Grain Size Hardening: Dislocation Sources and their Effects on Yield Strength

[tony_engin]

Hi all
I am learning about Grain Size Hardening, and find it difficult to understand some concepts.
With refer to the link:
http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=64&pageid=1000301064
What is that dislocation source, and why it emits dislocation when the stress is increasing?
For my understanding, dislocation are some imperfections already exist in the metals,so I find it very strange to have something called "source" to continuousy produce some dislocations. Can anyone help answer what's S1 and S2 and why's that? Please.

 

[PerennialII]

Hi Tony !

I'll get this started so we can delve deeper along the way :

The dislocation source (S1) can be for example a dislocation generator (like a true source a la Frank & Reed), an existing dislocation / or more like it, a "field" of dislocations (a dislocation density) or an imperfection (or something like it) giving rise to a field of dislocations. Dislocations are the fundamental mechanism of plasticity in metals (their movement that is), and the deformation caused by applied stress is understood as movement of dislocations. S2 is then a response of the adjacent grain to the dislocation pile-up caused by the grain containing S1 (and this links then to the whole idea of how grain size affects strength by handicapping dislocation movement), and as it states, on a macroscopic level these events sum to form what we observe as general yielding .

 

[wd40]

Hi,
i think the word "source" confused you, "source" refers to the location of the defect in the atom arrangement. when the stress is applied, the disclocation moves along the slip plane. it is easier to cause slip on a plane with dislocation.

hope this helps
cheers.

 

[Astronuc]

Each grain in a solid, particularly polycrystalline solid, has sources of dislocations. S1 and S2 are simply dislocation sources in two grains. Grain 1 is 'more favourably oriented' to the tensile stress in the example, so it achieves the critical shear stress to let dislocations glide along the slip planes before Grain 2, which does eventually experience dislocation movement.

With regard to dislocations, see - the previous page - http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=64&pageid=1000298442

Tony, What text are you using?

 

[Gokul43201]

It appears that the doubt here is not really regarding grain size hardening, but more specifically about the origin of dislocations, sources and deformation in the context of dislocations.

I would strongly recommend that you get a good introduction to dislocation theory (Reed-Hill or equivalent should have something) and go over that first (I would recommend the same for myself too ). But in terms of useful reminders, consider the following.

A translation of a lattice plane by one lattice spacing with respect to a neighboring plane can be visualized in terms of the transport of a (positive or negative) dislocation from one end of the specimen (or grain) to the other. This is really what shear is all about. Then you want to go over how an applied tensile load can give rise to shear stresses in the grains that depend on their orientations relative to the applied force. These shear stresses can result in shearing of the grain (or a relative displacement of lattice planes) only if they exceed a critical value (the CRSS). Finally, the shear stress is not uniform throughout the crystal. Cracks, particles and other imperfections cause local stresses to be significantly higher than the average values. Thus, the shear stress in the vicinity of an imperfection can exceed the CRSS, resulting in shear originating from this point/line. This shear can also be represented (or understood) as the movement of dislocations originating from the same point (as mentioned above).

So, in short, that's how a disclocation source 'works'.

Note : If the above is complete hogwash, the real experts (Astro and Perennial) will let you know.

 

[tony_engin]

hi, wd40!
But from the figure, dislocation is produced continuously and move continuously towards the boundary, isn't it?

 

[tony_engin]

Thanks PerennialII, Astronuc and Gokul43201 !
I know that dislocations exist in crystals and is the fundamental mechanisim of plasticity of metals. But I still have something don't really understand.
For example, there is initially 1 dislocation at place S1 in a grain of a polycrystalline solid. When a stress is applied, suppose the orientation of that grain is more favourable so that the dislocation can move first. But when that dislocation move, isn't the original position of the dislocation,S1, will recover? I mean when the dislocation move, there will no longer be dislocation at S1, isn't it? I don't understand why S1 will produce dislocation continuously. Please help.

By the way, I am using Callister's text.
Also, could you please give the full name of the book which is a good introduction to dislocation theory?

 

[Astronuc]

These might help.

http://www.nuc.berkeley.edu/thyd/ne161/jlrhoads/creep.html#defects

http://www.doitpoms.ac.uk/tlplib/dislocations/intro.php


Also interesting is -
http://www.metcer.ameslab.gov/Exploratory/Mechanics.html

And this, a discussion of superplastic deformation -
http://www.mse.mtu.edu/~drjohn/sp/deform/

Interesting paper on modeling materials with discussion on dislocations -
http://www.people.virginia.edu/~lz2n/mse201/mse201-modeling.pdf

List of abstracts from NIST Workshop on Work Hardening and Dislocation Patterning
http://www.metallurgy.nist.gov/reports/workharden/WSAbstracts.html
http://www.metallurgy.nist.gov/reports/workharden/WSReport.html

As for books, see if you can find one of these in a library

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471310433,descCd-tableOfContents.html

Theory of Dislocation J.P. Hirth and J. Lothe, 2nd, Wiley, New York, 1982.

Theory of Crystal Dislocation F.R.N. Nabarro, Clarendon, Oxford, 1967.

 

[enigma]

I have merged this thread with the one from ME&AE

 

[PerennialII]

Great links Astronuc as usual ... especially liked the computational one, marvellous stuff !

But I still have something don't really understand.
For example, there is initially 1 dislocation at place S1 in a grain of a polycrystalline solid. When a stress is applied, suppose the orientation of that grain is more favourable so that the dislocation can move first. But when that dislocation move, isn't the original position of the dislocation,S1, will recover? I mean when the dislocation move, there will no longer be dislocation at S1, isn't it? I don't understand why S1 will produce dislocation continuously. Please help.?

Trying to clarify this a bit further ... dislocations need to fulfill the same deformation compatibility (pretty much continuity) conditions as continuum description of deformation (if we wish to stick within classic theories), this is one of the main issues in understanding & modeling deformation at the lattice level and the interactive deformation behavior of different grains. I'd suggest you think of dislocations as what they are ... mechanisms & a 'medium' of deformation, and as such under applied stress (this is a crucial point to note especially in your case, the monotonicity of the deformation event) the dislocation pile - up in grain containing S1 and the response in S2 become a bit easier to comprehend ... as well as the 'dislocation production' (which in this case reads as movement, response to applied loading).

If you're in need of basic information about dislocations Callister will do you fine, lots of interesting really deep end stuff can be found from several books by Cottrell, Nabarro, Wirth, Read etc.

 

[tony_engin]

Really thank you all!
But after referring to the links, I still don't understand "why there exist something like a source producing dislocations"
As indicated by this animation:
http://www.doitpoms.ac.uk/tlplib/dislocations/videos/true-glide.mov
The dislocation moves as such.
That's all I know about dislocations...I don't know why there is "a source". I simply can't relate the dislocation with "the source producing dislocations continuously"..

 

[PerennialII]

Good that you're following the question through Tony !

Your dislocation source question is a really good one ... and actually goes pretty deep in the matter, so deep that a concise answer may be somewhat tough to come by.

The "easy way" out of this is to state that within a grain a great number of dislocations exist pre - applied stress, and the deformation is a continuous process of affecting the dislocation density, i.e. increasing it to extreme in areas favorable to slip, cause pile-ups etc. This is the usual way to understand this and in my mind suffices.

... the problem in generic sense if we start looking for a complete answer is a bit more complex. In addition to the above, dislocations are generated & affected by dislocation - dislocation interactions, dislocation - microstructure - lattice interactions & characteristics, specific dislocations generators, local damage and cracking etc., which dependent on the state of flow contribute different amounts to the distribution of the dislocation density within a set of grains.

 

[tony_engin]

Hi all!
Sorry for such a late follow-up.
I've just learned stuff abour frank-read sources, so I think I know what does it mean by a source.
Here comes another question about the effects of the size of the grains to the yield strength.
It is known that as the size of the grain increases, the yield strength would decrease, and a quantitative relation is given.
I would like to know if there is any physical interpretation of this result?
I am thinking if the following interpretation is correct:
When a shear stress is applied, dislocations are first produced continuously by the source of the best oriented grain. The dislocations flow until they meet the grain boundary and are stopped there.Given a fixed shear stress, the source will produce dislocations continuously until the dislocations pile-up at the boundary is so large that it prevent further production of dislocations to occur. So, for a bigger grain, since the distance between the source and the boundary is greater, the stress field produced by the stopped-dislocations will have less effect on the source. So, more dislocations can be produced and then pile up at the boundary in a bigger grain. Consequently, the other sources can be more easily triggered.
Is the above interpretation correct? It seems that sounds, isn't it? But I thinking if for bigger grains, the greater dislocation between the next source and the boundary will require equivalently more dislocations to be pile up at the boundary...