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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 

December 2006 

3. REPORT TYPE AND DATES COVERED 

Final Report 

December 2006 

4. TITLE AND SUBTITLE 

Fatigue Behavior of AAR Class A Railroad Wheel Steel at Ambient and Elevated 

Temperatures 

5. FUNDING NUMBERS 

RR28/DB032 

6. AUTHOR(S) 

* Fraser J. McMaster and Guadalupe B. Robledo 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

U.S. Department of Transportation 

Research and Innovative Technology Administration 

John A. Volpe National Transportation Systems Center 

55 Broadway 

Cambridge, MA 02142-1093 

8. PERFORMING ORGANIZATION 

REPORT NUMBER 

DOT-VNTSC-FRA-06-01 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 

U.S. Department of Transportation 

Federal Railroad Administration 

Office of Research and Development 

1120 Vermont Avenue, NW 

Mail Stop 20 

Washington, DC 20590 

10. SPONSORING/MONITORING 

AGENCY REPORT NUMBER 

DOT/FRA/ORD-06/15 

11. SUPPLEMENTARY NOTES 

*Southwest Research Institute 

6220 Culebra Road 

P.O. Drawer 28510 

San Antonio, TX 78228-0510 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 

This document is available to the public through the National Technical Information Service, 

Springfield, Virginia 22161. 

12b. DISTRIBUTION CODE 

13. ABSTRACT (Maximum 200 words) 

This report documents a test program to determine the material properties (chemical composition, tensile, and fatigue) at ambient 

and elevated temperatures of a Class A wheel steel as designated by the Association of American Railroads. The 3 temperatures 

examined included ambient room temperature, 500 °F, and 1000 °F. The fatigue properties determined at ambient temperature 

are required to address rail vehicle wheels equipped with disc brakes, which are not exposed to frictional heating during stopbraking. Researchers performed fatigue testing to determine the S-N curves at each of the three temperatures. Furthermore, the 

research team performed a large number of fatigue tests at R-ratios of -1.0 and 0.05 for each of the test temperatures to enable 

reliable estimates of the Sines parameters, A and α. 

14. SUBJECT TERMS 

Class A wheel steel, S-N fatigue testing, railroad wheels, fatigue specimens, loading conditions, 

stop-braking, tensile strength, Sines parameters 

15. NUMBER OF PAGES 

60 

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ENGLISH TO METRIC METRIC TO ENGLISH
 LENGTH (APPROXIMATE) 

1 inch (in) = 2.5 centimeters (cm) 

1 foot (ft) = 30 centimeters (cm) 

1 yard (yd) = 0.9 meter (m) 

1 mile (mi) = 1.6 kilometers (km) 

LENGTH (APPROXIMATE) 

1 millimeter (mm) = 0.04 inch (in) 

1 centimeter (cm) = 0.4 inch (in) 

1 meter (m) = 3.3 feet (ft) 

1 meter (m) = 1.1 yards (yd) 

1 kilometer (km) = 0.6 mile (mi) 

AREA (APPROXIMATE) 

1 square inch (sq in, in2

) = 6.5 square centimeters 

(cm2

) 

1 square foot (sq ft, ft2

) = 0.09 square meter (m2) 

1 square yard (sq yd, yd2

) = 0.8 square meter (m2) 

1 square mile (sq mi, mi2

) = 2.6 square kilometers 

(km2

) 

1 acre = 0.4 hectare (he) = 4,000 square meters (m2

) 

AREA (APPROXIMATE) 

1 square centimeter (cm2

) = 0.16 square inch (sq in, in2) 

1 square meter (m2

) = 1.2 square yards (sq yd, 

yd2

) 

1 square kilometer (km2

) = 0.4 square mile (sq mi, mi2) 

10,000 square meters (m2

) = 1 hectare (ha) = 2.5 acres 

MASS - WEIGHT (APPROXIMATE) 

1 ounce (oz) = 28 grams (gm) 

1 pound (lb) = 0.45 kilogram (kg) 

1 short ton = 2,000 pounds 

(lb) 

= 0.9 tonne (t) 

MASS - WEIGHT (APPROXIMATE) 

1 gram (gm) = 0.036 ounce (oz) 

1 kilogram (kg) = 2.2 pounds (lb) 

1 tonne (t) = 

= 

1,000 kilograms (kg) 

1.1 short tons 

VOLUME (APPROXIMATE) 

1 teaspoon (tsp) = 5 milliliters (ml) 

1 tablespoon (tbsp) = 15 milliliters (ml) 

1 fluid ounce (fl oz) = 30 milliliters (ml) 

1 cup (c) = 0.24 liter (l) 

1 pint (pt) = 0.47 liter (l) 

1 quart (qt) = 0.96 liter (l) 

1 gallon (gal) = 3.8 liters (l) 

1 cubic foot (cu ft, ft3

) = 0.03 cubic meter (m3) 

1 cubic yard (cu yd, yd3

) = 0.76 cubic meter (m3) 

VOLUME (APPROXIMATE) 

1 milliliter (ml) = 0.03 fluid ounce (fl oz) 

1 liter (l) = 2.1 pints (pt) 

1 liter (l) = 1.06 quarts (qt) 

1 liter (l) = 0.26 gallon (gal) 

1 cubic meter (m3

) = 36 cubic feet (cu ft, ft3) 

1 cubic meter (m3

) = 1.3 cubic yards (cu yd, yd3) 

TEMPERATURE (EXACT) 

[(x-32)(5/9)] °F = y °C 

TEMPERATURE (EXACT) 

[(9/5) y + 32] °C = x °F 

QUICK INCH - CENTIMETER LENGTH CONVERSION 

0 1 2 3 4 5

Inches 

Centimeters 0 1 2 3 4 5 6 7 8 9 10 11 12 13

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION 

°F -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°
 

°C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°
 

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98 

ii 
Table of Contents 

List of Tables ...................................................................................................................................v 

List of Figures................................................................................................................................ vi 

Acknowledgments......................................................................................................................... vii 

Executive Summary.........................................................................................................................1 

1. Introduction.................................................................................................................................3 

2. Material and Experimental Methods...........................................................................................5 

2.1 Material and Specimen Geometries.....................................................................................5 

2.2 Experimental Test Procedures .............................................................................................9 

2.3 Fatigue-Based Criteria .......................................................................................................10 

2.3.1 The Sines Criterion ...................................................................................................12 

2.3.2 The SNCF Criterion..................................................................................................13 

3. Test Results and Discussion .....................................................................................................15 

3.1 Material Characterization Results......................................................................................15 

3.2 Fatigue Test Results...........................................................................................................16 

3.3 Estimation of Sines Parameters .........................................................................................23 

4. Summary ...................................................................................................................................27 

5. References.................................................................................................................................29 

Appendix. Tensile and Chemical Properties.................................................................................31 

Acronyms and Symbols .................................................................................................................47 

iii 

List of Tables 

Table 1. Description of the Specimens Used During Tensile, Chemical Composition, and 

Fatigue Testing ................................................................................................................ 9 

Table 2. Chemical Analysis Results for the Class A Wheel Steel............................................... 15 

Table 3. Tensile Tests Results for the Class A Wheel Steel at Room and Elevated 

Temperature ................................................................................................................... 16 

Table 4. Summary of the Fatigue Tests Performed at Room Temperature for the Class A 

Wheel Steel .................................................................................................................... 17 

Table 5. Summary of the Fatigue Tests Performed at 500 °F for the Class A Wheel Steel ........ 18 

Table 6. Summary of the Fatigue Tests Performed at 1000 °F for the Class A Wheel Steel ...... 19 

Table 7. Regression Analysis of Fatigue Data for Each of the Three Test Temperatures........... 22 

Table 8. Sines Criterion Material Constant Estimates for the Three Test Temperatures ............ 26 

v 
List of Figures 

Figure 1. Schematic Showing Extraction of Sections from the Two Railroad Wheels................. 5 

Figure 2. Specimen Geometry Utilized for Assessing Tensile Strength of the Wheel 

Figure 6. Detailed View of Setup for 500 °F and 1000 °F High-Temperature S-N 

Figure 13. Endurance Limit Diagram for the Room-Temperature, 500 °F, and 

Figure 14. Representative Photographs of Room-Temperature Fatigue Specimens 

Material at 72 °F, 500 °F, and 1000 °F (Extracted from ASTM Standard E8 [4]) ........ 6 

Figure 3. Schematic Layout for the Tensile and Chemical Composition Specimens.................... 7 

Figure 4. Schematic Layout for the Fatigue Specimens in Each Wheel Section........................... 7 

Figure 5. Design Drawing for the Hourglass Fatigue Specimen ................................................... 8 

Fatigue Testing............................................................................................................. 11 

Figure 7. Overall Setup for High-Temperature S-N Fatigue Testing.......................................... 11 

Figure 8. Schematic of the SNCF MGD...................................................................................... 13 

Figure 9. Summary of Fatigue Tests Performed During Test Program....................................... 20 

Figure 10. Fatigue Test Results at Room-Temperature for the Class A Wheel Steel ................. 20 

Figure 11. Fatigue Test Results at 500 °F for the Class A Wheel Steel ...................................... 21 

Figure 12. Fatigue Test Results at 1000 °F for the Class A Wheel Steel .................................... 21 

1000 °F Tests ............................................................................................................ 23 

(a) R = -1.0 and (b) R = 0.05..................................................................................... 24 

Figure 15. Representative Photographs of 500 °F Fatigue Specimens (a) R = -1.0 and 

(b) R = 0.05 ............................................................................................................... 24 

Figure 16. Representative Photographs of 1000 °F Fatigue Specimens (a) R = -1.0 and 

(b) R = 0.05 ............................................................................................................... 25 

vi 
vii 

ACKNOWLEDGMENTS 

This work was carried out under the Rail Equipment Safety program sponsored by the Office of 

Research and Development, Federal Railroad Administration, U.S. Department of 

Transportation, under the direction of Ms. Claire L. Orth, Chief, Equipment and Operating 

Practices Research Division. Ms. Monique Stewart is the Project Manager for the research 

related to railroad wheel safety. Mr. Jeff Gordon of the Volpe National Transportation Systems 

Center was the Contracting Officer’s Technical Representative. The authors are grateful for the 

technical direction provided by Mr. Gordon. 

Gratitude is expressed to Ms. Susan McDonough (Foster-Miller) for overseeing this subcontract. 

Appreciation is further extended to Cameron Lonsdale (Standard Steel) for his efforts in 

procuring the wheels used herein. Thomas Luna, Ernest Montelongo, Ryan Whitaker, and 

Forrest Campbell from Southwest Research Institute all assisted in performing this testing. 

Finally, thanks to Loretta Mesa for patiently preparing this manuscript.

EXECUTIVE SUMMARY 

Service loading conditions for railroad wheels include those due to wheel-on-rail contact, as well 

as thermal loads from frictional heating during on-tread braking. Studies have shown that the 

wheel surface temperatures can reach 1000 °F during stop-braking. Current wheel design 

acceptance criteria deal primarily with wheel designs for North American freight applications, 

whereas the American Public Transportation Association (APTA) Passenger Rail Equipment 

Safety Standards Group is presently developing a companion fatigue-based standard for 

passenger and transit wheels. 

The group developing the new standard is exploring the potential applicability of two fatiguebased acceptance criteria. Unfortunately, limited fatigue data exists for wheel steels, especially 

in the as-forged service condition. This report documents a material property test program to 

determine the material properties (chemical composition, tensile, and fatigue) at ambient and 

elevated temperatures of a Class A wheel steel as designated by the Association of American 

Railroads (AAR). Previous testing focused on the fatigue performance of a Class B wheel steel. 

The 3 temperatures examined included ambient room temperature, 500 °F, and 1000 °F. The 

fatigue properties determined at ambient room temperature are required to address rail vehicle 

wheels equipped with disc brakes, which are not exposed to frictional heating during stopbraking. Researchers performed fatigue testing to determine the S-N curves for each of the three 

temperatures. Furthermore, a large number of fatigue tests was performed at R-ratios of -1.0 

and 0.05 for each of the test temperatures to enable reliable estimates of the Sines parameters, 

A and ". 

Chemical composition analysis indicated that both wheel samples were within the range for a 

Class A railroad wheel, as given in AAR specification M-107/208. Monotonic tensile tests were 

undertaken for the Class A wheel steel at room temperature, 500 °F, and 1000 °F. Roomtemperature test results were in accordance with AAR baseline values, as given in AAR 

Standard S-660. Similar ultimate tensile strength and yield stress results were found for the 

room-temperature and 500 °F tests. However, a 50-percent reduction in ultimate tensile strength 

and a 35-percent reduction in yield strength were observed for the 1000 °F tensile tests compared 

to both the room-temperature and the 500 °F tests. The research team observed a large decrease 

in the percent elongation and reduction in area for all 500 °F tests compared to room-temperature 

and 1000 °F tests. This variation in tensile properties was also observed during a previous test 

program utilizing a Class B wheel steel material. 

The vast majority of testing was performed at stress ratios of 1.0 and 0.05 to enable the full S-N 

curves to be developed. The remainder of testing was undertaken to obtain the endurance limit 

at 107

 cycles for R-ratios of 0.5 and 0.7. The degree of scatter for fatigue tests averaged 

approximately one order of magnitude (10x) for all tests performed at replicate stress levels. 

Endurance limit data was obtained for all R-ratios at each of the three test temperatures. For the 

1000 °F tests, however, the usual endurance limit transition did not appear at the lower stress 

levels, as was found with the room-temperature and 500 °F tests. Based on the endurance limit 

1 
data for R-ratios of -1.0 and 0.05, personnel conducting the tests obtained an estimation of the 

Sines parameters, A and ", for each of the 3 test temperatures. 

2 
1. Introduction 

The APTA Passenger Rail Equipment Safety Standards Group on wheel design is working 

toward the development of fitness-for-service design criteria for railroad wheels used in transit 

and passenger applications. Currently, AAR Standard S-660 specifies design acceptance criteria 

[1]. This standard deals primarily with wheel designs for North American freight applications, 

whereas the APTA Committee is seeking to develop an equivalent standard for passenger and 

transit wheels. 

The service loading conditions include those due to wheel-on-rail contact, as well as thermal 

loads from frictional heating during on-tread braking. Studies conducted at the Volpe National 

Transportation Systems Center (Volpe Center) [2] have shown that wheel surface temperatures 

can reach 1000 °F during stop-braking. Since the combination of contact and thermal loads 

results in multiaxial stress fields in wheels, no standard way exists to apply conventional 

acceptance criteria. 

The group developing the new standard is exploring the potential applicability of two fatiguebased acceptance criteria. Unfortunately, limited fatigue data exists for wheel steels, especially 

in the as-forged service condition. The objective of this program is to determine the material 

properties (chemical composition, tensile, and fatigue), at ambient and elevated temperatures, of 

Class A wheel steel as designated by AAR. Previous testing has focused on the fatigue 

performance of a Class B wheel steel [3]. The 3 temperatures examined included ambient room 

temperature, 500 °F, and 1000 °F. The fatigue properties determined at ambient room 

temperature are required to address rail vehicle wheels equipped with disc brakes, which are not 

exposed to frictional heating during stop-braking. 

This report documents the procedures and results obtained from constant amplitude fatigue 

testing at the Southwest Research Institute (SwRI). The report will discuss issues associated 

with the procedures used during testing, including test specimen machining and hightemperature test setup. The report presents tabular and graphical descriptions of the 

experimental results, estimates of fatigue parameters, and a discussion of the relevant trends and 

characteristics of the recorded data. The concluding section summarizes the results and provides 

a brief review of the major findings. 

3
 

2. Material and Experimental Methods 

2.1 Material and Specimen Geometries 

The AAR Class A railroad wheel steel used in this test program is designed for high-speed 

service with severe braking conditions and moderate wheel loads when used under passenger car 

service conditions. The AAR Class A wheel steel required for constant amplitude fatigue testing 

was supplied from two railroad wheels, sectioned into eight pieces per wheel, as schematically 

shown in Figure 1. Specimens for tensile, chemical composition, and fatigue tests were 

extracted from each of the railroad wheels. 

Figure 1. Schematic Showing Extraction of Sections from the Two Railroad Wheels 

5
 
Individual sections from each of the two railroad wheels were selected to enable a tensile and 

chemical test sampling of both wheels. The two wheels were produced in February 2003 from 

steel heat P9871 (Standard Steel, Burnham, PA). The basic geometries generally conformed to 

the relevant American Society for Testing Materials (ASTM) test specification [4]. The actual 

specification used to determine the properties evaluated, specimen geometry, and test 

procedures, however, depended upon the type of test performed: 

•	 Tensile testing: ASTM E8-00 (Standard Test Methods for Tension Testing of 

Metallic Materials) 

•	 Fatigue testing: ASTM E466-96 (Standard Practice for Conducting Force 

Controlled Constant Amplitude Axial Fatigue Tests of Metallic 

Materials) 

The various standards allow for a number of specimen shapes and sizes depending upon 

requirements of the particular test and raw material form. 

The tensile testing was subcontracted with specimen blanks supplied to the vendor (Staveley 

Services, Glendale Heights, IL). The blanks were machined into second-subsize specimens with 

gage length diameters of 0.250 inch, as illustrated in Figure 2. Elongation at failure was 

measured over the specimen’s total gage length. The tensile properties were determined only in 

the circumferential orientation for the railroad wheels, with this being the most relevant 

orientation in terms of the fatigue specimens. Figure 3 (tensile and chemical) and Figure 4 

(fatigue) show schematics indicating how the tensile, chemical, and fatigue test specimens were 

positioned in the actual railroad wheel. Figure 5 shows the actual fatigue specimen geometry. 

Figure 2. Specimen Geometry Utilized for Assessing Tensile Strength of the Wheel 

Material at 72 °F, 500 °F, and 1000 °F (Extracted from ASTM Standard E8 [4]) 

6
 
Figure 3. Schematic Layout for the Tensile and Chemical Composition Specimens 

Figure 4. Schematic Layout for the Fatigue Specimens in Each Wheel Section 

7
 
Figure 5. Design Drawing for the Hourglass Fatigue Specimen 

8
 
A basic code was used to form the identification numbers of the fatigue specimens. This code 

typically consisted of a number identifying the railroad wheel, a letter identifying the wheel 

section, and a multi-digit identifier qualitatively indicating position in the product, as outlined 

below: 

• Wheel 0 (Serial No. 02-3-14193), 1 (Serial No. 02-3-14202) 

• Wheel Section A-H (see Figure 1) 

• Specimen Position 1-10 (see Figure 4) 

The two chemical test specimens were identified by 0 and 1, indicating the wheel from which 

they were extracted. Similarly, the tensile test specimens were identified numerically from 1 to 

9, with their relevant position in the wheel shown in Figure 3. Table 1 provides a complete list 

of specimens extracted from the two wheels. 

Table 1. Description of the Specimens Used During Tensile, Chemical Composition, and 

Fatigue Testing 

Wheel Wheel Section Fatigue Specimen 

ID 

Tensile Specimen ID Chemical Specimen 

ID 

A 0A1 to 0A10 

B 0B1 to 0B10 

C 0C1 to 0C10 

D 0D1 to 0D10 

02-3-14193 

E 1 to 6 0 

F 0F1 to 0F10 

G 0G1 to 0G10 

H 0H1 to 0H10 

A 1A1 to 1A10 

B 7 to 9 1 

C 1C1 to 1C10 

D 1D1 to 1D10 

02-3-14202 

E 1E1 to 1E10 

F 1F1 to 1F10 

G 1G1 to 1G10 

H 1H1 to 1H10 

2.2 Experimental Test Procedures 

As indicated previously, testing was performed in the spirit of the ASTM test specifications and 

supplemented by experience gained over many years of similar testing. The purpose of this 

section is to provide additional detail concerning the methods used during tensile, chemical, and 

fatigue testing. 

Researchers performed tensile testing in complete accordance with ASTM E8-00. Three 

specimens were tested at each of the specified test temperatures: room temperature, 500 °F, and 

9
 
1000 °F. This resulted in a total of nine tensile tests. The quantities recorded during testing or 

derived from data included: 

• Ultimate tensile strength (σUTS) 

• Yield strength (σYS) 

• Percent elongation at failure 

• Percent reduction in area at failure 

Chemical analysis was performed on each of the two railroad wheels to provide verification that 

the material was within the specification for AAR M107/208 Class A steel. Analysis was 

performed in accordance with the standard ASTM test specifications [5,6]. 

The vast majority of testing focused on evaluating the fatigue behavior of the Class A steel under 

each of the three test temperatures. Four different R-ratios were evaluated during fatigue testing 

and included R = -1.0, 0.05, 0.5, and 0.7. The testing at R = -1.0 and R = 0.05 included 

sufficient specimens to generate the complete S-N curve. However, the testing at the higher Rratio conditions, R = 0.5 and R = 0.7, included only 6 specimens, nominally to determine the 

endurance limit. 

The fatigue testing was performed at SwRI in the Solid and Fracture Mechanics Laboratory 

using 2 closed-loop servo-hydraulic test frames with high-temperature furnaces required for the 

500 °F and 1000 °F tests. Figure 6 shows a photograph of the high-temperature test setup for the 

500 °F and 1000 °F tests. Figure 7 shows an overall view of the test setup, illustrating the 

complexity and multiple components. As shown in Figure 7, a step-down transformer was used 

to provide a variable high current, through water-cooled cables, to the heating plates. The hightemperature system provided a very controlled and stable temperature for the test specimens. 

Before starting each fatigue test, the controller set temperature was gradually increased to the 

desired level to avoid any temperature overshoot that may occur in the specimen during heating. 

Testing frequency was in the range of 10-25Hz, depending primarily on the R-ratio. All 

specimens were tested until failure (2 pieces) or until the runout level of 10 million cycles was 

reached. 

2.3 Fatigue-Based Criteria 

The two fatigue-based acceptance criteria currently under consideration by the APTA Passenger 

Rail Equipment Safety Standards Group are the Sines criterion [7] and the French Societé 

Nationale des Chemins de Fer (SNCF) criterion [8]. This section will provide additional details 

of the two criteria. Although the fatigue testing program described in the previous sections is 

primarily concerned with generating S-N curves for the Class A wheel steel, it is expected that 

material constants required in the Sines criterion will be able to be extracted from the 

experimental data. 

10
 
Figure 6. Detailed View of Setup for 500 °F and 1000 °F High-Temperature 

S-N Fatigue Testing 

Figure 7. Overall Setup for High-Temperature S-N Fatigue Testing 

11
 
2.3.1 The Sines Criterion 

In 1955, Sines [6] reviewed the results of experiments on the effect of different combinations of 

tensile, compressive, and torsional mean and alternating stresses on fatigue life. He reported that 

alternating shear stresses seemed to cause fatigue failure. Because of this, Sines studied the 

influence of mean static stresses on the planes of maximum alternating shear. From this study, 

he developed the relationship: 

1 2 2 2 (P − P ) + (P − P ) + (P − P ) + α(S + S + S ) ≤ A (1) 1 2 2 3 1 3 x y z 3 

where P1, P2, P3 = amplitudes of the alternating principal stresses 

Sx, Sy, Sz = orthogonal (any coordinate system) mean stresses 

A = material constant proportional to reversed fatigue strength 

" = material constant, which gives variation of the permissible range of 

stress with static stress 

A and " are materials properties for a given life level 

The first term on the left-hand side of Equation 1 is the octahedral shear stress, Joct. Sines 

suggested that Joct averages the effect of shear stresses on many differently oriented slip planes. 

In addition, a hydrostatic stress term is included in this model by the second term on the lefthand side of Equation 1. 

In Sines’s equation, A and " may easily be determined. For example, in a fully reversed uniaxial 

test, Equation 1 is: 

2 P = A (P2 = P3 = Sx = Sy = Sz = 0) (2) 3 1 

Letting P1 = f1 gives: 

A = 2 f1 (3) 3 

where f1 is the amplitude of reversed axial stress that would cause failure at the desired cyclic 

life. For 0 to Fmax loading (R-ratio = 0), 

S = P (P = P = S = S = 0) x 1 2 3 y z 

and Equation 1 becomes: 

2 P1 = A − αP1 (4) 3 

12
 
Letting P1 = f1 ′ yields: 

A 2 2 ⎛f1 ⎞

α = − = ⎜

⎜ −1⎟

⎟ (5) P 3 3 f ′ 1 ⎝ 1 ⎠

where f1 ′ is the amplitude of fluctuating stress that would cause failure at the same cyclic life as 

f1. Thus, A and α are described in terms of stress amplitudes f1 and f1 ′. 

2.3.2 The SNCF Criterion 

The second criterion currently under consideration is a modified Goodman diagram (MGD), as 

specified by SNCF in its wheel design specification [7]. Figure 8 shows a graphical example of 

the SNCF MGD. In this case, the mean and alternating stresses are the radial stresses in the plate 

and plate fillet of the railroad wheel. 

Figure 8. Schematic of the SNCF MGD 

The truncation of the MGD is based on empirical data gained from SNCF experience in 

designing wheels for rail applications. Finite element analysis, under both mechanical and 

thermal loading, is used to evaluate railroad wheel designs before introducing them into service. 

The largest values of the radial stresses, predicted using finite element analysis, are used to 

calculate the mean and alternating radial stresses at each node in the model as follows: 

(σR + σR ) (σR − σR ) max min max min σRmean = and σRalternating = (6) 2 2 

13
 
The mean and alternating stress pairs are then plotted on the graph shown in Figure 8 for each 

node in the finite element model. To enable the proposed wheel design to be accepted for 

service, all results must fall within the prescribed MGD envelope. 

14
 
3. Test Results and Discussion 

3.1 Material Characterization Results 

The following section provides tabular and graphical results of the tensile and chemical 

composition testing. This section also describes the most notable characteristics of the material 

property data for the tested Class A wheel steel and contrasts these data with the data given in 

the AAR specification for carbon steel wheels [9]. The tensile and chemical test result 

summaries are extracted from the actual data tabulated in the Appendix, Tensile and Chemical 

Properties. This appendix includes additional details regarding the specifics of all the tensile 

tests. 

Table 2 shows a summary of the chemical composition data, with the AAR specification 

allowables provided for comparison. The results given indicate that both railroad wheel samples 

contained the required elements within the specified range, below the maximum, or above the 

minimum given for the Class A steel, as specified in Section 8.1 of AAR Specifications M107/208 [9]. 

Table 2. Chemical Analysis Results for the Class A Wheel Steel 

Sample ID 

Element (Weight Percent) 

C Mn P S Si 

0 0.51 0.68 0.019 0.019 0.26 

1 0.51 0.68 0.019 0.020 0.27 

Minimum [9] 0.47 0.60 0.15 

Maximum [9] 0.57 0.85 0.050 0.050 

Table 3 shows tensile test results for each of the three temperatures, with the room-temperature 

baseline tensile data for Class A wheel steel [1] also included for comparison. Roomtemperature ultimate tensile strength (FUTS) was within the AAR baseline range specified. 

Two observations are apparent from the test data given in Table 3. First, a dramatic decrease in 

the ultimate tensile strength and yield strength occurred when testing at a temperature of 

1000 °F, with a 50-percent reduction in FUTS and a 35-percent reduction in FYS. Second, a 

decrease in the reduction in area and percent elongation for all 500 °F tests, compared to both 

room-temperature and 1000 °F tests, was observed. The actual tensile specimens were randomly 

selected for testing at the three temperatures, with each three-specimen group combined to 

include at least one specimen from each wheel, as previously shown in Figure 3. Therefore, it is 

unlikely that the difference in reduction of area for the three temperatures is a consequence of 

material variation in one specific wheel. This same variation in tensile properties for the three 

test temperatures was also observed during a previous test program utilizing a Class B wheel 

steel material. 

15
 
Table 3. Tensile Tests Results for the Class A Wheel Steel at Room 

and Elevated Temperature 

Temperature (°F) Specimen ID σUTS, ksi σYS, 

ksi 

ε, % RA, % 

1 136.9 93.5 16.0 33.8 

3 133.8 89.7 15.5 31.7 

Room Temperature 

8 132.3 87.2 15.0 31.5 

Average → 134.3 90.1 15.5 32.3 

Class A baseline [1] 125-160 

2 140.9 80.0 14.0 16.6 

4 147.9 95.7 15.0 16.0 

500 9 147.4 86.2 13.0 15.1 

Average → 145.4 87.3 14.0 15.9 

5 71.9 59.1 18.0 53.4 

6 69.2 57.5 19.0 57.6 

1000 7 68.5 53.9 20.0 57.3 

Average → 69.9 56.8 19.0 56.1 

3.2 Fatigue Test Results 

A total of 119 constant amplitude fatigue tests was performed at the 3 different test temperatures. 

Tables 4, 5, and 6 give a summary of all fatigue tests performed at room temperature, 500 °F, 

and 1000 °F, respectively. The tables present data in terms of R-ratio, maximum stress, actual 

stress range, and cycles to failure. The maximum stress given in the tables is not the stress at 

which the specimens were tested. Due to the specimen’s hourglass geometry, a stress 

concentration is produced in the specimen. Therefore, the effective test stress is calculated 

simply as: 

actual σ =

σ (7) effective
 Kt
 

where Feffective = stress used during test 

Factual = actual stress induced in specimen 

Kt = stress concentration due to hourglass geometry = 1.05 

16
 
Table 4. Summary of the Fatigue Tests Performed at Room Temperature 

for the Class A Wheel Steel 

R-ratio Test ID Maximum 

Test Stress 

(ksi) 

Actual Stress Range, 

KtΔσ (ksi) 

Cycles Comments 

0.05 1C-6 120 119.70 13,864 

1H-4 105 104.74 23,445 

0G-1 95 94.76 74,802 

1H-9 95 94.76 59,086 

0A-4 90 89.78 65,680 

1H-5 90 89.78 119,387 

0G-3 84 83.79 185,950 

0G-8 84 83.79 166,185 

0G-9 83 82.79 251,701 

0G-6 83 82.79 10,000,000 Runout 

0G-5 82.5 82.29 10,000,000 Runout 

0G-7 80 79.80 10,000,000 Runout 

-1.00 1H-6 85 178.50 2,781 

1H-2 75 157.50 8,201 

1C-3 75 157.50 8,895 

1G-5 70 147.00 28,724 

1C-7 70 147.00 21,983 

1H-8 60 126.00 68,519 

1C-1 60 126.00 169,414 

1G-4 59 123.90 66,377 

1H-7 58 121.80 194,086 

0G-10 56.5 118.65 2,973,242 

1G-6 56 117.60 2,692,003 

0A-9 55 115.50 156,852 

0A-8 55 115.50 200,000 

0A-3 55 115.50 89,881 

0A-10 55 115.50 10,000,000 Runout 

0A-2 54 113.40 155,25 

1C-8 53 111.30 309,058 

1E-4 52 109.20 6,476,442 

1E-5 51 107.10 179,372 

0A-5 50 105.00 10,000,000 Runout 

0.5 1E-1 114 59.85 235,950 

1E-8 110 57.75 293,281 

1E-9 106 55.65 381,213 

0D-5 104 54.60 10,000,000 Runout 

1F-7 103 54.08 10,000,000 Runout 

0D-3 100 52.50 10,000,000 Runout 

1E-7 95 49.88 10,000,000 Runout 

0.7 1F-2 135 42.53 316,072 

1A-5 135 42.53 10,000,000 Runout 

0D-1 130 40.95 10,000,000 Runout 

1A-6 120 37.80 10,000,000 Runout 

17
 
Table 5. Summary of the Fatigue Tests Performed at 500 °F for the Class A Wheel Steel 

R-ratio Test ID Maximum 

Test Stress 

(ksi) 

Actual Stress 

Range, KtΔσ (ksi) 

Cycles Comments 

0.05 0H-6 120.00 119.70 47,717 

0B-8 120.00 119.70 35,030 

0F-4 110.00 109.70 47,258 

0B-9 110.00 109.70 14,979 

1A-10 100.0 99.75 96,000 

0C-8 95.0 94.80 4,736,989 

0H-9 95.0 94.80 96,327 

0H-7 90.0 89.80 66,715 

1D-3 90.0 89.80 349,041 

1F-1 85.0 84.80 6,885,450 

0B-10 85.0 84.80 10,000,000 

1D-10 84.0 83.80 4,290,017 

1F-3 84.0 83.80 129,182 

1D-1 83.0 82.80 10,000,000 

0C-7 83.0 82.80 10,000,000 

1A-2 70.0 69.83 10,000,000 

-1.0 1D-8 80.95 170.00 6,198 

0F-7 80.95 170.00 4,573 

0F-2 71.43 150.00 14,349 

0B-4 71.43 150.00 41,979 

0C-6 69.05 145.00 59,980 

0H-4 69.05 145.00 10,260 

0H-2 66.67 140.00 135,956 

0F-1 66.67 140.00 178,894 

0C-5 61.90 130.00 2,845,416 

0B-7 61.90 130.00 162,093 

1D-6 61.90 130.00 77,024 

0C-4 57.14 120.00 743,846 

0B-5 57.14 120.00 4,922,716 

1D-5 57.14 120.00 10,000,000 

0.5 0F-6 140.00 73.50 95,867 

1D-2 131.43 69.00 3,755,883 

IF-9 127.62 67.00 10,000,000 

0C-9 123.81 65.00 10,000,000 

1D-4 106.67 56.00 10,000,000 

0H-8 102.86 54.00 10,000,000 

0.7 0B-2 139.68 44.00 1,252,549 

0B-3 139.68 44.00 630,157 

1D-7 136.51 43.00 10,000,000 

0B-1 133.33 42.00 10,000,000 

0H-3 126.98 40.00 10,000,000 

0B-2 46.00 14.49 10,000,000 

0F-8 44.00 13.86 10,000,000 

18
 
Table 6. Summary of the Fatigue Tests Performed at 1000 °F for the Class A Wheel Steel 

R-ratio Test ID Maximum 

Test Stress 

(ksi) 

Actual Stress Range, 

KtΔσ (ksi) 

Cycles Comments 

0.05 0A-2 60 59.85 1,527 

1C-2 60 59.85 1,249 

1E-3 55 54.86 48,351 

1G-2 50 49.88 58,949 

1C-5 50 49.88 128,400 

1H-1 45 44.89 665,484 

1G-3 45 49.89 295,851 

1G-8 40 39.90 577,411 

0A-6 35 34.91 1,369,530 

1C-4 35 34.91 1,392,951 

1G-1 30 29.93 4,440,274 

1C-10 30 29.93 6,048,120 

1C-9 28 27.93 7,745,408 

1H-10 27 26.93 10,000,000 Runout 

-1.0 0D-10 45 94.50 152,911 

0D-2 40 84.00 837,479 

1A-4 40 84.00 107,518 

1E-6 35 73.50 498,973 

1A-7 32 67.20 1,021,514 

1A-1 32 67.20 1,519,360 

0D-3 30 63.00 5,680,570 

0D-4 30 63.00 9,200,000 

1E-5 28 58.80 6,595,892 

1A-9 28 58.80 10,000,000 Runout 

1E-2 27 56.70 6,256,424 

0D-9 26 54.60 8,170,979 

0D-7 25 52.50 10,000,000 Runout 

0.5 0D-6 29 15.23 3,596,631 

1F-8 25 13.13 9,780,461 

1F-10 24 12.60 9,270,753 

1A-3 23 12.08 8,215,280 

1A-8 21 11.03 10,000,000 Runout 

0.7 1F-6 23 7.25 5,918,783 

0F-9 21 6.62 10,000,000 Runout 

0F-5 20 6.30 10,000,000 Runout 

Figure 9 shows a summary graph for all fatigue tests at each of the three temperatures and four 

R-ratios. To better highlight the differences at each temperature, Figures 10, 11, and 12 provide 

graphical summaries of the fatigue data for room temperature, 500 °F, and 1000 °F. For each 

graph, cycles to failure are given as a function of actual stress range, ΔS, which includes the 

stress concentration effect (Kt = 1.05). As expected, a certain degree of scatter in fatigue results 

is shown for each particular stress range, with the highest amount of scatter at the lower stress 

levels and therefore the higher life regime. 

19
 
Figure 9. Summary of Fatigue Tests Performed During Test Program 

Figure 10. Fatigue Test Results at Room Temperature for the Class A Wheel Steel 

20
 
Figure 11. Fatigue Test Results at 500 °F for the Class A Wheel Steel 

Figure 12. Fatigue Test Results at 1000 °F for the Class A Wheel Steel 

21
 
Each of the summary plots also provides regression curve fits for the data at the lower R-ratios 

of R = -1.0 and 0.05. Due to the limited amount of testing at the higher R-ratios of R = 0.5 and 

0.7, only the fatigue life at the 107

 life regime, termed the endurance limit, was obtained. To 

obtain the curves shown in Figures 10, 11, and 12, a simple linear regression on the fatigue data, 

up to and including the 106 life regime, was performed. A horizontal line, corresponding to an 

average stress level for all runout data, was then extended out to the 107 life regime. For the 

1000 °F high-temperature tests, the usual endurance limit transition did not appear to occur at the 

lower stress levels for each R-ratio, as was found with the room-temperature and 500 °F tests. 

Table 7 gives the power law functions for each of the regression fits shown in Figures 10, 11, 

and 12, with cycles given as a function of stress range. 

Due to the large amount of data produced in this fatigue test program over a wide variety of Rratios, it is possible to develop the endurance limit diagram for the three test temperatures. 

Figure 13 shows endurance limit diagrams for the room-temperature, 500 °F, and 1000 °F tests 

together for comparison. Due to the similarity of tensile and fatigue test results for the roomtemperature and 500 °F tests, it is not unexpected to see similar endurance limit diagrams for 

these 2 temperatures. In addition, the vast difference in tensile strength properties when testing 

at 1000 °F is indicative of the subsequent detrimental effect on the endurance limit diagram. 

Table 7. Regression Analysis of Fatigue Data for Each of the Three Test Temperatures 

Temperature (°F) R-ratio Stress Range, ΔS Power Law Constants Cycles to Failure 

(ksi) A b 

-1.0 

> 110.3 4.753x1023 -8.946 A S b N Δ=

Room Temperature 

≤ 110.3 Runout 

0.05 

> 81.6 1.291x1020 -7.734 A S b N Δ=

≤ 81.6 Runout 

500 

-1.0 > 120.0 4.213x1033 -13.419 A S b N Δ=

≤ 120.0 Runout 

0.05 

> 84.0 3.035x1014 -4.812 A S b N Δ=

≤ 84.0 Runout 

1000 

-1.0 > 55.7 1.666x1021 -8.171 A S b N Δ=

0.05 > 26.9 4.570x1020 -9.388 A S b N Δ=

22
 
Figure 13. Endurance Limit Diagram for the Room-Temperature, 500 °F, and 1000 °F 

Tests 

Figures 14, 15, and 16 are photographs of typical fracture surfaces for the room-temperature, 

500 °F, and 1000 °F tests, respectively. Both surface and sub-surface initiation sites were 

observed for all test temperatures. This indicates that preferential surface initiation did not occur 

due to the machining process performed on the specimens. In addition, no preferential initiation 

site appeared to exist at the point where the thermocouple was in contact with the specimen 

during high-temperature testing. 

3.3 Estimation of Sines Parameters 

Based on the results given in the previous section, it is possible to provide an estimation of the 

Sines parameters, A and ", for the 107

 life regime. Endurance limit data at the 107 life regime for 

R-ratios = -1.0 and 0.05 is required to calculate the 2 material constants (see Section 2.3.1). 

Using Equations 3 and 5, the constants A and " were estimated, with results provided in Table 8. 

23
 
(a) (b) 

Figure 14. Representative Photographs of Room-Temperature Fatigue Specimens 

(a) R = -1.0 and (b) R = 0.05 

(a) 

(b) 

Figure 15. Representative Photographs of 500 °F Fatigue Specimens 

(a) R = -1.0 and (b) R = 0.05 

24
 
(a) 

(b) 

Figure 16. Representative Photographs of 1000 °F Fatigue Specimens 

(a) R = -1.0 and (b) R = 0.05 

Similar Sines parameters were calculated for the room-temperature and 500 °F fatigue tests. The 

Sines parameters for the 1000 °F fatigue tests, however, are dramatically different from those of 

the lower temperature fatigue tests. This is not surprising considering the large difference in 

both tensile and fatigue properties obtained for the 1000 °F tests when compared to the roomtemperature and 500 °F tests. 

25
 
_______________________ 

Table 8. Sines Criterion Material Constant Estimates for the Three Test Temperatures 

Temperature (°F) R-ratio 

Sines Constants at Endurance Limit (107

 Life Regime) 

Stress Amplitude (ksi) 

A (ksi) 1 α

2 

f1 f1 ′ 

Room Temperature -1.0 55.1 

26.0 0.165 0.05 40.8 

500 

-1.0 60.0 

28.3 0.202 0.05 42.0 

1000 

-1.0 27.8 

13.1 0.499 0.05 13.5 

1 2 

A = f

1 3 

2 2 ⎛ f

1 ⎞ α = ⎜

⎜ − 1⎟⎟

3 ′ ⎝ f

1 ⎠

26
 
4. Summary 

The material property evaluations described herein provide an assessment of the chemical, 

tensile, and fatigue behavior observed for the Class A wheel steel material. Fatigue testing was 

performed to determine the S-N curves for each of the 3 temperatures: ambient room 

temperature, 500 °F, and 1000 °F. Furthermore, a large number of fatigue tests was performed at 

R-ratios of -1.0 and 0.05 for each of the test temperatures to enable reliable estimates of the 

Sines parameters, A and ". The following briefly summarizes chemical, tensile, and fatigue 

results, with the major conclusions indicated. 

1.	 Two chemical analysis tests and nine tensile tests were undertaken to characterize the 

Class A railroad wheel steel material. Individual sections from each of the two railroad 

wheels were selected to enable a material characterization test sampling of both wheels. 

2.	 Chemical composition analysis indicated that both wheel samples were within the range 

for a Class A railroad wheel, as given in AAR specification M-107/208 [9]. 

3.	 Monotonic tensile tests were undertaken for the Class A wheel steel at room temperature, 

500 °F, and 1000 °F. Room-temperature test results were found to be in accordance with 

AAR baseline values, as given in AAR Standard S-660 [1]. 

4.	 Similar ultimate tensile strength and yield strength results were found for the roomtemperature and 500 °F tests. However, a 50-percent reduction in ultimate tensile 

strength and a 35-percent reduction in yield strength were observed for the 1000 °F 

tensile tests when compared to the room-temperature and 500 °F tests. 

5.	 A large decrease in the percent elongation and reduction in area for all 500 °F tests 

compared to room-temperature and 1000 °F tests was observed. This variation in tensile 

properties was also observed during a previous test program utilizing a Class B wheel 

steel material. 

6.	 A total of 119 constant amplitude fatigue tests was completed at the 3 test temperatures. 

The vast majority of testing (75 percent) was performed at R-ratios of 1.0 and 0.05 to 

enable the S-N curves to be developed. The remainder of testing was undertaken to 

obtain the endurance limit at 107

 cycles for R-ratios of 0.5 and 0.7. 

7.	 The degree of scatter for fatigue tests averaged approximately 1 order of magnitude (10x) 

for all tests performed at replicate stress levels, with a scatter range of between 1.02x– 

111.3x. As expected, greater levels of scatter and less repeatability were apparent at the 

lower stress levels. 

8.	 Fracture surfaces indicated both surface and sub-surface initiation sites at all test 

temperatures. The thermocouple position during high-temperature testing did not appear 

to provide a preferential initiation site. 

27
 
9.	 Endurance limit data was obtained for all R-ratios at each of the three test temperatures. 

For the 1000 °F tests, however, the usual endurance limit transition did not appear to 

exist at the lower stress levels, as was found with the room-temperature and 500 °F tests. 

Endurance limit diagrams for the three test temperatures were constructed. 

10. Based on the endurance limit data for R-ratios of -1.0 and 0.05, an estimation of the Sines 

parameters, A and ", was obtained for each of the 3 test temperatures. Similar parameters 

were calculated for the room-temperature and 500 °F fatigue tests, with significantly 

different parameters obtained for the 1000 °F fatigue tests. 

28
 
5. References 

[1]	 Association of American Railroads, Standard S-660, Procedure for the Analytic Evaluation 

of Locomotive and Freight Car Wheel Designs, Manual of Standards and Recommended 

Practices, Section G, Wheels and Axles, 2004. 

[2]	 Gordon, J.E. and Orringer, O., Investigation of the Effects of Braking System 

Configurations on Thermal Input to Commuter Car Wheels, Volpe National Transportation 

Systems Center, Cambridge, MA. Report No. DOT/FRA/ORD-94-01, March 1994. 

[3]	 McKeighan, P.C., McMaster, F.J., and Gordon, J. Fatigue Performance of AAR Class B 

Railroad Wheel Steel at Ambient and Elevated Temperatures, ASME International 

Mechanical Engineering Congress and Exposition, 17-22 November 2002. New Orleans, 

LA. 

[4]	 Annual Book of ASTM Standards, Section 3: Metals Test Methods and Analytical 

Procedures, Vol. 3.01 Metals-Mechanical Testing; Elevated and Low-Temperature Tests; 

Metallography, 2000. 

[5]	 ASTM E1019-00, Standard Test Methods for Determination of Carbon, Sulfur, Nitrogen, 

and Oxygen in Steel and in Iron, Nickel, and Cobalt Alloys. Annual Book of ASTM 

Standards, Section 3: Metals Test Methods and Analytical Procedures, Vol. 3.05, 

American Society for Testing and Materials, West Conshohocken, PA. 

[6]	 ASTM E415-99a, Standard Test Method for Optical Emission Vacuum Spectrometric 

Analysis of Carbon and Low-Alloy Steel. Annual Book of ASTM Standards, Section 3: 

Metals Test Methods and Analytical Procedures, Vol. 3.05, American Society for Testing 

and Materials, West Conshohocken, PA. 

[7]	 Sines, G. Behavior of Metals Under Complex Static and Alternating Stresses. Metal 

Fatigue, G. Sines and J.L. Waisman, Eds., McGraw-Hill, New York, pp. 145-169, 1959. 

[8]	 Homologation Technique des Roues Monobloc. UIC Minutes, MTEL P 98016, October 

1998. 

[9]	 Association of American Railroads, Specification M-107/208, Wheels, Carbon Steel. 

Manual of Standards and Recommended Practices, Section G, Wheels and Axles, 2004. 

29
 

Appendix. 

Tensile and Chemical Properties 

Organization: Chemical composition analysis results 

Tensile test results 

Contents: Test data sheet (each specimen) 

31
 

Chemical Composition Analysis Results 

33
 
34
 
35
 

Tensile Test Results 

37
 
38
 
39
 
40
 
41
 
42
 
43
 
44
 
45
 
46
 
Acronyms and Symbols 

A Sines criteria material constant 

AAR Association of American Railroads 

APTA American Public Transportation Association 

ASTM American Society for Testing Materials 

f1 amplitude of reversed axial stress 

f

1

′ amplitude of fluctuating stress causing failure 

FRA Federal Railroad Administration 

Kt stress concentration factor 

MGD modified Goodman diagram 

N cyclic fatigue life of a given specimen 

Pi	 principal stress amplitude 

R stress ratio, ratio of minimum to maximum 

applied stress 

RA reduction of area at failure 

Si	 orthogonal mean stresses 

S-N stress-life 

SNCF Société Nationale des Chemins de Fer 

SwRI Southwest Research Institute 

VNTSC Volpe National Transportation Systems Center 

"	 Sines criterion material constant 

g	 percent elongation at failure 

)F	 effective applied stress range 

Fmax	 maximum applied stress 

FUTS	 ultimate tensile strength 

FYS	 0.2% yield strength 

Joct	 octahedral shear stress 

)P load range applied to specimen 

)S specimen section stress range (minimum 

diameter) 

47