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Critical Size of Stiff Islands on Stretchable Substrates due to Interface Delamination

Nanshu Lu's picture

One possible design of stretchable integrated circuits consists of functional islands of stiff thin films on a polymer substrate. When such a structure is stretched, the substrate carries most of the deformation while the islands experience little strain. However, in practice, the island/substrate interface can never cohere perfectly. Existing experiments suggest that, interface debonding occurs if the island is larger than a certain size. I am now studying the critical size of stiff islands on stretchable polymer substrates due to thin film delamination, using finite element simulations. We show that the maximum energy release rate of interfacial cracking goes down as island size or substrate stiffness decreases. As a result, the critical island size can be enhanced if the substrate is chosen to be more compliant. An approximate formula is given to predict the energy release rate for the configuration of stiff islands on very compliant substrate.


Is it in the nano-scale or micron? --

Nanshu Lu's picture

Thanks. The typical size of an island is in micron-scale. To determine the critical size we have to know the interface toughness at given mode mixity and compare with our calculated driving force.

Is there any question of the validity of continuum mechanics in this scale? If it is questionable, then the finite element equations are need to be reformulated. How do you measure the interface toughness? -

Nanshu Lu's picture

The length of the islands is in 100 micron and the thickness is in 1 micron. To be precise, we used continuum mechanics to analyze such structure and after normalization the thickness doesn't really matter. So the results will be valid for structures as small as continuum mechanics can apply.

I didn't do experiments to measure the interface toughness. What I did was to just provide the calculated energy release rate.

Tianlei Li's picture

Do you have any reference about that? Thanks.

Tianlei Li

Nanshu Lu's picture

1. Hutchinson 1996, Stresses and Failure Modes in Thin Films and Multilayers

2. Nix, 353 Class Notes on Thin Film Mechanics

3. Hutchinson and Suo 1992, Mixed mode cracking in layered materials

Actually we have a very good course of thin film fracture and delamination (ES 242r). Very completed resource there. 

Tianlei Li's picture

Thank you very much. It is a big help.

Can I ask how do you get the stress field in your project? FEM? I meet this problem when I am calculating the chemical potential of a void growing in a finite grain. I don't knwo what your model looks like, but I guess you may meet the same problem. Right now I'm trying to get the stress using traditional stress function method since the my model, represented as a rectangle within a circular hole, is not very complicated. Are you dealing your model using stress function too?


Nanshu Lu's picture

You are welcome.

I am now using the commercial FEM code ABAQUS v6.5 to do the calculation because it includes modeling and postprocessing capabilities for fracture mechanics analysis. I don't think ABAQUS is able to do chemo-mechanical coupled problems so you have to develop other feasible methods.

Henry Tan's picture

Can your finite element calculations match with the theoretical predications, or experimental results, on the critical size of stiff islands?

Nanshu Lu's picture

There's no very relavent experiments available for comparison. But the calculation does match our theory quite well. Please pay attention to our upcoming paper. Thanks.

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