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A Continuum Model for Dislocation Pile-up Problems (Accepted by Acta Materialia)

Xiaohan Zhang's picture


A continuum dislocation pile-up model is developed to solve problems with arrays of edge dislocations on one or multiple slip planes. The model solves pile-up problems in a discrete dislocation dynamics manner.  The effect of anisotropy and stacking fault energy can be naturally modeled. The model is validated by reproducing the solutions of problems for which analytical solutions are available. More complicated phenomena such as interlacing and randomly distributed dislocations are also simulated. 

PDF icon dislocation_array_acta.pdf1020.86 KB


dabiao liu's picture

It seems a very interesting work that may be related to my recent papers (2014. A continuum theory of stress gradient plasticity based on the dislocation pile-up model. Acta Mater. 80, 350-364.  2013. Towards a further understanding of dislocation pileups in the presence of stress gradients. Phil. Mag. 93, 2340-2362). I will read it in detail. Cheers.

Xiaohan Zhang's picture

Hi Dabiao,

Thanks. Yes, I have cited your acta-materilia work. One of the section is indeed devoted to improved the understanding of stacking fault in pile-ups. I will read the phil Mag paper in detail.  

Happy new year.

Shuozhi Xu's picture

Congratulations on the new paper, Xiaohan! At first glance, this paper concerns only the edge dislocations? How about a pile-up containing screw dislocations? Would the same model be directly applicable? Thanks.

Xiaohan Zhang's picture


How are you? Any updates ?

Yes, the equations in this paper are only for edge components. But including screw dislocations is doable. Basically, we will have to let alpha_23 be non-zero, and that results in two simultaneous equations, coupled through dislocation velocity term. However, how to solve the set of equations in a numerically faithful way is still an open question. 

Shuozhi Xu's picture

Thanks, Xiaohan!

Amit Acharya's picture

Yes, the model is directly applicable, almost word for word. Please see Appendix B of

A non-traditional view on the modeling of nematic disclination dynamics

So a screw pile-up should be exactly doable as in Xioahan's pile-up paper, only a bit easier since force equilibrium for anti-plane elasticity is always easier than full-plane elasticity problem (Poisson vs Navier equations).

As Xioahan says, dioing straight edge and screws in the same model is also possible - for the development of the model, one can see sec 4 of

A single theory for some quasi-static, supersonic, atomic and tectonic scale applications of dislocations

that has the 22 plastic strain component instead of the 32 required for screws, but otherwise the development would be pretty much the same. This would require a Generalized stacking fault energy profile to be included from aotmistics as designing the gamma-surface with two plastic strain components is significantly more involved. And, as said, the numerics also requires care as (unlike most other cases), with wave-propagation, a system of equations is an entirely different ball-game compared to a scalar equation. But can be done....


Shuozhi Xu's picture

Thanks for the comments and papers, Prof. Acharya!

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