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Size effects in pure and alloyed metals under dynamic loading

   School of Metallurgy & Materials

  Dr Beñat Gurrutxaga-Lerma  Applications accepted all year round  Funded PhD Project (UK Students Only)

About the Project

The strength of metals and metallic alloys is usually thought to be independent of the system’s geometry and dimensions. However, at the micron scale this ceases to be true. Broadly speaking, systems of the size of microns become increasingly stronger the smaller they are: the yield point and the plastic hardening rate, for instance, are known to increase with increasing system’s size. This “smaller is stronger” behaviour is known as a “size effect”. Size effects are particularly important in the thermal response of thin films on substrates, on indentation problems, on the plasticity at crack tips, and in the mechanical response of nanorods and other microsystems, amongst many other problems.

Size effects are well attested in a wide range of pure metals and alloys via experiments performed under various loading conditions: from torsional loads [1], through bending and compression of nanopillars [2], to nanoindentation[3,5], to the tensile testing of thin films [4,6]. Equally so, various theoretical and numerical models have

been proposed to study size effects, from continuum level phenomenological models reliant on strain gradient plasticity[1,6], to crystal plasticity[7], discrete dislocation dynamics[8], and molecular dynamics studies[9]. These studies have served to build a theoretical understanding of the physical mechanisms governing size effects, which are ascribed to dislocations operating at the microscale and their interactions with free surfaces, grain boundaries, and dislocation sources, as well as successful constitutive models of practical relevance.

Both experiment and theoretical studies of size effects tend to focus on very slow loading rates. That is to say, the loading rate of theory and experiments displaying size effects is typically quasistatic. Under these “low strain rate” conditions (usually below 10^1/s), the number of physical mechanisms responsible for size effects are well understood, particularly for simple metals. However, when the loading rate increases above 103s-1, many of the physical mechanisms believed to control size effects (e.g., dislocation starvation[10], obstacle-constrained plastic flow[1],...) become inoperative, or can be superseded by alternative mechanisms (e.g., heterogenous or homogeneous nucleation[11], surface sources, inertial effects in dislocation motion[12],...), so that whether or not size effects persist at high strain rates remains an open question that may impact shear band formation and other localisation effects. In particular, a threshold strain rate is postulated to exist (perhaps above 10^6/s), above which the time-dependencies in the plastic response completely overtake geometrical effects. The conditions that may lead to this are far from clear: very little experimental and theoretical work aimed at addressing the presence of size effects under high strain rate loads exists.

The project will be held at the School of Metallurgy and Materials at the University of Birmingham. The candidate will have at least a 2:1 class degree in Materials Science, Physics, Applied Mathematics, Engineering, or other relevant discipline. A background or interest in computer programming and applied mathematics would be advantageous. For further information, please contact Dr. Beñat Gurrutxaga-Lerma at

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Funding Notes

A fully funded (stipend+fees) PhD studentship is available for UK home students of this project.


[1] Fleck, N. A., et al. "Strain gradient plasticity: theory and experiment." Acta Metallurgica et materialia 42.2 (1994): 475- 487.
[2] Stölken, J. S., and A. G. Evans. "A microbend test method for measuring the plasticity length scale." Acta Materialia 46.14 (1998): 5109-5115.
[3] Stelmashenko, N. A., et al. "Microindentations on W and Mo oriented single crystals: an STM study." Acta Metallurgica et Materialia 41.10 (1993): 2855-2865.
[4] Venkatraman, R., and J. C. Bravman. "Separation of film thickness and grain boundary strengthening effects in Al thin films on Si." Journal of materials research 7.8 (1992): 2040-2048.
[5] Volkert, C. A., and E. T. Lilleodden. "Size effects in the deformation of sub-micron Au columns." Philosophical Magazine 86.33-35 (2006): 5567-5579.
[6] Haque, M. A., and M. T. A. Saif. "Strain gradient effect in nanoscale thin films." Acta Materialia 51.11 (2003): 3053- 3061.
[7] Bittencourt, E., Needleman, A., Gurtin, M. E., & Van der Giessen, E. (2003). A comparison of nonlocal continuum and discrete dislocation plasticity predictions. Journal of the Mechanics and Physics of Solids, 51(2), 281-310.
[8] Nicola, L., E. Van der Giessen, and A. Needleman. "Discrete dislocation analysis of size effects in thin films." Journal of Applied Physics 93.10 (2003): 5920-5928.
[9] Schiøtz, J., F. D. Di Tolla, and K. W. Jacobsen. "Softening of nanocrystalline metals at very small grain sizes." Nature 391.6667 (1998): 561
[10] Greer, J. R., W. C. Oliver, and W. D. Nix. "Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients." Acta Materialia 53.6 (2005): 1821-1830.
[11] Tschopp, M. A., and D. L. McDowell. "Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading." Journal of the Mechanics and Physics of Solids 56.5 (2008): 1806-1830.
[12] Gurrutxaga-Lerma, B., et al. "A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469.2156 (2013): 20130141.

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