Effects of self-accommodation and plastic accommodation in martensitic transformations and morphology of martensites
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I.
INTRODUCTION
COHENm showed that the strain-energy requirement of shape change for martensitic transformation is relatively large and plays a major role in the nucleation process. The lattice invariant shear occurs accompanying lattice deformation; thus, the strain energy can be reduced. The phenomenological crystallographic theory of martensitic transformations has been successfully applied to many alloy systems, but as shown by Christian, t21 in steels it can only be applied mainly to {259}- and {3,10,15}-type plates; {225 } plates and lath martensites have been proven difficult to explain. In the present work, the concept of the displacement vector of the lattice deformation is advanced, and two ways to reduce the strain energy are considered: (1) self-accommodation between different martensitic variants and (2) plastic accommodation between parent phase and martensite. The authors intend to connect the formation of an invariant habit plane with the self-accommodation process in ferrous twinned martensite and to answer why it is difficult to explain the {575} habit plane of lath martensites by means of the phenomenological crystallographic theory. Finally, the morphology of martensites will be discussed. II.
THEORETICAL BACKGROUND
Vi = [fcble b
D i = ([fcb]e -
Vi
=
Suppose a vector Vj becomes Vi due to lattice deformation, so the displacement vector D i for V i is then described as D~ = V ~ - V]
[1]
[2]
b
f
NANJU GU, Professor, XIAOYAN SONG, master; JIANXIN ZHANG, Lecturer; FUXING YIN, Associate Professor; and RUIXIANG WANG, Associate Professor, are with the Department of Material Science and Engineering, Hebei University of Technology, Tianjin 300132, Chian. Manuscript submitted September 7, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
[5]
= [fcb]e[bcf]b I1~
--.~f
where V y [ U V W]j is any vector in the parent phase; V7 = [U'V' W']f is the corresponding primary vector; [fcb]b and [bcf]~ are the Bain correspondence matrices for the orientation relationship of (111)i//(011)b,[10 - 1]f//[11 1]h(K - S)or [11 - 2]J/[01 - llb(N -- W) (Figure l(a)).
(mli) -1 0
1 0
;
Ebcf]h =
(,_l 1 0
1 0
The matrices [fcb]e and [bcf] e a r e determined by the orientation relationship between the parent and new phases, which can be calculated from Eq. [6]: t41
[bcf]e = aA/aM = [fcbMbcf]e
[41
[fCb]b ) [bcf]e
b
Referring to the authors' w o r k , [3]
V; = [fCb]b
f
[fcb]e
[ f c b ] b = 1/2
A. Displacement Vectors in Lattice Deformation
[3]
= [fcb]e[bcf] e
(
h 2 k 2 lZJ
0)(
)
|0
a2 0
h2 k2 12
h 3 k 3 13/b ~ 0
00l 3
h 3 13 l 3 f
[6] The matrix [fcb]e is the reverse of [bcf] e and also means the lattice correspondence after lattice deformation; in this case, (h i Id l%//(h i ki 13j- are three groups of parallel planes, c~i = (d)J(d3b, (~)j~ and (d3b are the lattice spacings of corresponding planes, and c~A and aM are lattice parameters of the parent and new phases. VOLUME 26A, AUGUST 1995 1979
B. Self-Accommodation in Twinned Martensitic Transformations In reference to Gu, t31the strain
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