Lecture 2

Lecture 2- Recovery, meta-dynamic recrystallisation & static grain growth

VIEPS/Mainz Microstructure Course

1) Recovery:

So called because it describes the processes that lead to a recovery of mechanical properties, since deformation of polycrystals at low temperature typically leads to the material gaining in strength (because the dislocations get tangled and can no longer move freely). Recovery processes are enhanced at higher temperatures, and occur both during deformation and subsequent to it, but are typically swamped by deformation processes during deformation. There are a number of competing processes that can lead to the observation of a recovered mechanical state:

mutual annihilation when dislocations of opposite sign meet up exactly. The two half planes of each dislocation become a full plane, and the two dislocations disappear. In the following example cross-slip occurs to allow this to take place.

pile-ups when dislocations are held up by, for example another type of dislocation or an impurity, it just sits there, because dislocations of like sign repel each other, the next dislocation will "wait" in the queue behind the first one, and so on. Each dislocation adds to the stress on the object blocking the way, until, sometimes that object may be overcome, and the dislocations may move freely again. The longer the pathway for the dislocations to build up the larger the obstacle that can be overcome, hence the Hall-Petch law which says the yield strength is proportional to 1/grain size.

climb Another way of clearing an obstacle is to climb over it. Climb is easier at higher temperatures, as it is a diffusional process.

polygonisation The movement of free dislocations (those not bound up in dislocation arrays) will eventually bring them into existing dislocation arrays, this reduces the energy state of the system, and is thus more stable, and the formation of these sub-grain boundaries is a typical microstructural response to recovery processes.

cross-slip Another form of dislocation motion can take place when the dislocation moves on a vector which is a combination of two or more existing slip systems. In this example double cross-slip occurs to avoid a fixed dislocation.

2) Recrystallisation:

The formation & movement of sub-grain & grain boundaries (definition of Urai et al 1986). There are again a number of distinct but interacting processes that are involved in recrystallisation.

Rotation recrystallisation

When a dislocation is added to a sub-grain boundary, it will change the angular mismatch between the two sub-grains. When dislocations of the same sign repeatedly become part of a single boundary, the two sub-grains either side become progressively misoriented with respect to each other, and eventually the mis-match may become large enough that the boundary becomes a grain boundary. The exact orientation at which this takes place is probably mineral dependent, however 10-15 degrees misorientation is commonly quoted.

ii) Grain boundary migration & pinning

Grain boundary migration refers to the movement of the boundary separating two grains. The movement takes place by the diffusion of single atoms from one grain across the boundary to the other grain. This motion results in the migration of the boundary in the opposite direction to the diffusion direction. There are several driving forces for grain boundary migration, in decreasing order of magnitude they are chemical, strain energy (stored as dislocations), and elastic energy. The driving force for migration is the difference between, for example, the dislocation energy state either side of the boundary. The rate at which a boundary migrates is both a function of this driving force, and the mobility of the boundary, which is an inherent property of a material (but which varies according to temperature, the presence or absence of fluids, the nature of the boundary, and the impurity content of both the grains and the boundary).
In the examples below we distinguish grain boundary migration in "clean" and "dirty" systems. Clean systems, like metals, many sub-grain boundaries and perhaps grain boundaries between quartz grains in a granite, can have grain boundary migration involving only the local readjustment of atoms at the boundary, and in an impure system. Dirty systems such as a schist resulting from the metamorphism of a pelite, where the grain boundaries will be rich in impurities, or where the grains may not even be in physical contact, have to diffuse material across a grain boundary of finite width. Impure systems will probably have lower grain boundary mobilities (velocity = mobility * driving force) than pure ones.

Second phase particles (small micas, for example) will hinder grain boundary migration by "pinning" the boundary locally. If there are enough particles in a rock, the grain size can be controlled entirely by the particle spacing.

Simulation of grain boundary migration in a clean system.

iii) What defines a (sub)grain boundary, and how do they vary?

iv) Static, Dynamic, Meta-dynamic Recrystallisation

These three terms refer to the processes of recrystallisation that occur without deformation, during deformation and following deformation respectively. The actual processes themselves are for the most part the same, but the driving forces that control them can vary enormously, so the resulting microstructures can look quite different.

3) What makes two grain behave differently?

mineralogy

b) crystallographic orientation Since during plastic deformation of a crystal the CRSS controls the movement of dislocations, grains which are well oriented for slip on a particular slip system will in principal be able to deform more easily than those whose slip system orientations result in low resolved shear stresses. The pair of images below are from Y. Zhang's PhD thesis and show a numerical simulation of deformation in a polycrystal with only one slip system, notice how in the second figure the three coloured grains have undergone virtually no deformation (yellow) a lot of deformation (orange) and a lot of deformation with internal kinking as well (green). The short lines within grains show the local slip system orientation.

c) shape The shape of any object will be an influence on its mechanical behaviour, elongate grains will be more prone to buckling than spherical ones, and if a series of elongate grains are all aligned, it makes it easier for them to deform by grain boundary sliding. Similarly elongate grains will have a mechanical coupling on them that will tend to rotate them with respect to the applied stress that spherical grains will not have.

d) neighbours The local neighbourhood relationships of grains will influence the local behaviour. If a weak mineral is surrounded by stiffer grains, it may be "shielded" by those grains and remain undeformed, even though it is inherently weak.

e) history As grains deform, their internal dislocation arrangement, shape and chemistry may change, which in turn leads to a change in mechanical properties.

f) grain size There are two main grain size dependent behaviours, one related to the Hall-Petch effect for plasticity, that makes smaller grains stiffer, the other for diffusional creep, that makes smaller grains less stiff.

g) grain boundary orientation certain grain boundary orientations allow easier grain boundary sliding, for example a brick wall texture in simple shear would allow easy grain boundary sliding because all the boundaries are aligned.