MSE 104 Questions:

The 'Question' is as posed by a student in the cohort (with some minor editing by me). The 'Answer' is my response. I've tried to include links to further (web) resources where I can. I will also respond to comments if you'd like!

Question: In the pile-up model, why does a larger grain size lead to a larger stress?

Answer: If we deform a metal to a fixed strain, then the total number of dislocations used to accommodate that strain is larger when we have a larger grain size, the number of dislocations is larger to accommodate the strain, as strain is "change in length over original length", change in length is related to the number of dislocations & the length of the Burgers vector, and the grain size is better.  The strain ahead of a dislocation pile up is proportional to square root of the number of dislocations.

Question: Please can you explain the field plots around the dislocations (page 181-184 of the notes)?

Answer: These are plots of the magnitude of the stress field with respect to position around a dislocation. The 'take home' messages from these stress fields are given in the following slides.

Question: What is the difference between a coherent and incoherent interface/boundary?

Answer: A coherent interface is where the two grains/phases match at the interface perfectly. An incoherent interface is where they do not match. In the context of precipitate hardening, this interface is between the parent matrix and the precipitate.
If you are interested - there is much more detail, for example, here: http://www.eng.utah.edu/~lzang/images/lecture-21.pdf

Question: Can you please share more information on the dislocation model presented in the lecture?

Answer: Yes - you can find it here. https://www-03.ibm.com/press/us/en/pressrelease/22038.wss
Note that I made a mistake in the lecture and incorrectly said this was a dislocation dynamics simulation. It is in fact a molecular dynamics simulation, sorry!

Question: For the Single Arm Frank-Read Source, is the mobile segment the slip plane?

Answer: This cannot be the case, as the dislocation is a line defect. The slip plane is a planar defect. 
The mobile dislocation segment is a dislocation segment that is contained on a glissile slip plane. This compares with the pinned, i.e. sessile, segment that is holding the single armed source in position.

Question: I have found several mistakes in the lecture notes and slides, please can you correct them?

Answer: Please can you direct me to where these mistakes are and I can assess where they are? There are a few minus sign errors that I have mentioned in the lectures themselves.

Follow-up question: There are many blank equations in the notes, such as the inter-atomic potential section.

Answer: These sections are intentionally blank in the lecture notes. The derivations were provided in the lectures themselves for you to include and annotate by hand. The blank spaces were provided for you to complete this activity.

Question: Why does the presence of a characteristic Burgers' vector for each dislocation mean that a dislocation must a dislocation terminate on another defect?

Answer: The Burgers’ vector is the characteristic feature of a dislocation and it is the ‘translation’ defect that is characteristic of the dislocation. At the ‘end’ of this dislocation, this defect must be ‘put’ somewhere (to sort of ‘cancel’ out). This can only be done on: (1) itself; (2) another dislocation; (3) or another defect like a grain boundary, surface, or phase boundary.

Follow-up question: Could you explain this another way?

Answer: Not that easily without invoking some other fields of study I am afraid. It is a geometrical requirement. Perhaps this may help: https://physics.stackexchange.com/questions/106679/why-cant-a-dislocation-terminate-in-the-bulk

Follow up answer #2 (following help from some Tweeps, answer courtesy of @egg_daddy): "The dislocation is the boundary between slipped and unslipped crystal. Boundaries can't just stop, cf coastlines."

Question: please can you supply more information about grain boundary characterisation?

Answer: You can find out more on this within Hull & Bacon. There are a few interesting resources on this:

https://en.wikipedia.org/wiki/Grain_boundary --> this is remarkably well written.


Question: What is the misorientation for a dislocation?

Answer: There is no ‘misorientation’ on a dislocation. A low angle grain boundary can be described in terms of an array of dislocations. More detail of this is discussed in Hull & Bacon.

There are some good pictures here - but the details are bit beyond the MSE104 course - http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_7/backbone/r7_2_1.html

Question: What is difference between simple shear and pure shear?

Answer: Consider the strain ellipse. In order for the simple shear to match the pure shear ellipse, there is a small rotation required.

These two web sites may help:



Question: For shear strain, why do we care about the directions the original length and the displacement?

Answer: By definition the shear strain is given as a change in angle, which therefore gives you the formulation as I show. This is evident in the recent derivation of the energy of the screen dislocation (see the relationship of gamma, b and the circumference of the roll).

Question: Could you explain the shear directions for pure vs simple shear (ref slides 33-34)?

In simple shear, imagine sliding a deck of cards. The object changes shape due to the desk shearing side ways.

In pure shear, imagine pulling across the diagonal of the rectangle. The object changes shape via shear (there's a change in angle involved). However these two different strain states are rotated by an angle with respect to each other.

You can find pictures of these states here: https://www.uwgb.edu/dutchs/structge/shear.htm

Question: Could you provide some examples of Mohr's circle?

Answer: A good question - there are examples in most engineering books. You can find some online here:

 http://users.ox.ac.uk/~kneabz/Stress6_ht08.pdf (stop at slide 15 for first year!)



(Sorry about the link – it’s a good explanation though!)

 There are some good examples here:


The wikipedia article is useful (but a bit more detailed that you might want...): https://en.wikipedia.org/wiki/Mohr's_circle