Plastic deformation in metallic glasses: mechanisms and models

1. Plastic deformation in metallic glasses: mechanisms and models Toren Grynbaum MS&E 410 Professor Shefford P. Baker Spring ‘06

2. Introduction: processing • Seminal discovery, 1957: Duwez (Au-Si). • Metal alloys could be solidified without crystallizing, by overshooting Tg amorphous glassy structure. • Early materials required high cooling rates (~1010K/s) thin dimensions.

3. Introduction: processing (cont) • Advances in the field lead to lower cooling rates (low as .1K/s) lead to bulk metallic glasses. • Pd40Cu30Ni10P20, by the Inoue group • Use of metallic glasses in structural applications implies need to understand mechanical properties, especially yielding criteria.

4. Introduction: properties • Strong: 2X strength of most Ti alloys with high elastic limit and recoverable elastic deformation. • However, fracture just beyond the yield point. • Not ductile at all. • Very brittle • Fail before almost any plastic deformation occurs. • Global plasticity often <1%. • Why is this??

5. Constraints on possible descriptions • Unlike polycrystalline alloys, there are no dislocations in metallic glasses. • Consequently, no strain hardening. • Exhibit asymmetric yield criteria for compressive vs. tensile stress. • Slip occurs on localized scale  shear bands. • Adiabatic heating. • Serrated yielding.

6. Constraints on possible descriptions (cont) • Deformation seems to be different for high vs. low T. • T<<Tg, a few thin shear bands occur. • At higher T (~.7Tg), there is some anelastic deformation before the yielding point. • Here deformation depends on the strain rate. • At high strain rates (~10-3/s) fracture takes place early (inhomogeneous flow), as in low T. • At low strain rates (~10-5/s), necking occurs, and deformation is actually more homogeneous.

7. Constraints on possible descriptions (cont) • Map of deformation mechanisms with different strain rates(taken from Anantharaman)  • Theories must, at the very least explain/be in accordance with these phenomena.

8. Argon’s model of free volume • One of the 1st atomistic descriptions of the plastic deformation in metallic glasses. • As in polycrystalline alloys, the structure inextricably linked to mechanism of plastic deformation. •  need accurate description of atomistic structure. • RDF no good because they are too average.

9. Argon’s model of free volume cont. • Consults a model describing localized regions of increased disorder. • There is lower coordination between atoms than in the rest of the material  called free volume sites. • Here, energetically more likely that inelastic relaxations will occur here, since they can occur without affecting the rest of the structure. • These relaxations occur by localized shear transformations.

10. Argon’s model of free volume cont. • Transition state theory applied: • to produce the free energy associated with these localized shear transformations • modes of rearrangement are established in order to map out the free energy associated with such rearrangements. • (procedures are beyond the scope of this discussion, but can be found in Kocks et al.)

11. Argon’s model of free volume cont. • Given stress, , less than the critical stress of transforming the free volume site, c • Find free energy of activation by finding the remaining free energy necessary to induce a transformation. • Use: G= F - W, where F and W are the Helmholz free energy of the system, and deformation work done on system from the state under consideration to that at localized shear transformation, respectively.

12. Argon’s model of free volume cont. • Therefore frequency of transformation of such a free volume site is controlled by the instances in which G (or greater) is supplied to the free volume site. • This is given by a Maxwell-Boltzmann distribution (Arrhenius plot). • The below plot maps the distribution of free volumes to the distribution of free energy barriers. • Inversion makes logical sense, since it is expected that at smaller free volumes there will be a larger free energy barrier for transformation.

13. Argon’s model of free volume cont. • Using this model, Argon postulated that, at low temperature, small applied stresses would activate only the largest free volume sites (those with the smallest free energy barriers.) • Correspondingly, at much larger applied stresses many free volume site will rearrange, until the localized sites of deformation converge and the whole material has lost memory of its initial structure, but producing the same structure again.

14. Indentation data corroborating Mohr-Coulomb description • While the above seems logical, there are some problematic consequences. • It implies a pressure sensitivity of deformation. • However, the observed pressure dependency of yielding is usually observed to be too small to justify this model.

15. Indentation data corroborating Mohr-Coulomb description • Vaidyanathan et al propose Mohr-Coulomb (M-C) model. • instrumetnal indentation experiment using Zr41.25Ti13.75Cu12.5Ni10Be22.5. • Compared 3D finite element generated computational model using M-C and von Mises (which is usually used for crystalline metals) with data.

16. Indentation data corroborating Mohr-Coulomb description • Von Mises: • M-C, which incorporates the effect of normal stresses on plastic deformation: • M-C was originally used for granular materials, where n is associated with the rearrangement of shuffling particles, and  is a sort of coefficient of friction. • Applies to metallic glasses because they are analogous to granular solids. • Motion of randomly positioned atoms similar to the sliding of granules.

17. Indentation data corroborating Mohr-Coulomb description • Both constitutive laws are used in the simulation and plotted along with load-depth data from indentation of Zr alloy: • M-C law follows the data very well. • Confirms the influence of a normal stress component on the yielding criteria of metallic glasses.

18. Sheer bands and pile-up • In micrographs taken at points of indentation, there are circular patterns of pile-up: • This is due to localization of strain and the incompressibility of plasticdeformation. • The metals flows up against the sides of the indenter

19. Sheer bands and pile-up • The wavy nature of the shear bands indicates presence of viscous phase flow. • Due to adiabatic heating • Thermodynamic calculations show that the (very local) release of elastic strain energy into adiabatic heating upon plastic deformation can even drive T above Tm very locally.

20. Further support for M-C criterion • Findings by Schuh and Lund further support validity of M-C law for yield criterion. • Rests on the model of fundamental unit of deformation being shear transformation zone (STZ) = local cluster of disordered atoms which reorganize under stress. • Use the following to simulate data points for n and : • Where V = volume of system considered,  = interatomic potential, rij = distance between atoms i and j, N= number of atoms in system considered, n = normal component of atomic separation, t = transverse component of atomic separation

21. Further support for M-C criterion • Model used to generate simulation. • Compared with M-C criterion. • Agrees well. • Asymmetric yield criterion satisfied.

22. References • VAIDYANATHAN et al. "STUDY OF MECHANICAL DEFORMATION IN BULK." Acta Metall 49 (July 2001): 3781–3789. • Schuh, CA, and AC Lund. "Atomistic basis for the plastic yield criterion of metallic glass." Nature Materials 2 (June 2003). • Anantharaman, TR. Metallic Glasses: Production, Properties and Applications. Switzerland: Trans Tech publications, 1984. • Argon, AS. "Plastic Deformation in Metallic Glasses." Acta Metall 27 (June 1978): 47-58. • Greer, A Lindsay. "Metallic Glasses." Current Opinion in Solid State & Materials Science 2 (1997): 412-416. • Leamy, HJ, HS Chen, and TT Wang. "Plastic Flow and Fracture of Metallic Glasses." Metallurgical transaction 3 (Mar. 1972): 699-708.

23. Thank you! Questions?