ANALYSIS OF MATERIALS STRENGTH DATA FOR THE ASME BOILER AND PR;:SS';K VESSEL CODE · 2005. 5. 3. · allowable stress levels for the ASME Boiler and Pressure Vessel Code have been

• . —

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

10

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

11

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

13

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.

16

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

17

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

18

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)

•

a .

£5?

A•ICL,

X

?

*

MPC 321IISS

--** • ? © 5

Heats91E D91A9 1 D <•"•

*t2G21C *213 *

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s

ib~c£ M

x:

cO.I]

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niv-s Hf"at3

9LE91A91D412631C219

•c

V*

V.

\

300 00 000

Temperature ("C)

300 450 «0d

Temperature (*C)

NRIM 321SS

*——_5 • ^ * *

HeataACAACBACCACCACHACJACLACMACN

* * a

DO

o4"•DE)B

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

MFC 321HSSH'F

im4125SIC

t 9

oAO7

\

ffl a miTemperature (*C)

730

«

«.

T.

•fc

;•: " S

NRIM 321SS

- ^ • • f , ,SJ LJ if oj ; 3 r - - - . j ^ _ — A

*' S fiT G

fleatsACA LJACBACCACGACItACJACLACMACN

I I |i: 5 3

o

g.F-B

1

orC

3U0 »M 600

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.

* . . . ' *

Heat aOtK Cl91A

41262IC2tB

o o

ooV

e

\

300 13CJ GOO

Temperature (*C)

faL" a

- _

MFC

— 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

•aD D

• O D D

"to-' i i i i

130 300 450 600 730Temperature (*C)

900

•

a.S

si

"̂^U

md

V+* 'n£

-fa

^ —&—

NRIM 321SSHeat ACA

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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