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

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Presentation transcript:

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

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

contraction expansion

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

u v A u v B Similarity transformation

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

similarity transformation

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

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

stretch and rotation

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

stretch and rotation

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

Smallest size possible in steel ?

Yokota & Bhadeshia, 2004

Pancaking

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

u v v = Su

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

courtesy of Rongshan Qin

Chae, Qin, ISIJ International 49 (2009) 115