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Homogeneous deformations

Crystallography. H. K. D. H. Bhadeshia. Homogeneous deformations. austenite. body-centred tetragonal cell of austenite. body-centred cubic ferrite. contraction expansion. pure strain matrix symmetrical referred to principal axes principal axes are unrotated

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Homogeneous deformations

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

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

  3. contraction expansion

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

  5. v u v A u B Similarity transformation

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

  7. similarity transformation

  8. general invariant-plane strain simple shear uniaxial dilatation s s d d 1 1 1 s=0.26 d=0.03

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

  10. stretch and rotation

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

  12. stretch and rotation

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

  14. Smallest size possible in steel ?

  15. Yokota & Bhadeshia, 2004

  16. Pancaking

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

  18. v = Su u v

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

  20. courtesy of Rongshan Qin

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

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