iMechanica - delamination - Comments

journal paper submitted

Rui Huang — Fri, 07 Dec 2007 23:28:05 -0500

A renovated version of this work has been submitted to International Journal of Fracture.

thanx Wei

shirangi — Thu, 31 May 2007 13:27:30 -0400

Hi Wei,

thanx for your kind answer. It seems that u know alot abou cohesive zone elements.

stay Happy and regards from Germany

Hossein

a very good idea

Zhen Zhang — Wed, 30 May 2007 11:47:55 -0400

Hi, Wei,

Thank you very much for your comment. This is a very good thought. Simple and easy to implement, but also capture the physics. You are always excellent.

Thanks a lot.

Zhen

2D vs 3D

Rui Huang — Tue, 29 May 2007 22:56:48 -0400

Zhen:

Very good point. I agree that the 2D solution could serve as a good approximation for rounded 3D corners. In this case, I believe the applicable area of the 2D plane strain solution would be limited by the rounded radius. For a 40 nm rounded corner, this area must be very small. Remember, we still have to take out the area really close to the corner for the k-annulus.

Thank you for the pointer to Dunn et al.'s paper. I should definitely check that out.

Interfacial heat transport

Wei Hong — Tue, 29 May 2007 11:43:28 -0400

Hi Hossein,

Similar as the mechanical cohesive model, what you need is a relation between the heat flux J, the temperture difference Δθ, and the displacement difference Δx.

More serious studies would require well designed experiments. However, as you are asking about the cohesive zone element, I assume that you only need a hand-waving model. Here is one:

If we still assume a linear kinetic law, say J = kΔθ, but take k as a function of Δx. Physically, we know that k→∞ when Δx=0, and k=0 when Δx>x0, where x0 is the distance over which the cohesive force is taken to be 0. A simple guess of the functional form would be k = k0 * (x0/Δx - 1), when Δx<x0 and k=0 when Δx>x0. But such singular form might not be usefull in numerical calculation. I would suggest using the form (for Δx<x0)

k = A * (x0 - Δx)n

where A is a big enough number and n is the index you can tune.

I wish I knew.

Zhen Zhang — Tue, 29 May 2007 10:09:35 -0400

Dear Hossein,

Thank you very much for your interest. I am so happy that we have the same interests.
In the problems I considered, there was no coupling of thermal conduction and mechanical failures yet. The only experience with cohesive zone element was described in my thesis, chapter 3. If there is any chance, I would like to do some in the problems you mentioned here.

Zhen

3D corner singularity can be approximated by 2D edge singularity

Zhen Zhang — Tue, 29 May 2007 09:53:30 -0400

Dear Rui,

Thank you very much for your interest.
As you pointed out, the delamination failure is most likely to occur at 3D corner, not only for chip-package structure, but also for others, e.g. SiN square pads on strained silicon. In order to avert the complexity of 3D corner singularities, we considered the 2D plain strain problems in our study. But, the 3D corner is more critical than 2D edge and therefore deserves attention. Dunn et al. (JMPS, 2001) had an asymptotic solution for the perfectly 3D corner. Here, we propose a 2D approximate solution for the 3D corner based on the following arguments. Since in practice, the 3D corner is formed by the perpendicular edges of pads on the substrate, and usually rounded with a radius. So it is not a perfectly sharp 3D corner. For example, in SiN pad on strained silicon, the rounded radius is much larger than atomic scale, e.g., 40 nm rounded radius for a 500 nm thick SiN pad in Kammler et al. (APL, 2005). The local stress state close to the root of 3D bimaterial interface is still in plain strain state (maybe this is a vague statement, but at least this is a good approximation). Hence, the singular stress expression of 2D plain strain problem still applies, except that the stress intensity factors need to be modified to include the effects of the stress overlapping from two adjacent edges. Then, the remaining complexity is from the 3D FEM calculation and the curve fitting.

Cohesive Zone Elements

shirangi — Tue, 29 May 2007 05:11:33 -0400

Dear Friend,

I saw your Dissertation and papers and I think that my PhD topic is very similar to yours. Actually I am doing my PhD in Germany at Fraunhofer Institut and my PhD is supported by Robert BOSCH company.

I wnated to ask, If you have any experience about cohesive zone elements. Do you know how you can bring thermal diffusion between to materials in interface?

stay Happy

Hossein Shirangi

How about a chip-package corner in 3D?

Rui Huang — Mon, 28 May 2007 22:37:37 -0400

Dear Zhen,

With interest I read your paper. I find the combination of analytical solutions and numerical modeling very powerful for understanding the basic mechanics in chip-package interactions. We have done many ABAQUS calculations of similar problems, for which I often find it difficult to draw any physical conclusions due to the complexity of the model. Now I think I have a clue to make the calculation more meaningful. For that I thank you.

As powerful as it is, I see one limitation of this work, that is, the 2D consideration. At most, the 2D model simulates the behavior at the edge of the chip, far away from the chip corner, where delamination failure is most likely to occur. I suspect a 3D configuration is required for the stress field near the real corner. Is it possible to develop an asymptotic solution in this case? If yes, it would be very useful, I think.

mode mixity w/ and w/o fillet

charliezhai — Wed, 25 Apr 2007 18:44:19 -0400

Zhen,

We consider the packages defective if we don't see proper formation of underfill fillet after underfill dispense, which speaks for the vital role of fillet to the reliability of flip chips.

Apparently the strength of singularity is totally different at die corner in cases of w/ and w/o fillet. In presence of corner defects, w/o fillet, the crack is almost dictated by the opening mode, with fillet the mode is rapidly shifting to shear mode. As you correctly pointed out, the fillet makes the crack much harder to grow.

Charlie

Zhen,

Yaoyu Pang — Wed, 11 Apr 2007 01:30:46 -0400

Zhen,

In the present work, we actually considered the coupling situation for steady state channel cracking, putting aside any complexities around the crack fronts and scenarios during the intermediate stage. So a 2D plane strain FEM model was set up and calculated, which I think is quite different from what N.Cordero have been doing.

But you did raise some interesting issues. Thanks for your nice input.

crack front morphology

Zhen Zhang — Tue, 10 Apr 2007 17:42:19 -0400

Hi, Yaoyu, this is a very nice work. When N. Cordero studied the channel cracking in hermetic coating for flexible electronics, we realized that we needed to do more to consider the coupling of channel cracking and interfacial delamination. Otherwise, the deformation in substrate around the channel crack front on the interface is too large and distorted, which is easily observed in FEM. Now you did this nice work before we move forward. And this is a nice paper.

Besides, I want to ask a question: how can you verify the whole crack front morphology, including the channeling front and the delaminated front, esp. around the vicinity of channeling crack front? You assume the shape is like that in Fig.1(b). Of course, your method circumvents this subtlety. I am just curious if you considered this point?

Hi Xiao, I am trying to

Biswas — Mon, 02 Apr 2007 03:18:33 -0400

Hi Xiao,

I am trying to implement a method to compute K for interfacial crack using ANSYS APDL. But my problem is to get the nodal force data at the crack tip (I am trying to use virtual crack closure technique). Could you please help me regarding this matter? If possible, please let me know the APDL command to get nodal force data.

Thanks.

Regards,

Biswas

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.