# Ballistics test

I have been given kind of a bonus question that requires a little thinking and I wanted to ask if I am going in the right direction with my thinking as I am new to Materials Science.

Given: Ballistics test in which a high velocity projectile is fired at a block of material. Isotropic. Does not go all the way through. High stacking fault energy. High friction.

x=point immediatly outside impact hole on surface
y=point at edge of surface furthest away from hole (horrizontally).

a) Plot a strain distribution curve from x to y.
I think that the strain will be very high near impact an decrease further away, so on a strain-vs-dist graph, I would make it a rounded "L" shape.

b) Assume that 100% recrystalization takes place at T1, what would be the distribution of the recrystalization grain size with distance?
I think that the grain size would increase as we move further from impact point.

c) If 100% recrystalization is controlled by conditions a "y" how will the grain size distribution change?
I dont understand what he is looking for here, any advice?

d) How can you produce a "uniform" grain size with distance (x--> y)?
Decreace temperature to decrease recrystalization time.

Any help would be greatly appreciated, thanks.

PerennialII
Gold Member
Interesting questions! I wasn't quite sure whether you were after recrystallization or dynamic recrystallization so wrote ideas to both (I was 99% sure the former, but out of interest wrote also something about the latter ---- yep, I'm a moron ).

Some "takes".

----------Recrystallization begins here

a) Plot a strain distribution curve from x to y.
I think that the strain will be very high near impact an decrease further away, so on a strain-vs-dist graph, I would make it a rounded "L" shape.

Yeah - rounded L shape, in principle quite similar to quasi-static contact ones as long as the hole isn't too deep and multiple nonlinearities of the problem don't come in to complicate, even then the rounded L shape still ok.

b) Assume that 100% recrystalization takes place at T1, what would be the distribution of the recrystalization grain size with distance?
I think that the grain size would increase as we move further from impact point.

Yeah, agree, the higher deformations near the impact helps develop smaller grains.

c) If 100% recrystalization is controlled by conditions a "y" how will the grain size distribution change?
I dont understand what he is looking for here, any advice?

The way I understood this was that he might just be after a "parametric" answer, like high initial deformation -> smaller grains and vice versa, higher temperature & long time -> large grains, and something along these lines.

d) How can you produce a "uniform" grain size with distance (x--> y)?
Decreace temperature to decrease recrystalization time.

Yeah, assuming the initial deformation distribution, working with time&temperature can be used to control the resulting grain size (complex, but in principle).

-----------DRX begins here

Given: Ballistics test in which a high velocity projectile is fired at a block of material. Isotropic. Does not go all the way through. High stacking fault energy. High friction.

Isotropic - helps in elimination of lengthy discussions and may actually enable a 'convergent' answer . High friction - possibility of high temperature. High stacking fault energy - this puzzles a bit, if remember about right low stacking fault energy in a way simplifies the picture by causing a discontinuous DRX by "ending" strain hardening and dynamic recovery, although with high you get a more interacting situation but the grain boundary formation may be simpler. Although higher stacking fault energy flow wise helps in "eliminating" hardening overall and leads to wavier glide. Not quite sure what is actually simplified if that is the aim.

b) Assume that 100% recrystalization takes place at T1, what would be the distribution of the recrystalization grain size with distance?
I think that the grain size would increase as we move further from impact point.

Agree, assuming that DRX can occur with the conditions over the distribution then the lower temperatures (if follow for example Zener-Hollomon type of a model for the DRX grain size) at same strain rate (which is a small unknown here for me at least?) would produce larger grains.

c) If 100% recrystalization is controlled by conditions a "y" how will the grain size distribution change?
I dont understand what he is looking for here, any advice?

I don't know if he's saying "even at y there will be 100% recrystallization", how will the strain rate and temperature profile affer the grain size distribution? Fuzzy. (The larger the strain rate the larger the grains, the lower the temperature the larger the grains .... but it get's mixed and becomes a material dependent to be able to provide an answer .... don't quite grasp the idea of the question)

d) How can you produce a "uniform" grain size with distance (x--> y)?
Decreace temperature to decrease recrystalization time.

Yeah, affecting either temperature or strain & strain rate suitably could get uniform sized grains - realistically though - well don't think need to concern with that since the question is "pretty" hypothetical.

DRX ones are somewhat difficult questions. There are lots of models available, but to my knowledge none of the master adequately all the angles of this complex phenomenon, in principle starting from some hypothesis with respect to material and behavioral model can arrive at conclusions, but I've seen different models and experiments produce quite a mix of results (and when viewing the phenomenon from a microstructural angle, can't help but to think this is one of those "everything affects everything" nightmares of a researcher). Perhaps been watching the wrong models , but even "standard" recrystallization is tough enough in that respect.

Thanks a lot, I was begining to think no one would reply!