". Acta Metallurgica 23 (4): 489–496. doi:10.1016/0001-6160(75)90088-7. ISSN 0001-6160. http://dx.doi.org/10.1016/0001-6160(75)90088-7. 
  14. ↑ Sergueeva, A.V., Mara, N.A. & Mukherjee, A.K. Grain boundary sliding in nanomaterials at elevated temperatures. J Mater Sci 42, 1433–1438 (2007). https://doi.org/10.1007/s10853-006-0697-0
  15. ↑ Wright, P. K. (1978-07-01). "The high temperature creep behavior of doped tungsten wire" (in en). Metallurgical Transactions A 9 (7): 955–963. doi:10.1007/BF02649840. ISSN 1543-1940. https://doi.org/10.1007/BF02649840. 
  16. ↑ 16.0 16.1 16.2 16.3 Raj, R.; King, G. W. (1978-07-01). "Life Prediction of Tungsten Filaments in Incandescent Lamps" (in en). Metallurgical Transactions A 9 (7): 941–946. doi:10.1007/BF02649838. ISSN 1543-1940. https://doi.org/10.1007/BF02649838. 
  17. ↑ 17.0 17.1 17.2 "100 years of doped tungsten wire" (in en). International Journal of Refractory Metals and Hard Materials 28 (6): 648–660. 2010-11-01. doi:10.1016/j.ijrmhm.2010.05.003. ISSN 0263-4368. https://www.sciencedirect.com/science/article/abs/pii/S0263436810000752. 




Retrieved from "https://handwiki.org/wiki/index.php?title=Physics:Grain_Boundary_Sliding&oldid=185286"