A study of stacking faults in deformed austenitic stainless steel by X-ray diffraction
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I.
(4 - ~/~r~lll r~2oo
INTRODUCTION
V ..-'/Z.~effz.~'eff
S I N C E the concept of stacking fault (SF) emerged, its effect on material properties has been studied deeply step by step. By means of direct or less direct methods, one can get some characteristic parameters, such as the effective particle size (EPS) Dell, the average dislocation density (ADD) /~, the average range of strain field Re, the average dislocation configuration parameter M, and the average elastic energy per volume ( E / V ) . II'2] Based on the studies of some face-centered cubic (fcc) ternary alloys, such as Cu-Ni-Zr and 1Cr18Ni9 stainless steels, the relation among the quantities mentioned above may be formulated as follows: I3,4,51 (1) The difference between the intrinsic stacking fault density a ' and the extrinsic stacking fault density a": - rr2120:2oo - 20~oo) - ( 2 0 f l l -- 20{ll) a' -
a"=
[1]
77.94(tan 020o + 0.5 tan Olll)
Here, the upper indices g a n d f d e n o t e the stretched samples that had or had not annealed, respectively. The terms 0200 and 0ill are the Bragg angles of diffraction peaks of (200) and (111), respectively.I7] (2) Let subscripts cg and p m stand for the center of gravity of the diffraction profile and the peak location, respectively. Then we have (,~.~lll __ ,)~111)
4.5a" +/3 =
-vcg
200
/2.31 Tmi n = 0 . 8 2 ~ e l f l f l
4Oma x - ~
l l tan 0ill + 14.6 tan 02oo
~
Dill eft
[31
eft t..,, eft
FENG-EN TENG, Associate Professor, and BENWE! YANG and YUMING WANG, Professors, are with the Institute of Materials Science, Jilin University, Changchun 130023, People's Republic of China. Manuscript submitted July 8, 1991.
O2~~
I
200
[5] 2
\)
V Tm i
[6]
Ill
is fulfilled when the TPS Do and the WSF T were measured from the lattice planes directed to [200] or [111], or the conditions T >> Do and Donl ~ Do2~176 are fulfilled. The term ao is a lattice parameter, t7,81 (4) Based on the assumption of random distribution of dislocations, the ADD may be determined as t41 p = (pp X ps) 1/2
[71
Here, pp = 3/D~ff and p, = K ( e ~ ) / b : , when there is a Gaussian strain distribution, then K = 6 ~r; for fcc, the Burgers vector b, directed along [110], is equal to ao/~/'2, and the SF energy Yl Gtooa3op "Yl
200 -- Deft
1.5(a' a") +/3 +/3 ==1.7637 1.7637 a0 a0 D 111T32oo 1.5(a' ++ a")
)
Defi~~
Here, it is presupposed that the relation
[2]
Here, a " is the extrinsic stacking fault density,/3 is the twin fault density, and the O's are Bragg angles specified by their superscripts and subscripts, t7,81 (3) Now let us deal with the true particle size (TPS) Do, the EPS Dell, the maximum particle size D .... the width of stacking fault (WSF) T, and the minimum value (mWSF) of WSF Tmi,. Then we have
1 ,-i
V~/---/'4D~ ~ V ~ D~f I ~
[4]
4D~f~ - V ~ FllllL~ef f
200
- v p m , - (20cg - (20pro)
METALLURGICAL TRANSACTIONS A
Do =
2 V 3 7ra
[8]
if taking 1 m J / m 2 or 1 e r g / c m 2 as a unit. Here G is the shear modulus, a (= a ' - a") is the net SF density, t4'5'61 and too is a constant parameter corr
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