1. Homogeneous deformations Crystallography H. K. D. H. Bhadeshia

2. body-centred tetragonal cell of austenite austenite body-centred cubic ferrite

4. contraction expansion

6. pure strain matrix symmetrical referred to principal axes principal axes are unrotated volume change = determinant of (A S A) =

9. u v A u v B Similarity transformation

10. homogeneous deformation leaves points originally in a line, colinear, and lines originally in a plane, coplanar

11. similarity transformation

12.  s 1 s 1  1 uniaxial dilatation simple shear general invariant-plane strain s=0.26  =0.03

16. Assignment Find and expression for the magnitude of a vector u in terms of the lattice parameters and angle β in a monoclinic lattice

17. stretch and rotation

22. three simultaneous equations solved three times by substituting each eigenvalue in turn

24. stretch and rotation

25. Refinement of austenite grain size repeated recrystallisation pancaking Refinement of ferrite grain size nucleation and growth

26. Smallest size possible in steel ?

28. Yokota & Bhadeshia, 2004

30. Pancaking

31. Singh & Bhadeshia, 1998 courtesy Rongshan Qin, GIFT, POSTECH

32. u v v = Su

36. Cross Rolling x x y y first pass second pass rotate 90°

41. courtesy of Rongshan Qin

42. Chae, Qin, ISIJ International 49 (2009) 115