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 passrotate 90°

courtesy of Rongshan Qin

Chae, Qin, ISIJ International 49 (2009) 115