Strange inversion of stress under shear deformation

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1

Hi,

I have attempted various methods of applying shear to a 3D simulation cell containing a dislocation dipole, and/or a single dislocation with a free surface.
No matter which method is applied (see the following detailed overview of methods), I find that the stress inverts periodically!?! In-plane shear stresses (τyz & τxy ) seem to interact.

You can see a simple example of my approaches and the inversion effect at the link:
https://drive.google.com/file/d/0B2_Hf1VNpOkpTmJoUWxwMHpmNlk/view?usp=sharing

To provide some context, I provide the following details.
Sorry for the wall of text which follows:

This does not occur as the dislocation crosses the periodic boundary, but rather what happens is the two complimentary shear components interact.

I evaluate the stress with respect to both the total volume and just the shear stress on the mobile atoms (i.e., sum of stress/atom of τyz & τxy components of mobile atoms only, divided by the approximate volume of the region containing mobile atoms).

I use zero normal displacement boundary conditions on the shear boundary layer, and periodic boundaries in the in-plane dimensions.

Shear is applied via several methods:

  1. Equal and opposite velocity applied to top and bottom layers (i.e., velocity topLayer set 1.0 0.0 NULL
    velocity botLayer set 1.0 0.0 NULL

  2. Velocity only applied to top layer

velocity topLayer set 1.0 0.0 NULL
velocity botLayer set NULL 0.0 NULL

  1. Force added to layers

velocity topLayer set NULL 0.0 NULL
velocity botLayer set NULL 0.0 NULL

fix addForceTop topLayer addforce 1.0 0.0 0.0
fix addForceBot botLayer addforce 1.0 0.0 0.0

  1. Setforce method

velocity topLayer set NULL 0.0 NULL
velocity botLayer set NULL 0.0 NULL

fix addForceTop topLayer setforce 1.0 0.0 0.0
fix addForceBot botLayer setforce 1.0 0.0 0.0

in all cases I use the following constraints:

fix nve BoundaryAtoms nve

fix nvt mobile nvt temp 300 300 100

2

Hi All,

Can I re-iterate this question - if anyone has any ideas why the application of shear forces at the surface layers causes stress to periodically invert (and how to fix this)?

Thanks,
Nathaniel

3

The only comment I have is that when you start

shearing a system with an instantaneous jolt,

e.g. set the velocity to a finite value, you induce

a shock wave in the system. Can be small or
big depending on how you do it. If

that moves thru a periodic system or reflects

off walls it could induce a periodic (in time)

blip in the pressure.

4

Hi Steve,

Thanks for your comment. I have carefully checked this and even implemented a method of slowly elevating the velocity. The shear stress is somewhat more steady, but still inverts periodically, for some strange reason. for example:

Stress_inversion_Shear_normal’.docx (109 KB)

5

Sorry, the previous email did not show the shear stress inversion (too short).

I know the attachment will be scrubbed anyway, so I just sent it to you.

Thanks for your thoughts and help in this,
Kind regards,
Nathaniel

Stress_inversion_Shear_normal.docx (139 KB)

6

HI all,

I will throw it out there again.

Has anyone else observed sudden inversion of the shear stress, and gradual increase/ decrease in the normal stresses when implementing shear via the velocity ramping or application of shear forces in the top and bottom layers of a 3D MD simulation?

Any ideas how to eliminate this would be appreciated.

(I have tried reducing the rate of velocity increase - it does not seem to be caused by a shockwave effect, due to the gradual nature of normal stress shifts anyway).

Kind regards,
Nathaniel

7

What did it mean exactly by inversion? Was it a sudden flip of sign with magnitude unchanged? Or was it a sharp decrease after an increase?

Have you noticed that your “equal and opposite” velocity set and fix addforce were all equal and of the same sign? Could that be a problem?

What were your units and how did you make sure the magnitude of 1.0 that was used in your input script was not beyond the speed of sound?

Ray

8

Thanks Ray,

All good questions.

  1. What did it mean exactly by inversion?

Yes it was a sudden flip with magnitude unchanged. Please refer to the google document:

https://docs.google.com/document/d/130M9fmKirgn2gyGZ79pYpncgxQCUDmuJmBg2zEQkRSU/edit?usp=sharing

  1. Have you noticed that your “equal and opposite” velocity/ fix addforce

They were definitely not of the same sign, and this is really not the issue because the same result occurs when I only shear either the top or the bottom layer.

  1. What were your units and how did you make sure the magnitude of 1.0 that was used in your input script was not beyond the speed of sound?

The same outcome occurs whether I slowly ramp the velocity from 0 - 0.25, which would occur if the velocity is set to 1.0. This is not a high velocity (at 300 K, the velocity of the x-component alone is up to 30 in the ‘mobile’ atoms).

Thanks for your consideration and insightful queries.

Kind regards,
Nathaniel

9

I am guessing there are no easy answers…

Has anyone obtained a steady shear stress, with a moving dislocation dipole? I am curious…

Has anyone on the forum actually ‘measured’ the shear stress, with respect to all 9 components of the stress tensor?

Thanks,
Nathaniel

10

This is not really a LAMMPS question, but a more general question about atomistic simulation of plastic response of dislocations under shear loading. There is a very well-developed literature out there on this subject. You should study it. Admittedly, most of it is non-thermal, so no velocities, only boundary displacements and energy relaxation, but people are starting to include temperature (Hale, Zimmerman, Weinberger, CMS (2014)).

Aidan

11

Hi Aidan,

Thanks for your comment.

I assume you are referring to the calculation of stress from an atomistic simulation, such as Hardy’s expression?

I agree that the virial stress approximation is not very effective for representing a true evaluation of the stress, in a conventional sense. However, the issue is not the magnitude of the stresses, but rather the transient behaviours (and this is mirrored in the dislocation response, which accelerates with the shear stress, than broadens and reverses upon shear stress inversion).

Another interesting point to note, is that when I control the stress with a barostat and periodic boundaries, I can retain a basically constant system stress (in terms of Virial). As a temporal average of a constant value, I think it is suitable to conclude that this is a fairly effective approximation of the stress. This is mirrored in a constant, steady-state dislocation response.

Cheers,

Kind regards,
Nathaniel

12

Read this paper: Hale, Zimmerman, Weinberger, CMS (2014)