MultiSil

Numerical experiments - another way to build up constitutive relations

ebarthel — 2018-01-12T10:49:00Z

There is only a limited number of experiments which can provide data suitable for the design of constitutive relations for amorphous silicates. However, numerical simulations can also help along the way.
Within the MultiSil consortium, we have pioneered the use of molecular dynamics (MD) to emulate typical calibration experiments which cannot be performed (yet) with amorphous silicates, such as plastic deformation in pure shear [1]. The key idea is that with MD, we can obtain structure information al along the deformation path, so that in principle, the internal variables parametrizing the deformation can be determined.

Figure : typical yield surface for sodosilicate glasses, with impact of strain hardening (in red) and loading states depending on test configuration.

In our recent work, the approach has been extended to depolymerized silica networks, in an attempt to model sodosilicate glasses [2]. The results have led us to develop a more elaborate functional form for the yield surface of silicate glasses [3]. We hope future experiments can provide quantitative data for identification of the parameters !

[1] Impact of pressure on plastic yield in amorphous solids with open structure
Mantisi, B. ; Kermouche, G. ; Barthel, E. ; Tanguy, A.
Physical Review E 93 (2016) 033001

[2] Densification dependent yield criteria for sodium silicate glasses - An atomistic simulation approach
Molnar, Gergely ; Ganster, Patrick ; Tanguy, Anne ; Barthel, Etienne ; Kermouche, Guillaume
Acta Materialia 111 (2016) 129-137

[3] Plastic response of amorphous silicates, from atomistic simulations to experiments - A general constitutive relation.
Molnar, G. ; Kermouche, G. & Barthel, E.
Mechanics of Materials 114 (2017) 1-8

Perfectly plastic flow in amorphous silica

ebarthel — 2017-03-28T14:17:00Z

Using in situ compression in a SEM, we have directly demonstrated plastic yielding in uniaxial compression for amorphous silica. A decent pîllar is turned into a pan-cake within dozens of seconds. Of course its (original) diameter is little more than 2 microns...

Figure : three stages of the compression of a silica pillar, a few microns across. The flattening without fracture is the result of extensive plasticity.

More quantitatively, we have demonstrated that this plastic flow occurs without hardening. On the theory side, this was expected since the amorphous structure leaves no mechanism for hardening... but experimetally not easy to prove, because it requires careful assessment of the section.

Reference :
Perfectly plastic flow in silica glass
Kermouche, G. ; Guillonneau, G. ; Michler, J. ; Teisseire, J. ; Barthel, E.
Acta Materialia 114 (2016) 146-153

Impact of pressure on plastic yield in amorphous silica

ebarthel — 2016-03-13T21:36:02Z

For the plastic flow of silicate glasses, the coupling between pressure and shear is still a debated issue. The problem is especially acute for amorphous silica, which is prone to densification due to large free volume. Here we have used Molecular Dynamics simulations of a model iono-covalent amorphous solid with large free volume to investigate this coupling. Of course this model tries to emulate amorphous silica.


Calculated silica yielf surface: Distribution of residual volumetric strain (densification) and residual shear strain as a function of loading (maximum hydrostatic pressure and maximum von Mises stress). This map delineates a yield surface with strain hardening. A simple buckling instability model predicts the overall parabolic shape of the surface quite accurately.

The most interesting result is the shape of the yield surface : the MD simulations result in a quasi parabolic yield surface (Figure). This is not too far from the elliptic shape we assumed for our previous constitutive equation (Kermouche et al. Acta Mat. 2008). The main discrepency lies near the pure shear regime, which is experimentally difficult to access.
Remarkably, this parabolic shape has been predicted by Lambropoulos (J. Am. Ceram. Soc 1993) a number of years ago, based on a simple buckling model. Therefore, the idea that buckling is key to the anomalous mechanical properties of amorphous silica pervades the plastic response as well.
The major remaining question is when do shear bands appear in amorphous silicates, and how can we deal with them at the continuum scale ?

Publication

- Boris Mantisi, Guillaume Kermouche, Etienne Barthel & A. Tanguy, Phys. Rev. E. 93, 033001 (2016) - Journal Page, Preprint (Hal)

Why plastic ?

ebarthel — 2014-05-10T09:22:11Z

The plasticity of amorphous silicates

People have dreamt for a perfectly plastic glass material for millennia : plastic glass is one of the many colourful inventions strewn around Petronius' Satyricon. In chapter LI, a glassmaker proudly presents the stunned emperor with a marvelous glassware, which, when thrown to the ground, does not shatter : the resulting bumps can even be mended with a hammer.

Indeed, brittleness actually results from a competition between plastic deformation and fracture. Hence for a given resistance to fracture (or toughness), a reduced brittleness may result from easier plastic deformation. Tempered steel is brittle...at the kilometer range (Y. W. Rhee et al., J. Am. Ceram. Soc. 84 (2001) 561).

Now glass does exhibit plastic deformations. The relevant lengthscale however is micrometric. Despite this fact, a singular feature of the ductile deformation of silicate glasses and most notably amorphous silica has been evidenced more than 30 years ago : it densifies (F. Ernsberger, J. Am. Ceram. Soc. 51 (1968) 545). In contrast to plastic deformation of metals, which occurs at constant volume, the plastic deformation of amorphous silica leads to permanent increase in density. Instead of deforming plastically by shear flow, silica deforms both by shear and by densification : the flow does not preserve the volume. The simplest evidence is that indented silica refracts visible light more than ordinary fused silica.

Plastic deformation of amorphous silicates

ebarthel — 2014-05-10T09:21:11Z

the dream for plastic glasses dates back to to millenia...(more)