Lecture 24: Strengthening and Recrystallization PHYS 430/603 material Laszlo Takacs UMBC Department of Physics

How can we make a material strong - have large yield strength? We need to make the motion of dislocations difficult. That can be achieved by: Decreasing the particle size of polycrystalline materials. Dislocation pile-up in one grain creates large stress in the neighboring grain, but the number of dislocations in a pile-up decreases with decreasing grain size. Work hardening. A dislocation in one slip plane acts as an obstacle for dislocations in another; locks form. Solution hardening. Size (parelastic) and shear modulus (dielastic) effect, ~ √c s for small solute concentration. Changing the separation between partials. Dispersion hardening. Finely dispersed particles are obstacles to dislocation motion. Precipitation hardening. Similar, but particle may be (semi) coherent. The above changes in a material influence many other properties. In particular, the motion of magnetic domain walls is similar to the motion of dislocations. What makes a material harder mechanically, usually also makes it harder magnetically.

Dispersion hardening Finely dispersed particles are obstacles for dislocation motion. Orowan mechanism: If the dislocation meets a pair of particles, it can only proceed by bowing out, similar to the principle of the Frank-Reed source. The stress needed to move the dislocation across this barrier is  = Gb/(l-2r) Introducing finely dispersed particles into a metal is often a difficult task, as the particles must be wetted by the matrix but not dissolved by it. Searching for a way to disperse aluminum oxide particles in Ni- based superalloys lead to the development of mechanical alloying in the late 1960s.

Precipitation hardening a form of dispersion hardening Precipitates are often coherent or semi- coherent. A dislocation can pass through a coherent precipitate, but it requires extra stress as a stacking fault results and creating it requires energy. This mode dominates, if the material contains many small particles. If the same total volume is in fewer but large particles, the Orowan mechanism is preferred. The largest hardness is achieved when the two mechanisms require the same stress; this happens at around 20 nm. Precipitates form when a solid solution becomes supersaturated during cooling and a second phase crystallizes in the matrix in the form of small crystallites. They are often coherent (like Ni 3 Al in Ni.)

In forming operations, sufficient external stress is applied to force plastic deformation in spite of the obstacles to dislocation motion. Plastic deformation results in substantial changes in the microstructure –Shear bands –Dislocation networks –Small/large angle grain boundaries –Grain refinement, rotation, texture Annealing can change the microstructure - recovery and recrystallization –Primary recrystallization - newly nucleated and growing, practically dislocation-free grains replace highly defected grains. –Grain growth - larger grains grow at the expense of smaller grains, decreasing the grain boundary energy. Read Chapters 7.1-3

The following images are from the site of Professor John Humphreys at the Manchester, Materials Science Centre, UK. There are also a few very illuminating in situ movies at Dislocation tangle in AlDislocation cell structure in Cu

Progressive misorientation of subgrains in a large grain of sodium nitrate, deformed in dextral simple shear. Note the migration of subgrain boundaries and the clear changes in morphology after the appearance of new high angle grain boundaries. Shear strain at the last photo is ~1. Long edge of each photo is 0.5 mm. M. R. Drury and J. L. Urai

Recrystallization of an Al-Zr alloy Notice the fine and oriented deformed structure and the growing, virtually defect- free recrystallized grains.

Strain rate dependence The time / strain rate dependence of the stress-strain curve is intuitively anticipated and clearly observed, but it is very difficult to explain quantitatively. Typically it is characterized by the strain rate sensitivity, m, defined as Ball milled and consolidated Cu, average particle size 32 nm. Babak Farrokh, UMBC

Temperature dependence The strain rate sensitivity is low at low temperature (T < 0.5 T m ) but increases at higher temperature. This is understandable, as atomic motion is more vigorous at higher temperature, diffusion is faster. High strain rate sensitivity is usually associated with larger strain to failure. Consider a tensile experiment. If a random cross section decreases in diameter, the strain rate at that cross section increases, with enough strain rate sensitivity the section becomes harder and no further reduction leading to failure occurs. In fine grained (<10 µm) materials close to T m very large strain rate sensitivity and strain to failure (up to 100-fold elongation) can be observed. This is called superplasticity. It depends on grain boundary sliding, rather than dislocation mechanisms. Nanocrystalline materials contain many grain boundaries, superplasticity should be more easily achieved.

Superplasticity of electrodeposited nc Ni and nc Al-1420 alloy and Ni 3 Al by severe plastic deformation Notice that superplasticity was achieved at a temperature much below typical for conventional materials; 350°C for Ni corresponds to 0.36 T m ! McFadden et al. (UC Davis, Ufa, Russia) Nature 398 (1999)

High RT ductility of a hcp Mg-5%Al-5%Nd alloy Ball milling results in repeated fracturing and agglomeration of grains, resulting in a nanometer scale microstructure (mean grain size probably 25 nm). Grain rotation and sliding results in high ductility even at room temperature and 3x10 -4 s -1 stress rate. (Recall that a hcp material is normally brittle.) L. Lu and M.O. Lai, Singapore

Ceramic nanocomposite of 40 vol.% ZrO 2, 30% Al 2 MgO 4, and 30% Al 2 O 3 shows superplastic behavior at 1650°C. Kim et al. (Tsukuba, Japan)

Creep Nabarro-Herring creepCoble creep mediated by volume diffusiongrain boundary diffusion mass flux

Anelasticity and viscoelasticity Small time dependent effects can be observed also for elastic deformation - e.g. related to reversible diffusion of C in a steel under stress. If a sample is vibrated close to resonance, the deviation from perfect elasticity, i.e. the existence of dissipative processes, results in a change of the resonance curve. While technologically unimportant, this is the way one can gain information about diffusion and other time dependent phenomena at low temperature, where their rate is very low and the macroscopic effects are not detectable. Anelastic: under constant stress Viscoelastic: