1. New grain New grains nucleate and grow into regions of high dislocation density. High dislocation density Experimental data usually fits a sigmoid curve

2. Rate of recrystallization in the early stages is limited by nucleation and grain boundary area Rate of recrystallization in the middle stage is a maximum because of the presence of many nuclei, high grain boundary area and limited impingement Rate of recrystallization in the late stage is limited by impingement and the lack of contact between grain boundaries and high dislocation density areas

3. Volume fraction transformed fits the curve Ќ is assumed to described a thermally activated process (diffusion, nucleation) Let X(t) specify the experimental data of volume fraction transformed as a function of time and Temperature

4. ln(t) 1/T

5. How can we get information about the physical process from n and Q? JohnsonMehlAvrami Equation Define the virtual volume fraction transformed-No impingement. For spherical grains this is G is the interface velocity (growth rate) of the grain boundary (m/s) N is the nucleation rate per unit volume (1/(m^3 s)) t is the clock time τ is the nucleation time

6. time R 1:00 am 1:01 am1:02 am1:10 am Nucleation time for the upper particle is 1:01 am and lower particle is 1:02 am Clock time for both particles is 1:10 am R=G(540 s) R=G(480 s) Volume of individual grain is How can we get information about the physical process from n and Q?

7. Johnson, Mehl, Avrami

8. How can we get information about the physical process from n and Q? Q is the activation energy for N and G n indicates the geometry of the particle--dimension = n-1

9. Growth rate controlled by diffusion Activation energy Nucleation rate/volume controlled by nucleation activation energy

10. Sphere n=4 Plate n=3 Rod n=2 r h n corresponds to shape

11. So how does this data on n and Q apply to a ‘real’ problem? T variation with time (position) Hot drawing of wire Modify the JMA equation so that we add up the amount of recrystallization occurring at each place (at each temperature)on the wire.