iMechanica - suo group research - Comments

Re. Question

Kejie Zhao — Tue, 29 Nov 2011 12:54:51 -0500

Hi Dibakar,

Thanks for the questions. We considered the amorphous lithiated silicon shell and crystalline silicon core is seperated by a sharp phase boundary, without more experimental evidence, we didn't describe details of such boundary, for example, how lithium assiste the reconstruction of the structure, if a small amount of lithium is dissolved in the crystalline silicon lattice ahead of reaction front, etc. There are still quite a bit open questions to make the picture clearer. Please let me know if I answered your concerns.

-Kejie

Question

Dibakar Datta — Tue, 29 Nov 2011 00:01:30 -0500

Kejie,

You have mentioned in the introduction section that the phase boundary between the crystalline silicon and the lithiated silicon has a thickness of ~1 nm as observed in experiment . However, in your model, you have not considered phase boundary. You have considered only LixSi zone . Any explanation ?

I am trying to do some work related to your work. Thanks .

Regards,
Dibakar Datta
Email : dibakar_datta@brown.edu
PhD Student ; Major : Solid Mechanics
Shenoy Research Group
Brown University
Providence 02912 , USA

Thank you

Kejie Zhao — Sun, 27 Nov 2011 19:27:00 -0500

Thank you Dibakar, hope you can find it interesting. -Kejie

Great Work

Dibakar Datta — Sun, 27 Nov 2011 17:42:16 -0500

Congrats Kejie .. Great Work ...

Regards,
Dibakar Datta
Email : dibakar_datta@brown.edu
PhD Student ; Major : Solid Mechanics
Shenoy Research Group
Brown University
Providence 02912 , USA

Thanks

Rui He — Sun, 02 Oct 2011 21:18:50 -0400

Hi, Yuhang, thanks very much for your reply, and I have read the paper and book you mentioned, they're very helpful, thanks!

Hi Rui, 1. The

Yuhang Hu — Tue, 27 Sep 2011 08:27:09 -0400

Hi Rui,

1. The poroelasticity theory which was orignially developed By Terzaghi and later genaralized by Biot has been studied for many years. There are many versions to define the poroelastic constants. But in general, there are five independent constants including the kinetic constant (diffusivity or permeability). In gel theory it is usually assumed that the individual polymer chains and solvent molecules are incompressible, so we are left with three paramters. For soil material, Darcy's law is addapted as kinetic model. The effective diffusivity is D=2(1-v)Gk/(1-2v)η, where k is the so-called permeability and η is the viscosity of the fluid. Details about how the expression is derived, you can refer to the following paper:

Jinhwan Yoon, Shengqiang Cai, Zhigang Suo, and Ryan C. Hayward. Poroelastic swelling kinetics of thin hydrogel layers: Comparison of theory and experiment. Soft Matter 6, 6004-6012 (2010). http://www.seas.harvard.edu/suo/papers/232.pdf

2. The inelastic deformation so fas has not been considered in the indentation method. About theory, it has long been studied for soil material. You may refer to the following book:

O. Coussy, Poromechanics, (2004)

one more question

Rui He — Sun, 25 Sep 2011 09:34:58 -0400

Hi, Yuhang, thanks very much for your reply. When comes to soil material, I still have some questions

1. There're only three constants in poroelastic gels, however, there're four poroelastic constants (Lame constant and two more Biot's constants) in soil material, and would you explain what "effective diffusivity" correspond to in soil?

2. In your experiment, the indentation can be treated as purely elastic, however, as you can imagine, lots of soil materials are very soft and inelastic (such as plastic) properties can easily comes out. Do you have any idea of how to treat this problem?

Hi Rui, theoretically it

Yuhang Hu — Fri, 23 Sep 2011 23:37:08 -0400

Hi Rui, theoretically it works for saturated soil material. Just several points need to be considered.

In our model, the individual solvent molecules and solid skeleton are assumed to be incompressible. The volume change of the material is due to the change of solvent concentration.

No inelastic deformation has been taken into consideration in our method.

a question

Rui He — Wed, 21 Sep 2011 08:41:14 -0400

Hello, Yuhang, I have read your paper, it's a good method, and I wonder whether your method can be used to determine the poroelastic constants of the saturated soil ?

Thank You Prof. Suo

Dibakar Datta — Tue, 13 Sep 2011 12:17:37 -0400

Dear Prof. Suo,

Thank you very much for sharing your work. I really enjoyed your recent talk in June at Brown University .

Regards,
Dibakar Datta
Email : dibakar_datta@brown.edu
PhD Student ; Major : Solid Mechanics
Shenoy Research Group
Brown University
Providence 02912 , USA

Thanks for sharing

Guangli — Mon, 12 Sep 2011 15:21:53 -0400

Dear Prof. Suo,

Thank you very much for posting the interesting seminar slides and video. I enjoyed it very much. The presentation is very clear and informative. I still remeber some of your slides when you did a related lecture at JHU a while ago.

Warm Regards,

Guangli

Re: Cu film SEM

Nanshu Lu — Wed, 06 Jul 2011 13:05:00 -0400

Hi, Oleksandr,

Thanks for the nice SEMs. The strain for crack initiation is around 10%, which actually matches well with the strain of resistance deviation. That's the point I tried to make in my paper.

You raised very good questions about the stress-strain and reloading behaviours of polymer-supported metal films. We didn't focus on the stress-strain because we wanted to mainly address the stretchability issues which is very pertinent to flexible electronics. I mentioned about the yield strengths of films with various thicknesses in the paper "The effect of film thickness on the failure strain of polymer-supported metal films " but not much about the overall stress-strain behaviour.

During unloading, as you pointed out, the substrate is elastic and recoverable but the elongation in the metal film is irreversible. So I suspect that the films have to deform plastically during the unloading. Although I haven't observed any buckling delamination of the film, I did see two cracked halves overlap onto each other.

Nanshu

cu film SEM

Oleksandr Glushko — Fri, 01 Jul 2011 07:01:04 -0400

Hi Nanshu!

the 5% strain example shown in my previous post is a pretty typical one.

The surface after 10% looks like this:

and after 15% like this:

By the way, there is something else that i don't understand. Why nobody is looking on stress-strain curves? Is it too trivial? I mean, even if the thickness of the substrate is ~ 100 times higher than the thickness of the metal film it is still interesting (at least for me) to compare bare substrate to film+substrate. For instance i can say that the yield strength of a film+substrate is higher than that of a bare substrate. Unloading is even more non-trivial: elastic substrate and ductile film, substrate "wants" to stretch back, film - doesn't. Did you observed any bending of your samples after a tensile test?

Best regards!

Thank you, Oleksandr

Nanshu Lu — Tue, 28 Jun 2011 17:09:51 -0400

Hi, Oleksandr,

Thank you very much for the figures. They are great illustrations.

Regarding to the first figure, since metal thin films cannot deform elastically up to 20% so we don't need to compare the circles to the stars at such strains.

For the second figure, if you have corresponding micrographs to show the cracking actually initiates around the strain of deviation, that would be awsome.

I observed very similar neckings for unannealed 200nm Cu film on Kapton substrate as your Figure 3.

Cheers,

Nanshu

Dear Nanshu, thanks a lot!

Oleksandr Glushko — Wed, 22 Jun 2011 04:16:44 -0400

Dear Nanshu,
thanks a lot! So, the initial part (elastic deformation) of a resistance change vs. length change should be a straight line. But since the yield strain is normally small (0.5%-2%) the difference between linear and square dependence is negligible. In the figure below the stars show the R/R0=(L/L0)^2 dependence while circles are for the first-order (elastic) volumetric change. During plastic deformation no change in lattice constant is assumed but dislocation generation and slipping. I understand, thanks!

I've already done some resistance measurements which look pretty similar to your published results, see the figure below. All curves are for 200 nm Cu film on PET.

Regarding necking of the films, at 5% strain we already observe what I called "homogeneous necking", see the figure below. Our films are not annealed and have very heterogeneous grain structure.

Hopefully, our discussion is at least a bit interesting for you too.

Thanks for your help!

Best regards,

Oleksandr