NEW NIST PUBLICATION

April 20, 1?8?

NISTIR 88-3899

Elevated Temperature

Deformation of Structural

Steel

B. A. Fields

R. J. Fields

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Metallurgy Division

Gaithersburg, MD 20899

December 1988

Issued March 1 989

Prepared for

American Iron and Steel Institute

Washington, DC

NISTIR 88-3899

Elevated Temperature

Deformation of Structural

Steel

B. A. Fields

R. J. Fields

U.S. DEPARTMENT OF COMMERCE

National Institute of Standards and Technology

(Formerly National Bureau of Standards)

Metallurgy Division

Gaithersburg, MD 20899

December 1988

Issued March 1989

National Bureau of Standards became the

National Institute of Standards and Technology

on August 23, 1988, when the Omnibus Trade and

Competitiveness Act was signed. NIST retains

all NBS functions. Its new programs will encourage

improved use of technology by U.S. industry.

Prepared for

American Iron and Steel Institute

Washington, DC

U.S. DEPARTMENT OF COMMERCE

Robert A. Mosbacher, Secretary

Ernest Ambler, Acting Under Secretary

for Technology

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Raymond G. Kammer, Acting Director
Abstract

The results of tensile and creep tests on steels close to the American

specification for ASTM A36 have been used to formulate an equation from which

elastic, plastic, creep and total strains can be calculated. Correlations

between measured and predicted strains for Australian AS A149 and Japanese SS41

steels, both close to the A36 specification, are shown and good agreement is

found.

The above mentioned equation is also used to construct deformation

mechanism (i.e., elastic, plastic, or creep) maps for times of 2 minutes to 4

hours at temperature. From these maps the deformation mechanisms operating at

a given temperature and stress can be seen. The dominant mechanism for each

set of conditions is given. In addition the maps show contours of total strain

values of 1, 2, and 5%.

2
TABLE OF CONTENTS

Abstract

1 . Introduction

2. Specimen Material

3. Calculation of Elastic Strain

4. Calculation of Plastic Strain

5. Calculation of Creep Strain

6. Calculation of Total Strain

7. Correlation of Measured and Calculated Plastic Strains

8. Correlation of Measured and Calculated Creep Strains

9. Correlation of Measured and Calculated Total Strains

10. Correlation of Measured and Calculated Strains for SS41

10.1. Plastic Strains

10.2. Creep Strains

11. Deformation Mechanism Maps

12. Construction of the Deformation Mechanism Maps

12.1. The Boundary At Which Fracture Occurs

12.2. The Boundary between ELASTIC and Elastic PLASTIC

12.3. The Boundary between Elastic CREEP and Elastic Plastic CREEP

12.4. The Boundary between ELASTIC and Elastic CREEP

12.5. The Boundary between Elastic PLASTIC and Elastic PLASTIC Creep

12.6. The Boundary between Elastic PLASTIC Creep and Elastic Plastic

CREEP

12.7. Total Strain Contours of 1%, 2%, and 5%

13. Conclusions

3
TABLES

Table 1 .

Table 2.

Table 3.

Table 4.

Table 5.

Table 6a

.

Table 6b.

Table 6c.

Table 6d.

Table 6e

.

Table 6f

.

Table 6 gTable 7.

Table 8.

Table 9a.

Table 9b.

Table 9c.

Table 9d.

Table 10.

Compositions and Tensile Properties for A36, AS A149, and SS41

Steels

Values of Plastic Strain for AS A149 from Knight ( 1

)

Values of Plastic Strain for AS A149 from Skinner (5)

Values of log F(t) and G(t) Where c p = FaG

Values of A(t), B(t) and C(t) Where e

c = AtB

cr c

Measured and Calculated Strains during Loading at 350 °C

Measured and Calculated Strains during Loading at 400°C

Measured and Calculated Strains during Loading at 450°C

Measured and Calculated Strains during Loading at 500°C

Measured and Calculated Strains during Loading at 550°C

Measured and Calculated Strains during Loading at 600°C

Measured and Calculated Strains during Loading at 650°C

Calculated Values of Plastic Strains

Measured and Calculated Plastic and Total Strains for SS41 Steel

Measured and Calculated Creep Strains for SS41 during Loading

at 350°C

Measured and Calculated Creep Strains for SS41 during Loading

at 450°C

Measured and Calculated Creep Strains for SS41 during Loading

at 550°C

Measured and Calculated Creep Strains for SS41 during Loading

at 600°C

Construction of a Deformation Mechanism Map for a Loading Time

of 60 mins

.

4
Table 10a. The Boundary

Table 10b. The Boundary

Table 10c. The Boundary

Table lOd. The Boundary

Table lOe. The Boundary

Table lOf. The Boundary

Table lOg,

Creep

Total Strain Contours of 1%, 2%, and 5%

5
FIGURES

Figure 1. Normalized yield stress versus temperature for A36 and similar

steels

.

Figure 2. The effect of temperature on the proof and flow stress of AS A149

steel at a strain rate of 2 x 10" 3 min" 1.

Figure 3a. Plastic strain versus stress at 350°C.

Figure 3b. Plastic strain versus stress at 400°C.

Figure 3c. Plastic strain versus stress at 450°C.

Figure 3d. Plastic strain versus stress at 500°C.

Figure 3e . Plastic strain versus stress at 550°C.

Figure 3f. Plastic strain versus stress at 600°C.

Figure 3g. Plastic strain versus stress at 650°C.

Figure 4. Log F versus temperature.

Figure 5. Constant G versus temperature.

Figure 6a. Creep strain versus time at 350°C.

Figure 6b. Creep strain versus time at 400°C.

Figure 6c. Creep strain versus time at 450°C.

Figure 6d. Creep strain versus time at 500°C.

Figure 6e . Creep strain versus time at 550°C.

Figure 6f. Creep strain versus time at 600°C.

Figure 6g. Creep strain versus time at 650°C.

Figure 7. Parameter B versus temperature.

Figure 8a. Creep strain versus stress at 350°C.

Figure 8b. Creep strain versus stress at 400°C.

Figure 8c. Creep strain versus stress at 450°C.

Figure 8d. Creep strain versus stress at 500°C.

6
Figure 8e

.

Creep strain versus stress at 550°C

.

Figure 8f

.

Creep strain versus stress at 600°C

.

Figure 8g- Creep strain versus stress at 650°C

.

Figure 9. Parameter C versus temperature.

Figure 10. Parameter A versus temperature.

Figure 11a. Correlation of measured and calculated plastic strain at 350°C

Figure lib. Correlation of measured and calculated plastic strain at 400°C

Figure 11c. Correlation of measured and calculated plastic strain >at 450°C

Figure lid. Correlation of measured and calculated plastic strain <at 500°C

Figure lie. Correlation of measured and calculated plastic strain .at 550°C

Figure Ilf. Correlation of measured and calculated plastic strain ,at 600°C

Figure 12a. Correlation of measured and calculated creep strain at 350°C

.

Figure 12b. Correlation of measured and calculated creep strain at 400°C

.

Figure 12c. Correlation of measured and calculated creep strain at 450°C

.

Figure 12d. Correlation of measured and calculated creep strain at 500°C.

Figure 12e. Correlation of measured and calculated creep strain at 550°C

.

Figure 12f

.

Correlation of measured and calculated creep strain at 600°C

.

Figure 12g. Correlation of measured and calculated creep strain at 650°C.

Figure 13a. Correlation of measured and calculated total strain at 350°C

.

Figure 13b. Correlation of measured and calculated total strain at 400°C

.

Figure 13c. Correlation of measured and calculated total strain at 450°C.

Figure 13d. Correlation of measured and calculated total strain at 500°C.

Figure 13e. Correlation of measured and calculated total strain at 550°C

.

Figure 13f

.

Correlation of measured and calculated total strain at 600°C.

Figure 13g. Correlation of measured and calculated total strain at 650°C.

7
Figure 14a. SS41 Steel - Correlation of measured and calculated creep strain

at 350°C

.

Figure 14b. SS41 Steel - Correlation of measured and calculated creep strain

at 450°C

.

Figure 14c. SS41 Steel - Correlation of measured and calculated creep strain

at 550°C

.

Figure 14d. SS41 Steel - Correlation of measured and calculated creep strain

at 600°C

.

Figure 15. Deformation modes for 2 minutes at temperature

.

Figure 16a. Deformation modes for 15 minutes at temperature

Figure 16b. Deformation modes for 15 minutes at temperature

Figure 17a. Deformation modes for 30 minutes at temperature

Figure 17b. Deformation modes for 30 minutes at temperature

Figure 18a. Deformation modes for 1 hour at temperature

.

Figure 18b. Deformation modes for 1 hour at temperature

.

Figure 19a. Deformation modes for 4 hours at temperature

.

Figure 19b. Deformation modes for 4 hours at temperature

.

8
SYMBOLS

c

e

- elastic strain, %

€p - plastic strain, %

€

c

- creep strain, %

e t

- total strain, %

T - temperature , C

a - stress, ksi

a

y

- yield stress, ksi

£7y r

t

- room temperature yield stress, ksi

aT

- tensile strength, ksi

E - Young's modulus, ksi

A - function of temperature

B - function of temperature

C - function of temperature

D - function of temperature

F - function of temperature

G - function of temperature

In this report the units used for temperature and stress are degrees C and ksi,

respectively. This was done to be consistent with the report* 1

}

from which the

original data was taken. To convert stresses from ksi to MPa the value of

stress in ksi should be multiplied by 6.89.

9
1 . Introduction

With the increase of steel skeleton high rise buildings, it is becoming

more important to be able to assess the damage sustained by such a building

during and after a fire. An analysis of the problem needs to be based on a

knowledge of certain basic facts. These include the determination of the

stresses and temperatures involved and the calculation of the resulting

strains. These strains can be subdivided into elastic, recoverable strain, c e ;

plastic, time independent strain, e p

; and creep, time dependent strain, e

c

.

It is the purpose of the present study to develop an equation predicting

the values of e e , e p and e

c under conditions of constant stress and

temperature, over a temperature range of 350 to 650°C, for periods of up to 4

hours. The empirical equation will have the form of

€ t = €

e + € P +C c (!)

or 6 t = Da + FaG + AtB a

c (2)

where c T is total strain and A, B, C, D, F, and G are all functions of

temperature. This equation will be used to construct deformation mechanism

maps showing the dominant mode of deformation for given conditions of

temperature stress and time.

Given the importance of the subject, it would be expected that there

would be a large body of data on which to base such a project. However, this

is apparently not the case. To the writers' knowledge there are only two

significant studies (1>2) available in the literature. The work reported by

Knight et al. (1) is particularly helpful as all their experimental data is

tabulated for temperature, time, stress and resulting strain. Using this data

10
a set of equations has been developed and used to construct deformation

mechanism maps. The work of Fujimoto et al. (2) has been used to test the

correlation between these predictions and separately obtained experimental

results

.

A future study might address the effect on the resulting strain, of

varying the temperature with time, i.e. increasing the temperature to a

maximum. The present assumption of constant temperature would certainly

predict conservative behavior for the same duration as compared to the heating

ramp that would occur in a fire.

2 . Specimen Material

The original purpose of this study was to develop deformation mechanism

maps for the American steel, ASTM A36. As stated in the introduction, only two

significant sets of data were available in the literature, neither of these

being obtained for A36 steel. The steel used by Knight et al. (1) was an

Australian steel, AS A149, while Fujimoto et al . ( 2

)

used a Japanese steel,

SS41 . The chemical compositions, yield strengths and tensile strengths for

A36, AS A149 and SS41 are given in Table 1. It can be seen that for all three

steels these values are not greatly different. There is, however, some

difference in the variation of yield stress with increasing temperature. This

can be seen in Figure 1 which includes results for A36 (3,4)

, AS A149 (5)

,

SS41 (2) and for BS4360 (6)

, a British steel which falls within the

specifications for A36 . The yield stresses have been normalized with respect

to the room temperature yield stress for each steel tested.

Considering the similarity between the Australian AS A149 and the ASTM

A36 specifications and the completeness of the Australian data, the object of

this project was pursued using the Australian data for creep and plasticity of

11
AS A149. Elastic behavior, which is rather insensitive to precise material

specification, was obtained from a variety of sources as noted in the report.

3 . Calculation of Elastic Strain

Since E = a/e for elastic behavior, where E is Young's Modulus, a is

stress and e is strain, the elastic component of strain, e

e , can be calculated

as follows

e. = ? x 102 % (3)

In order to calculate e

e at various temperatures, T, it is necessary to find E

as a function of T. The following empirical expression was obtained ( 7

}

using

data for a- iron given by Dever (8) over a temperature range of 0 to 650°C:

E = 29.3 x 103 - 12. 6T (4)

Values of E versus T are given by several authors for steels close to

A36 (2,3,9)

, but the results are not always consistent with each other. It was

found that the variations in e e caused by using these different values was

relatively small compared to the values of e T obtained at the same stress and

temperature. For example consider conditions at 600°C, where the values of E

show the biggest variation (21.7 x 10 3 ksi and 16.9 x 103 ksi, given by Dever

and De Falco, respectively). For a stress of 17.6 ksi the value of e e calculated using equation 4 was 0.081%, while that obtained using De Falco 's

value of E was 0.104%. Compared to the total strain observed after 2 minutes,

at this stress and temperature, e T = 0.41%, the variation in e

e was considered

relatively insignificant. Thus all values of € e were calculated using the

equation

< =

° X 102

%. (5)

(29.3 x 103 - 12. 6T)

12
4 . Calculation of Plastic Strain

The data given by Knight et al. are for various loads at temperatures

between 350 and 650°C for times of 2 to 960 minutes. An assumption was made,

by the present authors, that at 2 minutes any creep strain, c

c , was negligible

and that the strain observed at that time, € 2min , was due to elastic, c

e , and

plastic, e p

, components only. Obtaining e

e by using equation (5), one may

calculate e p

as follows:

€ p = e 2m i n

" C

e ( 6 )

Resulting values of e

e and e p

are given in Table 2. Since e p is time

independent, it is only necessary to find an equation linking e p

with the

stress, a , for a given temperature, T, i.e.,

£ p = FaG (7)

where F and G are functions of temperature. Data for e p and a were taken from

two reports, one by Knight, Skinner and Lay ( 1

5

and the other by Skinner (5)

, and

are listed in Tables 2 and 3, respectively. Using the second reference, data

was obtained from a graph reproduced here as Figure 2. This figure shows the

contours of strains from 0.01 to 5% during tensile testing at a strain rate of

2 x 10" 3 min" 1 over a temperature range of 0 to 650°C.

Figures 3a to 3g show values of e p plotted against a on a log- log scale.

It can be seen that for all temperatures the results are well represented by

straight lines, enabling calculation of the constants log F and G from equation

(7) at each temperature. The values of log F and G obtained in this manner are

given in Table 4 and are plotted against temperature in Figures 4 and 5. Least

squares fitting of the results gave

log F = -0.00041 * t

1 - 647 (8)

13
and

G = T/( 147 - 0.161 * T) (9)

Therefore

,

c = 1Q

-(0. 00041 * t

1 ' 647

) * aT/(147 - 0.161 * T)

( 10 )

5 . Calculation of Creep Strain

Because creep strain is time dependent it is necessary to find an

equation of the form:

€ c = AtB

<7 C (11)

where e

c is creep strain, t is time and A, B, and C are functions of

temperature. Values of e

c were found using equation (1)

Figures 6a to 6g show log- log plots of e

c versus t for different values

of o. The results are well represented by straight lines as shown. For each

temperature an average value of B was found (Table 5) and these were then

plotted linearly against temperature as shown in Figure 7. Least squares

fitting gave the equation

B = -1.1 + 0.0035 * T (12)

The same procedure was repeated for log- log plots of e

c versus a for different

values of t as seen in Figures 8a to 8g. Average values of C (Table 5) were

plotted linearly against temperature in Figure 9, but this time the results

were very scattered. Inspite of this, least squares fitting was used to obtain

a straight line resulting in the relationship

C = 2.1 + 0.0064 * T (13)

Values of the constant A in equation (11) were found by calculating

log e

c /tB

cr c for each stress and time at a given temperature (Table 5). The

results were averaged and plotted against temperature in Figure 10.

14
This time the points can be represented by two straight lines

intersecting at 500°C. The equations for the two lines in Figure 10 are:

for T < 500°C

for T > 500°C

A = 1 Q

-( 6.10 + °' 573 * T)

in -(13.25 - 0.00851 * T) A = 1U

(14)

(15)

Calculation of values of A at T = 500°C can be made using either of equations

(14) or (15). Having obtained values for constants A, B, and C equation (9),

e

c = AtB a

c can now be evaluated.

6 . Calculation of Total Strain

The total strain, e r , is the sum of the elastic, plastic and creep

strains

€ t = €

e + e P + €c (!)

where

e e = 102 * a/(29300 - 12.6 * T)

1Q

-(0. 00041 * T

1 ' 647

) * T/(147 - 0.016 * T)

(5)

( 10 )

and for T < 500 °C

in -(6.10 + 0.00573 * T) . (-1.1 + 0.0035 * T) , (2.1 + 0.0064 * T) ,,, N e

c = 10 * t * o (16)

or for T > 500°C

1

n

- (13 . 25 - 0.00851 * T) . (-1.1 + 0.0035 * T) . (2.1 + 0.0064 * T)

e

c = 10 * t * a

'

where T is in degrees C, a is in ksi and e is in %

.

Using these equations values of €

# , c p

, e

c and e T were calculated for

each temperature, stress and time reported by Knight et al. {1) The resulting

values are listed in Table 6 along with the data measured by Knight et al

.

15
7

.

Correlation of Measured and Calculated Plastic Strains

Values of plastic strain calculated using equation (10) are given in

Table 7. Figures 11a to Ilf show plots of measured and calculated plastic

strains versus stress for temperatures ranging from 350 to 600° C. The measured

values include results from both the creep studies of Knight et al . ( 1

)

and the

tensile testing work of Skinner (5) . As can be seen, the correlation between

results at all temperatures is good.

8 . Correlation of Measured and Calculated Creep Strains

Figures 12a to 12g show plots of measured and calculated creep strains

for temperatures of 350 to 650°C. The correlation of many of the results is

excellent while for some the agreement is not so good. Two things should be

noted: (1) Except in one case, the calculated values of creep strain are

higher than those measured, thus overestimating the strain achieved and giving

a conservative prediction. (2) During work at 550°C Knight et al. (1) carried

out two tests at the same stress of 23.4 ksi. As these gave different values

of creep strain both sets of results are included in Figure 12e. It can be

seen that one set is in better agreement with the calculated value than is the

other. A similar situation occurs at 350°C where two strains of 47.9 and 48.0

ksi were used. It can be seen in Figure 12a that there was apparently higher

creep strain resulting from the lower stress. These two cases are the only

indications of possible experimental error in the work of Knight et al.

9 . Correlation of Measured and Calculated Total Strains

Figures 13a to 13g show plots of measured and calculated total strains

for three different stress levels at temperatures between 350°C and 650°C for

times of up to 8 hours. Once again, in general the agreement is very good. As

16
for creep strain, where there are discrepancies the calculated result always

overestimates the total strain thus giving conservative values for any given

condition. As also noted in the last section, two sets of results for the same

stress were given by Knight et al. (1) at 550°C. Both are included in Figure

13e, thus giving an indication of possible experimental variations.

10. Correlation of Measured and Calculated Strains for SS41

As stated in the introduction, creep testing on SS41 , a steel close to

A36 specifications, was carried out by Fujimoto et al. (2) This work can be

used to test the correlation between values predicted by equations (16) and

(17) and separately obtained experimental results. Values of plastic, creep

and total strains measured by Fujimoto et al. were obtained from the figures

included in reference 2. These values are shown in Tables 8 and 9. It will be

shown that the agreement for creep strains is remarkably good, while this is

not so true for plastic strains.

10.1 Plastic Strains

It was noted in Section 2 that the temperature dependences of the yield

stresses are different for the various steels considered, as shown in Figure 1.

These differences are very marked for the two steels relevant to the discussion

here, i.e., AS A149 and SS41 . For example, at 400°C the values of ^y/^yrt are

0.81 and 0.63, respectively. Thus at a given temperature and load a specimen

made of SS41 steel will show a considerably larger plastic strain than will one

made of AS A149 steel. A comparison of results predicted by equations (16) and

(17) and those measured by Fujimoto is given in Table 8.

10 .

2

Creep Strain

Values of creep strain for SS41 are shown in Tables 9a to 9d. These

include results measured by Fujimoto et al. (2) and values predicted both by

17
Fujimoto and the present investigation. One point should be noted: The value

of t is the time during which creep occurred and does not include the time of

two minutes assumed by the present authors to involve only elastic and plastic

strains, see Section 4. Thus, before using equations (16) and (17) to predict

creep strains, two minutes needs to be added to each value of the time t as

given by Fuj imoto

.

Figures 14a to 14d show the correlation between the measurements and

both predictions for e

c during loading at temperatures of 350, 450, 550, and

600°C. Figure 14a shows the results for the highest stress level used at

350°C. In Figures 14a and 14b the correlations can be seen to be good. In

Figure 14c, at a temperature of 550°C and a stress of 17.8 ksi, it can be seen

that while the agreement between the present prediction and the measurements of

Fujimoto is not so good, it is considerably better than that for the prediction

of Fujimoto et al. themselves. In Figure 14d, at a temperature of 600°C and a

stress of 10.7 ksi, the prediction of Fujimoto is too low while that of the

present investigation is too high. For a stress of 14.2 ksi both predictions

are low but that from equation (17) is closer to the measured values.

It should also be noted that for each temperature, stress and time only

one specimen was tested. No indication is given of possible experimental

variation, such as that found in the two cases carried out by Knight et al. (1)

and mentioned previously.

11 . Deformation Mechanism Mans

A deformation mechanism map is a map that shows the deformation modes

operating under known conditions of time, temperature and stress. In the

present case the deformation consists of elastic, plastic, and creep modes.

Equations (16) and (17) and data from the tensile tests of Skinner (5) have been

18
used to construct such maps for times of 2, 15, 30, 60, and 240 minutes at

temperature, see Figures 15- 19b.

Figure 15 shows a map for conditions after two minutes at temperature.

As was stated in Section 4, it was assumed that at 2 minutes only the elastic

and plastic modes were operating and that creep was negligible. Thus this map

consists of only three areas, one of which is dominated by elasticity, one by

plasticity and one in which fracture has occurred. Also shown are the contours

of total strain values of 1, 2, and 5%. Figure 16a shows deformation modes

after 15 minutes at temperature and includes creep as a deformation mechanism.

Figure 16b shows the same map as 16a but includes total strain value contours

of 1, 2, and 5%. Figures 17a to 19b show maps obtained after 30, 60, and 240

minutes at temperature, respectively. In all the maps the dominant deformation

mode existing in each area is shown underlined. In the following section the

construction of a Deformation Mechanism Map for a loading time of 60 minutes is

considered.

12 . Construction of the Deformation Mechanism Maps

Many pieces of information have to be considered in order to construct a

deformation mechanism map. These include:

12.1 The Boundary at which Fracture Occurs

This boundary was deduced from the tensile test results of Skinner ( 5

)

as

shown in Figure 2. Values of aT , the U.T.S. are given in Table 10a. For

temperatures of 500°C and above values were taken directly from Figure 2.

Between 350 and 500°C the curve was extrapolated by eye.

12.2 The Boundary between ELASTIC and Elastic PLASTIC

This boundary, seen in Figure 15, is also present in all the other maps.

The critical condition was considered to be a plastic strain, e p

, of 0.1%.

19
When € p > 0.1% plasticity dominated while when e p

< 0.1% elasticity was the

dominant mode. The boundary had to be obtained for two ranges of temperatures

- above and below 350°C. Above 350°C, equations (15) and (16) were used to

calculate the stress causing € p = 0.1% for each temperature. Since the

equations were not valid for temperatures below 350°C the boundary in this

range was constructed using the contour of 0.1% proof stress taken from Figure

2 (5) . The results are shown in Table 10b. As would be desired both methods

gave close to the same value of stress at 350°C, so that the elastic/plastic

boundary was continuous across this temperature.

12.3 The Boundary between Elastic CREEP and Elastic Plastic CREEP

For conditions such that creep occurs this boundary will be a

continuation of the previous one between elastic and elastic plastic. See

Figure 16. The critical value of plastic strain was taken to be 0.1%.

12.4 The Boundary between ELASTIC and Elastic CREEP

Equations (16) and (17) were used to calculate conditions at which

e

c =0.1%. The results are shown in Table iOd. Above this boundary creep was

considered to be dominant.

12.5 The Boundary between Elastic PLASTIC and Elastic PLASTIC Creep

Once again it was necessary to calculate conditions at which €

c = 0.1%.

For temperatures above 350°C equation (16) was used. Below 350°C the curve was

extrapolated backwards by eye. The results are given in Table lOe. Above this

boundary, although there is some creep, plasticity remains the dominant mode.

12.6 The Boundary between Elastic PLASTIC Creep and Elastic Plastic

CREEP

For this boundary equation (16) were used to find the conditions at

which € p = €

c

, The results are given in Table lOf

.

Above the boundary

20
plasticity is dominant while below it creep dominates.

12.7 Total Strain Contours of 1%. 2%. and 5%

On Figures 16b, 17b, 18b, and 19b total strain contours of 1, 2, and 5%

are shown. At 350 °C and above these were calculated from equations (16) and

(17). Below 350°C these contours were taken from those shown in Figure 2. The

values of stress for these total strains are given in Table lOg.

13 . Conclusions

1. Using data for Australian steel A149 an equation has been developed

hat enables calculation of elastic, plastic, creep and total strains for given

conditions of stress and time, and for temperatures between 350 and 650°C.

2. Correlation between the measured and predicted strains is good.

3. The prediction for values of creep strain was tested against

separately obtained results for the Japanese steel, SS41 . The agreement is

good.

4. Deformation mechanism maps were constructed using the above

equation, for times of 2 to 240 minutes and temperatures of 350 to 650°C. The

dominant mechanism for any given condition of temperature, stress and time is

shown on the maps

.

Acknowledgements

We would like to thank the American Iron and Steel Institute (A.I.S.I.)

for financial support and encouragement of the study reported here. In

particular, the efforts of Mr. David Jeans and Mrs. Kathleen Almand of A.I.S.I.

to collect data from American steel producers and to disseminate the early

fruits of this work in order to stimulate industrial interaction is greatly

appreciated

.

21
References

1. Knight, D. , Skinner, D. H. , and Lay, M. G. , "Prediction of Isothermal

Creep," Broken Hill Proprietary Company, Clayton, Victoria, Australia.

Melbourne Research Lab. Report 18/2, April 1971, pp. 1-14.

2. Fujimoto, M. , Furumur, F. , Ave , T. , and Shinohara, Y. , "Primary Creep of

Structural Steel (SS41) at High Temperatures," Trans. A.I.J., No. 296, October

1980, pp. 145-157.

3. De Falco, F. D. , "Investigation of the Compressive Response of Modern

Structural Steels at Fire Load Temperatures," Doctoral Dissertation, University

of Connecticut, 1974, pp . 1-50.

4. Holt, J. M. , "Short-Time Elevated-Temperature Tensile Properties of USS

COR-TEN and USS TRI-TEN High Strength Low-Alloy Steels, USS MAN-TEN (A440) High

Strength Steel and ASTM A36 Steel," (57.19-901) (1) Progress Report (n-HS-2),

United States Steel, Applied Research Lab., Monroeville, Pennsylvania, October

1964.

5. Skinner, D. H. , "Determination of High Temperature Properties of Steel,"

Broken Hill Proprietary Company, Melbourne, Australia, Technical Bulletin, Vol.

16, No. 2, November 1972, pp . 10-21.

6. Jerath, V., Cole, K. J., and Smith, C. I., "Elevated Temperature Properties

of Structural Steel Manufactured by the British Steel Corporation," Report

T/RS/1189/1 1/80C , British Steel Corp., Teeside, England, July 1980.

7. Fields, R. J., "Fracture Mechanisms in Round Bars with a Detailed Study of

Finger-Like Crack Growth," Ph.D Thesis, University of Cambridge, 1978, p. 208.

22
8. Dever, D. J., "Temperature Dependence of the Elastic Constants in a-Iron

Single Crystals: Relationship to Spin Order and Diffusion Anomalies," J. Appl.

Phys., Vol . 43, 1972, p. 3293.

9. Brockenbrough , R. L. , "Investigation of Heat Curved Girders," Presented at

the Annual Meeting of the American Assoc, of State Highway Officials,

Minneapolis, Minnesota, December 1968.

23
Table 1. Compositions and Tensile Pronerties; for

ASTM A3 6. AS A149. and SS41 Steels

A3 6 A149UJ- SS41-12-*-

c 0.27 0.18

Si 0.128 0.24

Mn 0.65 0.73

P max 0 . 04 0.033 0.016

S max 0.05 0.041 0.017

Ni 0.086

Cr 0.16

Cu 0.01

ay psi 36,000 35,500 35,300

MPA 250 245 243

psi 58,000 to 80,000 70,500 62,400

MPA 400 to 550 487 431

24
Table 2. Values of Plastic Strain for AS A149 from Knight et al.^-

Temp

.

a E X 103 € 2 C ksi ksi

350 32.1 24.9

40.2 • 47.9 1 . 48.0 1 . 52.3 2.

56.2 3.

60.1 3.

61.0 3.

400 21.1 24.3

23.2 # 38.8 . 48.6 2.

51.7 2.

56.0 3.

450 21.1 23.6

23.2

31.9 . 41.8 1.

45.1 1.

46.7 2.

48.1 2.

500 21.0 23.0

23.4

28.1 # 31.1 # 32.2 m 34.0 1.

37.0 1.

550 16.1 22.4

18.5 . 20.3

23.4 m 23.4 . 25.0 . 26.7 •

600 9.7 21.7

12.0 . 12.8

16.5 . 17.6

.13 .15

.16 .68

.19 1.71

.19 1.49

.21 2.14

.23 3.07

.24 3.46

.25 3.43

.09 .04

.10 .08

.16 .79

.20 1.87

.21 2.30

.23 3.20

.09 .01

.10 .05

.14 .30

.17 1.03

.19 1.71

.20 2.11

.20 2.55

.09 .06

.10 .10

.12 .25

.14 .46

.14 .68

.15 .89

.16 1.12

.07 .02

.08 .04

.09 .15

.10 .19

.11 .24

.11 .32

.12 .58

.04 -.01

.06 .04

.06 .09

.08 .13

.08 .33

min

28

84

90

68

35

30

70

68

13

18

95

07

51

43

10

15

44

20

90

31

75

15

20

37

60

82

04

28

09

12

24

29

35

43

70

03

10

15

21

41

25
Table 2. (continued)

Values of Plastic Strain for AS A149 from Knight et

Temp

.

C

a

ksi

E X 103 € 2 n)in %

ksi = a %

Et

£ 2b i n %

650 4.8 21.1 .06 .02 .04

6.4 .07 .03 .04

8.8 .07 .04 .03

11.2 .20 .05 .15

26
Temp

.

C

350

400

450

Table 3. Values of Plastic Strain for AS A149 from Skinner4i-L

o

ksi

Et x 10 3 ksi

c p

+ €

e % e e = a %

Et

€ p%

21.6 24.9 .

.

— 0.01

24.8 0.05

26.2 0.10

27.2 0.25 0.11 0.14

29.1 0.20

32.4 0.5 0.13 0.37

39.3 1.0 0.16 0.84

44.5 1.5 0.18 1.32

49.2 2.0 0.20 1.80

53.4 2.5 0.21 2.29

56.4 3.0 0.23 2.77

58.8 3.5 0.24 3.26

61.1 4.0 0.25 3.75

62.7 4.5 0.25 4.25

64 .

4

5.0 0.26 4.74

20.6 24.3 .

.

0.01

23.1 0.05

26.0 0.10

27.2 0.25 0.11 0.14

29.1 0.20

32.1 0.5 0.13 0.37

38.1 1.0 0.16 0.84

43.3 1.5 0.18 1.22

47.3 2.0 0.19 1.81

51.1 2.5 0.21 2.24

53.2 3.0 0.22 2.78

55.1 3.5 0.23 3.27

57.0 4.0 0.23 3.77

58.3 4.5 0.24 4.26

59.4 5.0 0.24 4.76

19.9 23.6 _ _ _ _ 0.01

23.2 0.05

25.5 0.10

26.8 0.25 0.11 0.16

28.3 0.20

31.1 0.5 0.13 0.37

36.2 1.0 0.15 0.85

40.3 1.5 0.17 1.33

42.8 2.0 0.18 1.82

45.2 2.5 0.18 2.32

46.5 3.0 0.19 2.81

47.3 3.5 0.19 3.31

48.3 4.0 0.20 3.80

49.1 4.5 0.20 4.30

50.3 5.0 0.21 4.79

27
Table 3. (continued)

Values of Plastic Strain for AS A149 from Skinner-^-^-

Temp

.

a Et x 103

C p

+ C

e % € e = 2_% € p

%

C ksi ksi Et

500 20.2 23.0 - - . . 0.01

22.2 0.05

24.3 0.10

26.1 0.25 0.11 0.14

26.1 0.20

29.0 0.5 0.13 0.37

33.4 1.0 0.15 0.85

35.3 1.5 0.15 1.35

36.7 2.0 0.16 1.84

36.9 2.5 0.16 2.34

38.7 3.0 0.17 2.83

38.7 3.5 0.17 3.33

38.7 4.0 0.17 3.83

40.5 4.5 0.18 4.32

40.5 5.0 0.18 4.82

550 14.4 22.4 _ - - - 0.01

17.6 0.05

19.2 0.10

20.0 0.25 0.09 0.16

20.7 0.20

21.7 0.5 0.10 0.40

23.9 1.0 0.11 0.89

24.8 1.5 0.11 1.39

24.8 2.0 0.11 1.89

25.5 2.5 0.11 2.39

25.5 3.0 0.11 2.89

25.5 3.5 0.11 3.39

25.5 4.0 0.11 3.89

26.0 4.5 0.12 4.38

26.0 5.0 0.12 4.88

600 10.6 21.7 _ _ 0.01

12.9 0.05

13.9 0.10

13.9 0.25 0.06 0.19

14.7 0.20

15.5 0.5 0.07 0.43

15.5 1.0 0.07 0.93

16.3 1.5 0.08 1.42

16.3 2.0 0.08 1.92

16.8 2.5 0.08 2.42

16.8 3.0 0.08 2.92

16.8 3.5 0.08 3.42

17.3 4.0 0.08 3.92

17.3 4.5 0.08 4.42

17.3 5.0 0.08 4.92

28
Table 3. (continued)

Values of Plastic Strain for AS A149 from Skinneri-^-

Temp

.

C

650

o

ksi

Et x 103 ksi

+ <i% €

e = 2_%

et

e P %

8.1 18.1 . _ _ _ 0.01

9.7 0.05

10.3 0.10

10.3 0.25 0.06 0.19

11.1 0.20

11.1 0.5 0.06 0.44

11.1 1.0 0.06 0.94

11.1 1.5 0.06 1.44

11.1 2.0 0.06 1.94

11.1 2.5 0.06 2.44

11.1 3.0 0.06 2.94

11.1 3.5 0.06 3.44

11.1 4.0 0.06 3.94

11.1 4.5 0.06 4.44

11.1 5.0 0.06 4.94

29
Table 4. Values of log FCT) and GCT) where e p = FcrTemp . C log

350 -6

400 -7

450 -9

500 -11

550 -13

600 -13

650 -17

F G

406 3.918

838 4.816

657 6.062

16 7.315

44 9.703

79 11.40

68 17.00

30
Table 5. Values of ACT) . Bm and Cm where e

c = At^-

Temp . C A B C

350 8.04 0.15 3.8

400 8.48 0.31 3.9

450 8.74 0.45 4.9

500 8.9 0.58 7.2

550 8.61 0.71 5.9

600 8.2 1.00 6.5

650 7.6 1.24 4.7

31
Table 6a. Measured and Calculated Strains During Loading at 350C

Temp ExlO3 C ksi

350 24.9

350 24.9

350 24.9

350 24.9

o o t calculated strains % measured strains %

ksi

32.1

40.2

47.9

48.0

v Ft T mms e

0 €

c e T € 0 e r € j

.90 2 .13

P

.29 0 .42 .13

P

.15 0 .28

4 .03 .45 .07 .35

6 .03 .45 .07 .35

10 .04 .46 .07 .35

18 .04 .46 .07 .35

30 .04 .46 .07 .35

60 .04 .46 .08 .36

120 .05 .47 .07 .35

240 .05 .47 .07 .35

480 .06 .48 .07 .35

960 .06 .48 .12 .40

.13 2 .16 .70 0 .86 .16 .68 0 .84

4 .08 .94 .07 .91

6 .08 .94 .08 .92

10 .10 .95 .08 .92

18 .10 .96 .08 .92

30 .11 .97 .09 .93

60 .12 .98 .10 .94

120 .13 .99 .12 .96

240 .14 1.00 .14 .98

480 .15 1.01 .16 1.00

960 .17 1.03 .18 1.02

.35 2 .19 1.37 0 1.56 .19 1.71 0 1.90

4 .17 1.73 .20 2.10

6 .18 1.74 .21 2.11

10 .20 1.76 .22 2.12

18 .22 1.78 .23 2.13

30 .23 1.79 .25 2.15

60 .26 1.82 .27 2.17

120 .28 1.84 .30 2.20

240 .30 1.87 .34 2.24

480 .33 1.89 .38 2.28

960 .36 1.92 .44 2.34

..35 2 .19 1.38 0 1.57 .19 1.49 0 1.68

4 .17 1.74 .15 1.83

6 .18 1.76 .16 1.84

10 .2 1.77 .17 1.85

18 .22 1.79 .18 1.87

30 .24 1.81 .19 1.88

60 .26 1.83 .21 1.89

120 .28 1.85 .22 1.90

240 .31 1.88 .25 1.93

480 .34 1.91 .29 1.97

960 .37 1.94 .32 2.00

32
Table 6a. Continued

Temp ExlO3 C ksi

350 24.9

350 24.9

350 24.9

350 24.9

o o t calculated strains % measured strains %

ksi

52.3

56.2

60.1

61.0

O„ T> T mms e

0 € r

e

r e T

e

0 €- € j

1.47 2 .21 1.92 0 2.13 .21 2.14 0 2.35

4 .25 2.38 .21 2.56

6 .27 2.40 .22 2.57

10 .29 2.42 .23 2.58

18 .32 2.45 .24 2.59

30 .34 2.47 .27 2.62

60 .37 2.51 .29 2.64

120 .41 2.54 .34 2.69

240 .45 2.58 .39 2.74

480 .49 2.62 .47 2.82

960 .53 2.66 .55 2.90

1.58 2 .23 2.54 0 2.76 .23 3.07 0 3.30

4 .34 3.10 .40 3.70

6 .37 3.13 .43 3.73

10 .40 3.16 .46 3.76

18 .44 3.2 .48 3.78

30 .47 3.23 .50 3.80

60 .51 3.27 .55 3.85

120 .56 3.32 .61 3.91

240 .61 3.37 .69 3.99

480 .67 3.43 .83 4.13

960 .73 3.49 1.00 4.30

1.69 2 .24 3.29 0 3.53 .24 3.46 0 3.70

4 .45 3.99 .48 4.18

6 .49 4.02 .50 4.20

10 .53 4.06 .53 4.23

18 .58 4.11 .56 4.26

30 .62 4.15 .60 4.30

60 .68 4.21 .64 4.34

120 .75 4.28 .74 4.44

240 .82 4.35 .86 4.56

480 .89 4.42 .99 4.69

960 .97 4.50 1.19 4.89

1.72 2 .25 3.48 0 3.72 .25 3.43 0 3.68

4 .48 4.20 .55 4.23

6 .52 4.25 .58 4.26

10 .57 4.29 .60 4.28

18 .61 4.34 .64 4.32

30 .66 4.39 .67 4.35

60 .73 4.45 .70 4.38

120 .79 4.51 .79 4.47

240 .86 4.59 .89 4.57

480 .94 4.67 1.04 4.72

960 1.03 4.76 1.27 4.95

33
Table 6b. Measured and Calculated Strains During Loading at 400C

Temp ExlO3 o a t calculated strains % measured strains % c ksi ksi O,. p

*r mins €

c C T

€

c € j

400 24.3 21.1 .59 2 .09

F

.03 0 .12 .09 .04 0 .13

960 .05 .17 0 .13

400 24.3 23.2 .65 2 .10 .05 0 .15 .10 .08 0 .18

480 .07 .22 0 .18

400 24.3 38.8 1.09 2 .16 .60 0 .76 .16 .79 0 .95

4 .13 .89 .11 1.06

6 .15 .91 .13 1.08

10 .19 .95 .15 1.10

18 .23 1.00 .18 1.13

30 .28 1.04 .20 1.15

60 .35 1.11 .29 1.24

120 .35 1.19 .31 1.26

240 .53 1.29 .37 1.32

480 .64 1.41 .48 1.43

400 24.3 48.6 1.37 2 .20 1.80 0 2.00 .20 1.87 0 2.07

4 .44 2.44 .23 2.30

6 .50 2.50 .27 2.34

10 .58 2.58 .32 2.39

18 .70 2.70 .38 2.45

30 .81 2.81 .47 2.54

60 1.00 3.00 .57 2.64

120 1.23 3.23 .68 2.75

240 1.52 3.52 .89 2.96

480 1.87 3.87 1.17 3.24

400 24.3 51.7 1.46 2 .21 2.42 0 2.63 .21 2.30 0 2.51

4 .48 3.12 .29 2.80

6 .59 3.22 .34 2.85

10 .73 3.37 .41 2.92

18 .90 3.53 .49 3.00

30 1.06 3.70 .58 3.09

60 1.32 3.96 .72 3.23

120 1.64 4.27 .89 3.40

240 2.02 4.66 1.09 3.60

480 2.49 5.13 1.37 3 • e ®

400 24.3 56.0 1.58 2 .23 3.57 0 3.80 .23 3.20 0 3.43

4 .69 4.50 .53 3.96

6 .86 4.66 .62 4.05

10 1.06 4.86 .72 4.15

18 1.30 5.10 .88 4.31

30 1.53 5.34 1.03 4.46

60 1.92 5.72 1.29 4.7

34
Table 6c. Measured and Calculated Strains During Loading at 450C

Temp ExlO3 a

C ksi ksi

450 23.6 21.1

450 23.6 23.2

450 23.6 31.9

450 23.6 41.8

a t calculated strains % measured strains %

’.. r> >p mms € 0 € r

e

0 e_ € T

.59 2 .09 .02 0 .11 .09 .01 0 .10

4 .01 .12 .01 .11

6 .02 .13 .01 .11

10 .02 .13 .02 .12

18 .03 .14 .03 .13

30 .04 .15 .03 .13

60 .06 .17 .05 .15

120 .08 .19 .05 .15

240 .11 .22 .05 .15

480 .15 .27 .10 .20

.65 2 .10 .04 0 .14 .10 .05 0 .15

4 .02 .16 .01 .16

6 .03 .17 .01 .16

10 .04 .18 .02 .17

18 .05 .19 .02 .17

30 .06 .21 .05 .20

60 .09 .23 .07 .22

120 .13 .27 .10 .25

240 .18 .32 .13 .28

480 .25 .39 .16 .32

.90 2 .13 .29 0 .43 .14 .30 0 .44

4 .09 .52 .13 .57

6 .12 .55 .16 .60

10 .17 .60 .18 .62

18 .24 .67 .21 .65

30 .31 .75 .24 .68

60 .44 .87 .30 .74

120 .62 1.05 .37 .81

240 .87 1.30 .45 .89

480 1.21 1.64 .56 1.00

.18 2 .18 1.51 0 1.68 .18 1.02 0 1.20

4 .35 2.03 .48 1.68

6 .48 2.16 .56 1.76

10 .67 2.35 .67 1.87

18 .93 2.61 .82 2.02

30 1.21 2.89 .93 2.13

60 1.71 3.39 1.15 2.35

120 2.40 3.39 1.45 2.65

240 3.34 5.02 1.87 3.07

480 4.65 6.34 2.44 3.66

35
Table 6c. Continued

Temp

C

450

450

450

ExlO3 ksi

23.6

23.6

23.6

a

ksi

45.1

46.7

48.1

o t calculated strains % measured strains %

R T mms c r

€

c € j

e r € T

1.27 2 .19 2.38 0 2.57 .19 1.71 0 1.90

4 .50 3.08 .35 2.23

6 .70 3.27 .45 2.35

10 .97 3.55 .58 2.48

18 1.35 3.93 .75 2.65

30 1.76 4.33 1.05 2.95

60 2.49 5.07 1.31 3.21

120 3.49 6.06 1.73 3.63

240 4.87 7.45 2.28 4.18

1.32 2 .20 2.94 0 3.14 .20 2.11 0 2.31

4 .60 3.74 .44 2.75

6 .83 3.97 .56 2.87

10 1.16 4.30 .73 3.04

18 1.61 4.75 .97 3.28

30 2.10 5.24 1.22 3.53

60 2.97 6.11 1.64 3.95

120 4.16 7.30 2.27 4.58

1.35 2 .20 3.52 0 3.72 .20 2.55 0 2.75

4 .69 4.41 .78 3.53

6 .96 4.68 1.06 3.81

10 1.33 5.05 2.75 4.10

18 1.85 5.57 1.80 4.55

« 30 2.42 6.13 2.25 5.00

36
Table 6d. Measured and Calculated Strains During Loading at 500C

Temp ExlO3 C ksi

500 23.0

500 23.0

500 23.0

500 23.0

a

ksi

21.0

23.4

28.1

31.1

a t calculated strains % measured strains %

O.. TS mms €„ €

c € j

_ € 0 e r . T P

.59 2 .09 .03 0 .12 .09 .06 0 .15

4 .02 .14 .01 .16

6 .03 .15 .01 .16

10 .04 .16 .01 .16

18 .06 .18 .02 .17

30 .09 .21 .02 .17

60 .14 .27 .04 .19

120 .23 .35 .10 .25

240 .36 .49 .16 .31

480 .57 .69 .20 .35

.66 2 .10 .07 0 .17 .10 .10 0 .20

4 .03 .20 .04 .24

6 .04 .22 .05 .25

10 .07 .25 .08 .28

18 .11 .29 .10 .30

30 .16 .33 .13 .33

60 .26 .43 .20 .40

120 .41 .58 .30 .50

240 .64 .82 .48 .68

480 1.00 1.18 .70 .90

960 1.58 1.76 1.08 1.28

.79 2 .12 .29 0 .41 .12 .25 0 .37

4 .08 .49 .13 .50

6 .12 .53 .17 .54

10 .19 .60 .23 .60

18 .29 .71 .31 .68

30 .42 .84 .39 .76

60 .68 1.09 .55 .92

120 1.07 1.48 .77 1.14

240 1.69 2.10 1.04 1.41

480 2.65 3.07 1.37 1.74

960 4.18 4.59 1.99 2.36

.88 2 .14 .62 0 .76 .14 .46 0 .60

4 .20 .96 .23 .83

6 .27 1.03 .33 .93

10 .37 1.13 .43 1.03

18 .54 1.30 .51 1.19

30 .76 1.46 .75 1.35

60 1.19 1.95 1.03 1.63

120 1.87 2.63 1.60 2.30

240 2.93 3.69 2.05 2.65

480 4.60 5.36 3.28 3.88

37
Table 6d. Continued

Temp

C

500

500

500

ExlO3 a g_ t calculated strains % measured strains %

ks i ks i a.. R T mins e

0 € p _

23.0 32.2 .91 2 .14 .81

4

6

10

18

30

60

120

240

23.0 34.0 .96 2 .15 1.22

4

6

10

18

30

60

120

23.0 37.0 1.04 2 .16 2.30

4

6

10

18

30

60

c T

€

e

€ r

C

c € T*

0 .95 .14 .68 0 .82

.16 1.11 .35 1.17

.24 1.19 .46 1.28

.38 1.33 .60 1.42

.60 1.55 .82 1.64

.87 1.82 1.00 1.82

1.39 2.34 1.48 2.30

2.20 3.16 2.15 2.97

3.47 4.43 3.31 4.13

0 1.37 .15 .89 0 1.04

.21 1.58 .21 1.25

.33 1.69 .33 1.37

.51 1.88 .78 1.82

.80 2.17 1.09 2.13

1.15 2.52 1.41 2.45

1.85 3.22 2.16 3.20

2.94 4.31 3.31 4.35

0 2.46 .16 1.12 0 1.28

.32 2.79 .57 1.85

.51 2.98 .77 2.05

.80 3.27 1.05 2.35

1.25 3.72 1.46 2.74

1.81 4.27 1.97 3.25

2.91 5.37 2.88 4.16

38
Table 6e . Measured and Calculated Strains During Loading at 55QC

Temp ExlO3 C ksi

550 22.4

550 22.4

550 22.4

550 22.4

a a t calculated strains % measured strains %

ksi

16.1

18.5

20.8

23.4

—yRT

.45

mins

2

€ D

.07

-p—

.01

€

c

0

e T

.08

e

0

.07

€ p

.02

e

c

0

c T

.09

4 .03 .11 .06 .15

6 .05 .13 .07 .16

10 .09 .17 .09 .18

18 .16 .24 .10 .19

30 .26 .33 .15 .24

60 .47 .55 .25 .34

120 .84 .92 .44 .53

240 1.49 1.57 .81 .90

480 2.66 2.73 1.39 1.48

.52 2 .08 .04 0 .12 .08 .04 0 .12

4 .04 .16 .13 .25

6 .11 .23 .18 .30

10 .20 .32 .26 .38

18 .35 .47 .43 .55

30 .56 .68 .57 .68

60 1.02 1.13 .82 .94

120 1.83 1.94 1.23 1.35

240 3.26 3.37 1.93 2.05

480 5.78 5.91 3.23 3.35

.59 2 .09 .11 0 .20 .09 .15 0 .24

4 .12 .32 .19 .43

6 .22 .42 .29 .53

10 .38 .58 .44 .68

18 .68 .88 .68 .92

30 1.08 1.28 .94 1.18

60 1.96 2.16 1.46 1.70

120 3.53 3.73 2.29 2.53

240 6.29 6.49 3.81 4.05

.66 2 .10 .33 0 .43 .10 .19 0 .29

4 .24 .67 .38 .67

6 .42 .85 .55 .84

10 .74 1.17 .85 1.13

18 1.31 1.74 1.33 1.62

30 2.09 2.52 1.54 1.83

60 3.80 4.24 2.76 3.05

39
Table 6e . Continued

Temp ExlQ3 a a t calculated strains % measured strains %

C ksi ksi q„ R T mins e

c .

550 22.4 23.4 .66 2 .10

4

6

10

18

30

60

550 22.4 25.0 .70 2 .11

4

6

10

18

30

60

550 22.4 26.7 .75 2 .12

4

6

10

18

€ pe

c e T

€

0 € r € y

.33 0 .43 .10

P

.25 0 .35

.24 .67 .42 .79

.42 .85 .65 1.00

.74 1.17 .97 1.32

1.31 1.74 1.22 1.57

2.09 2.52 2.10 2.45

3.80 4.24 3.46 3.81

.61 0 .72 .11 .32 0 .43

.34 1.06 .35 .78

.61 1.33 .60 1.03

1.08 1.80 .89 1.32

1.90 2.63 1.50 1.93

3.02 3.74 1.95 2.38

5.52 6.24 2.95 4.38

1.13 0 1.25 .12 .58 0 .70

.50 1.74 .85 1.55

.88 2.12 1.31 2.01

1.56 2.80 2.05 2.75

2.77 4.01 3.30 4.00

40
Table 6f. Measured and Calculated Strains During Loading at 600C

Temp ExlO3 a

C ksi ksi

600 21.7 9.7

600 21.7 12.0

600 21.7 12.8

600 21.7 16.5

600 21.7 17.6

a t calculated strains % measured strains %

O-, r> X mms € r

e T

€ r £ T

.27 2 .04 0 0 .04 .04 0 0 .03

4 .01 .06 .02 .05

6 .02 .07 .03 .06

10 .04 .09 .05 .08

18 .08 .13 .06 .09

30 .15 .19 .09 .12

60 .30 .35 .15 .18

120 .62 .66 .26 .29

240 1.24 1.29 .51 .54

480 2.49 2.53 1.00 1.03

.34 2 .06 0 0 .06 .06 .04 0 .10

4 .04 .09 .04 .14

6 .07 .13 .07 .17

10 .15 .21 .13 .23

18 .30 .35 .26 .36

30 .52 .57 .34 .44

60 1.07 1.12 .58 .68

120 2.18 2.24 .95 1.15

240 4.39 4.45 1.93 2.03

480 8.83 8.88 2.85 3.95

.36 2 .06 .01 0 .06 .06 .09 0 .15

4 .05 .12 .07 .22

6 .11 .17 .13 .28

10 .22 .28 .20 .35

18 .43 .50 .39 .52

30 .76 .82 .60 .75

60 1.57 1.64 1.10 1.25

120 3.20 3.26 2.20 2.35

240 6.25 6.51 4.33 4.48

.46 2 .08 .12 0 .19 .08 .13 0 .21

4 .24 .44 .20 .41

6 .49 .68 .38 .59

10 .98 1.17 .79 1.00

18 1.96 2.15 1.44 1.65

30 3.43 3.62 2.54 2.75

.50 2 .08 .25 0 .33 .08 .33 0 .41

4 .36 .69 .73 1.14

6 .71 1.05 1.24 1.65

10 1.44 1.77 2.11 2.52

18 2.87 3.20 3.79 4.20

41
Table 6p. Measured and Calculated Strains During Loading at 650C

Temp ExlO3 a

C ksi ksl

650 21.1 4.8

650 21.1 6.4

650 21.1 8.8

650 21.1 11.2

a t calculated strains % measured strains %

<7V ft T mins €

0 ec 6? € 0 €- € t

.14 2 .02

F

0 0 .02 .02

P

-

.04 0 .06

4 0 .02 0 .06

6 0 .02 0 .06

10 0 .03 0 .06

18 .01 .03 0 .06

30 .02 .04 0 .06

60 .04 .06 0 .06

120 .10 .12 .07 .13

240 .22 .24 .13 .19

480 .49 .52 .46 .52

.18 2 .03 0 0 .03 .03 .04 0 .07

4 0 .03 .02 .09

6 .01 .04 .03 .10

10 .02 .05 .06 .13

18 .06 .09 .10 .17

30 .11 .14 .33 .40

60 .25 .28 .38 .45

120 .58 .61 .42 .49

240 1.32 1.35 1.14 1.21

480 3.00 3.03 3.58 3.65

.25 2 .04 0 0 .04 .04 .03 0 .07

4 .04 .08 .06 .13

6 .08 .12 .14 .21

10 .18 .22 .27 .34

18 .41 .45 .55 .62

30 .78 .83 .96 1.03

60 1.84 1.89 1.96 2.03

120 4.25 4.29 4.19 4.26

.31 2 .05 .03 0 .08 .05 .15 09 .20

4 .16 .24 .27 .47

6 .36 .45 .45 .65

10 .81 .90 .93 1.13

18 1.83 1.92 1.85 2.05

30 3.54 3.63 3.35 3.55

42
Table 7. Calculated Values of Plastic Strain

Temp

.

a € p

C ksi %

350 25.0 .11

32.1 .29

40.2 .70

47.9 1.37

52.3 1.92

56.2 2.54

60.1 3.29

61.0 3.48

62.5 4.45

65.0 4.45

66.0 4.72

400 27.0 .12

31.0 .20

35.0 .37

38.8 .60

48.6 1.80

51.7 2.42

56.0 3.56

58.0 4.23

60.0 4.99

450 27.0 .11

31.9 .29

34.0 .43

37.0 .72

40.0 1.16

41.8 1.51

45.1 2.38

46.7 2.94

48.1 3.52

49.0 3.94

50.0 4.45

50.5 4.72

500 24.5 .10

28.1 .29

31.1 .62

32.2 .81

34.0 1.22

37.0 2.30

39.0 3.42

550 20.8 .11

23.4 .33

25.0 .61

26.7 1.13

43
Table 7. (continued) Calculated Values of Plastic Strain

Temp. a e p

C ksi %

600 16.5 .12

17.0 .16

17.6 .25

650 11.2 .03

44
Table 8. Measured and Calculated Plastic and Total Strains

for SS41 Steel

Temp

.

a ExlO3 «p

+ 6

e % c e =£% € p

% € p%

- * € j %

a *

€ t %

C ksi ksi E Fuj imoto Fields Fuj imoto Fields

350 35.5 24.9 1.13 .14 .99 .43 1.20 .68

39.0 1.52 .16 1.36 .62 1.62 .89

42.6 1.82 .17 1.65 .87 1.95 1.19

400 21.3 24.3 .18 .09 .09 .03 .23 .14

24.9 .35 .10 .25 .07 .43 .21

28.4 .53 .12 .41 .13 .63 .33

32.0 .88 .13 .75 .24 1.03 .51

35.5 1.27 .15 1.12 .39 1.51 .77

450 17.8 23.6 .09 .07 .02 .01 .11 .10

21.3 .18 .09 .09 .03 .28 .18

24.9 .37 .11 .26 .07 .55 .30

28.4 .69 .12 .57 .15 1.0 .51

32.0 1.02 .14 .88 .30 1.43 .88 ,

500 14.2 23.0 .06 .06 .00 .00 .09 .08

17.8 .11 .08 .03 .01 .22 .15

21.3 .24 .09 .15 .04 .59 .28

24.9 .44 .11 .33 .12 1.08 .58

28.4 .88 .12 .76 .32

550 10.7 22.4 .05 .05 .00 .00 .11 .10

14.2 .07 .06 .01 .00 .29 .30

17.8 .18 .08 .10 .02

21.3 .50 .10 .40 .13

600 7.1 21.1 .03 .03 .00 .00 .06 .08

10.7 .06 .05 .01 .00 .42 .59

14.2 .17 .07 .10 .02

*

e T

- total strain after 60 min. at temperature.

- these specimens fractured before 60 minutes at temperature.

The values of strain are those measured by Fuj imoto and calculated by Fields.

45
Table 9a. Measured and Calculated Creep Strains for

SS41 During Loading at 350°C

€

c % C

c % %

Temp a t measured by calculated by calculated by

C ksi mins

.

Fuj imoto Fields Fuj imoto

350 35.5 2 .028 .045 .023

5 .036 .051 .029

10 .042 .056 .034

20 .049 .061 .042

37 .054 .065 .048

62 .068 .070 .055

99 .081 .074 .062

156 .097 .078 .070

250 .12 .083 .078

355 .13 .087 .086

350 39.1 2 .036 .069 .036

5 .050 .077 .045

10 .056 .084 .054

20 .070 .092 .064

37 .082 .099 .076

63 .10 .106 .087

99 .12 .11 .097

159 .14 .12 .11

249 .16 .13 .12

370 .19 .13 .14

350 v£> CM 2 .046 .10 .054

5 .064 .11 .069

10 .073 .12 .082

20 .085 .13 .097

37 .10 .14 .11

63 .13 .15 .13

100 .15 .16 .15

155 .18 .17 .16

248 .21 .18 .18

354 .24 .19 .20

46
Table 9b. Measured and Calculated Creep Strains for

SS41 During Loading at 450°C

% % C

c %

Temp

.

a t measured by calculated by calculated by

C ksi mins

.

Fuj imoto Fields Fuj imoto

450 17.8 2 .019 .005 .016

5 .025 .008 .021

10 .031 .011 .026

19 .034 .014 .032

33 .039 .019 .038

58 .044 .024 .046

91 .046 .030 .053

144 .050 .037 .061

227 .055 .046 .071

350 .058 .057 .081

450 21.3 2 .03 .012 .034

4 .05 .017 .043

10 .06 .026 .057

19 .07 .035 .070

33 .09 .045 .084

58 .10 .059 .10

90 .11 .073 .12

144 .13 .091 .13

232 .14 .114 .16

450 24.9 2 .059 .026 .067

5 .090 .040 .089

9 .11 .053 .11

19 .13 .076 .14

32 .15 .097 .16

56 .18 .12 .19

90 .20 .16 .22

143 .23 .20 .26

226 .25 .25 .30

450 28.4 2 .074 .05 .12

5 .11 .08 .16

9 .15 .10 .19

19 .20 .15 .24

32 .26 .19 .28

56 .31 .24 .34

88 .36 .30 .39

144 .43 .38 .46

228 .48 .47 .53

336 .55 .57 .60

47
Table 9b. (continued) Measured and Calculated Creep Strains for

SS41 During Loading at 450°C

€

c % C

c % Cc %

Temp

.

a t measured by calculated by calculated by

C ksi mins

.

Fuj imoto Fields Fuj imoto

450 32.0 2 .11 .09 .20

5 .17 .14 .26

9 .22 .19 .31

18 .28 .26 .39

32 .35 .34 .47

56 .41 .44 .56

90 .49 .55 .65

141 .59 .68 .75

225 .67 .85 .87

333 .75 1.03 .99

48
Table 9c. Measured and Calculated Creeo Strains for

SS41 During Loading at 550°C

€

c % €

c % «c %

Temp

.

a t measured by calculated by calculated by

C ksi mins

.

Fuj imoto Fields Fuj imoto

550 10.7 2 .015 0 .018

5 .023 .006 .026

10 .028 .011 .033

19 .036 .019 .043

34 .044 .030 .053

57 .055 .046 .065

93 .065 .069 .078

147 .077 .10 .093

236 .086 .15 .11

349 .097 .20 .13

550 14.2 2 .044 .014 .057

5 .071 .030 .081

10 .098 .054 .11

19 .14 .092 .13

33 .18 .14 .17

56 .22 .22 .20

91 .27 .33 .24

142 .33 .48 .29

230 .42 .72 .35

345 .54 1.00 .41

550 17.8 2 .18 .051 .14

5 .33 .11 .20

9 .48 .18 .25

19 .70 .32 .33

32 .98 .51 .40

60 .85 .51

90 1.19 .59

120 1.51 .66

247 .92

362 1.00

550 21.3 2 .41 .14 .29

5 .78 .30 .41

9 1.2 .49 .51

20 .94 .69

30 1.31 .80

60 2.33 1.05

49
Table 9d. Measured and Calculated CreeD Strains for

SS41 During Loading at CT> oo

0 O

% €

c % €c %

Temp

.

a t measured by calculated by calculated by

C ksi mins

.

Fuj imoto Fields Fuj imoto

600 7.1 2 .013 .002 .010

5 .016 .004 .015

10 .021 .008 .019

20 .024 .016 .026

35 .028 .033 .032

60 .032 .049 .040

99 .035 .081 .050

155 .040 .13 .060

247 .042 .20 .073

378 .046 .31 .087

600 10.7 2 .054 .019 .048

5 .090 .047 .070

10 .12 .094 .093

19 .18 .18 .12

34 .25 .32 .15

58 .36 .55 .19

93 .50 .88 .23

146 .68 1.38 .28

238 .87 2.24 .34

600 14.2 2 .28 .10 .14

5 .61 .25 .21

9 .96 .45 .27

15 .75 .33

20 1.00 .37

30 .44

60 .59

50
Table 10. Construction of a Deformation Mechanism Map

for a Loading Time of 60 mins

.

Table 10a. The Boundary at Which Fracture Occurs

Temp

.

°7 -2.7-

C ksi aYR7 Reference

350* 70.6 1.99 (5)

400* 62.5 1.76

450* 51.8 1.46

500 40.6 1.14

550 26.9 .76

600 17.3 .49

650 11.3 .32

Estimated from Figure 2 (reproduced from Skinner ( 5

)

) by extrapolating the

curve to lower temperatures by eye.
c

20

49

98

150

198

250

301

350

400

410

420

10b. The Boundary between ELASTIC and Elastic PLASTIC

a a €

e

c p

e

c ksi ^YRT % % % Reference

35.5 1.0 .12 .10 0 (5)

34.8 .98 .12 .10 0

33.4 .94 .12 .10 0

31.7 .89 .11 .10 0

30.0 .85 .11 .10 0

27.5 .77 .10 .10 0

26.1 .73 .10 .10 0

24.1 .68 .10 .10 .01 Equation

26.8 .75 .11 .10 .06

27.0 .76 .11 .10 .08

27.1 .76 .11 .10 .10

52
Table 10c. The Boundary between Elastic CREEP

Elastic Plastic CREEP

Temp

.

a a

C ksi aYRT %

425 27.0 .76 .11

450 26.7 .75 .11

475 25.8 .73 .11

500 24.4 .69 .11

550 20.6 .58 .09

600 16.3 .46 .07

625 >UTS

€ pC

c % % Reference

.10 .11 Equation (16)

.10 .18 Equation (16)

.10 .27 Equation (16)

.10 .33 Equation (17)

.10 1.92 Equation (17)

.10 6.84 Equation (17)

53
c

420

425

450

475

500

525

550

575

600

650

lOd. The Boundary between ELASTIC and Elastic CREEP

a a €

e

€ pe

c ksi <7 Y r T % % % Reference

27.1 .76 .11 .10 .10 Equation (16)

26.5 .75 .11 .09 .10 Equation (16)

23.7 .67 .10 .05 .10 Equation (16)

21.3 .60 .09 .03 .10 Equation (16)

19.6 .55 .09 .02 .10 Equation (17)

15.4 .43 .07 0 .10 Equation (17)

12.2 .34 .05 0 .10 Equation (17)

9.8 .28 .04 0 .10 Equation (17)

8.0 .23 .04 0 .10 Equation (17)

5.5 .15 .03 0 .10 Equation (17)

54
Table lOe. The Boundary between Elastic PLASTIC and Elastic PLASTIC Creep

Temp

.

a o €

e

£ p

€

c C ksi aYRT % % % Reference

267* 70.6 1.99 Equation (16)

287* 57.5 1.62 Equation (16)

306* 50.1 1.41 Equation (16)

325 44.8 1.26 .18 1.12 .10 Equation (16)

350 39.0 1.10 .16 .62 .10 Equation (16)

400 29.7 .84 .12 .17 .10 Equation (16)

* curve extrapolated backwards by eye

55
Table lOf. The Boundary between Elastic PLASTIC Creep and

Elastic Plastic CREEP

Temp

.

a o € e

€ p

€

c C ksi <7 yRT % % % Reference

420 27.8 .78 .12 .12 .12 Equation (16)

425 33.3 .93 .14 .31 .31 Equation (16)

430 37.8 1.06 .16 .64 .64 Equation (16)

440 44.2 1.24 .19 1.78 1.78 Equation (16)

450 46.8 1.32 .20 2.98 2.98 Equation (16)

460 49.0 1.38 .21 4.98 4.98 Equation (16)

56
Temp

C.

20

47

99

145

197

245

297

350

400

450

500

550

600

650

Table lOg. Total Strain Contours of 1%. 2%. and 5%

€ t = 1% € t = 2% € t 5%

a 1a Temp

.

a <7 Temp

.

a <7

ksi a ?rt C. ksi a,i RT C ksi a,

If R T Ref.

38. 3 1 .08 23 45. 8 1 .29 21 58. 2 1 .64 (5)

38. 8 1 .09 49 46. 2 1 .30 47 59. 2 1 .67

39. 7 1 .12 99 47. 3 1 .33 99 61. 7 1 .74

41. 3 1 .16 147 50. 3 1 .42 115 63. 0 1 .77

42. 5 1 .20 197 54. 1 1 .52 146 66. 8 1 .88

41. 6 1 .17 246 51

.

7 1 .46 167 70. 3 1 .97

40. 0 1 .13 297 49. 8 1 .40 174 70. 9 2 .00

40. 5 1 .14 350 49. 2 1 .39 350 62. 8 1 .77 Eq. (16)

37. 5 1 .07 400 44. 5 1 .25 400 54. 4 1 .53 Eq. (16)

32. 9 .93 450 37. 8 1 .06 450 45. 0 1 .27 Eq. (16)

27. 7 .78 500 31. 3 .88 500 36. 6 1 .03 Eq. (17)

18. 1 .51 550 20. 5 .58 550 24. 1 .68 Eq. (17)

11

.

7 .34 600 13. 2 .37 600 15. 5 .44 Eq. (17)

7. 9 .22 650 8. 9 .25 650 10. 3 .29 Eq. (17)

57

A36

STEEL

NORMALIZED

YIELD

STRESS

VERSUS

TEMPERATURE o

CDO

inoooo

coo

04oo Od

LUQ

LU

dc3£

DC

LU

CL2

LU

h-

(XH)

K

OI

Ko

Figure

1.

Normalized

yield

stress

versus

temperature

for

A36

and

similar

steels.
Figure 2. The effect of temperature on the proof and flow stress of

AS A149 steel at a strain rate of 2 x 10" 3 min_1 (5)

.
PLASTIC

STRAIN

VS

STRESS

AT

350

DEG

CM

oo

H

(/)

CO

</)

LjlI

QC

1—

(/)

% NIVyiS OllSVld

Figure

3a.

Plastic

strain

versus

stress

at

350
PLASTIC

STRAIN

VS

STRESS

AT

400

DEG

o

H

COV

<0

CO

LJ

QC

1—

CO

% NlVdlS OllSVld

Figure

3b.

Plastic

strain

versus

stress

at

400
PLASTIC

STRAIN

VS

STRESS

AT

450

DEG

CJ

o

H

CO

NZ

CO

CO

hJ

CtC

1—

CO

% NlVdiS GllSVld

Figure

3c.

Plastic

strain

versus

stress

at

450
PLASTIC

STRAIN

VS

STRESS

AT

500

DEG

CM

Oo

H

CO

CO

CO

Ld

QC

1—

<f)

% Nivais onsvid

Figure

3d.

Plastic

strain

versus

stress

at

500
PLASTIC

STRAIN

VS

STRESS

AT

S50

DEG

% NlVdlS OllSVld

STRESS

KSI
PLASTIC

STRAIN

VS

STRESS

AT

600

DEG

% NlVdlS OllSVId

Figure

3f.

Plastic

strain

versus

stress

at

600
PLASTIC

STRAIN

VS

STRESS

AT

650

DEG

% NlVdlS OllSVld

Figure

3g.

Plastic

strain

versus

stress

at

650
LOG

F

VS

TEMPERATURE

CD LO © LD ©00

OJ — —

O 0)u

3

j son

TEMPERATURE

DEG
CONSTANT

G

VS

TEMPERATURE

©

© LD © LO ©CO

CM —

O

(1) U

3

u

Rj

•H

Uh

9 1NV1SN00

TEMPERATURE

DEG
CREEP

STRAIN

VS

TIME

FOR

T

=

350

DEG

% NlVdlS d33d3

Figure

6a.

Creep

strain

versus

time

at

350
CREEP

STRAIN

VS

TIME

FOR

T

=

400

DEG

CO

oo

CO

z:H

21

LU

ZH

I

% Nivais d33d3

Figure

6b.

Creep

strain

versus

time

at

400
CREEP

STRAIN

VS

TIME

FOR

T

=

450

DEG

CO

o

Ld

xH

h-

% NlVdlS d33d3

Figure

6c.

Creep

strain

versus

time

at

450
CREEP

STRAIN

VS

TIME

FOR

T

=

500

DEG

m

CO

z

H

Z

u

H

% NlVdlS d33d0

Figure

6d.

Creep

strain

versus

time

at

500°C.
CREEP

STRAIN

VS

TIME

FOR

T

=

550

DEG

% NlVdlS d33d0

Figure

6e.

Creep

strain

versus

time

at

550
CREEP

STRAIN

VS

TIME

FOR

T

=

600

DEG

m

</)

H

21

LlJ

XH

I

% NlVdlS d33d0

Figure

6f.

Creep

strain

versus

time

at

600°
CREEP

STRAIN

VS

TIME

FOR

T

=

650

DEG

o

(0

LU

X

H

H-

% NlVdlS d33d0

Figure

6g.

Creep

strain

versus

time

at

650°C.
PARAMETER

B

VS

TEMPERATURE




LO — LO ©00

<S>

a

TEMPERATURE

IN

DEG
CREEP

STRAIN

VS

STRESS

FOR

T

=

350

DEG

% NlVdlS d33d0

STRESS

KSI
CREEP

STRAIN

VS

STRESS

FOR

T

=

400

DEG

CM

o

0

H

CO

(/)

CO

LU

1—

(/)

% NlVdlS d33d3

Figure

8b.

Creep

strain

versus

stress

at

400
CREEP

STRAIN

VS

STRESS

FOR

T

=

4S0

DEG

CM

U

H

00

CO

CO

hi

QCH

00

% NlVdlS d33d0

Figure

8c.

Creep

strain

versus

stress

at

450
CREEP

STRAIN

VS

STRESS

FOR

T

=

500

DEG

CM

H

co

co

co

L±J

QC

1

in

o

o

% NlVidiS 633X3

Figure

8d.

Creep

strain

versus

stress

at

500
CREEP

STRAIN

VS

STRESS

FOR

T

=

5S0

DEG

Od

u

H

00

V

00

CO

Ll!

cy:

1—

00

% Nivais 633X3

Figure

8e

.

Creep

strain

versus

stress

at

550°
CREEP

STRAIN

VS

STRESS

FOR

T

=

600

DEG

CM

H

COV

CO

CO

LlI

QC

1—

CO

o

o

% NlVdlS d33d0

Figure

8f.

Creep

strain

versus

stress

at

600
CREEP

STRAIN

VS

STRESS

FOR

T

=

6S0

DEG

C\J

H

CO

co

CO

LjJ

C£

I

CO

o

o

% NlVdlS d33d0

Figure

8g.

Creep

strain

versus

stress

at

650
PARAMETER

C

VS

TEMPERATURE

G>

o

0} 3

u

tou

au

•rH

o a3i3wvavd

TEMPERATURE

DEG
PARAMETER

A

VS

TEMPERATURE

<s

(0 1^-00 0) <5)00

I I I I —

o

4) u

3

iJ

COu

a>

bo

tik

V d3i3WVdVd

TEMPERATURE

DEG
PLASTIC

STRAIN

VS

STRESS

AT

350

DEG

C o

oO

in

m

OJ

tfl C

•t-i cC

>-( 4J

10o

•HU

W

tfl —Ia

a)

a)

v-i u

oo

cfl

0) J-l 3

to

•H

IS» SS3dlS

PLASTIC

STRAIN
PLASTIC

STRAIN

VS

STRESS

AT

400

DEG

C

IS* SS3dlS

PLASTIC

STRAIN
PLASTIC

STRAIN

VS

STRESS

AT

450

DEG

C

IS* SS3dlS

PLASTIC

STRAIN

%
PLASTIC

STRAIN

VS

STRESS

AT

500

DEG

IS» SS3dlS

PLASTIC

STRAIN
PLASTIC

STRAIN

VS

STRESS

AT

550

DEG

IS>I SS3dlS

PLASTIC

STRAIN
PLASTIC

STRAIN

VS

STRESS

AT

600

DEG

uoO

o

VOV

(0c

•H

03Vi 4JW

O

i-lW

03 —

)

CV

•u

cd

•—

i

0)

Vio

CJ

4-1

0)Vi3

W)

•H

u,

ISX SS3diS

PLASTIC

STRAIN
% NlVdlS d33d3

u

oo

LDcnu

cdC

*r-l cOU

4Jw

a*

a>0)

>-i o

to

0) 4-) CO f—

I

3o

•—

H

COo

TOc

CO T5 0) 4l 3w

COe

4-1Oc

o

•HU

cO

*—

i

a)4i u

ou

cO CM

a)4i 3

WD

•H

u*
AS

149

STEEL

-

CREEP

STRAIN

VS

TIME

AT

400

DEG

% NlVdlS d33d0

Figure

12b.

Correlation

of

measured

and

calculated

creep

strain

at

400°
AS

149

STEEL

-

CREEP

STRAIN

VS

TIME

AT

450

DEG

<5>

<f>

H

LU

H

hOo

% NlVdiS d33d0

Figure

12c.

Correlation

of

measured

and

calculated

creep

strain

at

450
AS

149

STEEL

-

CREEP

STRAIN

VS

TIME

AT

500

DEG

o

^r

ir>

lo oo (\i —

% NlVdlS d33d0

Figure

12d.

Correlation

of

measured

and

calculated

creep

strain

at

500°
AS

149

STEEL

-

CREEP

STRAIN

VS

TIME

AT

550

DEG

o

©

lr> ©

CO

©

©

CO

CO

©©

CO

©

OJ

©

CO

©

CM

©

CO

©

o

o

LU

xH

HLD

^

00 (\J — ©

% NlVdiS d33d0

Figure

12e.

Correlation

of

measured

and

calculated

creep

strain

at

550
AS

149

STEEL

-

CREEP

STRAIN

VS

TIME

AT

500

DEG

j LO 00 <\J ®

% NlVdlS d33d3

Figure

12d.

Correlation

of

measured

and

calculated

creep

strain

at

500
AS

149

STEEL -

CREEP

STRAIN

VS

TIME

AT

550

DEG

©

^r

O LO©

00©

CM

^r©

CD

CO©©

CO©

CNJ ©

00©

OJ©

<0© oo

LUH

hL0 CO OJ — © % NlVdlS d33d0

Figure

12e.

Correlation

of

measured

and

calculated

creep

strain

at

550
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

350

DEG

C

oo

% Nivais 1V10JL

Figure

13a.

Correlation

of

measured

and

calculated

total

strain

at

350
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

400

DEG

C

x

o

o

% Nivais ivioi

Figure

13b.

Correlation

of

measured

and

calculated

total

strain

at

400
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

450

DEG

C




o

CO

z:H

T.

kJ

z:H

hCO LO CO C\J — <S>

% Nivais ivioi

Figure

13c.

Correlation

of

measured

and

calculated

total

strain

at

450°
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

500

DEG

C

o

% Nivais ivioi

Figure

13d.

Correlation

of

measured

and

calculated

total

strain

at

500°
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

550

DEG

©

oo

LU

:eH

I

% Nivais ivioi

Figure

13e.

Correlation

of

measured

and

calculated

total

strain

at

550
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

600

DEG

C




o

CO

zH

z

UJ

z:H

H

% nivsis ivioi

Figure

13f.

Correlation

of

measured

and

calculated

total

strain

at

600
AS

A

149

STEEL

-

TOTAL

STRAIN

VS

TIME

AT

650

DEG

C

% Nivais 1V101

Figure

13g.

Correlation

of

measured

and

calculated

total

strain

at

650
SS41

STEEL

-

CREEP

STRAIN

VS

TIME

AT

350

DEG

C

CD

LlI

H

h-

% NlVdlS 633H0

Figure

14a.

SS41

Steel

—

Correlation

of

measured

and

calculated

creep

strain

at

350°C
SS41

STEEL

-

CREEP

STRAIN

VS

TIME

AT

450

DEG

C




LO — LD ®

<S>

LJ

z:H

• VoOm

'•d'

4-1 COc

•H

COu

4-> w

ex

<u

QJ

J-l o

"O

Q) U

CO i1

3

u

I—

I

COu

-oc

CO -a

CDu

3

w

co

QJE

m

o

c

o

•H

4-1 CO r—

t

CDU

U

0O

1

CDa»

4-1 co

co

co

j=>

<uu

3

OO

•HCL

% NlVdlS 433X3
SS41

STEEL

-

CREEP

STRAIN

VS

TIME

AT

550

DEG

C

LlI

H

h-

% NlVdiS d33d3

Figure

14c.

SS41

Steel

-

Correlation

of

measured

and

calculated

creep

strain

at

550°C.
SS4

1

STEEL

-

CREEP

STRAIN

VS

TIME

AT

600

DEG

G>

CD O CO


 ©

CO




C\i

CO

z:H


 X

00

LlJ

H

o

00

G>

CO

G>

LO LO <S>

G>

v/ NlVdlS d33d3

Figure

14d.

SS41

Steel

-

Correlation

of

measured

and

calculated

creep

strain

at

600°C
A36

STEEL

DEFORMATION

MODES

FOR

2

MIN.

AT

TEMPERATURE

SS3U1S Q13IA Td

SS3U1S Q3HddV

Figure

15.

Deformation

modes

for

2

minutes

at

temperature.
A36

STEEL

DEFORMATION

MODES

FOR

15

MIN.

AT

TEMPERATURE

O

d

LUQ

111

IT

<

DC

LU

CL

S

LU

ISS301S Q13IA Td

SSBdlS OBIlddV

Figure

16a.

Deformation

modes

for

15

minutes

at

temperature.
DEFORMATION

MODES

FOR

15

MIN.

AT

TEMPERATURE

SS3H1S Q~I3IA TO

SS3U1S Q3llddV

Figure

16b.

Deformation

modes

for

15

minutes

at

temperature.
A36

STEEL

DEFORMATION

MODES

FOR

30

MIN.

AT

TEMPERATURE

cm Ln

'I— in o

SS3U1S CH3IA JLU

SS3U1S Q3HddV

100

200

300

400

500

600

TEMPERATURE

(DEG.

C)
A36

STEEL

DEFORMATION

MODES

FOR

30

MIN.

AT

TEMPERATURE

o

0

LU

Q

LU

DC

DC

LU

CL

• 0) J-l o

ssaais anaiA xu

ssHdis aanddv

Figure

17b.

Deformation

modes

for

30

minutes

at

temperat
A36

STEEL

DEFORMATION

MODES

FOR

1

HOUR

AT

TEMPERATURE

mm

CM IT) LO

o

SS3U-LS QT3IA Tbi

SS3U1S Q3ITddV

TEMPERATURE

(DEG.

C)

Figure

18a.

Deformation

modes

for

1

hour

at

temperature.
I.

LU

X

LUI— T—

CO DC

CD

O

00 LL <

CO

111 Q

SS3dlS QH3IA XU

SSBdlS Q3llddV

<u3u

ctJ u

0)aE

(V 4J

JJ

tc

J-i 3OX

Vjo4-1 W

a> •ooECO

•H

4J

rtE5-1 o

4-1

a) Q

X)

00ou3

oo
DEFORMATION

MODES

FOR

4

HOURS

AT

TEMPERATURE

O

SS3H1S CD3IA XM

SS3U1S Q3nddV

Figure

19a.

Deformation

modes

for

4

hours

at

temperature.
A36

STEEL

DEFORMATION

MODES

FOR

4

HOURS

AT

TEMPERATURE

o

LU

Q

LU

DC

DC

LU

Q.

LU

ISS301S Q13IA Td

ss3dis asnddv

Figure

19b,

Deformation

modes

for

4

hours

at

temperature.
NBS-H4A 'Rev. 2-80

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publ ication Date

BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions) NISTIR 88-3899 MARCH 1989

4. TITLE AND SUBTITLE

Elevated Temperature Deformation of Structural Steel

5. AUTHOR(S)

B.A. Fields and R.J. Fields

6. PERFORMING ORGANIZATION (11 joint or other than NpS. see in struction s) National Institute of Standards and Technology

BATKHMSLXEtt REJC B XHXSK/OCX**DCX

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Coverec

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

American Iron and Steel Institute

1133 15th Street, N.W.

Washington, DC

10. SUPPLEMENTARY NOTES

~1 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The results of tensile and creep tests on steels close to the American specification

for ASTM A36 have been used to formulate an equation from which elastic, plastic,

creep and total strains can be calculated. Correlations between measured and

predicted strains for Australian AS A149 and Japanese SS41 steels, both close to the

A36 specification, are shown and good agreement is found.

The above mentioned equation is also used to construct deformation mechanism (i.e.,

elastic, plastic, or creep) maps for times of 2 minutes to 4 hours at temperature.

From these maps the deformation mechanisms operating at a given temperature and

stress can be seen. The dominant mechanism for each set of conditions is given.

In addition the maps show contours of total strain values 1, 2, and 5%.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) A.S.T.M. A-36 steel; creep deformation; elastic deformation; fire resistance;

plastic deformation, structural steel.

13. AVAILABILITY

| Uni imited

|

1 For Official Distribution. Do Not Release to NTlS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

14. NO. OF

PRINTED PAGES

120

15. Price

fX ' Order From National Technical Information Service (NTIS), Springfield, VA. 22161

$19.95

U SCOMM-DC 6043-P80

N1STIR

88-3899

Jun

13,

2016