ANALYSIS OF MATERIALS STRENGTH DATA FOR THE ASME BOILER AND PR;:SS';K VESSEL CODE · 2005. 5....
Transcript of ANALYSIS OF MATERIALS STRENGTH DATA FOR THE ASME BOILER AND PR;:SS';K VESSEL CODE · 2005. 5....
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ANALYSIS OF MATERIALS STRENGTH DATA FOR THEASME BOILER AND PR;:SS'";K VESSEL CODE
M. K. Booker
B.L.P. Booker
Mechanical Properties Data Analysis CenterOak Ridge National Laboratory*
Oak Ridge, Tennessee
ABSTRACT
Bv decant ,nco o ) , h l , J M l ( : l e , h e
Pulji.iho. or , e c , D , en , a c k n o » , m
cover,ng the j r , , , jL .
MAST!Tensile and creep data of the type used to establish
allowable stress levels for the ASME Boiler and PressureVessel Code have been examined for type 321H stainless steel.Both inhomogeneous, unbalanced data sets and well-plannedhomogeneous data sets have been exaained. Data have beenanalyzed by implementing standard "manual" techniques on amodern digital computer. In addition, more sophisticatedtechniques, practical only through the use of the computer,have been applied. The result clearly demonstrates theefficacy of computerized techniques for these types ofanalyses.
INTRODUCTION
The bo i le r and Pressure Vessel Code of the American Society of
Mechanical Engineers conta ins extensive guide l ines for the design of
components in various i n d u s t r i e s . One of the most important aspects of
these guidelines is the establishment of alienable design stresses for
the various materials listed in the code. Although the exact criteria
for setting allowable stresses vary from situation to situation (in
particular, elevated temperature nuclear criteria are more detailed),
the basic materials properties addressed include:
*Operated by Union Carbide Corporation for the U.S. Department ofEnergy under contract W-7405-eng-26.
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1. yield strength (0.2% offset),
2. ultimate tensile strength,
3. stress to produce a secondary creep rate of 0.01% per 1000 h,-
and
4. stress to produce rupture in 100,000 h.
In the most general case, both average and "minimum" properties are
of interest. A large number of data for many materials might be
involved in the above analyses. Variables of interest include
temperature, chemistry, grain size, product form, section size, heat
treatment, and others. In the past, most analyses have been performed
by primarily manual techniques. The results of these analyses have
generally been satisfactory, but the growing number of available data
makes such analyses more and more tedious for the analyst.
The sheer mass of available data increasingly suggests the use of
the modern digital computer for handling and analysis. Computerized
systems are now available to perform a full range of data storage,
retrieval, display, and analysis. The advantages of computerizing the
management of large sets of data are obvious. In terms of analysis,
computerization allows implementation of a variety of sophisticated
techniques with a maximum of ease and efficiency. This paper
illustrates the use of the computerized Mechanical Properties Data
Analysis Center (MIDAC) at Oak Ridge National Laboratory in analysis of
material strength data of the type used by the ASME Code. The data used
fcr illustration involve type 321H stainless steel, but similar
techniques would of course apply to other msierials as veil.
ANALYSIS OF TENSILE PROPERTIES
Data
The tensile data examined include a set supplied to MPDAC by the
Metal Properties Council (MPC)* and a set obtained from the Japanese
National Research Institute for Metals (NRIH).1 (The NRIM data are
referenced* as pertaining to type 321 stainless steel, but as far as can
be determined the material falls within specifications^ for type 321H.)
Methods
The method commonly used for evaluation of yield and tensile
strength data for ASME Code purposes involves Smith's "ratio"«
technique.•* Briefly, strength values for a given heat at elevated
temperatures are divided by the corresponding room temperature strength,
yielding a series of strength ratios as a function of temperature. This
method seeks to achieve two main goals. First, if the curves of log
strength vs temperature are parallel for different heats, then the data
for different heats will collapse onto a single strength ratio vs
temperature "trend curve." The existence of this trend curve both
simplifies the analysis and protects the results from various spurious
effects caused by inhomogeneous and incomplete data distributions.
Second, if the ratios for different heats do not collapse onto a single
*A11 data supplied by MPC were compiled under the direction tfW. E. Leyda of Babcock and Wilcox Company. There is no implication thatr.he data were generated in MPC ^sting programs or that MPC has endorsedthe accuracy and consistency of the data.
curve, then this lack of collapse may point up features of behavior that
were formerly hidden by data scatter. Of course, in no way does the
ratio technique decrease scatter in the data — that scatter is real and
must be dealt with.
Note that in the first case above the ratio trend curve represents
the behavior of strength ratios as a function of temperature for all
heats. In the second case there is no unique trend in the ratios, since
the trend will vary from heat to heat. In this case the best fit trend
curve seeks to represent average behavior among the available heats.
Thus, more data are required to define the trend curve in the second
case than in the first. In either case data scatter and other effects
will yield some variation in behavior about the mean trend curve.
Average values of strength as a function of temperature can be
defined by multiplying the average room temperature strength by the
ratio trend curve. Minimum values can be defined by multiplying the
specified room temperature minimum strength by the trend curved This
relationship between the specif:cation minimum and the minimum strength
used in setting allowable stresses is clearly desirable. However, it
should be noted that the resulting minimum strength curve lias no
statistical meaning. Also, due to the average nature of the trend
curve, there is a 50% chance that data for a heat just meeting the room
temperature specification strength will fall below the predicted
elevated temperature minimum strength. (There is also a chance that the
heat will no longer meet the room temperature minimum upon retest.)
The ratio technique was developed for use with existing manual
analysis methods, but i t can easily be implemented by computer, saving
considerable time and labor. Results are illustrated below. The
historical success of ".he ratio technique indicates that its basic
premise is sound. Probably the major fault of the technique is i ts
heavy reliance on the accuracy of available data at room temperature.
(In most analyses done at MPDAC, we have found that room temperature
data exhibit at least as much scatter as corresponding elevated
.temperature data.-)- Thus,—the question arises: can modern computer
techniques produce an analysis method that uses assumptions identical to
the ratio technique but utilizes all data for normalization, not just
room temperature data? The answer is yes.
Yield and tensile strength are often expressed as simple
polynomial functions of temperature:
1 • j y •where
S - the predicted yield or tensile strength,
T = temperature, and
u = constants whose values are estimated by regression or other
techniques.
In essence, che ratio technique involves an implicit' assumption that
different heats display parallel curves of log strength vs
temperature.''* As a f i rs t step toward implementing this assumption in a
direct data f i t , Eq. (1) can be rewritten as
log 5 = I b'/r1 . (2)
This equation is not equivalent to Eq. (1) but would be expected to
describe the data equally as well.
Next, one employs a technique of centering the data for each heat
as has been reported for creep data by Sjodahl.-* The equation thus
becomes
l 5N
log 5W - log Sh = ] i r [ ^ - 2j] , (3)
•where the barred symbols represent average values of each variable for
each heat. The index ^ again refers to the power of temperature, J
refers to the particular test, and a refers to the particular heat.
Equation (3) can be arranged as
N _. N ~r
J -t=l j i—1
or as
/ \ N —7 N .
log S = (log 5, - ib.Tb + lb,Th, . (5)h
Note that the terra in parenthesis is a constant ( ^ ) for a given heat.
The other tern on the right side of the equation is a function of
temperature but not of heat. Thus, a fit of Eq. (3) to the available
data will yield predictions for the different heats that are parallel in
log S vs T but that have different intercept values. These intercept
values are determined by a regression fit to all data, not merely by the
room temperature strength asff in ratio technique. In fact, heats for
which no room temperature data at all are available can be included in
the heat-centered analysis. Such heats would, of course, have to be
excluded from the ratio analysis. Note that since each heat has its own
intercept, no explicit intercept term is required in the model in Eq. (3).
If the assumption of log S— T parellelism is not met, plots of
strength ratio vs temperature tend to emphasize effects which cause the
lack of parallelism. Likewise, residual plots of (log S— log S) vs T
from the above regression technique will point up such effects (S is the
observed strength, S is the predicted strength). The regression tech-
nique can be used to determine a statistically defined average or mini-
mum curve (see Appendix), or these predictions can be keyed to room tem-
perature values as in the ratio technique. Thus, the technique pre-
sented here includes all the advantages of the ratio technique but
avoids its major disadvantages. This technique is, however, suited only
to computer analysis — not to manual analysis.
Results
Data for yield strength and ultimate tensile strength from the two
available data sets were analyzed both by the ratio technique and by the
technique of heat-centered regression analysis. The ratio technique was
lmpleraeated by fitting the ratio data as a function of temperature using
the form
Ratio = 1 + ax{T-To) + a2(f-Tj)2 + a 3 ( M ) 3 ( 6 )
where a\, a-^t and a-^ are least-squares regression constants, and?" is
room temperature. This equation form assures that the various strength
ratios will be unity at room temperature, as desired.
The heat-centered regression was performed based on models of the
form
log 5 = Ck + at T + a2 T1 + a2 T
3 (7)
except for the NRIM data for yield strength, o , which were described by
log a = Ch+ ax T . (8)
The C, values are the heat constants for the equations (see above and
Appendix). Constants for the individual heats and average heat
constants for each equation are piven in Table 1. Table 2 l i s t s the
between-heat, within-heat, and total variances determined for these
equations.
Figure 1 displays the results obtained for the various data sets
using the ratio technique, while Fig. 2 shows the results obtained with
the heat-centered regression technique. In both Figs. 1 and 2,
"minimum" behavior has been calculated by normalizing the appropriate
trend curve to the room temperature specified minimum strength (207 HPa
for yield strength, 517 MPa for ultimate tensile strength).
In Fig. 3, "minimum" predictions are made with the heat-centered
regression technique by the quasi-statistical procedure of subtracting
two standard errors in log strength from the predicted log average.
(The standard error is the square root of the total variance.) Finally,
Figs. 4 and 5 compare predictions from the two methods with data on an
individual heat basis. The ratio technique, being rigidly tied to the
roon temperature data, cannot in general describe the higher temperature
data as well as can the heat-centered regression technique.
Tables 3 and 4 compare results from the two techniques for the
present data. Also shown are results derived by Smith" from a data base
that presumably was similar to the MPC data, although i t included both
321 and 321H material. Since all data are involved in determining the
strength level (heat constant) for each heat, the heat-centered
regression fits the data for each individual heat better than does the
ratio technique. In terms of average predictions, the two methods yield
generally similar results. The exception occurs for the MPC yield
strength data, where the unusual behavior of heat 41 causes the ratio
technique to predict unrealistic trends. The heat-centered regression
technique does predict realistic trends, similar to those predicted by
Smith. (Smith used the ratio technique, but several data were omitted
from the analysis to force realistic predictions.)
Predicted minimum values based on the room temperature minimum
strength are also generally similar for the two methods, again with the
exception of the MPC yield strength data. Also, a l l yield strength
minima predicted by this technique are unconservative for these data
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because many of the data do not aect the specification. Minima
determined by average ninus two standard errors (an empirical approach
based on MPDAC experience) describe the data better in general than the
specification-based minima. For the URIl-l ultimate tensile strength data
predictions from both techniques are similar.
In summary, the heat-centered regression analysis yields a clearly
superior description of individual heat behavior. For well-balanced
multi-heat data sets the techniques yield similar predicted trends. For
sparse, ill-conditioned data the regression technique appears to be less
affected by "quirks" in the data and therefore describes the data
better. The ability of the regression technique to yield minimum
predictions based on the data rather than on specification also has
advantages in data description. The ratio technique was formulated
specifically to allow treatment of sparse data sets and minima
prediction, yet the regression technique is superior to the ratio
approach on both of these counts. The advantages of the regression
method are therefore obvious, both on a theoretical basis and on the
basis of application to real data. A more complete discussion of these
results can be found in Ref. 4.
ANALYSIS OF CREEP PROPERTIES
Data
Only data for rupture life will be examined in this paper, but
similar methods can be used for the description of minimum creep rate
data if they are available. Again, both data from US sources (supplied
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by MPC) and data from the Japanese NRIM (obtained, as were the tensile
data, from the MPDAC computer files) were used.
The original 191 MPC rupture data (several were later excluded from
the analysis) represented 66 heats of material, with the majority of the
heats having seen only one or two tests each. Of these 191 tests, 161
were conducted at a temperature of b4y°C (1200°F), with the remaining
data scattered over the range 593-816UC (1100-1500°F) in temperature.
Thus, it can be seen that these data represent an extreme example of the
data distribution problems often encountered in Code analyses. The
available data were not generated as part of a comprehensive program
designed to develop a well-balanced data base for analysis. Rather, the
data probably represent an historical collection of tests conducted in
several unrelated programs with different goals in mind. These data
should therefore present a severe test of any analytical method.
By way of contrast, the NRIM data represent a very well-planned,
systematic, well-balanced set of tests that is ideally suited to the
types of analyses involved in setting allowable stresses. The two data
sets examined thus repi^sent opposite ends of the spectrum of that would
be encountered in such analyses.
Methods
Methods commonly used for evaluation of creep rupture and minimum
creep rate data for ASME Code purposes are discussed in Ref. 3. The
methods historically used fall into two basic categories: (1) direct
extrapolation of isothermal log a—log t curves, and (2) analysis by
standard iiMc-tonper;itutv par i:~.i.-tor '•. The d i rec t ex t rapo la t ion '••:•
comnio;ily In no on -in Individual lot has i.: , v i th thy l'j -h rupture
strength values fro:n t h" individual lots l a t e r used to e s t a b l i s h a
s t rength trend curve vs r er-'porature. The parametric an.ily-~.is is
typ ica l ly done nsin,", .ill data .is a single population, if only h-jc.iu.se
there .ire seldom suf f ic ien t data to perfurn such -in ana lys is uri em :i lot
s epa ra t e ly .
The d i r ec t isothermal ext rapola t ion approach can be implemented
a n a l y t i c a l l y but has usual ly been performed via n manual extrapol. i t ion
on log-log paper. This technique d i r e c t l y addresses the problem of
l o t - t o - l o t var ia t ions and is in that sense coi::mendable. I t s
shortcomings include the following:
(1) The graphical ex t rapola t ion can require considerable judgement
on the part of the a n a l y s t .
(2) Uncer ta int ies are great ly increased if the log O— log t
isotherms are nonlinear . Conversely, assumption of such l i n e a r i t y may
sometimes be 4**rrt5 erroneous-by, introducing addi t iona l e r r o r s on
ex t r apo la t ion .
(3) Since only data at one temperature are t reated at any time,
i n f o r m t i o n froui other temperatures is ignored. Moreover, if data for a
given lo t are not su f f i c i en t to determine a given isotherm, Lhcse data
must be ignored. Thus, the method does not make e f f i c i en t n.-.e of the
ava i lab le information.
(4) Data at d i f f e ren t temperatures may represent d i f f e r e n t l o t s .
Thus, what nay appear to be a temperature e f fec t may l a r g e l y be an
effect of differences between l o t s .
The parametric approach h;is tho advantage of treating all data
together. However, that method also involves sever '1 Inherent
disadvantages.
(1) The problem of lot-to-lnt variations is not directly
addressed. Ignoring this significant effect may result in large errors.
For example, a few points tor unusually strong or weak heats can
significantly distort the shape of the best fit curve.
(2) Any given parameter involves very specific and rigid
assumptions about behavior. If the wrong parameter is used (i.e., if
the assumptions are not met), the results may contain significant
errors.
(3) Literally hundreds of parameter forms are available. Choice
of the correct parameter can be a formidable task..
(A) Available data are often dominated by tests run at a single
temperature (as in the current MPC data). In these cases it may be very
difficult to accurately determine temperature dependence by standard
parametric techniques.
Several recent advances'>° in the use of computerized analytical
techniques for the treatment of creep and creep rupture d-ita have
. brought new hrpe that previously insoluble problems such as those
mentioned above might be conqueied. The power of the modern digital
computer ha? made possible the achievement of new strides in the
treatment of lot-to-lot variations, selection of model forms, and
statistical analysis of results. It is to be hoped that any methods
springing forth from this new technology wuuld be iubued with a wide
range of advantages, including those listed below.
(1) Ability to treat the quest. Ci, ,.f lo t - to- lo t variations as an
Integral part of the analysis;
(2) Sufficient f lexibil i ty to al! r.-.; f i t t ing a wide range of
behavior, such as by automatic consideration of a -ide variety of
models;
(3) Ability to establish a s t a t i s t i ca l ly viable estimate of
average and minimum behavior;
(4) Minimized vulnerability to "bad" data dis t r ibut ions , such as
concentration of the data over a narrow temperature range or
avai labi l i ty of only a few data for each of several lo t s ; and
(5) Ease of applicabili ty ar.d minimization of manual labor
involved in producing resul ts , especially for large data se ts .
"Computerized" techniques otjfer a wide range of possible
approaches. This report presents results obtained using an approach
which was felt to be adequately suited to the data at hand. Other
approaches are certainly possible, and in fact the current analysis
represents the f i r s t time this particular approach was ^sed at MPDAC.
Similar techniques have since been used successfully for several other
data se ts , however. Thus, experience has been gained through implemen-
tation of the analysis in a variety of s i tuat ions. The method is essen-
t i a l l y a synthesis of those previously used by Sjodahl^ and by
Booker,' and in that sense the authors feel that i t represents a step
forward in the technology of such analyses.
The heart of the current method involves the use of "heat-centered'
data as proposed by Sjodahl.-* This method provides the maximum
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protection against poorly Ji.-.iribuied data bases, and it.:; use here was
actuated by the particularly "ncssy" distribution of the data supplied
by MPC. However, it will be seen that the method is also .advantageous
for the well-distributed NRIM data.
First assume that the loftarithn of rupture life (lop, t )* has been
i V3-en as the dependent variable for the analysis. Label log tt as y.
Now assune that Y can be expressed as a linear function (in the
regression sense) of tern? involving stress (a) and temperature (?').
Label these terms as A'. . In general form we thus have
where the c's are constants estimated by regression, and ^ is the
predicted value of log rupture life at the Xth level of the independent
or predictor variables, X.-, • Note that X is always unity and that a
is a constant intercept term.
As the next step, each variable (}' and all X's) is "heat centered,
and the equation becomes
*The debate that has sometimes arisen over this choice is notcentral to the results obtained and will not be discussed here.References 5, 7, 8, and 9 address the subject. The authors frankly donot feel there is any legitimate question over the choice of dependentvariable.
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where the bar rod variables represent average values for a given lot and
h represents the Lndex of the lot involved. The prediction of log
rupture life itself will then be given by
:/ _ :VY.- = y. - 7 a'X.. . [ a'.X..,. . ( 1 1 )
t r — -L L- J.
NThe term 1\ — £ a'X., is a constant for a given heat and replaces
the intercept term a in the uncentered analysis. Thus, each heat will
have a different intercept terra, but all other coefficients £„• will be
common to all heats. (Ti-.ere is no separate a' term, since it would be
superfluous,)
Heat centering of the data involves no complicated mathematics and
can be done by anyone who can add, subtract, and divide. However, for
large data sets these simple operation?- can become quite tedious, and
Che centering is best done by computer. Implications of the
heat-centering are also straightforward, although a f irs t glance at
Eq. (11) can leave one lost in a maze of variables and subscripts.
As pointed out above, different lots are treated as having
different intercept values, but all other equation constants are
lot-dependent. Thus, al l heats vary in similar manner in the
independent variable, but any two heats will always be separated by a
constant increment in log t space. This assumption of parallelism may
or nay not be a good one in any given case. For both data sets examined
here the assumption was judged to be appropriate. Adjustments that
might be made to the method in the case of lack of parallelism were
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therefore not attempted. Such adjustments s t i l l need to be examined for
ocher data sets.
If any lot is represented by a single datum, nil heat-centered
variables will be zero, and that lot will not contribute to
establishment of stress and temperature dependence, although ic will
contribute to the calculation of average and minimum values as described
below. If all data for a given lot occur at a single temperature, all
pure temperature variables will be zero, and that lot will not
contribute to the estimation of temperature dependence. Thus, criteria
(1) and (4) above are already met — lot-to-lot variation is addressed
directly and vulnerability of the method to "bad" data distributions is
minimized.
Use of heat-centered models to predict average, and minimum behavior
is described in detail in the Appendix. Suffice i t to say here that the
method certainly presents an estimate of the average far superior in
reliabili ty to that obtained from fitting the entire data base as a
single population without regard to lot-to-lot: variations. In its
ability to separate the within-heat and between-heat variances, the
method also offers superior possibilities for the estimation of minima.
Thus, c iterion (3) is met.
The selection of the particular model form to use in Eqs. (9—11)
can be performed exactly as previously described by Booker.^ Details of
the model selection procedure will not be repeated here except to
reemphasize the power and flexibility of the techniques involved.
Literally tens of thousands of potential models can be explored then
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reduced to a handful and finally to one with a ^inimun of tediun for the
analyst. Some judgement is s t i l l involved, but that is considered more
asset than l iabi l i ty. Any method relying strictly on computerized
calculations without the opportunity for appropriate human intervention
is dangerous at best. Criterion (2) above is well-satisfied.
The analyst makes several decisions along the way, but all actual
computations are performed by machine. The final result is a single
equation with perhaps three or four regression constants to describe a
data set such as that supplied here by MPC. Thus, the fifth and last
criterion mentioned above is met by this approach. S t i l l , the true test
of the method is in i ts actual application to the data, as described in
the next section.
Results
The current data were analyzed using five different approaches:
(1) graphical extrapolation of individual heat data (where possible);
(2) isother.al fitting procedures; (3) modeling of individual heat data;
(4) fitting of standard parameters to all data as a single population;
and (5) the above heat-centered regression and generalized n;ndel
selection procedure. Results from each approach will be presented and
then compared in this section.
Individual heat graphical extrapolation was not attempted for most
of the MPC data since most data were at a single temperature. Also,
most heats were represented by only two data, which the authors do not
consider sufficient to yield meaningful extrapolations. Graphical
results (in tercis of 10^-h rupture strengths) are presented for the NRIM
data and MPC Heat 41 in Table 5. Most log a—log t isotherms for these
data appeared to be curvilinear, and extrapolations were raade
accordingly. Such curvilinearity greatly increases the uncertainty in-
graphical extrapolations, but the current extrapolations are relatively
short due to the amount of long-term data available. The results in
Table 5 should therefore be fairly reliable although not exactly
reproducible.
Isothermal f i ts to the scatter band of available data were
performed for the NRIM data and for the MPC data at 649°C (1200°F). For
the NRIM data terras higher than linear in log ° were found to be
insignificant in these f i ts , although the data again show clear signs of
curvature on an individual heat basis. The MPC data were best fit by a
cubic stress dependence, similar to Eq. (12) below, but this equation
was ill-conditioned upon extrapolation. Thus, all of these isothermal
f i ts resulted in choice of linear log a—log t models even though such
behavior is inconsistent with the data. Table 6 gives 10^-h rupture
strengths estimated from this approach.
Individual heat data for all NRIM heats and for heat 41 of the MPC
data were fit both by standard parameters and by generalized model
selection procedures. It was discovered that the data for all heats
could be adequately represented by an equation of the form
log tp= aQ+ ajUog o)2 + ^( log 0)3 + Oj/T , (12)
where the <2's are coefficients determined by least squares for each
heat. Values of stress ( o) were expressed in MPa, time ( t,) in h, and
temperature (21) in K. Mote that Eq. (12) is a form of the common
Orr-Sherby-Dorn tine-temperature parameter.1"3 Predicted 105-h rupture
strengths from these fits are given in Table 7.
All MPC and all N'RIM data were separately analyzed as single
populations using the Orr-Sherby-Dorn,10 Larson-Miller,11 and
Manson-Siiccop1^ time-temperature parameters. A cubic log stress
dependence was assumed for all models. Such an approach is clearly
dangerous since it ignores the significant heat-to-heat effects apparent
in the data. The approach is a common one, however, and one hopes
(rightfully or not) that al l the errors and uncertainties will somehow
cancel cut and yield reasonable results. Values of the coefficient of
determination,/?-, and the standard error of estimate, SEE, from these
fits are given in Table 8. (This standard error includes a mixtare of
between-heat and within-hcat variations, and i ts real meaning is
unclear.) The Orr-Sherby-Dorn parameter provides the best overall fits
for both data sets, but the differences among the three parameters are
not large. Table 9 shows predicted v: _ues of lO^-h rupture stress from
the standard parameters. Also shown are "minimum" values determined by
subtracting two standard errors of estimate from Table 8 from the
predicted average log time, since log time was regarded as the dependent
variable in these analyses.
Finally, the available data were analyzed by the heat-centered
regression and generalized model selection procedure described in t -
last section. As a f i rs t step data were plo'ted in terms of log a vs
log tj and several preliminary runs were made. A few data were omitted
as outliers as a result of these* runs. The conclusion from those
"preasse ssnents" was that the assumption of parallel"" :..i among heats was
a good one for these data and that Che data could be described by models
involving the terns listed i". Tauit 10. Thus, a total of 1474 nodels
were examined at t'r.is stage.
After this run the ten best models with 2, 3, and 4 terras were
selected for further study. Of these 30 models most were rejected
because of poor behavior on extrapolation or other undesirable
characteristics. (Most fit the actual data approximately equally well,
as shown in Table 11.) Models chosen for final study (with s ta t is t ics)
are listed in Table 12. Again, most of these models fit the data about
as well as all the others; all also behave well on extrapolation.
Therefore, one could defend the choice of any of these candidate models.
For the I-tpr data three of the final candidates were forms of the
Orr-Sherby-Dorn parameter; one was a Larson-Miller parameter. In
general, the OSD model forms fit these data slightly better than the LM
forms, so the LM parameter was rejected. Among the three OSD forms, any
could equally well be chosen. We chose model 456 bar.ed largely on the
fact that i t provided the best fits to the N'RIM data (below). This
criterion was used because the NRIM data set is much better balanced and
included longer term data. Therefore, the N'RIM data would be expected
to better characterize trends in behavior.
Following the procedures described above and in the Appendix,
individual heat constants, the average constant, and the variance
components were estimated for all of the candidate models. For the
final selected raodel the best-fit equation is
22
log t = C, - O.26909(log o ) 2 - 0.32703(log a ) 3 + 17549/r , (13)v n
where
a = stress (MPa), and
T = temperature (K).
Values of C, for the individual heats are given in Table 13. The
average heat constant was —11.363. Figure 6 displays typical
comparisons of predicted and experimental MPC data, while Table 14 shows
estimated values of the lO-'-h rupture strength from the above model.
The log a-log t isotherms predicted from Eq. (13) are concave3?
downward when plotted in the conventional fashion, as are those
predicted from all models in Table 12. One might argue that these
predictions are overconsei/vative, especially since the curvature upon
extrapolation is generally more pronounced than that predicted from the
NRIM data. Certainly one could choose a model that f i ts slightly more
poorly to yield more optimistic extrapolations, or one could adjust Eq.
(13) to ., ield more opLimistic results. However, based on these data
alone, such procedures would clearly be presumptuous. The uncertainty
caused by the sparseness of the data could potentially yield large
errors on extrapolation. Therefore, the conservatism of Eq. (13) is
welcome and justified based on the MPC data alone. Possibly a better
way to treat chose data would be to combine them with the NRIM data. //'-•'</
The pooled data sets would then yield optimum predictions based on al l £'/«/c
available infe'nation. However $ the ASME Code has traditionally frowned / t
on the use of foreign data in allowable stress assessments, so this /
combination was not attempted.
23
Examination of data plots, model forms, etc., for the NRIM data led
to the choice of model 456 as the optimum, although all of the models in
Table 12 yielded very similar results. For this model the best-fit
equation is
log t = C, - 1.0520 (log a)2 - 0.06884(log o ) 3 + 16752/j . (14)
Values of C, for the individual heats are again given in Table 13. The
average heat constant was —9.229. Figures 7 and 8 compare predictions
from Eq. (14) with available NRIM data. The fits are in all cases
excellent, with only very slight deviations from the predictions even
though heat-to-heat variations are significant,
For both data sets the heat-centered regression approach describes
the behavior of individual heats well, describes the mean trend well,
and yields good predictions of minimum behavior, even when those
predictions are based on an empirical definition. The method provides
reasonable extrapolations, though it is never possible by any method to
determine the actual accuracy of any extrapolation in the absence of a
detailed physical model for the subject process.
Comparison of Methods
The five methods used for the rupture data analysis can be compared
in various ways, the first comparison that comes to mind involves the
actual calculated values of the lO^-h rupture strength. Unfortunately,
this comparison is somewhat artificial since the correct value of this
strength is unknown. For the NRIM data the value can be reasonably
estimated, however, since many data are available up to and beyond
5 x lCr h. A comparison of Tables 5, 7 and 14 show the predicted
individual heat results are quite similar whether the heats are treated
separately (Tables 5 and 7) or all together in the heat-centered
regression. Given that the results are conparable for individual heats,
the advantages of pooling the data together are obvious. Table 15
compares predicted average strengths, with all methods again being
generally comparable. Note, however, that of the raultiheat approaches
the heat-centered regression results are most similar to the averages of
the individua1 neat analyses. For the MPC data comparisons are
difficult. By intentional design the heat-centered regression results
are slightly more conservative than the others, but no significant
conclusions can be drawn.
Figures 9—11 present some additional comparisons of the current
results with those reported earlier^ by Smith for this material. Again,
the data base used by Smith was similar (but not identical) to the "MPC"
data base used herein. Smith's results were obtained from individual
heat graphical fits and extrapolations followed by determination of a
linear relationship between log rupture strength and temperature.
The average predictions are fairly similar except that the current
MPC data results become relatively more and more conservative at higher
temperatures, as expected. The data are not sufficient to determine
which of the two sets of predictions is more accurate.
Figure 11 compares minimum SLrength predictions from the two
sources. Smith1r minimum strength values were obtained by multiplying
the average strengths by tha ratio of average minus 1.65 times the
standard error at 649°C to the average at 649°C. This procedure is
equivalent to subtracting 1.65 SEE in log strength from the average aL
all temperatures. Minimum values from the current heat-centered
25
analyses were determined by subtracting 2 SEE in log time from the
average predicted log t values at each temperature. A comparison of
Figs. 10 and II shows that the current safety factors involved in the •
minimum definition are slightly larger than those used by Smith.
However, the available data indicate that the current predictions are
not overcont>ervative.
The various methods can also be compared on the basis of several
general criteria, as described below.
(1) OVERALL USEFULNESS: The heat-centered regression results are
clearly the =:.--• t generally useful of the five methods. One simple
equation describes both individual and multiple heat (average and
minimum) behavior. Setting of statistical bounds are also possible
since the method yields a clear estimate of variance components. None
of the other methods come close in terms of all-around utility of the
results.
(2) STATISTICAL SIGNIFICANCE: The heat-centered regression
technique is igain the only one of the five methods that even approaches
statistical rigor. Therefore, it is the only method with the potential
for yielding meaningful statistical inferences such as tolerance limits,
• etc.
(3) ANALYST JUDGEMENT: Requirement of judgement on the part of
the analyst is b->rh a positive and negative factor in assessing a
method. It is desirable to allow inte^ction of the analyst and to
provide capability for input of engineering judgement. I t is also
desirable to provide standardized results that are relatively
independent of individual preferences. In these regards the isothermal
26
and parametric senior band fits require the least judgement on the [>-.rt
of the analyst v/hile also providing the least opportunity for
interaction on the part of the analyst. On the other hand, the
graphical extrapolation and heat-centered regression approaches require
Che most judgement but provide tnaximura opportunity fo- thi. analyst to
use his knowledge and experience to influence the results.
(A) DATA INFLUENCES: All of the methods work, best with good,
balanced data sets. The heat-centered regression approach is also
particularly well-suited to the analysis of "bad" data sots. The
graphical approach also allows one to use judgement in negating *"he
effects of unbalanced data. the heat-centered regression approach
performs this negation automatically, however, as well as providing more
efficient use of the full data base.
(5) ABILITY TO DESCRIBE DATA: For the very "good" MRIM data
results from different methods are qui^e comparable. However, only the
heat-centered regression results provide a complete description of both
single and multiheat data. For "bad" data the method also yields
reasonable descriptions. No other method provides such comprehensive
descriptions. The parametric methods yield no predictions beyond the
range of data in some cases at high temperatures; the graphical and
isothermal fitting approaches do not include comprehensive estimates of
temperature dependence, and so on.
Using the above criteria, Table 16 cor pares the various methods
based on the opinion of the authors. Other reviews might reach slightly
different conclusions, but we believe the overall superiority of
heat-centered regression a:.d similar automated techniques to be obvious.
If nothing else, automation allots one to try a wi Jor ranp.i' of
approaches than rnip.ht be practical nanually.
Limit Setting
The analysis of rupture data for design purposes generally has two
goals. One goal involves an attempt to describe actual material
behavior. That goal has been dealt with above. The other goal involves
setting safe design lower limits on behavior so that rupture of
components in service 'ill be precluded. A detailed discussion of such
lirait-setting procedures is beyond the scope of this report. However,
the regression models developed by the current methods are particularly
amenable to limit-setting treatments. Therefore, a brief description of
some possible lirait-setting procedures will be given here.
Limit setting procedures can be either statistical or engineering
in nature. Statistical limits may include several basic types,
including confidence limits, prediction limits, and tolerance limits. A
general discussion of statistical limits is given in kef. 13. The
advantage of these limits is that they are well defined and have clear,
quantitative implications. However, they involve certain assumptions
such as that the experimental data obey a certain distribution (usually
normal). Violation of these assumptions removes the quantitative
meaning of the limits and can in fact make them misleading. Also, these
limits are intended primarily for use within the range of the
experimental data. Use of such limits for extrapolation beyond the data
base (such as is generally necessary with creep data) is dangerous at
best.
28
Engineer ing-type limits ha'.'.-• r!;<> <! i ̂ advantage that they are
somewhat arbitrary In nature and cin r"!y heavily on the judgement of
the Lnd ividuaL analyst . Hovevcr, they hive the advantage of being
flexible enough to yield a "reasor.at 1 ••" estimate of lover l ini t behavior
even In the extrapolated region. They also do not necessarily rely on
specific assumption1-, as to else data d is t r ibut ion. A corcnon method of
se t t ing such Un i t s involves subtracting a constant multiple of the
standard error of estimate, SEE, from the mean value of stress at a
given rupture time or rupture time at a given s t r e s s .
The choice of the particular method to use depends on factors such
as the specific purpose of the analys is , dis t r ibut ion of the available
data, e tc . Most design codes specify that an additional safety factor
(allowable stress reduction) be applied to the "lower l imit" value for
•additional conservatism, whichever method is used. The regression
approach described above his the advantage of being easi ly adaptable to
any of the limit se t t ing techniques discussed above.
Figures 10 and 11 present only an indirect comparison of the common
Code method for basing the minimum on a set decrement from average log
s t ress with the procedure used herein of basing the safety factor on
time. The comparison in Fig. 12 i s more d i rec t . Here, the individual
heat graphical extrapolations have been analyzed as a function of
temperature per Smith's approach in Ref. 6. The average values thus
obtained for ICH-h rupture strength are essential ly identical to those
derived from the heat-centered regression aproach. At the higher
temperatures the regression minimum values become progressively more
conservative than the graphically derived values, however. This trend
29
occurs because the regression Diniaa include a fixed safety factor on
time; as the slope of the log stress-log tine curves increases at the
higher temperatures, this fixed time factor corresponds to a
progressively larger factor on stress. In fact, Fig. 12 indicates that
the graphically-derived results become continuously less conservative as
Che temperature increases. The regression results, on the other hand,
remain in approximately the same relation to the actual individual heat
minimum graphical predictions, indicating greater consistency with data
trends.
A final possible approach would be to use the heat-centered
regression analysis to define rupture strength values for individual
heats and then to treat those values by the strength trend curve
approach. Note that in constructing the trend curves strength values
for a given heat were used only for temperatures at which data for that
heat were available. Additionally, only values for temperatures up to
704°C were used to assure a linear relationship between log strength and
temperature.
Shown in Table 17 are average, average — 1.65 SEE, and average — 2
SEE predictions from both approaches for 1CH, 10', and lO-'-h rupture
strength at various temperatures. Note that the choice of the SEE
multiplier (1.65 or 2) is somewhat arbitrary. These two values are
typical of those .̂omnionly used and are shown for comparison. (Assuming
a normal distribution, 1.65 is a lower limit on the value of this
multiplier if one seeks a lower limit in strength above which one has a 95%
confidence that the true mean lies.)
For iho well-balanced NRi:t data the results fron the t'-'o nethods
are fairly similar, though again the minima based on stress becone
increasingly less conservative in a relative sense for higher
temperatures and longer times, when the stress exponent tends to
increase.
The extreme inhomogeneity in the MPC data base makes the strength
trend curve analysis susceptible to large errors and biases, whereas the
heat-centered regression approach is inherently protected against such
biases. The trend curve results are still fairly similar to the
heat-centered regression results, although the values at 538°C are
consistently and significantly higher from the former approach. Note
that this temperature is slightly below the lowest temperature
represented in the data. the above comment concerning decreased
conservatism in the stress-based minima at higher temperatures still
applies. A nore cosaplete discvission of these results can be found in
Ref. A.
SUMMARY AND CONCLUSIONS
The results presented above clearly demonstrate the applicability
of modern computeri?.ed techniques for the analysis of material strength
data such as those required for setting allowable stresses for the ASME
Boiler and Pressure Vessel Code. These techniques, when used in
conjunction with modern computerized system for data storage and
retrieval, provide an efficient means for data processing that far
outstrips the capabilities of older manual data analysis techniques.
Specific conclusions follow.
31
1. The well-known ratio technique for analysis of yield and
tensile strength data can easily be implemented by computer. However,
a heat-centered regression technique thnt involves similar assumptions
about material behavior can also be inplemented. This latter technique
makes more efficient use of available data, since it bases the strength
of a given heat on all data for that heat, not just on the room
temperature strength. As a result, even heats for which no room
temperature data are available can be analyzed with this technique.
2. The computer is a useful tool in facilitating analysis of
creep-rupture data by many standard techniques. Moreover, it opens up
the possibility of additional analysis techniques that would be too
cumbersome to implement manually.
3. For the data sets examined in this paper (type 321H stainless
steel), a computer-implemented heat-centered regression aproach used in
conjunction with a generalized model selection procedure was found to be
superior to the standard techniques applied. This superiority was
evidenced by increased accuracy in data fitting, more efficient use of
available data, less susceptibility to biases caused by inhomogeneous
data distributions, and increased precision of available statistical
information to describe the fits.
4. The superiority of the heat-centered regression approach for
treatment of both tensile and creep-rupture data persists whether the
data base examined is extremely inhomogeneous and poorly balanced or
whether it is very homogeneous and well-balanced. However, these
techniques are particularly useful for the inhomogeneous data sets due
Co Che protection they provide against potential lar^e biases that could
be caused by the data distribution.
ACKNOWLEDGMENTS
This work was supported by the Mei.il Properties Council, Inc.,
using funding provided hy cho American Society of Mechanical Engineers.
The authors gratefully acknowledge the support of these organizations.
We would also like to thank the United States Department of Energy (DOE)
for permission to do the work at the DOE facilities at Oak Ridge
National Laboratory. The cooperation of G. M. Slaughter and C. R. Brinkraan
in this regard is also appreciated. We would like to thank
and for reviewing the contents of this manuscript
and Linda Pollard for typing the draft.
33
REFERENCES
1. "Data Sheets on the Elevated Temperature P rope r t i e s of IB Cr-8
Ni-Ti S ta in less Steel for Boiler and Heat Exchanger Seamless Tubes
(SUS 321 HTB)," NRIM Creep Data Sheet N'o. 5A, Uatior^i', Research
Institute for Me talc, Tokyo '(1978).
2 . "Standard Speci f ica t ion for Seamless and Welded Aunt • u t i c
S ta in le s s Steel P ipe , " ASTM Designation A312-74, 1975 Annual Book
of AST!-! Standards, Part 1, American Society for Tes t ing and
Mate r ia l s , Ph i lade lph ia , 1976, pp. 209-215.
3 . G. V. Smith, "Evaluation of Elevated-Temperature Strength Data,"
J. Materials 4 ( 4 ) : 378-908 (December 1969).
4 . M. K. Booker and B.L.P. Booker, Automated Analysis of Creep and
Tensile Data for Type 321H Stainless Steel, r epor t prepared for the
Metal Propert ies Council, Inc. (September 1979).
5 . L. H. Sjodahl, "A Comprehensive Method of Rupture Data Analysis
with Simplified Models," pp. 501—515 in Characterization of
Materials for- Service at Elevated Temperatures, MPC-7, American
Society of Mechanical Engineers, 1978.
6. G. V. Smith, An Evaluation of the Yield, Tev.sile, Creep and
Rupture Strengths of Wrought 304, 316, 321, and 347 Stainless Steels
at Elevated Temperatures, ASTM Publication DS 5S2, American Society
for Testing and Materials, Philadelphia, 1969.
7. M. K. Booker, "Use of Generalized Regression Models for the
Analysis of Stress-Rupture Data," Characterization of Materials
for J^rv'.cc at Elcvaied ?~s:rrcr"zzicre;:, MPC-7, A m e r i c a n S o c i e t y of
Mechanical rlngineers, 1973, pp. 459—499.
8 . D. R. Runmler, "Stress-Rupture Data Correlat ion — Generalized
Regression Analys is , An Al ternat ive to Parane t r ic Methods, in
Reprodu:-iiility and A^-r.^zcy of yectizKical Tests, ASTM,
Phi ladelphia , 1977.
9 . G. J . Hahn, General E lec t r i c Conpany, Presenta t ion to Workshop on
Needs and Solut ions to Problems in the Area of Useful Application
of Elevated Temperature Creep and Rupture Data, Cleveland, Ohio,
August 30-31, 1977.
10. R. L. Orr, 0. D. Sherby, and J . E. Dorn, "Corre la t ion of Rupture
Data for Metals at F.levated Temperatures," Trzr.s. ASy.E 46: 113-123
(1954).
1J. F. R. Larson and J . Miller , "A Ticie-Tempei'atare Relat ionship for
Rupture and Creep S t re s ses , " Tvarr.c. ,\Sy.F.l^: 765—761 (1952).
12. S. S. Manr.on and G. Succop, "Stress-Rupture P rope r t i e s of Inconcl
700 and Corre la t ion on the Basis o1: Several Tiue-TenporaLure
Paraaeters," Sij"z:csiicn or. MeiaZt'ic i-'aterials fev Service Above
lC00°FJ ASTM STP 174, American Society for Test ing and Mater ia l s ,
Phi ladelphia , 1956, pp. 40-46.
13. G. J . Hahn, " S t a t i s t i c a l I n t e rva l s for a Normal Populat ion, Part 1,
Tables , Examples, and Appl ica t ions , " J. Quzliiy Technology 2 ( 3 ) :
115-125 (1970).
Table l. Heat Constants Determined from Heat-Centered Regression on Tensile Data
Unafncd L
Average91E91A91D412621C21B
MPC Data
Yield StrengthConstant
2.3422.3452.2912.3692.425
" 2.3932.2732.316
Ultimate StrengthConstant
2.7672.7722.7642.7902.7232.7852.7812.776
AverageACAACBPCCACoACHACJACLACMACN
NRIM Data
Yield StrengthConstant
2.3772.3462.3932.3872.4492.4392.4632.3042.3432.266
Ultimate StrengthConstant
2.7912.7872.8032.7892.8022.7932.8192.7802.7792.768
Table 2. Variance Values2 Obtained by Heat-CenteredRegression on Tensile Data
0.
0.
0.
0.
V00226
00169
0448
00216
variances
0.
0.
0.
0.
V °w
00219
.00932
,00315
.00160
0.
0.
0.
0.
V00445
0110
0530
00376
MPC Yield Strength
MPC Ultimate Strength
NRIM Yield Strength
NRIM Ultimate Strength
CA11 variances in terms of log strength for strengthvalues in MPa.
'"•Between-heat variance.c.Within-heat variance.dTotal variance; VT = VD + V .
Table' 3. • Predicted Values of Yield Strength
Tern°C
26031637142748253359 3649704760
260316371427432538593649704760
perature(°F)
RT(500)(600)(700)(800)(900)(1000)(1100)(1200)(1300)(1400)
RT(500)(600)(700)
(aoo)(900)(1000)(1000)(1200)(1300)(1400)
Average^MPa
20513112512111711711511310810296
(ksi)
(29(19.(18,
(17,
(17.(17.(16.(16.
(15.(14.(13.
.7)
.0)• 1 )
.5)
.0),0)7)4)7)8)
9)
Ratio Technique
Average12
MPa
207130125122122123125127127126122
251201194188182178173169165161156
(ksi)
(30(18(18(17(17(17(18(18(18(IS,
(17,
(36.(29.(28.(27.(26.(25.
(25.(24.(23.(23.(22.
.0)
.8)
.1)
.7)
.7)
.8)
.1)• 4).4).3)
.7)
.4)2)
1)3)4)8)1)5)9)4)6)
Minimum^MPa
MI'i
2071301251221221231251271271.26122
(ksi)
C Data
(30.0)(18.8)(13.1)(17.7)(17.7)(17.8)(18.1)(18.4)(18.4)(18.3)(17.7)
NRIM Data
207166160155150147143140136132123
(30.0)(24.1)(23.2)(22.5)(21.8)(21.3)(20.7)(20.3)(19.7)(19.1)(13.6)
1
Average
MPn
20514 3139136134132129125119111IU1
23420319 7190134178172166161156150
leat-Centered Regression
(ksi)
(29.(20.(20.(19.(19.(19.(18.(18.(17.(16.(14.
(33.(29.(28.(27.(26.(25.
(24.(24.(23.(22.(21.
7)7)2)7)'01)7)1)2)1)6)
9)4)6/6)7)3)9)1)4)6)8)
Minimum^MPa
20714414013?135JJ3130120120.112
102
20,1791 7 j.
168162157152147142 '
137133
(ksi)
(30,(20,(20(19,
(19,(19,(18.(18,(17.(In.(14.
(26.(25.(24.(23.(22.(22.(21.(20.
(H.(19.
.0)
.9)
.3)
.9)
.6)
,3).8).3)
.'0,2)
.«)
0)0)1)4)5)8)0)3)6)
9)3)
Minimum0
ML'a
1501.05102
lnu'JH
y'>
9 2
6 I
Ml
i'.
16814614113613212712 3119115111108
(kai)
(21.(15.(14.(14.(14.(14.(13.(13.(12.ill.
•; IO .
(24.(21.(20.(19.(19.(18.(17.
(17.(16.(16.(15.
8)2)8)5)2)1)H)3)6)7)7)
4)2)4)7)1)4)3)2)7)1)7)
"Predictions reportes by Smith, AST>I Publication DS5S2. All other results were obtained from present
< analysis.^Minimum values obtained based on room temperature specified minimum strength.
^'Minimum values obtained by subcontracting two standard errors in log strength from the predicted
average log strength.
°c
2603163714274825385 9 3
649704760
26031637142748253859 3
649704760
perature
(°K)
RT(500)(600)(700)(300)(900)(1000)(1100)(1200)(1300)(14U0)
RT(500)(600)(700)(800)(9U0)(1000)(1100)(1200)(1300)(1400)
Table 4
Average^Ml'a
5644 4 6
4624 7 4
4 7 9
468446499344276209
(ksi)
(81.8)(64.7)(67.0)(68.7)(09.5)(67.9)(64.7)(58.0)(49.9)(40.0)(30.3)
. Predicted V;
Ratio
Avt.
MPa
54444945U452453448435410369310228
5754 4 3
44 2
445448447438417379324241
llueS
Technique
>r;j;;e
(ksi)
(78.9)( h i , . 1 )
( 6 5 . 3 )( 0 5 . 6 )
1 0 5 . 7 )
( 6 5 . 0 )
( 0 3 . 1 )
C9.5)(5 3,5)
(45.0)(33.J)
(83.4)("4.2)
(04.1)
(04.5)
(05.0)
(04.8)
(63.5)
(.00.5)
( '•> 5 • L))
(4 7.0)
(35.0)
o f U l t i m a t e
Minimi):'?
Ml'a
31742742 8
4 30
4 31
4274143903512'i 5
217
N K I M
5173 9 8
3 9 7
4 0 0
4034023 9 4
3/5341291217
(ks
IKi_t,-|
(75(<'l("2(62(02(01(00(50(50(42(31
Data
(75.(57.(57.(58.(58.(58.(57.(54.(49.(42.(3L.
i)
.0)
.9)
.1)
.4)• 5)
.9)
.0)
• 6)
.9),8)
.5;
.0)"7(,6)
0)4)3)1)4)4)2)5)
Tensile Strength
1!
AverageMl1 a
5374 16
4 254 37
4 40
*474 34
4U335429 1
220
57344 2
4464514 55
4534 4 04 1 4
JM.318254
(ks
(77(00(0 1
( 0 3(04( ( , 4
(62(58(51(42(31
(83,(04.(64,(6 5.
(60.
«,'>.(0 3.(.60.
(JJ.(40.(30.
cat-Centered Re
1)
.y)• 3)
• '•>)
.4)
.7)• 8).9)
• •')
• i)
• 2)
-y)
• i)
.1), 7)
<<)0)
7)8)o)8)
1)8)
Mini nunMl'a
5174014094214 29
4 30
4 IB
3dB341280212
51739940240 7
410
40939 7373JJ5287
Us
(75OS'. 5 -'(0 1
U'2(02(60(5d149
(40(30
(75(57158(VJ.
(59,
(59,
(57.154.(>'. 8 .
(41.133.
greus ion
i)
.0)
.2)
.3)
.0)
.2)
.4)
.0)
.3)
.4)
.6)
.7)
.0)
.9)
.3)
.0)
. 5)
,3)0), 1 )
d )
6)2)
Minimuw-
XI'a
4 6 0
35t.3n43 7-'<
IblMM372(4 5
303249lti»
5244044ua41241 6
414•'i i) 2
3 7">
JJ929 1
232
(ks
(60(51(52(54(55155(54150(43(3d12 7
(7(3
15b,
1V»,
('.'»,
lt)0,
(00.155.(5'i.
(•'.').
(42.(33.
i)
.7)
.0)
• » )
.2)
.4)
. '))
.0)
.u)
.'*)
.1)• 3)
• 0)• 0)
.2)
,3)
O)3)D)
2)2)6)
a l ' r e d i c t l o n s r e p o r t e d by Smi th , ASMT L ' u b l l c u . i o n US5S2. A l l o t h e r r r s u l t s were obt.uiueil from t h epresent analysis.
^Minimum values obtained based on room temperature specified minimum strength.eMliiitnum values obtained by aubcontracting two standard errors in log strength from tlie predicted
average log strength.
? ' ^ ; - ; - ._ ' "_ Table 5. Graphically Estimated 105-h Rupture Strengths (MPa) fromTreatment of Individual Heat Data
TemperatureOf / 0 C\
600 (1112)
650 (1202)
700 (1292)
750 (1382)
ACA
135
iZ50
28
ACB
135
89
52
30
ACC
128
77
49
24
ACG
84
54
30
16
He
ACH
86
53
29
18
:at«
ACJ
92
60
42
21
ACL
100
64
44
26
ACM
96
62
41
24
ACN
120
70
45
29
41
170^
75^
28^
?Heat 41 from MPC data. All others from NRIH data.H/alue at 566°C (1050°F)^Value at 649°C (1200°F)
Value at 732°C (1350°F)
Note: 1 ksi = 6.395 MPa
Table 6. Estimated 10--h Rupture Strengths (MPa]from Isothermal Fits-: to Multiheat Data
as a Single Population
Temperature°C (°F)
649 (1200) MPC 65 52
600 (1112) NRIM 98 73
650 (1202) NRIM 61 45
700 (1292) NRIM 43 33
750 (1382) NRIM 22 15
aAll data sets were fit by logt = a + a, loga.
^Estimated from average minus two standard errorsin log time.
Note: 1 ksi = 6.895 MPa
Table 7. Estimated 105-h Rupture Strengths (MPa) from Parametric F i t sto Individual Heat Data
Temperature°C (°F)
600 (1112)
650 (1202)
700 (1292)
750 (1382)
ACA
140
84
48
26
ACB
138
85
48
e
ACC
127
76
43
21
ACG
88
51
28
15
Heata
ACH
89
51
27
e
ACJ
95
60
37
22
ACL
106
67
42
27
ACM
102
64
40
25
ACN
120
74
46
29
41
1636
70c
—
^ 41 from MPC da ta . All others from NRIM da ta .^Value a t 566CC (1050°F)^Value a t 649°C (1200°F)"Value a t 732°C (1350°F)eModel ill-conditioned - does not yield reasonable predictions in
this case.
Note: 1 ksi = 6.895 MPa
Table 8. Statistics Determined from Fits of StandardParameters to Data as a Single Population
Parameter
Orr-Sherby-Oorn
Larson-Miller
Manson-Succop
R2
77
76
76
MPC
.4
.1
.0
Data
SEE*
0.310
0.319
0.319
NRIM
R2 (%)a
83.2
83.0
83.3
Data
SEE3
O.?93
0.296
0.293
aR 2, the coefficient of determination, gives thepercentage of data variations described by the model.
^SEE, the standard error of estimate, is the squareroot of the variance from the equation fit.
Table 9.Fits
Estimated 105-h Rupture Strengths (MPa)of Standard Parameters to Multiheat Data
as a Single Population
from
Temperature°C (°F)
566 (1050)593 (1100)621 (1150)649 (1200)677 (1250)704 (1300)732 (1350)
600 (1112)650 (1202)700 (1292)750 (1382)
Orr-Sherby-Dorn
151117896643bb
986034b
(121)a
( 92)( 67)( 42)bbb
( 72)( 40)( 18)b
Parameter
Larson-Miller
HPC Data
' 153 (123)120 ( 97)94 ( 72)70 ( 50)49 ( 29)29 bb b
NRIM Data
100 ( 76)63 ( 45)37 ( 25)20
Manson-Succop
14511592705132b
986337b
013)( 91)( 68)( 49)( 31)bb
( 72)( 44)( 23)b
Predictions in parenthesis determined from average minus twostandard errors in log time.
^Parameter does not yield reasonable predictions due toinflection in "master curve."
Note: 1 ksi = 6.895 MPa
3T Ll-.i Or " Table 10. Terms Used for Generalized Model Selection2
Term Number Term
1 o2 logo
3 l/o4 (logo)2
5 (logo)3
6 1/T
7 o/T8 (loga)/T9 './(oT)
10 (loga)2/T
11 (loga)3/T
aAll models considered were composed of termstaken from this list.
Table 11. Values of R2 for the Ten Leading Models with2, 3, and 4 Terms (Heat-Centered Regression)
Two
Terms'3
1,62,65,86,116,85,104,64,36,105,6
5,82,85,106,112,64,85,66,106,84,6
Terms
RH%)b
88.189.790.092.892.892.993.493.794.094.1
92.192.994.396.096.897.197.397.497.597.7
Three
Tennsa
MPC
4,5,65,6,71,5,63,6,82,4,66,8,92,3,62,6,94,6,93,4,6
Terms
RH%)b
Data
94.194.294.294.294.294.294.394.394.394.3
NRIM Data
2,3,62,5,64,6,91,4,64,6,74,5,62,4,63,4,64,6,114,6,10
97.797.797.797.797.797.797.797.797.797.7
Four Terms
Terms
2,6,9,102,3,6,112,6,9,111,2,6,91,2,3,62,6,7,92,3,6,71,8,10,111,5,7,107,8,10,11
2,3,6,75,6,8,105,6,8,115,6,10,113,4,6,91,6,7,101,6,7,81,8,10,113,4,8,93,5,9,10
RH%)°
94.394.394.394.494.494.494.494.494.494.4
97.797.797.797.797.897.897.897.897.897.8
&Terms as l i s t ed in Table 10; -?Coeff icient of determination.
-ST -_I^£ >' " Table 12. Final Candidate Rupture Models Chosen for Detailed Study.
Termsa
4,5,66,8,10,112,4,5,65,6
4,5,62,5,66,8,10,112,4,5,63,4,8,93,5,",106,8
R U)D
94.194.294.394.1
97.797.797.697.897.897.897.5
V
MPC Data
0.0.0.0.
NRIM Data
0.0.0.0.0.0.0.
aw
0158015801560158
0118011801240119,01160116,0128
"a" :I
0.0559 '0.05600.05550.0550
0.03740.03750.08330.08740.08760.08740.0834
?Terms as l is ted in Table 13.^Coefficient of determination.^Within-heat variance.Between-neat variance.
_ Table l". Individual Heat Constants from Heat-Centered Regression Fits" of Creep Data
HEAT
i 171 16
1 1 5I 141 1 31 1 211 11 1 01 0 91 0 ?1 0 7
1 0 6
1 0 51 0 4
1 0 31 0 2
1 0 11 0 0
9 9
9 b
9 7
9 6
9 59 4
9 3
CON STAN T
- 11 . 4 4 1- 1 1 . 4 4 1- 11 . 730- 11.553- ) 1 .387- 1 I . 4 ^ 3- 1 1 . 3 ft e- 11 . 0 7 7- 1 1 . 3 0 ?- J 1 . ?.? 9- l i . 4 3 1- 1 ! . 4 a 3- 1 1 . 4 2 5- 1 I . E32- 1 1 . 4 6 4- 1 1 . 5 1 ?- 1 1 . 4 O 7- 1 1 . 3 9 f- 1 1 . 2 2 £- 1 1 . 4 7 4
- 1 1 . 3 5 0- 1 1 .384- 1 1 . 122-11.531- 1 I .65?
H£A
9 286*3S 5 T
8 27 8-17 6 1
7CC7 0"!7C.X6 9
::S
. , 76 66 5
6 4564-\6 336 3-\5 4
5 35 2515 04 OP4 4P
CONSTANT
- 1 1 . 635
- 1 1 . 5 1 9
-11 .421-1 I . 1 66
- 1 I .348- 1 I . 7 09- 1 0.951- I I .270- I I .324-1 I . 054
- 1 1.0 65-1 I .357- 1 1 . 1 16
-1 1.031
-1 1 . I 36
-11.121-1 1.4^4
-1 1 .4H6- 1 1 . 7 35
-13.713
-1 I . IHR- I 0. 775
-10.826
- I I .325-11 .433
HEAT
24C-Q24 53-9
2 3"?23 A
2 2 C2 2 C37 D8 1
7 27 9 R24 A-2 A
291 E91 A
91 O4 1ACA
AcnACC
ACGA C H
AC J
A C LACM
A C N
C0N3
- 1 1 .
- 1 1 .
- 1 1 .
-I I.-1 1.-11.-11.-11.-I I.-I I.
-1 >..-12.-I 1 .
-1 I .
-1 1 .-1 I .
- 3 .- < } .
- H .- O .
- 9 .- 9 .- 9 .- 9 ,- 9 .
T ANT
1 1 21 0 6 !20 0
45 I3 9 55 6 ?24 33 27
040 ;3 6 54 9 6
0 4 06 4 9
6 5 0
S 9 91 7 67 d 63 5 7
9 37
6 0 05 6 43 2 5
20 J3 2 7
0 4 6
Table 14. Estimated 105-h Rupture Strengths (MPa) fromHeat-Centered Regression Approach
Temperature°C (°F)
566 (1050)593 (1100)621 (1150)649 (1200)677 (1250)704 (1300)732 (1350)
600 (1112)650 (1202)700 (1292)750 (1382)
Avg
110674023
Mina
81472714
Average
1451108159422919
ACA ACB
130 12782 7951 4930 29
Ml
M
PC Data
in i mum'
11685624229189
NRIH Data
ACC
121754627
ACG
90533117
ACH
92553218
Heat 41
1551208965473422
ACJ
103623721
ACL
109664023
ACM
103623721
ACM
117724426
"Minimum" predictions determined from average minus two standard errorsin log time.
Note: 1 ksi = 6.895 MPa
Table i s . Comparison of Predicted Average Values of 105-h Rupture Strength
MPC 649°CNRIM 600°CNRIM 650°CNRIM 700°CNRIM 750°C
6598614322
9b
66986034/
Values from
14G
59110674023
Table
Sd
108684224
f
112684024
^Isothermal f i t s to multiheat data as single population.OSD parametric f i t s to multiheat data as single population.
c-Heat-centered regression.Average of single heat graphical extrapolations.
^Average of single heat parametric f i t s .•'Parameter does not yield reasonable predictions due to inflection
in "master curve."
Note: 1 ksi = 6.395 MPa
Table 16. Comparison of Methods for Rupture Data Analysis Based on Several Criteria
Ranking
1
2
3
4
5
OverallUsefulness
a
Cr i lo r ia
Stat is t ics
E
C
A
D
B
Least LeastJudgment AffectedRequired by Bad Data
EngineeringInteraction
DataDescription
B
D
C
E
A
E
A
B
D
C
A
E
C
B
D
E
A
C
D
B
Letters refer to the fo l l ow ing techniques:
A: Ind iv idua l heat graphica l ex t r apo la t i onB: Isothermal scatterband f i t sC: Ind iv idua l heat parametr ic f i t sD: Scatterband parametr ic f i t sE: Heat-centered regress ion
NOTE: On the basis of 5 points f o r f i r s t , 4 f o r second, e t c . , the ove ra l l rankingsare: 1 . E(26); 2. A(18) ; 3. C(17); 4. D(15) ; 5. B(14).
Table 17. Comparison of Different Estimates of Average and Minimum Behaviorfrom Multi-Heat Analyses
R u p l ' j r e S t r i - r t r , t h , "T.I ( k s l )
Tecperature
*C
533
593
649
704
533
593
649
704
538
593
649
704
600
650
700
750
6 0 0
650
700
750
600
650
700
750
(*F)
(10O0)
(1100)
(1200)
(1300)
(1UO0)
(1100)
(1200)
(1300)
(1000)
(1100)
(1200)
(1300)
(1112)
(1202)
(2192)
(13:52)
(1112)
(1202)
(1292)
(1382)
(1U2)
(1202)
(1292.)
(1382)
aSEE •= standard
SHE •» standard
Heat-C
Avera,,c A-
3 6 0 ( 5 3 . 1 )
237 ( 3 4 . 4 )
152 ( 2 2 . 0 )
9 5 . 5 ( 1 3 . 3 )
268 ( 3 8 . 9 )
166 ( 2 4 . 1 )
9 3 . 5 ( 1 4 . 3 )
5 6 . 5 ( 8 . 2 )
190 ( 2 7 . 6 )
110 (16.0)
5V ( 8 . 6 )
29 ( 4 . 2 )
24o ( 3 5 . 7 )
164 ( 2 3 . a )
110 ( 1 6 . 0 )
7 4 . 5 ( i n . S i
167 ( 2 4 . 2 )
103 ( 1 5 . 7 )
69 (10.0)
4 3 . 5 ( ^ . 3 )
110 ( l b . O )
66.5 C>.6)
40 (5.8)
23 ( 3 . 3 )
error or estimate
error of estir-ite
e n t e r e d Rc^r
g - I . u 5 S'_t."
) 2 O <'">.-•)
: o 4 , : • » . * . )
12!> ( 1 . H . 3 )
77 ( 1 1 . 2 )
2 3 2 ( 3 3 . 6 )
1 4 0 ( 2 0 . 3 )
79. 5 ( 1 1 . 5 )
43 («. .2)
162 ( 2 3 . i )
39 .5 ( 1 3 . 0 )
45 ( 6 . 5 )
1 9 . 5 ( 2 . B )
202 ( 2 9 . 3 )
132 ( 1 9 . 1 )
8 7 ( 1 2 . f > >
57 (6.3)
135 (19.6)
34.5 U 2 . 2 )
5 2 . 5 ( 7 . 6 )
32 (4 .6)
86 (12.5)
50.5 (7 .3)
29 (4 .2)
15 .5 (2 .2 )
in U T H S of
in t e rms of
t- .s i. n
Avg • 2 : ,[ , , ; :
SrC P.il.i - i 0 ! !i
311 ( 4 j . l )
H i ( 2 S . 4 )
122 ( 1 7 . 7 )
73.5(10.b)
MPC Data - 101* h
224 ( 3 2 . 5 )
134 ( 1 9 . 4 )
7t> (IV.0)
40 . r> 1.3 .9)
J|pr _fnta_-_ l».\j i
156 (27.6)
85 .5 112 .4)
4 2 . 5 ( 6 . 2 )
1 7 . 5 ( 2 . 5 )
Nit LN U.ir.i - ID3 h
194 ( 2 3 . 1 ;
126 ( IS.3)
S2.5 (12.0)
54 (7.8)
SKIM Data - lu" h
128 (18.6)
30 (11.b)
49.5 (7 .2)
29 .5(4 .3 )
KKIM Iiatu - lo'J h
b l . 5 ( 1 1 . S )
47 .5 (6 .9 )
27 (3 .9)
14 (2.0)
lo£ tr from heat-center
Average
3S2 ( 5 5 . 4 )
2 3H ( 3 4 . 5 )
143 i 2 1 . 5 )
92 ( 1 3 . 3 )
290 ( 4 2 . 0 )
16 7 ( 2 4 . 2 )
9 b ( 1 3 . 4 )
55 (8.0)
223 (32.3)
113 (16.4)
56 .5(5 .2)
28 .5(4 .1)
251 (3*.. 4)
168 (24.4)
112 Uh.2)
75 (10.9)
170 (24.6)
109 (15.8)
70 (10.2)
45 (b.5)
111 (16.1)
67 .5 (9 .8 )
41 (5.9)
25 (3.6)
t'ti regression
lot! a from strength trpnd rurvp F i r« .
Strength Trend Curve
Avg - 1.65 SFFP
3 2 4 ( 4 / . U )
2 0 2 ( 2 ' » . 1 )
1 2 6 V I S . 3 )
78 (11.3)
238 (34.5)
137 (19.9)
79 ( U . 4 )
45 (6.5)
173 (25.1)
87 (12.b)
44 ( 6 . 4 )
22 ( 3 . 2 )
2US ( 3 0 . 2 )
134 ( 2 0 . 2 )
93 (13.5)
6 2 ( 9 . U )
13a (20.0)
59 (12.9)
57 (8.3)
36.5 (5.3)
88 (12.8)
53.5(7.8)
32.5(4.7)
20 (2.9)
f i t s to data.
AvB - 2 SEt*
31 1 (45.4)
l '»5 ( 2 3 . 3 )
121 (17.5)
75 (10.9)
228 (33.1)
V31 (19.0)
75 .5(10 .9)
43 (6.2)
163 (23.6)
83 (12.0)
41 (5 .9)
21 (3.0)
200 (29.0)
134 (19.4)
89 (12.9)
60 (5.7)
132 (19.1)
85 (12.3)
54.5(7.9)
35 (5.L)
83.5(12.1)
5O.a(7.4)
31 (4.5)
19 (2.8)
•
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MPC 321IISS
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Temperature ("C)
300 450 «0d
Temperature (*C)
NRIM 321SS
*——_5 • ^ * *
HeataACAACBACCACCACHACJACLACMACN
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DO
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c
NRIM 321SS HeatsACAACBACCACCACHACJACLACMAC.N
uO
07*•t*&
a
m <» cooTemperature (*C)
300 00 SOO
Temperature (*C)
Fig. 1. Comparison of Data with Predictions from Ratio Technique.Solid lines represent predicted average; dashed lines are keyed to roomtemperature specification minima.
HI
•a
MFC 3:HISSHP.1t 3
DIE9!A
41
ZIC
I.
c
V*
m uo raTemperature ('C)
•fa
in
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im4125SIC
t 9
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730
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•fc
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NRIM 321SS
- ^ • • f , ,SJ LJ if oj ; 3 r - - - . j ^ _ — A
*' S fiT G
fleatsACA LJACBACCACGACItACJACLACMACN
I I |i: 5 3
o
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Tcrr.pnrature (*C)
•faP
NRIM 321S3
fr 2
FeatsACAACBACCACCACHACJACLACMACN
uOflO"<•
&K
Temperature (*C)
Fig. 2. Comparison of Data with Predictions from Heat-CenteredRegression. Solid lines represent predicted average; dashed lines arekeyed to room temperature specification minima.
"5
MPC
v - . ~~~&-—" " • * - . *
32HISS
o
i" e"~* • * IT.
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Heat aOtK Cl91A
41262IC2tB
o o
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e
\
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Temperature (*C)
faL" a
- _
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— gi. A
321HSS
'—'=• * . .*,
H
91L
0!D^ j
2S
•i*
ao07
S
\
•xA
(*C)
NRIM 321SSHenta
AC A.ACBACCACGACHACJACLACMACN
DOAC-V•0Ba
i—|—§_ I •
300 OG eooTempei-attLre ("C)
fi3b.
• f a -
• .
NRIM 321SS HeatsACAACBACCACCACHACJACLACMAOT
-1ilva
DOA
oV<.&
K
Temperature ("C)eoo
Fig. 3. Comparison of Data with Predictions from Heat-CenteredRegression. Solid lines represent predicted average; dashed linesrepresent minimum predictions based on average minus two total standarderrors in log strength.
MPC 3211ISSHeat 41
Q.T—t
Mr
e
a:
a .
12'130 300 isa roa
Temperature ("C)7S0 900 *so coo
Temperature (*C)750 900
C
NRIM 321SSHeat ACA
a
B--
GOO
T-mporature ("C)
• ' i730 9O0
a,
NRIM 321SSHeat ACA
-.Brrrr
150 300 .730Temperature ("C)
900
Fig. 4. Comparison of Data with Predictions for Individual Heatrfrom Heat-Centered Regression. Solid lines represent predicted average;dashed lines represent average minus two within-heat standard errors.
IB
a.
Cau
• * - •
en
coE-
t l -
MPC 321HS5Heat 41
150 300 AX 600
Temperature (*C)750 900 130 300 *50 600
Temperature ("C)730 900
NRIM 321SSHeat ACA
CV
u
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"to-' i i i i
130 300 450 600 730Temperature (*C)
900
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si
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md
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n n n n
130
Temperature ("C)
Fig. 5. Comparison of Data with Predictions for Individual Heatsfrom the Ratio Technique.
• - " • • " • " « !
na,
a .
10* 101 10*Rupture Life (Hr)
Heats
5023A91A
108
MFC 321HSS
10' ID" 10* 101 10*Rupture Life (Hr)
r. 2"n
LEGENDc =~566.C
732.C
MPC 321IISS
Heat 41
101 10* 10s 10*Rupture Life (Hr)
10'
o _enU
MPC 321HSS649°C
- i — i r i i i i—i• i i 11 ii| 1—iii
10" icr io3 io'Rupture Life (HR)
Fig . 6. Comparison of Stress-Rupture Data from UPC with Pred ic t ionsfrom Heat-Centered Regression, Showing Ind iv idua l Heat and Mult iple HeatP red i c t i ons . Solid l i n e s represent p red ic ted average; dashed l i ne srepresent average minus two within-heat (a -c ) or t o t a l (d) standarderrors.
o.L
LEGENDo = 600.Ca « 650.C+ <= 700.Cx -- 750.C
NRIM 321SS
Heat ACA
10' 10* 101 10*R u p t u r e Life (Hr)
7;
LEGENDo = 600 C^ = 650.C+ =700C> = 750 C
NRIM 321SS
Heat ACC
10 10* 10J 10*R u p t u r e Life (Hr)
O J
LEGENDo = 600.Cfi = 650.C+ = 700.C* = 750.C
NRIM 321SS
Heat ACH
10 10 D 10s 10*R u p t u r e Life (Hr)
10s
**.*• • •
«". —1
<n&>* - »
V.
LEGENDJ - GOO.Ct =- 650.C* =* 700.C- - 750 C
NRIM
Heat-. a
321SS
ACN
- - -i '" --T~ - _ . -4.^ * -»
x " - - . • ^
10" 10e 10' 10'R u p t u r e Lifp (Hr)
10
Fig. 7. Comparison of Stress-Rupture Data from NRIM with Predictionsfrom Heat-Centered Regression for Individual Heats. Solid lines representpredicted average; dashed lines represent average minus two within-heatstandard errors.
101 o' io a i.o4
Rapture LifeLO3
102 103 10*Rupture Life (HR)
10'
1Q3 10*R u p t u r e Life (HR)
103
ri
oCT.
NRIM 321SS7D0°C
; t : •, 11 1 I •! I i M i | ' 1 — I " I I I 1 1 1 1 ' — I ' l
1Q2 103 10*Rupture Life (HR)
10
Fig. 8. Comparison of Stress-Rupture Data from NRIM with Predictionsfrom Heat-Centered Regression for Multiple Heats. Solid lines representpredicted average; dashed lines represent average minus two total standarderrors.
rig. 9.i . - • • H I , i ; , - . , - . . • ,
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