iMechanica - Delamination of stiff islands patterned on stretchable substrates - Comments

Response to your question

Rongmei niu — Wed, 28 Mar 2007 20:40:02 -0400

Hi Nanshu,

Cracks density is the total cracks length per unit area in this paper. in case of parallel channel cracks , the average crack spacing is often used. Howerver, as to the zigzag cracks, i thinkit is reasonable to use cracks length per unit area.

I donot understand what is you meaning of the second question. And the modulus of Cu from my test is about 80~100GPa. How about you?

Regards!

Rongmei

Justification for 2D modeling of island delamination

Nanshu Lu — Wed, 28 Mar 2007 12:05:23 -0400

Xuanhe, very interesting question.

You're right, from engineering point of view the ideal modeling should be 3D, multilayer structure, true flaws... as real as possible. Intuitively, the corners of a square shape island should have higher driving force so that these areas are more susceptible for debonding. However, here I can give three justifications for our 2D modeling of island delamination.

First, from some experimental pictures of island delamination (Fig. 7 in Lacour et al, JAP 100 014913, 2006 and Fig. 11 in Bhttacharya et al, JES 153 (3) G259, 2006) we can see debonding occurs at both corners and laterals of the square island. Thus our 2D modeling is reasonable for the later one.

Second, even if the crack front is a 2D curve (many people modeling the 3D corner crack with quarter circular front) our delamination criterion says the energy release rate of each point on the front should reach interface toughness Γ(Ψ), where Ψ is the mode mix angle. So sometimes this 3D problem can be reduced to a 2D problem.

Last but not least, the main purpose of our scientific research is to try to understand the natural laws and intrinsic mechanisms. We make as many as possible simplifications so that the main object gets emphasized. Starting from 2D study we can find out how elastic mismatch, island size and crack size can influence the energy release rate, which is of great guidance for 3D problem. Meanwhile, 3D modeling is of high calculation and time cost. Comparing the gain and cost we just adopted 2D modeling.

Corner Effects.

Xuanhe Zhao — Tue, 27 Mar 2007 18:48:25 -0400

Hi Nanshu,

Very interesting work. A question. I noticed that you used plane strain assumption for your calculation, because the island's width is usually much higher than its thickness. Have you ever considered the effects of the island's corners, which in my opinion are the highest stress concentration points in this kind of structure, and therefore maybe the crack initiations? In this way, do you you need a 3D simulation to analyse the problem?

-Xuanhe

Nice job

Nanshu Lu — Mon, 26 Mar 2007 22:38:40 -0400

Dear Rongmei,

Congratulations to your new paper and thanks so much for sharing with us. It is very nice work and exactly what I am looking for. I just had a glance and have two questions needing your help,

1. How do you define and measure the crack density?

2. To obtain Cu yield strength did you take the tensile system compliance into account? What Young's modulus for film Cu did you get?

I'll read it more carefully later.

Nanshu

attatchment

Rongmei niu — Mon, 26 Mar 2007 21:29:15 -0400

Dear Nanshu,

I am sorrry for missing the attachment. This paper has been accept, and may be referenced to your experiments.

Regards!

Rongmei

Nice work, Nanshu.

Teng Li — Mon, 26 Mar 2007 17:14:17 -0400

Nanshu,

Very nice work. Thanks for this a wonderful addition to the March Journal Club issue.

I was away in the last several days, and it seems I missed the instructive discussion here. I've added a link in the March issue of Journal Club to this active discussion.

-Teng

My pleasure to answer your question

Nanshu Lu — Mon, 26 Mar 2007 13:13:36 -0400

Dear Rongmei,

Thanks for your recommendation very much. Now with the platform of imechanica, mechanics people can communicate freely all over the world. We are able to find speeches, lecture notes, manuscripts and many other resources here. Actually all of us are fortunate, right?

Regarding to your question about "island", it is actually a very nice design in flexible electronics. In order to be flexible, we need to fabricate inorganic brittle material onto flexible PI substrate. Since the brittle film can only sustain little strain, the film cannot continuously cover the whole substrate surface. Instead, we fabricate a lattice of brittle islands with metallic interconnections. When the substrate is stretched, the deformation is mainly accommodated by the substrate, so that the island and functional materials on it experience relative small strains.

Regarding to "coating", we use it to refer an additional continuous layer covering all over the islands and substrate. It can significantly reduce corner singularity and suppress delamination. A recent study from our group is here.

Regards

pleasure to discuss with you!

Rongmei niu — Mon, 26 Mar 2007 10:58:09 -0400

Dear Nanshu,

I am very pleasure to recommend excellent references to you! but you will find that most of them are from your group. Another paper in Journal of the Mechanics and Physics of Solids48 (2000) P1107――Crack patterns in thin films by Z. Cedric Xia, John W. Hutchinson, may be useful.

I admire and congratulate you that you are so fortunate in a great group, and conveniently communicate and discuss with great people. My major is materials science and engineering, and i only did some experiments, the attatchment in the following is part of the experiments, i sincerely hope it helpful to you! To be frankly, i still did not completely understand your paper. Why use "island" instead of "film or coating"? In the actual application, the films are continuous. Regards

Reply to mode mixity

Nanshu Lu — Sun, 25 Mar 2007 17:21:31 -0400

Thanks, Charlie.

When you request history output for the domain of contour integral there are several choices of the type. To obtain energy release rate only, we just choose "J-integral". To obtain both ERR and Ks, we choose "Stress intensity factors", with prescribing a crack initiation criterion. After calculation is completed, from the history output we can get both K1 and K2 as well as ERR estimated from Ks.

You are right, to present the ABAQUS results in the paper I just assume ε=0 and get my mode mixity simply from tanΨ=K2/K1. This is because our main purpose is to study the behavior of energy release rate.

mode mixity

charliezhai — Sun, 25 Mar 2007 15:09:05 -0400

Nanshu,

Nice work. Just a bit confused how you got K2 and K1 in Abaqus if you opted to use J-integral, and what is the characteristic length for you to calc mode mixity unless you neglected the ossicillatory index?

Charlie Zhai, AMD

Thanks very much

Nanshu Lu — Sun, 25 Mar 2007 11:24:47 -0400

Dear Rongmei,

Thanks very much to point out the mistake. Nice to meet you :)

Actually I am also doing some experiments of metal films on Kapton substrate in Vlassak's group. I have read your previous discussions carefully and I am wondering is there any paper published on this topic by your group? Or any crucial references you can recommend to me?

Thanks.

Nanshu

Good paper

Rongmei niu — Sun, 25 Mar 2007 00:19:15 -0400

hi Nanshu,

Thanks, and i have learnt very much from your paper! But it seems wrong in Page 8 the third line---" Es=200GPa ...." should be reversed, Es-- Ef, Ef -- Es .

I am a third year Phd in Xi'an Jiaotong university in china, and have done some experimental work in Cu films on PI substrates. Accordingly, i am very interesting to your group's research.

wedge singularity and Williams singularity

Zhen Zhang — Sat, 24 Mar 2007 19:01:07 -0400

Dear Rui,

I am not sure that what you mean by the so-called Williams singularity. Is that a crack perpendicular to the interface?

Here are my two cents about the wedge singularity and crack singularity.

1. for the wedge singularity of rigid film on substrate, alpha=1, the singularity exponents are -1/2+i*epsilon, the same as interfacial crack.

2. for Zak-William singularity, i.e. a crack in mat#2 perpendicular to the interface, the singularity exponents can vary from 0 to 1 for the whole alpha-beta plane.

Zhen

This solves my problem!

Rui Huang — Sat, 24 Mar 2007 18:48:08 -0400

Thank you again, Zhigang.

It is always a pleasure to read your paper. Now with iMechanica, I can learn more from the discussions, just like those days back in Princeton.

Zak-Williams vs. islands.

Zhigang Suo — Sat, 24 Mar 2007 18:39:29 -0400

Dear Rui: In the Zak-Williams problem, a crack impinges upon an interface. This would correspond to a limiting case in our problem when two islands approach each other. For us, we need to consider a corner singularity.

When the islands are rigid, the Zak-Williams problem will prescribe displacement on the entire interface. However, at the edge of an island (our problem), we will only prescribe displacement underneath the island, leaving the other part of the substrate surface traction-free.

Delamination of stiff islands patterned on stretchable substrates

Nanshu Lu — Fri, 23 Mar 2007 12:12:59 -0400

As another celebration of March Journal Club of Mechanics of Flexible Electronics, this paper has just been submitted.

Abstract

In one design of flexible electronics, thin-film islands of a stiff material are fabricated on a polymeric substrate, and functional materials are grown on these islands. When the substrate is stretched, the deformation is mainly accommodated by the substrate, and the islands and functional materials experience relatively small strains. Experiments have shown that, however, for a given amount of stretch, the islands exceeding a certain size may delaminate from the substrate. We calculate the energy release rate using a combination of finite element method and complex variable method. Our results show that the energy release rate diminishes as the island size or substrate stiffness decreases. Consequently, the critical island size is large when the substrate is compliant. We also obtain an analytical expression for the energy release rate of debonding islands from a very compliant substrate.

Keywords: flexible electronics, island size, delamination, complex potential