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Effects of grain boundary adhesion and grain size on ductility of thin metal films on polymer substrates

Teng Li's picture

We study the effects of grain boundary adhesion and grain size on the ductility of thin metal films well bonded to polymer substrates, using finite element method. It is shown that the ductility of polymer-supported metal films increases approximately linearly as the grain boundary adhesion increases, and as the grain size decreases. A rule-of-thumb estimate of the ductility of polymer-supported metal films agrees well with the simulation results.

In press, Scripta Materialia, 2008 

DOI: 10.1016/j.scriptamat.2008.06.058

PDF icon TengLi-Pub24-SMM-2008.pdf256.49 KB


Xiaodong Li's picture

Thanks Teng. Excellent. I very much like this paper. Your paper can well explain our previous experimental results about thin film magnetic tapes. We performed in situ tensile tests under AFM on thin film/polymer systems. Your paper can help us a lot to get in-depth understanding of the cracking in thin film magentic tapes.

Xiaodong Li, Weijie Xu, Michael A. Sutton, and Michael Mello, "Nanoscale Deformation and Cracking Studies of Advanced Metal Evaporated Magnetic Tapes Using Atomic Force Microscopy and Digital Image Correlation Techniques," Materials Science and Technology, 22 (2006) 835-844.

Teng Li's picture


Thanks for your kind words and pointing out your related publication.  The decreasing crack spacing in the film under increasing tensile strain has been observed in various experments, including those in your above paper.  Such observations need to be considered in our further simulations.


I find the topic discussed here most interesting, as I am working on various instability phenomena (including localizations) analytically.


Hi, Teng,


I have read the paper entitled 'Deformability of thin metal films on elastomer substrates' co-authored by you and Z. Sou with great interest. I understand that you used the finite element code of ABAQUS to compute the localization solutions. Could you clarify some issues regarding computing the post-bifurcation solutions by ABAQUS?  Thanks.


1. When there are multiple solutions (which typically arise in a bifurcation problem), how does ABAQUS select the solution to compute?


2. There could be mutiple nontrival post-bifurcation solutions. Can ABAQUS determine how many nontrival solutions there are? I have encountered some cases that there exist a single-neck solution and some mutiple-neck solutions.

3. If the number of nontrival solutions can be determined, can ABAQUS compute all them?

4. If there is a snap-through phenomenon, how does ABAQUS deal with it to get the post bifurcation solution?

Recently, we have managed to construct the analytical solutions for localization in a slender cylinder compose of a hyperelastic material and all post-bifurcation solutions are obtained (see International Journal of Solids and Structures 45 (2008) 2613–2628). The results reveal that the thickness plays important role in several aspects. If ABAQUS can deal with the issues raised above, it will be interesting to compare the numerical results with our analytical one.



Teng Li's picture


Glad to know your interest in our papers.

In the abovementioned IJSS paper , we investigate the strain localization in the thin metal films on polymer substrates.  The bifurcation analysis predicts the bifurcation deformation in the metal film at short wavelengths.  In the FEM, an initial imperfection (a shallow V-shaped notch) is introduced to initiate the necking of the metal film.  Although the same shape of initial imperfection is introduced in the model with various metal/polymer stiffness ratios, the spacing between the multiple necks in FEM simulations agrees well with the short wavelength predicted by the bifurcation analysis.  It seems ABAQUS (the FEM codes we used) can pick up the neck spacing corresponding to the lowest bifurcation strain of the metal film. For comparison, we also run the similar model but w/o initial imperfection. In such cases, the metal film can deform to rather large strains w/o necking formation. My understanding is that ABAQUS cannot deal with the above bifurcation analysis, but can be used to simulate the nonlinear post-bifurcation deformation.  I'm not sure of the detail algorithm used in ABAQUS to deal with post-bifurcation analysis. I'll suggest to look into their documentation or contact their tech support to double check.

Hope this is helpful.




Thanks a lot for your very helpful comments.


I also thought that ABAQUS could not deal with the bifurcation analysis but was not so sure. While a linear stability analysis is very valuable, fully nonlinear stability analysis is also often needed. I believe that your work and others on the strain localizations of thin films on polymer substrates provide good motivations for further such analysis. 





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