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Chester F. Jatozak
The Timken Co.
Canton, OH
Congress and Exposition
Cobo Hall, Detroit
February 25-29,1980
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ISSN 0148-7191
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Chester F. Jatczak
The Timken Co.
Canton, O H
ABSTRACT
This paper shows that retained austenite (R.A.) exists in many hardenable
steels and that its presence can induce both
positive and negative changes in various
mechanical and engineering properties. The
economic considerations of these changes
are particularly important in such finished
products as bearings, gears and tool steels.
Discussed in the paper are the following
aspects of the R.A. problem; (1) origin of
R.A., (2) methods for its control, (3) quantity levels in various steels, and (4)
various methods for its measurement. The
x-ray diffraction technique of R.A. measurement is shown to be a very accurate and fast
tool for the quantification of R.A. in the
microstructure of such products whether
subjected to measurement after heat treatment, or after deformation processing and
return from service.
RETAINED AUSTENITE (R.A.) IS A REMNANT
PRODUCT which may coexist with martensite
or ferrite in many quenched and tempered
hardenable steels. Its presence in the
hardened microstructure generally induces
significant changes (both positive and negative) in certain mechanical, engineering and
processing properties of the steels. The
economic considerations of these changes in
properties are particularly important in such
finished products as bearings, gears, tool
steels, and high strength steels. Consequently, techniques allowing accurate measurements of retainedaustenite, as well as
methods for its control during processing,
have grown in importance in the quality control of these and related items of manufacture.
This manuscript concerns itself with two
aspects of the retained austenite problem,
methods for its control and techniques for
its measurement. Section 1 considers the
origin of retained austenite, the factors
which promote or control its presence, typical
ranges of retained austenite developed in various
hardenable steels, the specific effects of retained austenite on various mechanical, engi-
neering and processing characteristics of steel
and finally various methods which can or have
been applied to retained austenite measurements.
Section 2 describes the principles of the
x-ray diffraction technique for measurement of
R.A. Discussions of the theoretical aspects of
x-ray diffraction are purposely held to a minimum. Instead a "cook book" approach is favored
in which the most important steps and procedures
involved in making R.A. measurements by the x-ray
technique are described to guide even the inexperienced neophyte through an accurate R.A.
measurement. Examples of typical diffraction
patterns produced by hardened steels when
irradiated with various x-ray sources are given
along with specific instructions as to how diffracted x-ray intensities should be measured and
especially which (hkl) peaks to consider for most
accurate R.A. determination. Basic equations
that readily convert the measured diffracted
intensity values into volume fractions of R.A.
are enclosed to permit accurate R.A. values even .
in heavily textured specimens. Examples of
typical R.A. measurements and data collection are
shown. A listing of the various factors which
influence precision and accuracy of intensity and
R.A. measurements is made, but not discussed.
The reader is referred to the parent SAE manual,
SP453 for a detailed coverage of these items.
KINETICS OF RETAINED AUSTENITE IN STEEL PRODUCTS
ORIGIN OF RETAINED AUSTENITE - Austenite is
a face-centered cubic phase which in hardenable
steels, is stable at temperatures above the Ac^
and Ac phase boundaries, but is unstable below
these temperatures. On cooling from the stable austenitic region, austenite may therefore undergo
decomposition or transformation to one of several
constituents, the type of which depends on three
factors: (1) chemical composition, i.e. alloy and
carbon content in solution at the moment of
quenching (this may be different than the base
composition, if undissolved carbides or other
"This paper is an abbreviated version of two sections from an SAE Manual SP453 on the same subject. Manual SP453 is being prepared by the
X-Ray Division of the SAE Fatigue, Design and
Evaluation Committee and will be published in
1980.
0148-7191 /80/0225-0426302.50
Copyright © 1980 Society o f A u t o m o t i v e Engineers, Inc.
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2
constituents coexist with the austenite), (2)
rate of cooling, and (3) the temperature of the
quenchant or the lowest temperature reached
prior to tempering. When the cooling is relatively slow, austenite transformation involves
diffusion processes which may lead to formation
of free ferrite, or of aggregates of ferrite and
carbide termed pearlite and bainite. The ferrite in all these products is a body centered
cubic phase. Under slow cooling conditions,
austenite decomposition can be made total, so
that no austenite survives at room temperature.
If on the other hand, cooling is rapid
enough to prevent significant diffusion of
carbon and alloy, martensite, a hard body
centered tetragonal product is formed instead of
the diffusional transformation products by a
displacive body shear mechanism.
Martensite
usually forms at a characteristic temperature
called Ms and continues to form with decreasing
temperature until Mf, the temperature of essentially 100% transformation is reached. However,
in many hardenable steels, the Mf temperature
may be well below room temperature (R.T.), so
that a considerable quantity of untransformed
austenite may be retained at room temperature
(1-7). Obviously, less retained austenite
(R.A.) will be present if the cooling is continued to sub-zero temperature (prior to tempering). These circumstances are well illustrated
in Figures 1 and 2 which are transformation
diagrams for a Tl~high speed tool steel and for
the 1.14% carbon level in the carburized case of
a Ni-Cr-Mo carburizing grade steel.
FACTORS WHICH PROMOTE AND/OR CONTROL
RETAINED AUSTENITE - The principal factors which
promote retention of austenite in as-hardened
microstructures are the same ones which affect
the formation of martensite:
(1) chemical
composition, (2) the lowest temperature to which
the steel is cooled, and (3) the rate of cooling
from the hardening temperature and within the
Ms-Mf range. The specific influence of the
first two factors has been quantitatively established by Koistinen and Marburger (4) for a
range of lean alloy medium and high carbon
steels (carburizing grades included) which are
ordinarily oil quenched (see Figure 3 ) . The
following equation is the result:
% R.A. ~ exp. [-1.10 x 1 0 ~
2
(Ms - T q ) ]
(1)
where Tq is the lowest temperature reached
in quenching and the Ms temperature is
either measured or calculated from composition using the following equation (9,10):
Ms (°C) = 500° - 333 C - 34 Mn ~ 35 V 20 Cr - 17 Hi - 11 Mo - 10 Cu - 5 W + 15 Co
+ 30 Al + 0 Si
(2)
Note that carbon is much more potent in promoting
R.A. than the standard alloying elements and
that the lower Tq is made, as for instance by
cold treating at sub-zero temperatures after
hardening (prior to tempering), the lower will
be the retained austenite. Higher austenitizing
temperatures which promote better solution of
carbon and alloying elements in high carbon
steels will also produce higher R.A. contents
since both depress the Ms temprature.
Figure 4 shows that R.A. calculations based
on Equation 1 compare well with measured values
for most of the standard high carbon and carburizing steels. However, equation 1 cannot be
used for highly alloyed steels such as high
chromium (>5.0%) die steels and high speed
steels. Additionally, it cannot provide
accurate R.A. values even for the standard
steels covered in Figure 4 when the rate of
cooling to martensite and through the Ms-Mf
range differs greatly from that of oil. The
reason for this is that faster cooling rates,
such as provided by water or brine quenching,
transformation of austenite, due to
higher transformation stresses. Therefore less
R.A. than calculated is observed in water
quenched microstructures (1-3). By constrast
slower cooling treatments such as air hardening
or isothermal and retarded cooling in the Ms-Mf
range (as experienced in martempering or salt
hath quenching operations) promote significant
5.^5.^1 ll2£tlon. or retention of austenite (11-17).
The result is higher R.A. values than for
straight oil quenching (see Figure 5 ) .
After quenching , two additional factors,
tempering and cold deformation, will generally
reduce the amount of R.A. finally observed in
the finished part or after it is returned from
service (7,8,18,19). Tempering reduces the
retained austenite in steels by promoting, the
following microstructural changes:
(1) In stage 1, 80/200°C (3,7,8,18) epsiIon carbide precipitates and high carbon martensites degrade to a low carbon martensite of
about 0.25%C with a total loss of tetragonality.
Retained austenite remains unchanged.
(2) In stage 2, 150/300°C, retained austenite transforms to bainite. In most standard
steels this transformation is completed by
tempering for two hours at 250°C (500°F);
however, where the bainite nose is.far removed
to the right as in steels containing more than
5% Cr (A2, D 2 , 400C, M50, M 2 , in Table 2 ) ,
essentially nothing happens to the retained
austenite until a temperature of 450/650°C is
reached (3,5) (see Stage 4 below).
(3) In stage 3, 200/500°C, the epsilon
carbides formed in lean alloyed standard steels
convert to cementite (M^C) and the low and high
carbon martensites go to essentially zero-carbon
ferrite.
(4) In stage 4, 450/650°C, which only
occurs in steels containing large contents of
carbide-forming elements, alloy carbides such as
M.^Cg, ^ 2 ^ ' ^ P
ipi
•
The austenite is
thus conditioned (depleted of carbon) and transforms to new martensite on cooling to room
temperature since conditioning raises the Ms
r e c
t a t e
t
"Numbers in parentheses designate references
at end of paper.
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3
temperature. If held for long periods of time
at 450/650°C retained austenite may also transform directly to ferrite and alloy carbides.
Cold deformation which is often generated
incrementally in service from periodic overloads
will cause direct transformation of retained
austenite to martensite as cited in the table
below. Bearings made of carburized 8720 steel
were run at an overload condition of 3.1 GPa
(451 ksi) for the cycle times indicated. Subsurface (.125 mm/.005 in.) retained austenite
levels and residual stresses (R.S.) were then
measured on the cone or inner race. The results
were as follows:
or surface rolling can be applied to work harden
the austenite (8,20) and to improve its bend
strength and fatigue resistance.
3.
It improves impact fatigue strength of
the same steels at all R.A. levels (25,26).
4.
It improves ductility and fracture
toughness at high strength levels in maraging,
trip, and standard high strength steels (28-30).
5It improves the corrosion resistance of
martensitic high carbon steels (31).
Note that as the R.A. decreased with time, the
newly formed martensite resulted in higher
compressive stresses.
RANGE OF RETAINED AUSTENITE IN STEEL
PRODUCTS - Retained austenite can be expected in
the as-hardened microstructures of all plain
carbon and alloyed steels containing more than
about 0.4%C. High strength steels such as 4340,
300M, and 4150, as well as high carbon and
carburized low carbon grades such as used for
bearings, gears, and cold work tool steels
always contain R.A. in varying degrees in the
as-hardened and also the tempered microstructures since these steels are generally tempered
in the range 150/260°C (300/500°F). R.A. may
also be expected in the higher alloyed Cr, Mo,
and W high speed tool steels which are usually
tempered in the secondary hardening range of
480/590°C (900/1100°F). Tables 1 and 2 illustrate the R.A. levels generally present in many
common cold work and high speed tool steels.
Figures 3 and 4 demonstrate the levels of R.A.
to be expected in bearing and gear steels.
The important negative effects of R.A. in
hardened microstructures are:
1.
It may cause undesirable growth of
dimensions in finished gears, bearings and tools
and gages during service if such items are subjected to temperatures at which R.A. can transform
isothermally (1-8,32,33).
2.
R.A. lowers the aggregate compressive
yield and ultimate strengths and thereby the load
carrying capacity of martensitic/austenitic
structures (22).
3.
It lowers aggregate hardness and resistance to scuffing and indentation (22).
4.
It increases susceptibility to burn and
heat checking in grinding operations (7,22).
Although other factors may undoubtedly be
added to these lists of good and bad effects of
R.A. in hardened microstructures, the economic
significance of the above items alone is sufficient to demonstrate the advisability and/or need
to monitor and control R.A. in many industrial
products,
TECHNIQUES FOR MEASUREMENT OF RETAINED
AUSTENITE - Many different techniques have been
applied successfully to the measurement of
retained austenite in martensitic and ferritic
structures. Quantitative optical microscopy is
generally satisfactory as long as the austenite
content is high (12-15,35,36). However, optical
microscopy becomes unsatisfactory below about 15%
in many steels due to etching and resolution
difficulties. Recently a new etch reagent containing CuSO^ in a slightly acidified water
solution was developed (34) which is claimed to
provide good resolution of austenite down to 2%.
INFLUENCE OF R.A. ON MECHANICAL OR
ENGINEERING PROPERTIES AND PROCESSING
CHARACTERISTICS OF STEEL - Retained austenite in
martensitic microstructures provides both positive and negative effects with respect to the
general properties and processing characteristics
of the base steel composition. Some of the most
significant positive effects are:
1.
It improves contact fatigue life in
gears and bearings made from carburizing or
homogeneous high carbon steels (8,20-24).
2.
It generally improves bending fatigue
resistance of the same steels (25,26). However,
there is a maximum R.A. content above which
bending fatigue resistance suffers; in such
cases plastic deformation such as by shot peening
The most accurate R.A. measurement technique
is the x-ray diffraction method which is described
in this text. It is essentially absolute and
independent of external calibration and can be
used to easily measure low austenite contents
(>2%) with excellent precision. It is also
non-destructive in that no specimen cutting need
be involved and very large objects can be measured
for R.A. in place with portable units (47). The
outstanding features of the method are its simplicity, the use of automatic equipment and the
short times required for a single determination.
Accurate results can be obtained in less than a
half-hour using either recorded traces of the
diffraction pattern or electronic scan-counting
of peak intensities obtained from the specimen.
A portable x-ray unit described by Cohen and
Condition
As hardened and
tempered
After 1x10^ cycles
6
After 2x10 cycles
Residual Stress
MPa
ksi
% R-A.
31.3
-133.2
-19.3
29.7
-423.7
-61.4
23.5
•1077.8
-156.2
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4
James (47) which uses a position sensitive detector to record the complete line profiles for
austenite and martensite, can reportedly be used
to make a satisfactory R.A. measurement in 20
seconds. The results of a single fast determination will be within 1/2 to 2% of the true austenite content.
• Other worthwhile techniques employed in the
past for R.A. measurement are: electrical
resistivity (12,17), magnetic permeability (13
,42), dilatometry (14), and thermal analysis
(15). All of these are, however, more amenable
to measurement of the austenite present during
transformation than that retained in the final
microstructure. Several of the above techniques
can, however, be calibrated with the x-ray or
optical methods to provide satisfactory R.A.
results, but they are usually cumbersome and not
worth the effort. Except for dilatometry, which
is used extensively to determine CCT diagrams of
the type illustrated in Figure 2, the other
techniques are not often used.
PRINCIPLES OF R.A. MEASUREMENT BY X-RAY
DIFFRACTION
THEORETICAL CONSIDERATIONS - When a
crystalline substance is irradiated by x-rays,
it produces a characteristic diffraction pattern
which is determined by the crystal structure of
all phases existing within that substance
(36-50). Peaks of varying height corresponding
to diffraction of x-ray energy from various
(hkl) planes in the crystal structure of each
phase will be observed in the diffraction pattern
at discete 26 angles. The specific 28 locations
of the peaks depend on the "d" spacings of the
planes and on the wavelength of the x-ray
radiation used. Typical x-ray diffraction
patterns for a hardened and tempered steel
showing specific reflections (diffraction peaks)
for martensite (or) and austenite (y) phases are
shown in Figs. 6 and 7. These were obtained
with Chromium, Copper and Molybdenum radiations
respectively. Note that more diffraction (hkl)
peaks appear with the shorter wavelength Cu and
Mo radiations than with Cr. This follows from
Braggs' Law, xxK - 2dsin8, which predicts that
in a given 26 space more (hkl) lines will be
made available for observation with shorter
wavelength radiation (see Table 3 for the
specific wavelenghts of Cr, Cu, Co and M o ) .
Quantitative determination of the relative volume fractions of martensite and austenite can be made from such x~ray diffraction
cftarts because the x-ray intensity diffracted
from each phase is proportional to the volume
fraction; of that phase. Furthermore if the
phase contains a completely random arrangement
of crystals and is of infinite thickness, so
that x-rays do not pass through the sample,
the diffracted intensity from any single (hkl)
plane within that phase is also proportional to
the volume fraction of that phase. Thus in
random specimens measurements of diffracted
intensity need only be made on one (A) austenite
and one (M) martensite (hkl) line to accurately
establish the volume fraction of each phase. By
contrast if preferred orientation (P.O.) or
texture exists within the specimen, intensity
measurements may have to be made on many austenite and martensite lines each to provide an
accurate result by averaging (52,53).
EQUIPMENT AND SUPPORTING INSTRUMENTATION - A
typical x-ray diffractometer set-up for the
generation of diffraction patterns is illustrated
in Fig. 8. All elements of the system from the
power supply, to sample positioning, to beam
generation and pickup and recording of the diffracted x-ray pulses are shown. Because the
description and discussion of each of these
elements is quite lengthy and is covered in great
detail in the parent manual SP453, no discussion
of specific equipment functions, operating
characteristics and methods of performance optimization will be presented herein. A thorough
discussion of the x-ray procedure itself is
planned instead.
TYPICAL X-RAY PROCEDURE FOR MEASUREMENT OF
R.A. - In practice the procedure for measuring
R.A. by x-ray diffraction is a rather simple
routine. It generally involves the following six
steps (1) selection of the proper radiation, (2)
running of the diffraction pattern, (3) selection
of the optimum M and A peaks for comparison of
diffracted intensities, (4) actual measurement of
the diffracted intensities under each selected
peak, (5) a comparison of two austenite line or
peak intensities to establish the degree of
preferred orientation (P.O.) or texture if present
in the specimen, and (6) application of the
appropriate equations to convert the measured
intensity values to volume fractions of austenite.
This procedure may be reduced to four steps,
namely 2, 4, 5 and 6 if one has prior knowledge
of the degree of P.O. in the specimens to be
surveyed for R.A. since the selection of radiation and optimum M and A peaks for comparison of
diffraction intensities can be fixed for all
specimens. Each of the six steps is described in
more detail below.
Selection of Radiation - One of the following four radiation sources, chromium, molybdenum,
cobalt or copper is generally employed in x-ray
measurements of R.A. Chromium (Cr) is the most
used choice when the P.O. is known to be absent
or at worst moderate in degree," because as shown
in Fig. 6 its long wavelength provides widely
dispersed M and A peak shapes for study of diffraction intensities (except for the 110M and
111A lines). The 200A, 220A, 200M and 211M lines
are so well separated from each other, that none
interferes with the other hence interfering or
overlapping lines produced by carbides (C) and/or
other intermetallic phases present within
''The various degrees of P.O. orientation will be
described later.
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5
the steel specimen can be easily unfolded or
separated. Cr radiation also produces high
relative intensities (see comparative R-values
in Table 3 ) , high peak to background (P/B)
ratios and the shortest test times per each
R.A. determination.
Molybdenum (Mo) is the preferred x-ray
radiation when specimens with severe P.O. have
to be assessed for R.A. Mo radiation offers
many M and A lines (see Fig. 7 and Table 3) for
comparison and provides even higher relative
intensities (R-values) and P/B ratios than Cr.
It will be shown Chat four or more M and A lines
must be averaged to assure accurate R.A. values
in specimens with severe P.O. Mo fulfills this
requirement much better than Co and Cu which
also provides at least four M and A lines for
observation, (see Fig. 6 and Table 3 ) . Co and
Cu radiations, both suffer from the handicap
that they cause fluorescence of the iron (Fe)
in the specimen, which must then be reduced by
special filtering, careful pulse height discriminator (PHD) settings or the use of a
crystal monochromator to achieve low backgrounds
and high P/B ratios. Mo does not suffer from
this handicap; however compared to Cr, irradiation with Mo (and Co and Cu as well) has two
distinct disadvantages which should be noted.
First the unfolding of overlapping and interfering intensities from carbide, and intermetallic lines is much more difficult to achieve
and two, the times required to complete a R.A.
measurement are very much longer, even when such
measurements are made on specimens containing
no P.O. and only two or three lines need be
scanned. Reasons for these facts are given in
the parent Manual SP453.
Selection of M and A Lines - The selection
of the optimum M and A lines, as well as the
number of lines whose intensities must be
measured to assure an accurate measurement of
R.A. is dependent on three factors: (1) the
radiation selected or available, (2) the degree
of P.O. present in the specimen, and (3) whether
interference with carbide or other lines can be
expected in the diffraction pattern. When low
to moderate P.O. exists the following M and A
lines are most often selected for comparison of
diffracted intensities (see Figs. 6 and 7 ) ;
Cr Radiation
Co Radiation
Cu Radiation
Mo Radiation
200A,
220A,
220A,
220A,
200M, 220A
2 1 J M , 311A
211M, 311A
211M, 3 1 1 A
When P.O. is severe, specific lines cannot
be pre-selected beforehand, however it is.
necessary to measure as many M and A lines as
possible as will be described below to provide
a true picture of the average diffracted intensity from M and A lines so that an accurate
value of volume fraction R.A. can be derived.
Measurement of X-Ray Diffracted Intensities - In measuring diffracted line intensities it is essential that integrated Intensity
be measured and not maximum intensity. This is
so because large variations in line shape and
broadening can occur in hardened and plastically
deformed steels due to variations in microstrain
and particle or grain size. These changes in
line shape will not affect the integrated intensity, but they can make the values of maximum
intensity absolutely meaningless, even when
apparently sharp lines are present.
Two techniques are available for evaluating
diffracted intensities from a specimen:
(1)
measurement of areas above background for each
line or peak automatically recorded on chart
paper, and (2) electronic integration of the area
using the scaler circuit.
In the chart method, the area (intensity)
under each peak can be evaluated either by a
planimeter or by using the product method of peak
height times peak width at half height to represent area (59) (see Figure 9 ) . When the peak
height times peak width technique is used,
symmetrical peaks must be generated. How this
is done by selection of time constant and diffractometric scanning speeds is shown in the
parent Manual SP453.
The electronic integration technique is
applied as follows (refer to Figure 10). Each
peak is first scanned at a constant rate making
certain that the 20 range scanned is wide enough
to include the whole peak (two peaks when a
tetragonal doublet is present) but no portion of
another peak. This scan rate may range from as
high as 4°/minute for Cr radiation to as low as
0.1°/minute for Mo radiation, and in extreme
cases may consist of step-scanning the peak at
very small increments of 29. The scaler is used
to count the total pulses, 1^ emitted by the
counter tube during the scanning period. Next
the x-ray pulses emitted at the start 20 (BG^,^)
and finish (BG ) 20 position are counted for a
fixed period of time (BG ) . The integrated
background intensity (BG) is found using:
B
G
^
B b
Cl
+
B
° C 2 x scan width x
2
scan rate
60
(3)
BG^
where the units are:
for BG^j and B G ^ ™ total counts accumulated at the two
locations C^ and C^
for scan width
- degrees
for scan rate
- degrees/minute
for B G
- seconds
t
The integrated intensity is then obtained as
I = 1^ - BG. Typical. 29 scanning ranges for
electronic integration of peaks generally used
with Cr, Co, Cu and Mo radiations are given in
Table 5. As a general rule, the electronic
integration technique is much less time consuming
than the chart method, but it has one serious
drawback; this is that sample positioning and/or
machine or electronic difficulties with the
equipment may go unnoticed. These are easily
picked up in recorder traces.
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6
Detection of Preferred Orientation - P.O.
or texture can be formed within a steel when it
is exposed to heavy cold (or hot) deformation or
in castings during solidification. Recrystallization textures can also form in hardening.
The influence of such textures is to enhance
diffraction intensity for those (hkl) planes
which lie parallel to the surface (perpendicular
with the x-ray beam) and to diminish or totally
eliminate diffraction from planes lying perpendicular to the surface. Because of this fact,
R.A. measurements on specimens containing severe
orientation must involve (as already mentioned)
intensity measurements from a minimum of four M
and A lines (44,52,53). These lines should
preferably include the corner (hkl) planes of
the stereographic triangle; that is (100, 110,
and 111) as either first or second order reflections. Planes of lower symmetry such as the
(211) for M and (311) for A, which are near the
average planes when the cubic stereographic
triangle is integrated may also be included in
the n -n =4 line requirement, for analysis.
However,""the use of such "average" lines alone
to establish R.A. in specimens showing heavy
P.O. is not recommended since this can lead to
large errors.
Miller (42) has shown that the problem of
severe P.O. can be better handled by the use of
a mechanical tilting and rotating (T.R.) stage,
in which the specimen is tilted back and forth
at least ±5^.7° while being simultaneously
rotated. This in effect randomizes all (hkl)
reflections within the stereographic triangle and
reportedly provides a near random oriented
diffraction pattern from very textured and/or
large grain-sized specimens. Figures 11 and 12
taken from Kim (61) illustrate this rather
effectively for cast iron. The major drawback
of this technique when using Mo radiation is
that slow scanning speeds and high time constant
are required to assure "random" diffraction
patterns and hence the process may be as time
consuming as running an eight line diffraction
analysis at normal scanning speeds. Also, the
specimen size must be limited. An attractive
option exists, however in that once it is proven
that a random pattern is being produced only one
or two M and A lines need be scanned; hence Cr
radiation and fast scanning speeds can be
employed. This will, shorten machine time and
still provide the necessary accuracy.
The use
of the T.R. procedure with Cr radiation is
described in Section 4 of the parent Manual
SP453. A test of the measured intensity ratios
between any two austenite (or two martensite)
lines to determine whether the theoretical ratio
has been achieved will establish whether all of
the P.O. orientation was accounted for by the
tilting and rotating procedure.
In practice preferred orientation or texture in the specimen is generally detected by
comparing the measured intensities of two austenite lines if it is not obvious from the
diffraction pattern itself. P.O. is said to be
present when the intensity ratio of the two
lines being compared, as for instance the
I220A/I200A line ratio (when Cr radiation is
u s e d ) , differs significantly from the
(R220A/R200A) ratio which can be obtained from
Table 3 and which shows what the theoretical
diffraction intensity ratio for these lines
should be in a randomly oriented specimen.
Table 3 shows that when Cr radiation is employed,
the R220A/R200A ratio should be 41.6/28.2 or
1.47 for austenite of 1.0% Carbon content.
However in practice the sample is considered to
be random if the measured (X220A/I200A) ratio is
between 1.2 and 1.8, an approximate ±20% deviation from the random value of 1.47.
Moderate P.O. is considered to be present
when the measured intensity ratio for the two
austenite lines selected for comparison differs
by ±(20 to 200%) from the random R-ratio for
the same .lines in Table 3. Severe P.O. is said
to be present when the measured intensity ratio
for the two austenite lines differs by more
than 200% from the random or theoretical
R-relationship for the two lines. Similar
guidelines apply when other than Cr radiation is
employed. The I311A/I220A ratio has been
satisfactorily applied for this purpose with Co,
Cu and Mo radiations. Refer to Table 3 for
typical R values.
CONVERSION OF MEASURED INTENSITIES TO VOLUME
FRACTION R.A. - Basic equations which are used to
convert measured intensity values from the
various (hkl) reflections in martensite and austenite in the specimen are listed below. The
derivation of these equations is given in the
parent SAE manual.
Case 1 - Specimens with Random or Low P.O. When the P.O. ranges between values of 1.2 and
1.8, the following equation should be used to
calculate volume fractions from measured intensity values:
Volume
Fraction ~ V
a
~
hkl hkl
I
/R
T
/ n
A
A
+
A
(4)
hkl hkl
A
A
hkl hkl ^ hkl hkl
*
/R
C
T
/r>
X
/ R
T
/ n
+
M
M
T
:
/ D
/ R
C
h k l ,hkl
, hkl
. .
. , . .
A'
M'
C
8
d
~
sities measured for a single preselected austenite, martensite and,carbide lipe respectively.
The factors R^
, R^
and R
are theoretical intensity values for the same (hkl) planes.
R-factors are calculated from basic principles
by a process described in detail in Manual SP453.
An example calculation of R-values is, however,
given in Table 4 for the (200A) line in a
carburized 8620 steel along with the equations
and functions involved in the calculation.
Table 3 contains a compilation of all R-values
one may ever need to calculate R.A. by the x-ray
diffraction technique. Specific R-values are
given for all consecutively diffracting (hkl)
lines of austenite and martensite for the four
radiation source already mentioned; Cr, Co, Cu
and Mo.
T
T
a
a
r
e
i n t e
r a t e
Q
1 J l t e n
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7
Equation 4 above may be re-written in the
following form which is sometimes more convenient when intensity measurement are not made
on carbide lines but the carbide volume measured
or estimated optically instead;
The following equation is recommended by
Miller- (41) when Mo radiation is employed to
handle specimens with moderate P.O.:
1.4
- VC
1
(5)
, hkl, hkl>
1 +
(R
A
/R
r T
)
M
h k l , hkl
/I
CI
M
A
)
Equations 4 and 5 may be satisfactorily
employed to measure retained austenite in
hardened and in tempered steels because in
these conditions the majority of steels contain
low P.O. Thus, accurate results may be obtained
quickly from intensity measurements of only one
A and one M line. It is good practice, however
to scan and compare at least one other austenite
line since one cannot assume that P.O. is not
present. Two independent
values will then
be obtained in this fashion. These can be used
to confirm the first result or to detect
possible errors in observation or calculation
if present. The lines generally recommended
for this purpose with each radiation have
already been noted under selection of M and A
lines.
Case 2 - Specimens With Moderate P.O. When the measured intensity ratio of aforementioned two austenite lines differs by more than
20 to 200% from the theoretical R-ratio of 1.47
for the same two lines, the following equation
must be used to give acceptable accuracy to the
volume fraction value calculated:
V
A
I„
=
V
A1
+
( I
A1
+
:
a
r
(6)
r
1+R„
VH
hl>
T
a
r
hkl
Al
hkl
e
1
1
(7)
.200
+ 4.10
-200
+ I
220
200
where the constant 4.10 is R or [ ( R
+
A
220
200
^A
^ ^
hardened ^ subsequently
tempered steels.
has a value of 4.27 for
hardened, non-tempered steels.
T
o r
a n <
( I
AZ-,o
hki hki
/ R
(9)
|1
}
C I
+
hkl ,„hkl.
A
/ A >
R
( I
hki
/ R
hki
) + V c
.hkl
A2
1^ and
the measured integrated
intensities of two different (hkl) austenite
lines, 1^ is the intensity of a martensite line
generally located between the two austenite
lines and R ^ is the ratio (RAJ + ^ A 2 ^ ^ M
values taken from Table 3. Equation 6 can be
used with any radiation that provides two austenite lines and one martensite for analysis
of diffracted intensities. For example with Cr
radiation the aforementioned 200A and 220A
lines are ordinarily compared with the 200M line
located between them (see Fig. 6 ) . The appropriate version of equation 6 is then;
V,
(8)
A
+ 1.4 I
The 200A and the 3 1 1 A peaks and the 211M peaks
located between them (see Fig. 7) m u s ^ ^ e scanned
to use this^^uation where 1^ •+-.^I
(I
and 1^ - 1^
. This equation was developed
empirically from intensity measurements on an
Fe-20%Ni alloy, but Is a special version of
equation 6.
Case 3 - Specimens With Severe P.O. - When
severe P.O. exists in the specimen, the diffraction spectrum will be severely warped as
shown in Fig. 11, in that certain (hkl) lines
for both phases may be greatly more intense
than would be observed in random steels, while
others may be much less intense. In fact in some
cases, certain lines may not appear at all if
such (hkl) planes lie perpendicular to the
specimen surface and Bragg reflections are not
produced. To obtain accurate measurements of
R.A. under these circumstances, intensity measurements have to be made on as many different
(hkl) austenite and martensite lines as possible
and then averaged according to equation 9 below:
n
+
( I
I
V is again the volume of carbide measured
optically or by x-rays as discussed previously
and n^ and n^ are the numbers of (hkl) lines for
which integrated intensities have been measured.
Note that missing lines must be counted as zero
intensity when determining n in this equation.
Table 3 can help in detecting such missing lines.
Dickson (53) states that at least four diffraction line pairs, n,, = n^ - 4 are required to
handle the severe P.O. present in sheet and wire
after cold draw or rolling. More than four line
pairs may have to be scanned and evaluated in
coarse grained castings and heavily deformed
non-recrystallized materials.
p
Because the time requirement to scan more
than eight lines is usually prohibitive in
production evaluations of R.A., a second method
for determining R.A. in specimens containing
severe P.O. should be listed which is much less
time consuming. This is the Miller (42) method
described earlier in which the specimen is tilted
and rotated in a special (TR) stage while being
irradiated.
In this fashion many additional
plane orientations are placed into position for
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8
diffraction and a continuous trace of diffraction lines and intensities is obtained
which corresponds closely to that presented
by a randomly oriented specimen, compare
Figs. 11 and 12. Because the TR stage effectively randomizes specimens with severe P.O.
comparison of one line pair will generally
suffice to establish R.A. in textured specimens.
This mechanical method of handling specimens
with severe P.O. is described in detail in the
parent Manual SP453 and will not be discussed
further.
EXAMPLES OF X-RAY DATA COLLECTION - Intensity data collected on four specimen ranging in
R.A. content from about 5 to 35°/ are tabulated
in Table 6 (60). These data were obtained with
Cr Ka radiation using the electronic integration
(E.I.) and chart techniques (C.T.) both to
establish integrated intensities for the 200A, .
220A and 200M lines. Since the P.O. ranged
from 1.0 to 1.7, equations 5 and 7 were both
used to calculate the R.A. present in each
specimen. Note that equation 7 which should be
used preferredly with this P.O. range yields
results about midway between those obtained
with equation 5 when used to compare the
200A/200M and 220A/200M lines individually.
Also, note that the R.A. results obtained on each
specimen are similar whether the E.I. or the
C.T. method was used to measure intensities.
Each R.A. value obtained with equation 7 on
a given specimen is within ±0.5% of the average
value for that specimen. The subject of precision and accuracy of R.A. measurements is
handled in detail in the Manual SP453.
The base chemistry of the austenitic and
ferritic or martensitic phases should preferredly
be the same or as close as possible. AISI 440C
steel treated as follows will provide both
phases:
100% Austenite Sectors
440C steel oil-quenched
from 2100°F (1150°C),
not tempered
100% Ferritic or
Martensitic Sectors
440C steel oil-quenched
from 1800°F (932°C) and
tempered at 1100°F
(593°C)
0
COMPARISON OF X-RAY MEASUREMENTS WITH OTHER
TECHNIQUES - X-ray R.A. results were obtained
for a series of bearing steel specimens containing up to 4 3 % R.A. (43). These were compared
with metallographic and magnetic evaluation of
the same steels. The data are plotted in Fig. 13.
Although a good correlation was obtained with
the optical point counting and magnetic susceptibility techniques, neither of these techniques
are very reproducible below about 15%. Fig. 14
shows why this is so - with the metallographic
technique it is very difficult to get the proper
resolution of austenitic areas at these low
contents.
CALIBRATION OF X-RAY R.A. METHOD - The
x-ray technique can be calibrated very conveniently with the following procedure. Pieshaped segments are made of two materials, one
yielding pure austenite and the other pure
ferrite or martensite. These are then fitted
together in various combinations. The assembled
disc is then rotated in its own plane in a
sample spinning stage. The proportion of
austenite can be determined from the angular
ratio of the pie-shaped austenite sections to
360°.
If eighteen (18) 20° pie-sections are
made, austenite contents from 0 to 100% can be
measured in 5 % increments.
440C is a 17% Cr-steel containing 1.0% C.
Use of the same steel for both phases obviates
differences in R-factors due to variation in
chemistry.
PRECISION AND ACCURACY OF INTENSITY
MEASUREMENTS AND R.A. RESULTS - The precision
and accuracy of R.A. measurements with the x-ray
diffractometric technique is considerably
improved if the resulting diffraction patterns
and/or intensity measurement techniques provide
the following characteristics:
(1) high diffracted intensities for each (hkl) line of martensite and austenite, (2) a high peak to background (P/B) ratio, (3) a wide dispersion and
resolution of all (hkl) lines in the pattern,
(4) minimum interference from overlapping
carbide lines, (5) a low and straight background
over the entire scan of 26, (6) high counting
statistics and finally, (7) a stable irradiation
source, with optimum electronic discrimination
of line as well as machine noises.
Factors which influence these characteristics or parameters may be subdivided into three
categories:
(1) equipment or instrumental
variables, (2) specimen variables, and (3)
technique variables.
The influence and optimization of these
variables is described in detail in the parent
Manual SP453. However, to properly conclude
this paper, some of the most important items are
listed below for the benefit of the reader.
Those not previously listed in this manuscript
are:
1.
Equipment and Instrument Variables
a.
b.
c.
d.
e.
f.
g.
h.
Selection of filters
Selection of tube voltage and milliamp
setting
Selection of detector systems
Selection of pulse-height discriminator
Use of monochromators
Selection of slit system
Selection of diffractometer scanning
speeds
Selection of recorder scan speeds
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9
2.
Specimen or Material Variables
a.
b.
c.
d.
Influence of chemistry
Influence of absorption
Influence of extinction and grain size
Influence and separation of carbide
interference and/or superposition or
overlap of other lines with M and A
lines
Influence of specimen surface condition
Specimen preparation techniques
e.
f.
3.
Technique Variables
a.
b.
c.
d.
Overall uncertainty in x-ray R.A.
measurements
Errors due to uncertainties in calcul a t i o n and proper use of the theoretical intensity factor - R
Experimental errors in measurement
of diffracted intensities
Errors due to variations in chemistry
and specimen geometry
REFERENCES
1.
P. Gordon, M. Cohen and R. S. Rose,
"Kinetics of Austenite Decomposition in High
Speed Steel." Trans. A.S.M., 1943.
2.
A. Rose and H. P. Hougardy, "Transformation Characteristics and Hardenability of
Carburizing Steels." "Transformation and
Hardenability in Steel", Climax Molybdenum Co.
of Michigan, U.S.A., Symposium, 1967.
3.
M. Cohen, "Retained Austenite."
Trans. A.S.M., 1948.
4.
D. P. Koistinen and R. E. Marburger,
"A General Equation for Austenite - Martensite
Transformation in Pure Carbon Steels." Acta
Met., Vol. 7, 1959.
5.
C. F. Jatczak, "Graphitic Cold Work
Tool Steels." A.S.M. Paper No. C72-25.2,
1972.
6.
A. Gulyayev, "Martensite Transformation in High Speed Steels." Katchestvennaya
Stal, 5, No. 1, 1937.
7.
K. R. Kinsman and C. L. Magee, Editors,
"Symposium on Formation of Martensite in Iron
Alloys." in Trans. A.I.M.E., Vol. 12, Sept.,
1971.
8.
G. Parrish, "Influence of Microstructure on Properties of Case Carburized Components." Part 4 - "Retained Austenite", Heat
Treatment of Metals, 1976-4.
9.
E. S. Rowland and S. R. Lyle, "The
Application of Ms Point to Case Depth Measurements." Trans. A.S.M., Vol. 37, 1946.
10. L'. D. Jaffe and J. H. Hollomon,
"Ferrous Metallurgical Design." John Wiley,
New York, N.Y., 1947.
11. P. Gordon, M. Cohen and R. S. Rose,
"Effect of Quenching Bath Temperature on
Tempering of High Speed Steel." Trans. A.S.M.,
33, 1944.
12. E. S. Machlin and M. Cohen, "Burst
Phenomenon in Martensitic Transformation."
Trans. A.I.M.E., 191, 1951.
13. H. R. Woherle, H. R. Clough, and
G. S. Ansell, "Athermal Stabilization of
Austenite." J. Iron and Steel, 203, 1965.
15. B. Edmondson, "Thermal Stabilization
of Austenite in 10% Ni, 1% C, Steel." Acta
Met., 5, 1957.
16.
W. J. Harris and M. Cohen, "Stabilization of the Austenite - Martensite Transformation." Trans. A.I.M.E. 180, 1949.
17. S. R. Pati and M. Cohen, "Nucleation
of Isothermal Martensite." Acta Met., 17, 1969.
18. B. S. Lement, B. L. Averbach and
M. Cohen, "Microstructural Changes on Tempering
Iron-Carbon Alloys." Trans. A.S.M., Vol. 46,
1954.
19. 0. Zmeskal and M. Cohen, "The Tempering
of Two High Carbon - High Chromium Steels."
Trans. A.S.M. 31, 1943.
20. C. Razim, "Effect of Retained Austenite on Pitting and Bending Fatigue."
Thesis, Techn. Hochschule, Stuttgart, 1967,
also Harterei Tech-Mitt, Vol. 28. 1968.
21. F. T. Krotine, M. F. McGuire and
A. R. Troiano, "Influence of Case Properties and
Retained Austenite on Behavior of Carburized
Components." Trans. A.S.M., Vol. 62, 1969.
22. R. Widner, H. Burrier and C. F. Jatczak,
"Influence of Retained Austenite on Compressive
Properties, Contact Fatigue and Scoring Resistance of Carburized Steels." Interim Report,
The Timken Company, 1973.
23. B. Prenosil, "Effect of Retained
Austenite on Strength of Cemented and Nitrided
Steels Under Alternating Loads." "Symposium
on Metal Fatigue", Prague, I960.
24. H. Muro, et al., "Effect of Retained
Austenite on Rolling Fatigue of Carburized
Steels."
12th Japan Congress on Materials
Research, Metallic Materials, March, 1969.
25. R. A. DePaul, "High Cycle Bending and
Impact Fatigue of Carburized Gear Steels."
A.S.'M. Metals Engineering Quarterly, Vol. No.
10, Nov., 1970.
26. R. H. Richman and R. W. Landgraf,
"Some Effects of Retained Austenite on Fatigue
Resistance of Carburized Steel." Met. Trans.,
Vol. 6A, May, 1975.
27. G. S. Reichenbach, et al., "Yield
Behavior of Certain Alloy Steels at Low Strain
Values." Trans. A.S.M., Vol. 54, 1961.
28. G. Y. Lai, W. E. Wood, R. A. Clark,
V. F. Zackay and E. R. Parker, "The Effect of
Austenitizing Temperature on the Microstructure
and Mechanical Properties of As Quenched 4340
Steel." Met. Trans., Vol. 5, July, 1974.
29. D. Bhandakarar, V. F. Zackay and
E. R. Parker, "Stability and Mechanical Properties of Some Metastable Austenitic Steels."
Met. Trans., Vol. 3, Oct., 1972.
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30. E. R. Parker, ''Interrelations of
Composition, Transformation Kinetics, Morphology,
and Mechanical Properties of Alloy Steels."
Met. Trans., Vol. 8A, July, 1977.
31. R. W. Krieble and T. V. Philip, "Effect
of Retained Austenite on Copper Sulfate
Corrosion Resistance of 440-C Stainless Bearing
Steel." A.S.M. Materials Engr. Congress,
Chicago, 1973.
32. S. C. Fletcher, B. L. Averbach and
M. Cohen, "The Dimensional Stability of Steel."
Part 1, Trans. A.S.M., Vol.. 34, 1945.
33. Ibid, Part 2, Vol. 4 0 , 1948,
34. E. J. Klimek, "A Metallographic
Method for Measuring Retained Austenite."
Metals Engineering Quarterly, Vol. 15, No. 1,
February, 1975.
35. W. J. Harris, Jr., "Comparison of
Metallographic and X-Ray Retained Austenite
Measurements." Nature, 161, February, 1948.
36. B. L. Averbach and M. Cohen, "X-Ray
Determination of Retained Austenite by Integrated Intensities." Trans. A.I.M.E., 176,
1948.
37. W. E. Littmarm, "An X-Ray Spectrometer
Determination, of Retained Austenite in Steel."
MS Thesis, MIT, 1952.
38. H. H. Erard, "Technique for Measuring
Low Percentages of Retained Austenite Using
Filtered X-Ray Radiation and an X-Ray Diffractometer." Adv. in X-Ray Analysis, Vol. 7,
1963, Plenum Press, New York, N.Y.
39. R. E. Ogilvie, "Retained Austenite
by X-Rays." Norelco Reporter, May, 1959.
40. R. Lindgren, "Calculated Intensity
Ratios of X-Ray tines from Austenite and
Martensite, Report No. 8503, The Timken Company,
1964.
41. R. L. Miller, "A Rapid X-Ray Method
for the Determination of Retained Austenite."
Trans. A.S.M. 5 7 , 1964.
42. R. t. Miller, "Volume Fraction. Analysis of Phases in Textured Alloys." Trans.
A.S.M., 61, 1968.
43. J. Durnin and K. A. Ridal, ''Determination of Retained Austenite in Steel by X-Ray
Diffraction." J.I.S.I., January, 1968.
44. R. D. Arnell, "Correction for
Preferred Orientation." An Answer to Above
Reference, J.I.S.I., October, 1968.
45. K. E. Beu, "Modification of an X-Ray
Method for Measuring Retained Austenite in
Hardened Steel." Trans. A.I.M.E., 194, 1952.
46. L. Leonard, S. J. Luszcz and
J. D. Meakin, "Non-Dispersive X-Ray
Techniques in Retained Austenite Determinations, A.S.M., 197347. M. R. James and J. B. Cohen, "A
Portable Residual Stress Analyzer." Tech.
Report 19, Dept. of Materials Science Northwestern University, Evanston, Illinois, 1977.
48. B. D. Cullity, "Elements of X-Ray
Diffraction.*
Addison-Wesley, Reading,
Massachusetts, 1956.
49. A. Taylor, "X-Ray Metallography."
John Wiley & Sons, New York, 1961.
1
50. H. D. Klug and L. L. Alexander, "X-Ray
Diffraction Procedure." J. Wiley & Sons, New
York, 1970.
51. L. I. Mirkin, "X-Ray Analysis of Polycrystalline Mterials." Consultant Bureau, New
York, 1964.
52. R. Gulberg and R. Langneborg, "X-Ray
Determination of the Volume Fraction of Phases
in Textured Materials." Trans. A.I.H.E., Vol.
236, October, 1966.
53. M. J. Dickson, "The Significance of
Texture Parameters in Phase Analysis by X-Ray
Diffraction." J. Applted Crystallography, 2,
1969.
54. C. S. Roberts, "Effect of Carbon on
the Volume Fractions and Lattice Parameters of
Retained Austenite and Martensite." Trans.
A.I.M.E., February, 1953.
55"International Tables for X-Ray
Crystallography." Kynoch Press, Birmingham,
Volume III, 1962.
56. J. Taylor and W. Parrish, "Absorption
and Counting and Efficiency Data for X-Ray
Detectors." Rev. Scientific Instr., Vol. 26,
1955.
57. P. H. Bowling, et al., "Counters for
X-Ray Analysis." Philips Technical Rev., Vol.
18, 1956/1957,
58. S-A.E. Handbook J784a - Residual Stress
Measurement by X-Ray Diffraction, S.A.E., New
York, 1971.
59. C..F. Jatczak, ''Product Method for the
Determination of Retained Austenite." Report
No. 9321, The Timken Company, 1966.
60. C. F. Jatczak, "Precision of X-Ray
Retained Austenite Measurements -" Report No.
172R, The Timken Company, 1970.
61. C. Kim, "X-Ray Method of Measuring
Retained Austenite in White Cast Iron."
AM Foundry Soc., 1978.
62. W. B. Pearson, "Handbook of Lattice
Spacings and Structure of Metals and Alloys."
Pergamon Press, N. Y., 1967.
63. R. Lindgren, "On the Accuracy of X-Ray
Retained Austenite Measurements," Metal Progress,
April, 1965/
64. R. A. Armstrong, "Some Developments in
the Analysis of Retained Austenite by X-Ray
Diffraction." Report No. SR75-86, Scientific
Research Lab., Ford Motor Company, 1975.
65. Minutes of X-Ray Division Meeting,
Rackaam Building, Detroit, Michigan, Aprl 23,
1964,
66. D. A- Pearson, "Summary of Techniques
and Procedures for Retained Austenite Determinations by X-Ray Diffraction." X-Ray Subcommittee
Meeting Report, April 28-29, 1965.
67. W, J. Youden, "Graphical Diagnosis of
Interlaboratory Test Results." Industrial
Quality Control, May, 1959.
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11
Table 1 - Retained Austenite in As Quenched Cold
Work Tool Steels
(% - X-Ray Retained Austenite-)
A10
D2
13.0
20. 0
~
—
—
26. 0
--
--
21.0
22.0
15.0
34. 0
--
25.5
25.0
--
27.5
18.0
45. 0
--
32.0
29.0
6..0
36.5
22.0
58..0
—
—
—
—
49.0
27.0
68..0
—
—
37.0
JO
70.0
—
74..0
20.0
28..0
--
—
77..0
23.0
45-0
37..0
—
--
—
26.0
—
48..0
—
79..0
37.0
—
--
50.0
—
60.0
—
72.0
Temp. , °F (C)
F2
01
06
A2
A4
1400 (760)
—
9.5
—
--
1450 (788)
1570
14.5
16.0
1500 (816)
19.5
17.0
1550 (843)
27.5
1600 (871)
—
1650 (899)
1700 (927)
—
1750 (954)
—
1800 (982)
—
1850 (1010)
1900 (1038)
—
--
--
65 .0
1950 •(1066)
__
—
—
73 .0
--
—
2000 (1093)
A6
--
-R.A. measured by x-ray intensity comparisons of (200)M and (220)A peaks
corrected for carbide content. A2 and D2 data from Zmeskal et al. (19)
confirmed by author
Bands denote recommended hardening range
Table 2 - Retained Austenite and Hardness in Cold Work Die
Steels After Tempering (2 Hours)
A.
X-Ray Retained Austeni.te__2_%
Tempering
Temp., °F, (C)
52100
1500°F*
01
1500°F
06
1475°F
A2
1750°F
A4
1550°F
A6
1575°F
A10
1475°F
D2
1825°F
As Quenched
300 (149)
400 (204)
500 (260)
600 (316)
700 (371)
800 (427)
900 (482)
1000 (538)
1100 (593)-
13.0
18. 0
15. 5
11. 5
3. 0
0
17..5
16..5
10.• 5
""3 •
.0
.0
28..0
28..0
28!.0
20..0
13..5
22.. 5
17..0
5..5
2.J>
26.5
26.5
16.5
3.0
.0
20.0
20.0
14.0
30.
27..5
26..0
23..0
22..0
21..5
9..0
.0
.0
•A
31..0
27..0
25. 5
24..5
27..0
26..0
26..5
23..0
__3.J>
66..0
63..5
61..0
59..5
58..5
58,.0
57.• 5
58.. 5
57..5
65.0
62.0
59.5
58.0
56.5
64..0
62..0
59..0
58..5
56.• 5
55.. 5
53..0
52..5
47..5
65.. 5
63..0
61..0
59.. 5
59..0
59..0
59..5
60..5
59..0
B.
lT.
5"
7.5
.0
.0
_
"Z. 6
.0
M50
2040°F
M2
2250°F
_.
23.0
----
--
10. 0
8. 0
6. 0
3. 0
3.J>
-20.0
10.0
3.0
2.0
Hardness, Rockwell "C"
As Quenched
300 (149)
400 (204)
500 (260)
600 (316)
700 (371)
800 (427)
900 (482)
1000 (538)
1100 (593)
67.0
64.0
63.0
62.0
60.0
57.0
65. 0
63. 5
61. 0
59. 0
57. 0
"Hardening temperature
Bands denote usual tempering ranges
66,.0
63.. 5
61..5
6 1 . .0
60..0
56..0
65.0
60.5
58.5
56.5
55 .5
_„
65.0
„.
--
56. 0
58. 0
60. 0
60. 0
55. 0
--61.0
64.0
65.0
64.0
Downloaded from SAE International by University of New South Wales, Monday, August 27, 2018
12
o
Chromium R a d i a t i o n
Cubic
J
-
2.29092 A
Fe
°
1.31
JL
LP
e
o
0.2 C
15.4
948
12
4.29
0.956
2.872
IS.3
936
8
4.25
0.956
2.854
590
15.5
951
4
4,47
0.957
2.983
590
12.5
625
6
2.80
0.913
-2
12.4
615
4
2.82
0.913
2.854
590
-2
12.8
655
2
2.73
0.920
2,983
590
12.9
-2
10.9
475
24
9,06
0.875
a
26
\
lis
2.027
68.80
0.246
17.4
-2
11 OM
2.018
69.17
0.248
17.3
-2
101M
2.062
67.18
0.242
17.5
-2
J .433
106.00
0.34!!
14.5
-2
20QM
5,427
106.78
0.350
14.4
. 0O2M
1.491
100.35
0.335
14.8
1.171
155.60
0.426
110M
200M
2
iff!
d
hkl
k
(f-4f)
Sin 0
Tetragonal
1.0 C
v
0.2 C
ULC
27.6
50.7
5.6
1.173
154.92
0.426
12.9
-2
10.9
475
16
8.80
0.874
2.854
590
99.1
1.199
145.43
0.417
13.0
-2
11.0
484
8
6.20
0.879
2.983
590
35.8
2.078
66.90
0.241
17.5
-1
15.5
3844
8
4.55
0.960
20OA
1.799
220A
5.272
Cobalt R a d i a t i o n
A
79.10
128.40
0.278
0.393
16.3
13.5
o
=
-2
-2
=,
1.7902!A
14.3
11.5
3271
2116
6
12
3.31
3.96
0.944
0.900
3.564
16.3
161.1
561
112M
3.564
79.2
17.1
211M
111A
R
l.OC
I
55.6
561
2.872
R
5.0 C
83.2
561
2.872
R
0.2 C
3.599
2049
2173
65.0
3.599
2049
2173
29.9
28.2
44.5
41.6
R
H
1.0 C
3.564
3.599
2049
2173
o
o
l.OC
V
0.2 C
1.0
134.9
61.3
1 .026
a
Cubic
hkl
Tetragonal
Sin o
26
hkl
no
1Q1M
?0OM
\
lis
m
Af
-2M
JL
c
LP
e
0.2 C
2.872
2
v
2
c
OAS
2.027
52.40
0.246
17.4
-4
13.4
718
12
7.85
0.956
2.018
53.66
0.248
17.3
-4
13.3
708
8
7.76
0.956
2.854
590
71.2
2.062
51.45
0.242
17.5
-4
13.5
729
4
8.18
0.957
2.983
590
38,7
1.433
77.30
0.348
14.5
-4
10.5
441
6
3.45
0.913
115.3
561
2.872
1.427
77.70
0.350
14.4
-4
10.4
433
4
3.41
' 0.913
2.354
590
002M
1.491
73.76
0.335
14.8
-4
10.8
467
2
3.74
0.920
2.983
590
1.171
99.60
0.426
12.9
-4
8.9
317
24
2.73
0.875
211H
1.173
99.42
0.426
12.9
-4
8.9
317
16
2.72
0.874
2.854
590
mw
1.199
96.53
0.417
13.0
-4
9.0
324
y
2.73
0.879
2.983
590
1.011
123.90
0.493
11.7
-4
7.7
237
12
3.58
0.850
22GM
1.009
125.02
0.495
11.7
-4
7.7
237
8.
3.66
0.834
2.854
590
202M
1.031
120.48
0.485
11.8
-4
7.8
243
4
3.36
0.840
2.983
590
0.906
162,20
0.552
10.9
-4
6.9
190
12
12.63
0.803
31 OM
0.902
165.31
0.554
!0.8
-4
6.8
185
4
15.39
0.797
2.854
590
103M
0.939
144,83
0.532
11.1
-4
7.1
202
4
6.08
0.811
2.983
590
6.8
301M
0.906
161.92
0.552
TO. 9
-4
6.9
190
4
52.43
0.793
2.854
590
12.8
220M
31 OM
2.872
56!
2.872
9.1
5.4
14.5
32.4
565
2.872
109.9
14.8
561
ZOOM
tim
i; R
l.OC
20,4
10.5
30.9
15.4
561
9.8
4.6
14.4
41.2
15.4
1!1A
2.078
51.00
0.241
17.5
-4
13.5
2916
8
8.27
0.960
3.564
3.599
20*19
2173
90.4
85.2
200A
1.799
59.60
0.278
16.3
-4
12.3
2421
6
5.86
0.944
3.564
3.599
2049
2173
39.2
37.0
220A
1.272
89.40
0.393
13.5
-4
9.5
1444
12
2.84
0.900
3.564
3.599
2049
2173
21.6
20.4
311A
1.085
111.20
0.463
12.2
~4
8.2
1076
24
2.96
0.855
3.564
3.599
2049
2173
31.9
30.1
222A
1.039
119.00
G.'481
11.9
-4
7.9
999
8
3.28
0.850
3.564
3,599
2049
2173
10.9
10.3
35.0
Downloaded from SAE International by University of New South Wales, Monday, August 27, 2018
13
Tfeble 3 (Continued) - Calculation of Theoretical Line Intensities (R-Values)
for the Martensite and Austenite Phases in Steel Using Cr, Co,
Cu and Mo Hadlation
o
C.
Copper R a d i a t i o n
Cubic
a
=
1.54178 A
Tetragonal
x
Ci/ Fe
Sin e
__i
J
=
-2M
11.3!
0.956
2.872
0.956
2.854
590
11.72
0.957
2.983
590
6
4.84
0.913
666
4
4.77
0.913
2.854
590
708
2
5.32
0.920
2.983
590
520
24
3.13
0.875
13.4
520
36
3.33
0.874
2.854
590
11.5
529
8
3.25
0.879
2.983
590
416
32
2.73
0.850
17.4
-1.5
15.9
101!
12
17.3
-1.5
15.8
999
8
0.242
17.5
-1.5
16.0
1024
4
65.00
0.348
14.5
-1.5
13.0
676
1.427
65.40
0.335
14.4
-1.5
12.9
1.491
62.24
0.335
14.8
-1.5
13.3
1.171
82.20
0.426
12.9
-1.5
11.4
211H
1.173
82.13
0.426
52.9
-1.5
112M
3.199
79.99
0.41J
13.0
-1,5
1.014
98.90
0.493
11.7
-1.5
10.2
44.60
2.018
44.91
101K
2.062
43.90
1.433
ZOOM
002M
20GM
21 IK
220M
,2
11.13
0.246
0.248
2.027
11CM
HOM
2
0.2 C
o
0.2 C
flf
...iL.
'I
G_
Us,
20
ItkZ
LP
M l
a
V
1.0 C
1.009
99.63
0.495
11.7
-1.5
10.2
416
8
2.73
0.334
2.854
590
202M
1.031
96.77
0.485
13.8
-1.5
10.3
412
4
2.73
0.840
2.983
590
0.906
116.60
0.552
10.9
-1.5
9.4
353
12
3.16
0.803
2.872
561
3iOM
0.90?
117.33
0.554
30.8
-1.5
9.3
346
4
3.19
0.797
2.854
10311
0.811
110.37
0.532
11.1
-1.5
9.6
369
/"
2.91
0.811
2.983
301M
0. 798
116.54
0.552
10.9
-1.5
9.4
353
4
3.15
0.798
0.827
137.40
0.604
10.1
-1.5
8.6
296
8
4.89
0.780
0.835
3 31.56
0.598
10.2
-1.5
8.7
303
8
4.54
0.767
•
19.7
11.7
20.5
6.4
6.0
590
5.9
590
6.0
34.3
43.60
0.243
17.5
-1.5
16.0
4096
8
13.93
0.960
3.564
3.599
2049
2173
182.8
172.4
1.799
50.80
0.278
16.3
-1.5
34.8
3505
6
8.42
0.944
3.564
3.599
2049
2173
81-6
76.9
2?m
1.
m
74.60
0.393
13.5
-1.5
32.0
2304
12
3.66
0.900
311A
1.085
90.60
0.463
12,2
-1.5
10.7
1832
24
2.80
0.855
"
44.4
41.9
51.3
48.4
14.8
222A
1.039
96.0
0.481
13.9
-1.5
10.4
1731
8
2.74
0.85O
15.7
400A
0.899
117.9
0.556
10.8
-1.5
9. i
1384
6
3.22
0.800
10.4
9.8
331A
0.825
137.9
0.606
10. 1 -1.5
8.6
1183
24
4.99
0. 7 78
53,3
50.7
420A
0.805
146.5
0.621
9.9
8.4
1129
24
6.89
0. 762
69.5
65.5
0.71069 P
W
FQ
=
-1.5
0.407
a
Cubic
Tetragonal
....
. A.
o
o
1-0 C
c
Us.
Af
(f-Af)
ILL.
-L
..kt.... e
0.2 C
2.872
V
2
his
2
V
2-027
20.20
0.24'fi
17.4
+0.3
17.7
3253
12
62.12
0.956
2.030
20.28
0.248
37.3
+0.3
17.6
3 239
8
63.59
0.956
2.854
590
101M
2.062
19.84
0.242
17.5
+0.3
17.8
3 267
4
64.44
0.957
2.983
590
1.^33
28.70
(5.348
14.5
+0. 3
14.3
876
6
29.96
0.933
2G0M
561
2.872
561
1 .'12 7
28.84
0.350
14.4
+0.3
14.7
864
4
29.43
0.913
2.854
590
1.491
27.57
0.335
14.3
+0.3
15.1
912
2
32.39
0.920
2.983
590 .
7.171
35. 30
0.426
12.9
'0.3
13.2
697
24
19.14
0.875
529.7
157.4
92.1
1.1/3
36.25
0.426
12.9
'0. 3
13.2
697
16
19.07
0.874
2.854
590
112H
1.199
34.47
0.417
13.0
'0. 3
13. 1
708
8
20.04
0.879
2.983
590
1.014
41.20
0.493
31.7
'0-3
12.0
576
12
13.5?
0.850
220M
1.009
43.24
0.495
13.7
+0-3
12.0
576
8
13.49
0.834
2.854
590
2G2M
1.031
40.32
0.485
11.8
+0.3
12.1
586
4
14.18
0.840
2.983
590
0-906
46.20
0.552
10.9
+0. 3
11.2
502
12
30.55
0.803
310M
0.902
46.37
0.554
10.8
+0.3
11.1
493
4
10.36
0.797
2.854
590
27.6
3 03H
0.939
44.47
0.532
11.1
+0.3
3 1.4
520
4
11.38
0.811
2.983
590
32.5
30 HI
0.906
46.17
0.552
10,9
+0.3
11.2
502
4
30.46
0. 798
2.854
590
0.(327
50.80
0.604
10.1
'0.3
10.4
432
8
8.42
0.780
0.836
50.32
0.598
10.2
+0. 3
10.5
441
8
8.60
0.767
0. 767
55.40
0.654
9.5
+0.3
9.8
384
48
6.9!
0. 750
32 I H
0.765
55.35
0.653
9.5
+ 0.3
9.8
384
36
6.92
0.729
2.854
590
52.5
213M
0.784
53.87
0.637
9.7
+0. 3
10.0
400
16
7.36
0.637
2.983
590
50.9
132M
0.772
54,80
0.647
9.6
+ 0.3
9.9
392
16
7.08
0.733
2.864
590
0.677
63.60
0. 741
8.5
+0.3
3,8
310
24
5.07
0.690
411M
0.674
63.61
0.74!
8.5
'0.3
8.8
310
16
5.07
0.666
2.854
590
28.4
114H
0.699
61.06
0.715
8.7
+0.3
9.0
324
8
5.55
0.685
2.983
590
16.7
2.078
1. 799
1.272
1.086
1.039
0.899
0.826
0.805
0.735
19.80
22.80
32.40
38.2
39.91
46.46
51.0
52.40
57.80
0.24!
0.278
0.393
0.463
0.48!
0.556
0.606
0.624
0.680
17 5
16 3
13 5
12 2
11 9
10 8
10 1
9 9
9 2
+0.3
+0.3
+0.3
+0.3
+0.3
+0,3
+0.3
+0.3
+0.3
17 8
16 6
13 8
12 5
12 2
11 1
10 4
10
9 5
5069
4409
3047
2500
2381
1971
1730
1665
1444
8
6
12
24
8
6
24
24
24
66 12
48 30
22 92
15 80
11 52
10 32
8 34
7 78
6 97
0.960
0.944
0.900
0.856
0.850
0.800
0.778
0.762
0.750
31 OH
nm
zzm
4n«
2
561
2.872
561
2.896
2 872
3.564
"
590
169.1
2049
484.5
87.9
47.3
135.2
28.4
88.5
39.4
39.4
40.5
590
170.3
561
3.599
"
315.4
91.0
561
2.872
249-5
141.6
561
2.872
1519
499.4
561
2.872
R
989.2
211M
zzm
I
256.3
200M
2.872
R
U>.£
1592
002M
211M
R
L_Q_c
11OM
1 tOM
U1A
2G0A
220A
311A
222A
400A
331A
420A
42 2A
S_i_n v
17.9
590
2.078
=
19.2
16.1
ma
•
59.1
12.8
200A
Molybdenum R a d i a t i o n
31.4
38.6
590
561
2.896
222.0
19.2
.
2.854
2.872
77.9
20.6
561
220M
3! OH
144.1
60.9
561
2.872
E R
1.0C
31.9
56!
2.872
R
3.Q C
233.8
561
2.872
R
0.2 C
55.2
358.6
46.4
2173
1256 1
588 9
368 1
395 6
114 7
47 6
131 5
115 6
88 4
1184.5
655.1
347.1
373.0
108.2
44.9
124.0
109.0
83.4
45.1
Downloaded from SAE International by University of New South Wales, Monday, August 27, 2018
14
Table 4 - Sample Calculation of R-Factor for Austenite (200)
Line in 8620 Steel, Cr Radiation
Equation:
R
[ jFFJ
= -j-
A f 2 0 0 )
p • LP] e ~
2 M
20 = 79.40° for (200)A line, measured from diffraction pattern.
Volume of Unit Cell"
v
=
(a )
= 2048.739 (Example 1)
= 2173.157 (Example 2)
where a = 3.555 + 0.044x
x = weight percent carbon
= 0.20% for Example 1
= 1.00% for Example 2
Atomic Scattering Factors for Alloyed AISI 8620"
sin 0/A = .278 for CrKa
Element
Wt. %
Element
f + Af
F = Structure Factor = 4(f - Af) - 4 f
•
2
Multiplicity Factor
e
p = 6
-2(0.37 (siaSA)
-
0
*From Cullity (48)
""Ratio ACr/AMn, etc. used to establish
anomalous scattering correction - Af
sin 0 cos 0
Results:
Example 1 - R( 00)A = 30.03 for austenite of 0.20% C
2
=
2
8
,
2
^
=
Lorentz-Polarization Factor
TP
2
1.208
1.540
1.107
3.696
1.314
.109
.090
.062
.055
14.007
14.323
i + cos^je
Example 2 - R( 00)A
A/Xk**
Temperature Factor - e
IFF! = 16f' = 16 (14.323) = 3282
2
(Wt. Frac.)
(f )
f*
(-2.1) = 13,,60
( - 1 . 7 ) = 16.,30
(-2.7) = 12.,30
(-1.3) = 27..50
(-2.0) = 14..30
15..70
18..00
15..00 +
28.,80
16..30 +
Mn
.80
Ni
.55
Cr
.50
Mo
.20
Fe
97.95
f (Weighted-Sum)
=
3
f
°
r
a
u
s
t
e
n
i
t
e
o
f
l
-°^>
C
=
3
_
3 1 0
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Table 5 - Typical 20 Scanning Ranges
for the Various Radiations
Chrome Radiation
Molybdenum_Radiation
Peak
From
To
Width
Peak
From
To
Width
200A
200M
220A
76°
97°
123°
82°
113°
135°
6°
16°
12°
220A
211M
311A
31°
33.5°
37.0°
33.5°
37.0°
39-0°
2.5°
3-5°
2.0°
Co£per Radiation
Cobalt Radiation
Peak
From
To
Width
Peak
From
To
200A
200M
220A
58°
72°
87°
86°
93°
92°
108°
62°
81°
93°
92°
105°
104°
115°
4°
9°
6°
220A
211M
311A
72°
79°
88°
76°
85°
92°
211M
311A
Width
4°
6°
'
12°
7
o
Table 6 - Example X-Ray Retained Austenite Measurements Using the
Electronic Integration and Chart Methods to Establish Intensities
(% Austenite Calculated with Equations 5 and 7)
A.
Electronic Integration Technique
Operating Conditions:
CrKa radiation with .0015" V-filter
40 kV, 28 mA, 3°/0.5° slit combination
scan rate, 4°/min., proportional detector
26 scan ranges: 200A
74/82°
200M
97/113°
220A
121/137°
Integrated Intensity for
Indicated Peak, Total Counts
Calculated % Austenite
Specimen
Number
200A
200M
220A
200A+220A
P.O.*
200M
200A
200M
220A
200M
200A+220A
1
2
3
4
78,700
10,440
23,080
9,679
81,240
100,540
99,010
86,149
93,740
17,330
34,900
13,842
172,440
27,770
57,980
23,521
1..2
1..7
1..5
1..4
35.,9
5..7
11..9
6., 1
32..3
6..6
12..7
6.,2
33..9
6..2
12..4
6..2
B.
Chart Technique - using product method (peak height times peak width at half
height) to measure integrated intensity
Operating Conditions:
CrKa with .0015" V-filter
40 kV, 28 mA, 3°/0.2° slit combination
scan rate, 2°/min., proportional counter
^
chart speed, 2 cms/min., scale factor 1 x 10 cpm
time constant, 3 sec; statistical error, 1%
Specimen
Number
v
1
2
3
4
Integrated Intensity for
Indicated Peaks, Arbitrary Units
200A
200M
220A
200A+220A
108.4
29.4
64.1
31.2
104.9
271.9
258.9
267.8
112.2
37.6
81.0
49.9
220.6
67.0
145.1
81.1
*P.O. = ratio I220A/I200A
Calculated % Austenite
1.0
1.3
1.3
1.6
200M
200A
200M
220A
200M
200A+220A
37.5
5.9
12.5
6.3
30.7
5.4
11.5
7.2
33.7
5.6
11.9
6.7
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16
Fig. 1 - TTT diagram for Tl (18-4-1) high speed
steel austenitized at 1290C (2350°F). Note
influence of cold temperature on austenite
transformation (1)
Fig. 3 - Influence of Ms and Tq temperatures
on the volume of austenite retained at room
temperature in low alloy, high carbon and
carburized steels. (4) Band denotes range
to be expected in oil quenched bearing and
gear steels
70
60
I I
O
®
+•
A
I I
Rose and Hougardy
David B r o w n Gear Industries
Krotine et al.
Others
50
c
y
A
.40
ifjr 1
-
o
—i
f
'
60
70
130
x
£j o
• 20
<
10
1
10
10
2
10
3
I0
4
10-
10
20
30
40
50
% Retained austenite — measured
Cooling Time to 500 C (930 Fi, seconds
Fig. 2 - CCT diagram with related hardness and
microstructures for a 20 NiMoCr 6 steel carburized to 1.14%C - austenited at 930C (I706°F)
(8)
Fig. 4 - Correlation between measured and
calculated retained austenite contents using
equation listed in Fig. 3 (8)
Fig. 5 - Stabilization of retained austenite in
M2 high speed steel by interrupted quenching.
Specimens were quenched from 1217C (2225°F)
to indicated temperature, and directly
tempered at 565C (1050°F) for 2-1/2 hours (16)
Fig. 6 - Diffraction spectra for a randomly
oriented 52100 steel. Upper chart - made
with monochrontated Cu radiation. Lower chart an expanded trace made with Cr radiation
showing the three austenite and martensite
lines available for comparison of integrated
intensities
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18
<2ll)a
Fig. 9 - Example of line intensity measurement
by the product method (I x B ) (59)
allO
Fig. 10 - Example of line intensity measurement
by the electronic integration method (59)
Kill
Fig. 7 - Typical diffraction patterns for a
randomly oriented 52100 steel made with Mo
radiation. Upper chart shows peaks which are
ordinarily compared in R.A. measurements with
this radiation
'A- RAV DIFPEaC T MEl-KB
1.
ISCBEiWl 'IC)
9.
PiUor
10.
Geigor Countc
IX.
nonjonwtor True*
X-»ay Tube
2.
X~Eay Tube Window
4.
Priiaory Bfca
. Vertical Defining
12.
Strip Cliurt kccoidtr
H.
Tlraor
13.
Scalar Counting Unit
6.
Biffractotl Uoams
15.
Kilovolt Control
(KVP)
7.
Diffracted Bear HorlKontal Defining Slit
10.
Jiilliaran Control
{W
8.
sample Hounteti on Simple Holder
17.
Scatter Shield
a200
Fig, 8 - X-ray diffractometer setup and equipment used for retained austenite measurements
7220
a2U
y 3 1 1 ..x220
u 3 1 0 , Vi00
Fig. 11 - Diffraction patterns from three
mutually perpendicular faces (X, Y, and Z)
of a hardened white cast iron showing severe
preferred orientation, Mo radiation (61)
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19
(X)
(V)
0
1
I
<
1
11
30
ii
40
1
t
t
t
10
20
POINT
30
COUNT y
40
50
%
ft
y 3 H Y2'2> u220
Fig. <r200
12 - Same V220
materiala21l
run with
rotating and
tilting specimen stage. Note that all
austenite and martensite lines show about the
same intensities on all three faces, i.e. a
random response (61)
0
10
MAGNETIC
20
30
SUSCEPTIBILITY,
40
%
Fig. 13 - Comparison of retained austenite
measurements made by metallographic point
counting, magnetic susceptibility measurements
and the x-ray method (43)
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A
B - 20.6%
- 13.9%
3C * - ~
C - 27.0%
* -
ff- 35.0%
l
r
i. fj"
ft,
/
Fig. 14 - Chart for estimating retained austenite
in high carbon (1.0%) steels by optical metallography. Note x-ray measurements are used as
reference, 500x reduced by 1/2 (60)
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