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dynamic failure of nanocrystalline copper

Large scale molecular dynamics simulations are aimed at understanding the micromechanisms of nucleation, coalescence, and growth of voids in nanocrystalline metals (Cu, Al). Current focus is on systems with grain sizes between 2 nm to 15 nm for strain rates > 10^7 /s. Voids nucleate at grain boundary junctions and grow by the shearing of neighboring atoms. Void growth is accompanied by the formation of a disordered region surrounding the void which later recrystallizes due to the increase in temperature associated with the plastic deformation. The snapshots of a section of the system at (a) 362 ps, (b) 366 ps, (c) 370 ps, (d) 374 ps, (e) 390 ps, and (f) 400 ps, showing the growth of the void under conditions of triaxial tensile strain at a constant strain rate of 10^8 s-1. The atoms are colored using common neighbor analysis. [Phys Rev B 80, 104108 (2009)]

PDF icon DONGARE_Voids_PRB_80_104108_2009.pdf2.95 MB


Kejie Zhao's picture

Hi amdongare,

This is a nice and comprehensive study.  I did a simulation on the failure of nanoporous single crystal Cu, which may be of interest to you.


Dear Dr. Kejie,

Thank you for your comments. Is your manuscript published anywhere? Your work on the Gurson's model is very interesting. We have carried out a similar study for single crystal Cu (but we focus on calculating a biaxial yield surface(stress only in x and y; stress in Z direction is = 0). A short summary of this work is recently being published in the proceedings for Shock Compression of Condensed Matter (SCCM) 2009. I would be happy to send you the article in case you are interested. Thanks,


Kejie Zhao's picture

Hi Avinash,

Thanks. Please send me your article. My email is

This manuscript is in press, and should appear in journal soon. We have not incorporated appropriate model for size effect on the yield surface though. If you have any comments on it, please let me know. Thanks



Hi, Avinash, 

At first thought, I was surppried that Cu could fail in this way, i.e.,  nucleation, coalescence, and growth of void because due to their high plastic deformation ability (the small unstable stacking fault engergy to stable stacking fault energy ratio).

Then after I realized that you are applying triaxial tensile loading, the confusion was gone because the hydrostatic pressure will hypothetially constrain other plastic deformation mechanism like dislocation slip, twinning, grain roation etc.   

I did some work on this topic but in uniaxial tensile loadin of NC Ni, which shows some similar results as you do. The link is here: Welcome discussions.



Hi Ajing,

Yes you are right.  Triaxial loaidng would haveslightly lesser dislocation activity, but it is present. If you see the snapshopts above, the red atoms correspond to stacking faults. Graib boundry slip/rotation is present as well. Your study on loading/unloading/loading is very interesting. Thank you for sending me your paper.


I have one question though. In your simulations, for teh continuous loading one, you mention that after the stress reaches a maximum strength of 5.2 GPa at 4% total strain, the curve shows a negative slope which is responsible for the formation of damage (nanovoids). To me, the negative slope of the stress strain curve is related to the flow of the material (softening) and hence the peak stress is defined as the flow stress. But I have run simulations of nanocrystalline Ni with garin sizes upto 20 nm upto 12% strain. We've never encountered formation of voids during continuous loading. The same is the case for copper as you can see in the paper by Schiotz in Science. []. You mention in the paper that the system was equilibrated only for 20 ps. This equilibration time to me is very small given the nature of the as-created grain boundaries.


Do let me know what you think.



HI Avinash,

Yes, the two possibilities for stress reduction after peak stress are
softening (continuously except localization) and cracking (a little bit
sudden). The stress-strain curve in our paper showed a small drop after
peak stress, which we believe is corresponding to the void formation (and we
did observe them in snapshots).
I think flow stress is distinguished
from peak stress (yield stress). The former is the initiation of flow and the
latter is for sustaining flow. And accordingly strain softening and strain
hardening define how flow stress continues with strain with respective to the
peak stress. Again in our case, with bond breaking involved, the
relative sudden stress drop is more likely due to the formation of nano-voids. Otherwise,
the stress-strain curve should be flat resulting no softening as seen in NC Cu
in our simulations and Schiotz et al.
On the opposite, I've not seen voids
occurred in my simulations up to 12% strain, which is similar to the paper by
Schiotz in Science you mentioned above. The reason for you did not see the void
formation in Ni is probably due to the inter-atomic potential. I would
suggest you use Mishin potential (references therein) for the accurate
description of general stacking fault energy cure, which is critical to
simulate mechanical properties involving plasticity. 





I'm sorry for the bad format. I dont why the post looks like this and how to revise it.

Click on the html editor and remove the text between <!-- and --> before posting the comment.

-- Biswajit 

Dear Ajing,

Thanks for the input. I will look at the effects of interatomic potential. 


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