Homogeneous deformations
description
Transcript of Homogeneous deformations
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