Residual Stress in Rails Effects on Rail Integrity and Railroad Economics Volume II Theoretical and Numerical Analyses by Oscar Orringer, Janusz Orkisz, Zdzisław Świderski (eds ) (z-lib org)

Prévia do material em texto

RESIDUAL STRESS IN RAILS 
ENGINEERING APPLICATION OF FRACTURE MECHANICS 
Editor-in-Chief: George C. Sih 
VOLUME 13 
The titles published in this series are listed at the end oj this volume. 
Residual Stress in Rails 
Effects on RaiI Integrity and Railroad Economics 
Volume II: Theoretical and Numerical Analyses 
Proceedings of a conference held at the Cracow Institute of Technology, 
Cracow, Poland, sponsored by the Office of Research and Development, 
Federal Railroad Administration, United States Development of Transportation 
Edited by 
Osear Orringer 
U.S. Department of Transportation, 
Cambridge, U.S.A. 
J anusz Orkisz 
Cracow Institute of Technology, 
Cracow, Poland 
and 
Zdzislaw Swiderski 
Central Research Institute ofthe Polish State Railways, 
Warsaw, Poland 
SPRINGER SCIENCE+BUSINESS MEDIA, B.V. 
ISBN 978-94-010-4786-9 ISBN 978-94-011-1787-6 (eBook) 
DOI 10.1007/978-94-011-1787-6 
Printed on acid-free paper 
All Rights Reserved 
© 1992 Springer Science+Business Media Dordrecht 
Originally published by K1uwer Academic Publishers in 1992 
Softcover reprint ofthe hardcover 1 st edition 1992 
No part of the material protected by this copyright notice may be reproduced or 
utilized in any form or by any means, electronic or mechanical, 
including photocopying, recording or by any information storage and 
retrieval system, without written permission from the copyright owner. 
Table of contents 
Series on engineering application of fracture mechanics 
Foreword 
Editors' preface 
Contributing authors (Volume II) 
Glossary and conversion factors 
Contents of Volume I 
Chapter 1. Catastrophic web cracking of railroad rail 
R.K Steele, M.W. Joerms, D. Utrata, and G.F. Carpenter 
1.1 Introduction 
1.2 Laboratory tests 
1.3 Tou~ess considerations 
1.4 ReSidual stresses 
1.5 Summary 
References 
Chapter 2. Rail fracture inspection on the heavily 
loaded railway line Tczew • Katowice 
Z. Swiderski 
2.1 Introduction 
2.2 Factors causing rail failures 
2.3 Verification of rail quality improvement 
2.4 Concluding remarks 
References 
Chapter 3. Detail fracture growth rates in curved track 
at the Facility for Accelerated Service Testing 
P. Clayton and Y.H. Tang 
3.1 Background 
3.2 Experiments on curved track 
3.3 Results 
3.4 Discussion 
3.5 Conclusions 
Acknowledgements 
References 
Chapter 4. Plans and progress of controlled experiments on 
rail residual stress using the EMS-60 machine 
, 
Z. Swiderski and A. W6jtowicz 
4.1 Introduction 
4.2 Experiment design 
References 
xi 
xiii 
xv 
xvii 
xix 
1 
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2 
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9 
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66 
vi 
Chapter S. Modification of the EMS-60 testing machine 
to simulate rolling contact loads in service 
J. Piotrowski 
5.1 Introduction 
5.2 The EMS-60 testing machine 
5.3 Methods of loading 
5.4 Available range of parameters influencing contact force 
5.5 Numerical prediction of contact forces 
5.6 Conclusions 
References 
Chapter 6. Effect of train load spectra 
on crack growth in rail steel 
DA. Jablonski and R.M. Pelloux 
6.1 Introduction 
6.2 Theoretical model 
6.3 Experimental procedure 
6.4 Discussion 
6.5 Conclusions 
References 
Chapter 7. Self-adaptive guide for scheduling 
rail inspection in service 
D. Drringer 
7.1 Background 
7.2 Defect population characteristics 
7.3 Damage tolerance 
7.4 Nondestructive inspection 
7.5 Inspection guide 
7.6 Evaluation 
7.7 Discussion 
7.8 Conclusions 
References 
Chapter 8. Comparative evaluation of several alternative 
methods for measuring rail residual stress 
C.H. Cundiff and R.C. Rice 
8.1 Introduction 
8.2 Experiment configuration and baseline results 
8.3 Alternate destructive procedures 
8.4 Alternate semi-destructive procedures 
8.5 Conclusions 
References 
Table of contents 
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84 
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139 
142 
Table of contents 
Chapter 9. Neutron diffraction determinations of 
residual stress patterns in railway rails 
GA. Webster, P J. Webster, MA.M. Bourke, K.S. Low, 
G. Mills, HJ. MacGillivray, D.F. Cannon, and RJ. Allen 
9.1 Introduction 
9.2 Experiments 
9.3 Results 
9.4 Summary 
Acknowledgements 
References 
Chapter 10. Moire interferometry and its potential for appli-
cation to residual stress measurements in rails 
R. Czarnek, J. Lee, and S.-Y. Lin 
10.1 Introduction 
10.2 Measurement of residual stresses 
10.3 Experiment 
10.4 Discussion 
10.5 Conclusions 
References 
Chapter 11. Experiences in ultrasonic measurement 
of rail residual stresses 
J. Deputat, J. Szelazek, A. Kwaszczynska-Klimek, 
and A. Miernik 
11.1 Introduction 
11.2 Measurement of residual stresses 
11.3 Measurement of thermal stresses in CWR 
11.4 Welding stresses 
11.5 Conclusions 
References 
Chapter 12. Investigation of residual stress 
by penetration method 
M. Bijak-Zochowski 
12.1 Introduction 
12.2 Investigations of uniformly stressed bodies 
12.3 Investigation of a non-uniform stress distribution 
12.4 Investigation of residual stress with variation 
of material properties in surface layer 
12.5 Conclusions 
References 
Chapter 13. Residual stress measurements at 
rail surface and inside rail head 
R. Radomski 
13.1 Introduction 
13.2 Results 
13.3 Conclusions 
vii 
143 
143 
145 
146 
151 
151 
152 
153 
153 
156 
158 
162 
167 
167 
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169 
171 
175 
179 
181 
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185 
185 
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viii 
Contents of Volume II 
Chapter 1. Residual stresses and web fracture 
in roller-straightened rail 
SJ. Wineman and FA. McClintock 
1.1 Introduction 
1.2 Determination of residual stresses 
1.3 Effects of residual stresses on web fracture 
1.4 A saw-cutting test to quantify 
severity of residual stresses 
1.5 Stress transients and short cracks at rail ends 
1.6 Creation of residual stresses: 
anal~ the roller-straightener 
1.7 ConclUSIOns 
Acknowledgements 
References 
Chapter 2. Some factors influencing the transition 
from shelling to detail fracture 
T.N. Farris, Y. Xu, and L.M. Keer 
2.1 Introduction 
2.2 Crack path stability of statically growing shells 
2.3 Dynamic crack curving 
2.4 Calculation of shell growth rates 
2.5 Conclusions 
Acknowledgement 
References 
Chapter 3. Analysis of crack front propagation in contact 
M. Olzak, J. Stupnicki, and R. %jcik 
3.1 Introduction 
3.2 Existing theories and research objective 
3.3 Two-dimensional model 
3.4 Method of solution 
3.5 Results 
3.6 Conclusions 
3.7 Appendix - matrix equations for contact solution 
References 
Chapter 4. Effect of load sequence 
on fatigue life of rail steel 
G.C. Sih and D.Y. Jeong 
4.1 Introduction 
4.2 Strain energy density criterion 
4.3 Material characterization 
4.4 Load spectra 
4.5 Finite element analysis 
4.6 Discussion and conclusions 
References 
Table of contents 
1 
1 
1 
3 
4 
9 
16 
20 
21 
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27 
34 
41 
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49 
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68 
73 
74 
81 
84 
Table of contents 
Chapter 5. On residual stresses in 
corrugated rails and wheel/rail interactiOD 
R.Bogacz 
5.1 Introduction 
5.2 Simple models of wheel/rail interaction 
5.3 Simulation of rolling contact process 
5.4 Measurements of residual stresses in corrugated rail 
55 Final remarks 
References 
Chapter 6. Prediction of actual residual stresses 
by constrained minimization of energy 
J.Orm 
6.1 Introduction 
6.2 Mechanical models 
6.3 Numerical models 
6.4 Optimization strategy 
65 Numerical results 
6.6 Concluding remarks 
References 
Chapter 7. Hybrid finite element method for 
estimation of actual residual stresses 
M. HoIbwiAski and J. Orkisz 
7.1 Introduction 
7.2 Numerical approach 
7.3 Performance tests 
7.4 Example analysis of a rail 
7.5 Discussion and conclusions 
References 
Chapter 8. Application of the constrained minimization 
method to the prediction of residual stresses 
in actual railsections 
A.B. Perlman and J.E. Gordon 
8.1 Introduction 
8.2 Background 
8.3 Analysis method 
8.4 Results 
85 Discussion and conclusions 
References 
ix 
87 
87 
88 
90 
97 
97 
100 
101 
101 
103 
109 
110 
113 
118 
123 
125 
125 
127 
134 
143 
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154 
161 
164 
171 
176 
x 
Chapter 9. Estimation of actual residual stresses 
by the boundary element method 
W. Cecot and J. Orkisz 
9.1 Introduction 
9.2 Estimation of residual stresses by the BEM 
9.3 Results of numerical examples 
9.4 Conclusions 
References 
Chapter 10. A new feasible directions 
method in nonlinear optimization 
J. Orkisz and M. Pazdanowski 
10.1 Introduction 
10.2 New algorithm 
10.3 Tests and comparisons 
10.4 Concluding remarks 
References 
Chapter 11. Enhancement of experimental results 
by constrained minimization 
W. Karmowski, J. Magiera, and J. Orkisz 
11.1 Introduction 
11.2 General formulation of the problem 
11.3 Tests of enhancement concept 
11.4 Conclusion 
References 
Chapter 12. On future development of the con-
strained energy minimization method 
J.Orkisz 
12.1 Introduction 
12.2 Continuation of current work 
12.3 New topics 
References 
Table of contents 
179 
179 
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232 
Series on engineering application of fracture mechanics 
Fracture mechanics technology has received considerable attention in recent years and 
has advanced to the stage where it can be employed in engineering design to prevent 
against the brittle fracture of high-strength materials and highly constrained structures. 
While research continued in an attempt to extend the basic concept to the lower strength 
and higher toughness materials, the technology advanced rapidly to establish material 
specifications, design rules, quality control and inspection standards, code requirements, 
and regulations for safe operation. Among these are the fracture toughness testing 
procedures of the American Society for Testing and Materials (ASTM), the American 
Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Codes for the design 
of nuclear reactor components, etc. Step-by-step fracture detection and prevention 
procedures are also being developed by the industry, government, and university to guide 
and regulate the design of engineering products. This involves the interaction of 
individuals from the different sectors of society that often presents a problem in 
communication. The transfer of new research [mdings to the users is now becoming a 
slow, tedious, and costly process. 
One of the practical objectives of this series on Engineering Application of Fracture 
Mechanics is to provide a vehicle for presenting the experience of real situations by those 
who have been involved in applying the basic knowledge of fracture mechanics in practice. 
It is time that the subject should be presented in asystematic way to the practising engineers 
as well as to the students in universities, at least to all those who are likely to bear a 
responsibility for safe and economic design. Even though the current theory of linear 
elastic fracture mechanics (LEFM) is limited to brittle fracture behavior, it has already 
provided a remarkable improvement over the conventional methods not accounting for 
initial defects that are inevitably present in all materials and structures. The potential of 
the fracture mechanics technology, however, has not been fully recognized. There remains 
much to be done in constructing a quantitative theory of material damage that can reliably 
translate small specimen data to the design oflarge size structural components. The work 
of the physical metallurgists and fracture mechanicians should also be brought together 
by reconciling such details of the material microstructure with the assumed continua of 
the computational methods. It is with the aim of developing a wider appreciation of the 
fracture mechanics technology applied to the design of engineering structures such as 
aircraft, ships, bridges, pavements, pressure vessels, off-shore structures, pipelines, etc. 
that this series is being developed. 
Undoubtedly, the successful application of any technology must rely on the soundness 
of the underlying basic concepts and mathematical models and how they reconcile with 
each other. This goal has been accomplished to a large extent by the book series on 
Mechanics of Fracture started in 1972. The seven published volumes offer a wealth of 
information on the effects of defects or cracks in cylindrical bars, thin and thick plates, 
shells, composites, and solids in three dimensions. Both static and dynamic loads are 
considered. Each volume contains an introductory chapter that illustrates how the strain 
energy criterion can be used to analyze the combined influence of defect size, component 
geometry and size. loading. material properties. etc. The criterion is particularly effective 
for treating mixed mode fracture where the crack propagates in a non-self-similar fashion. 
One of the major difficulties that continuously perplex the practitioners in fracture 
mechanics is the selection of an appropriate fracture criterion. without which no reliable 
prediction of failure could be made. This requires much discernment, judgement. and 
experience. General conclusions based on the agreement of theory and experiment for a 
limited number of physical phenomena should be avoided. 
Looking into the future. the rapid advancement of modem technology will require more 
sophisticated concepts in design. The micro-chips used widely in electronics and advanced 
composites developed for aerospace applications are just some of the more well known 
examples. The more efficient use of materials in previously unexperienced environments 
is no doubt needed. Fracture mechanics should be extended beyond the range of LEFM. 
To be better understood is the entire process of material damage that includes crack 
initiation, slow growth. and eventual termination by fast crack propagation. Material 
behavior characterized from the uniaxial tensile tests must be related to the more 
complicated stress states. These difficulties should be overcome by unifying metallurgical 
and fracture mechanics studies. particularly in assessing the results with consistency. 
xi 
xii Series on engineering application offracture mechanics 
This series is therefore offered to emphasize the applications of fracture mechanics 
technology that could be employed to assure safe behavior of engineering products and 
structures. Unexpected failures mayor may not be critical in themselves but they can 
often be annoying, time-wasting, and descrediting of the technical community. 
Bethlehem, Pennsylvania 
1987 
G.C. Sib 
Editor-in-Chief 
Foreword 
Rail integrity is a current application of engineering fracture mechanics at a practical 
level. Although railroad rails have been manufactured and used for more than a 
century, it is only in the last ten years that the effects of their crack propagation and 
fracture characteristics have been considered from a rational viewpoint. The J,Jractical 
objectives are to develop damage tolerance ~delines for rail inspection and to improve 
the fracture resistance of new rail productiOn. 
Rail fatigue crack propagation rates and fracture resistance are strongly influenced 
by residual stresses, which are introduced into the rail both during proouction and in 
service. Therefore, the rail residual stress field must be well understood before fracture 
mechanics can be usefully applied to the subject of rail integrity. 
The three-dintensional character of rail and its stress fields make it essential to apply 
both experimental and analytical methods in order to twderstand the effects of pro-
duction and service variables on residual stress and the effects of the stress on fatigue 
crack propagation and fracture. This volume brings to~ether field observations and 
experimentalstress analysis of railroad rails in the Umted States and Europe. The 
ongoing search for an efficient and accurate technique is emphasized. A companion 
volume brings together several analytical investigations, based on advanced compu-
tational mechanics methods, for correlation of the experimental data as well as eval-
uation of the effects of residual stress on rail integrity. 
Bethlehem, Pennsylvania 
1991 
xiii 
G.C. Sih 
Editor-in-Chief 
Editors' preface 
The theoretical developments presented in this volume represent significant progress along 
a tortuous path which, we hope, will ultimately lead to a systematic understanding of 
fatigue crock propagation and fracture in rails subjected to typical service conditions. The 
theories are based on fundamental principles of mechanics - principles which are not easy 
to apply to complex bodies like rails. As was shown in Volume I, experiments on rails 
are also difficult. Synthesis poses a dilemma which is well described by a popular joke: 
"When a theoretical result is presented. no one believes it except the author. When an 
experimental result is presented. everyone believes it except the author." With the satire 
factored out, this tells us that the theoretician must be willing to accept the discipline of 
conforming his model to test results, and the experimentalist must be willing to question 
results which do not conform to the theory, if any genuine understanding is to be achieved. 
Most of the early attempts to systematize crock propagation in rails were based on linear 
elastic fracture mechanics (LEFM). The LEFM-based models have generally included 
simplifying assumptions about the rail and its stress fields - assumptions which in some 
cases had to strain credulity if anything at all was to be calculated. Of course, there was 
not much to be gained then from more sophisticated models, since only the vaguest notions 
were available about one of the most influential variables: the internal residual stress field 
in the rail head. 
Much more quantitative information is now available about rail residual stresses, and 
the fracture mechanics theoreticians have also gained a better understanding of crock 
propagation in rails under mixed-mode conditions. Thus, we are now beginning to see 
the second generotion of crock propagation models, which take much better account of 
the recent experimental results. Chapters 2 through 4 are examples of such models. 
The remainder of this volume presents the results of theoretical work aimed at 
understanding the relations between residual stress, manufacturing process variables, and 
the service environment. Chapter I deals with the problem of estimating the level of 
residual stress induced by roller straightening, the process now used by most mills to meet 
the tolerances required for continuous welded rail. In Chapter 5, the problem of wheel/rail 
contact is revisited from the viewpoint of the influence of the service loads on rail running 
surface corrugation, as well as residual stress. Chapters 6 through 12 present the results 
of a joint research progmm undertaken with the aim of predicting the rail residual stress 
fields which may result from service conditions. The frrst and last of these chapters contain 
an introductory overview and expectations for the future, respectively, while the other 
chapters delve into various specifics. 
We wish to acknowledge several members of the U.S. Department of Transportation, 
whose efforts made this conference and these volumes possible. Mr. R.L. Krick. Deputy 
Associate AdministmtorforTechnology Development, Mr. W.B. O·Sullivan. Chief. Trock 
Standards Division. and Mr. W.R. Paxton, Chief. Trock Research Division, of the Federal 
Railroad Administration. provided patient guidance and support for much of the work 
reported in these volumes. Mr. AJ. Bang. International Progmms Officer. Federal Railroad 
Administration, and Mrs. M.S. Allen. International Cooperation Division, Office of the 
Secretary. were instrumental in the organization of the joint projects. We also thank the 
Office for Research and Experiments of the International Union of Railways. the Chicago 
Technical Center of the Association of American Railroads, and the Polish Academy of 
Sciences for their contributions to the conference progmm. 
Cracow. Republic of Poland 
April. 1990 
xv 
O. Orringer 
J. Orkisz 
z. Swiderski 
Volume Editors 
Contributing authors (Volume II) 
R. Bogacz 
Institute of Fundamental 
Technological Research 
Polish Academy of Sciences 
Warsaw, Republic of Poland 
W. Cecot 
Cracow Institute of Technology 
Cracow, Republic of Poland 
T.N. Farris 
School of Aeronautics 
and Astronautics 
Purdue University 
Lafayette, Indiana, USA 
J.E. Gordon 
U.S. Department of Transportation 
Volpe National Transportation 
Systems Center 
Cambridge, Massachusetts, USA 
M. Hotowmski 
Cracow Institute of Technology 
Cracow, Republic of Poland 
D.Y.Jeong 
U.S. Department of Transportation 
Volpe National Transportation 
Systems Center 
Cambridge, Massachusetts, USA 
W. Karmowski 
Cracow Institute of Technology 
Cracow, Republic of Poland 
L.M.Keer 
Department of Civil Engineering 
Northwestern University 
Evanston, Illinois, USA 
J. Magiera 
Cracow Institute of Technology 
Cracow, Republic of Poland 
FA. McClintock 
Mechanical Engineering Department 
Massachusetts Institute 
of Technology 
Cambridge, Massachusetts, USA 
M.Olzak 
Warsaw University of Technology 
Warsaw, Republic of Poland 
J.Orkisz 
Cracow Institute of Technology 
Cracow, Republic of Poland 
M. Pazdanowski 
Cracow Institute of Technology 
Cracow, Republic of Poland 
A.B. Perlman 
Mechanical Engineering Department 
Tufts University 
Medford, Massachusetts, USA 
G.C.Sih 
Institute of Fracture 
and Solid Mechanics 
Lehigh University 
Bethlehem, Pennsylvania, USA 
J. Stupnicki 
Warsaw University of Technology 
Warsaw, Republic of Poland 
SJ. Wineman 
Mechanical Engineering Department 
Massachusetts Institute 
of Technology 
Cambridge, Massachusetts, USA 
R. W6jcik 
Warsaw University of Technology 
Warsaw, Republic of Poland 
Y.Xu 
xvii 
School of Aeronautics 
and Astronautics 
Purdue University 
Lafayette, Indiana, USA 
Glossary and conversion factors 
Since the general reader may not be acquainted with the many abbrevations, acronyms, 
and special terms used in the railroad industry, the editors have tried to provide 
explanations at appropriate points in the volume. Since railway engineermg and 
research in the United States IS still carried out in English units, we have also included 
conversions from English to SI units, or vice versa, in each chapter. The following is 
a summary of common abbrevations and acronyms, as well as a few conversion factors 
for some uncommon units. 
AAR 
AREA 
ATSF 
BNA 
CNTK 
CWR 
EMAT 
FRA 
FAST 
MGT 
ORE 
PKP 
Association of American Railroads. 
American Railway Engineering Association. 
Atchison, Topeka, and Santa Fe Railroad. 
Barkhausen noise analysis. 
Centrum Naukowo Techniczne Kolejnictwa 
(Central Research Institute of the Polish State Railways). 
Continuous welded rail - lengths of 39 or 78 feet in North America, or 15 
to 30 m in Europe, joined after manufacture by means of flash butt 
welds to produce strings typically 1/4 mile (400 m) long. After placment 
in track, CWR strings are generally joined by means of field welding 
techniques. 
Electromagnetic acoustic transduction - a method for nondestructive 
internal inspection of metal bodies, currently under investigation for 
application to rail inspection. 
Federal Railroad Administration, U.S. Department of Transportation 
Facility for Accelerated Service Testing (a dedicated closed-loop track at 
the U.S. Transportation Test Center). 
Million gross tons - unit of rail traffic measurement commonly used in 
North America 
Office de Recherches et d'Essais (Office of Research and Experiments) 
of the VIC 
Polskie Koleje Panstwowe (Polish State Railways). 
Railsections 
132 RE Typical examJ.>les of North American nomenclature. The number 
136 RE dermes the nul weight in lb./yd.; the code RE identifies the profile as a 
section design approved by the AREA. 
S49 
S60 
VIC 60 
RO.2 
Rm 
SP 
Tangent 
track 
Tg 
TIC 
VIC 
Typical examples of European nomenclature. The number defines the 
rail weight in Kgf/m; the code UIC identifies the profile as a section 
design approvea by the VIC. 
Tensile 0.2% offset yield strength. 
Ultimate tensile strength. 
Southern Pacific Railroad. 
Term used in North America to describe track designed to have zero 
curvature. 
Teragram (1012 gm) - unit of rail traffic measurement used in some 
countries in Europe 
U.S. Transportation Test Center, located in Pueblo, Colorado. 
Union Internationale des Chemins de Fer 
(International Union of Railways). 
xix 
xx Glossary and conversion/actors 
Unit train A long freight train consisting of identical cars. The most common unit 
trains in North America carry coal, grain, or iron ore and may contain 
100 to 110 cars. 
UP Union Pacific Railroad. 
Conversion factors 
0/00 
degree 
Unit of track grade (1 0/00 = 0.1 %) 
When used to specify track curvature (North American practice), the 
curve radius (ft) = 5730/degree. For example, the radius of a 5-degree 
curve is 1146 ft. 
1 ksi = 6.895 MPa 
1 ksi.[ill. = 1.099 MPa .[ffi 
1 MGT = 1.101 Tg 
1 ton = 0.907 tonne 
SJ. WINEMAN and F.A. McCLINTOCK 
Residual stresses and web fracture 
in roller-straightened rail 
1.1. Introduction 
Over the past ten years, several accidents involving web fracture of roller-straightened 
rail, both before and in service, have raised questions on the safety of such rail. This 
work reviews progress in quantifying the tendency of residual stresses to drive fracture 
in roller-straightened rail. The available residual stress data and their reliability are 
discussed. The stress intensity on a long running web crack due to release of the 
mid-rail longitudinal residual stress field is mentioned. A saw-cutting test has been 
developed to quantify the severity of residual stresses in roller-straightened rails by 
relating the curvature changes of the cut ends to the stress intensity K I on a web 
crack at the saw-cut location. Since web cracks actually occur most often at or near 
rail ends, the stress transients near a cut rail end are calculated and the stress intensity 
on a short web crack at the rail end is estimated. Lastly, a discussion is given of ongoing 
work in analyzing the roller-straightening process, to predict the formation and 
modification of residual stresses for eventual process improvement. 
1.2. Determination of residual stresses 
Data 
Residual stress data for roller-straightened rail were taken from several sources 
[1.1-1.5). In these works, values of residual stress at points on the periphery of the rail 
were obtained by placing strain gauges on the rail surface and cutting to relieve residual 
stresses. Although both longitudinal and transverse stresses were measured, it was 
shown by Wineman and McClintock [1.6] that the longitudinal residual stress is the 
key component in web fracture. A scatterband of the longitudinal residual stress 
measurements is shown in Figure 1.1. 
O. Orringer et al. (eds.l. Residual Stress in Rails. Vol. II. 1-22. 
© 1992 Kluwer Academic Publishers. 
2 Chapter 1 
COMPRESSION TENSION 
- 40 - 20 o 20 40 (ksi) 
-300 -200 -100 o 100 200 300 MPa 
Figure 1.1. Scatterband of longitudinal residual stress. 
(As-manufactured roller-straightened rail and typical measurement locations.) 
Equilibrium conditions on residual stresses 
Stress gradients should satisfy the local equilibrium equations: 
o i,j=x,Y,Z ( 1.1 ) 
Also, stress distributions should satisfy global equilibrium equations for zero net force 
V qi and moment M qi over a cross section A q , with i,q = x,y,z; no summation 
over q: 
V qi o ( 1.2) 
f f E ijk X j ( 1 - 1) jq) a qk d A q o ( 1.3) 
where E ijk is the alternating unit tensor and 1) jq is the Kronecker delta. 
Residual stresses and web fracture in roller-straightened rail 3 
Application of equilibrium checks to data 
Checks oflocal equilibrium were performed [1.6) from data developed by Groom [1.7] 
on press-straightened, service-worn rail for equilibrium in the vertical and lateral 
directions. These checks gave non-zero sums of gradients which were of the order of 
the gradients themselves. Checks of some of the global equilibrium equations were 
performed for data from both press-straightened and roller-straightened rail. The 
global checks showed non-zero net longitudinal forces and vertical and lateral bending 
moments, which were small compared to those producing overall yield (about 1 to 
12%), but large compared to those expected in service (as much as 91% of the 
longitudinal force expected in service for one case of roller-straightened rail, with the 
other cases ranging from 10 to 45% of expected service values). The non-zero forces 
and bending moments were also not negligible compared to those required to produce 
tensile and bending stresses of the order of the maximum longitudinal residual stress. 
Such uncertainties, measured by global and local equilibrium checks, suggest that the 
current residual stress data are only accurate within a factor of two. Although these 
uncertainties still allow predictions of the effects of residual stresses on web fracture, 
they are probably too large for use in predicting, for example, growth of cracks in the 
rail head during service, where accurate and detailed knowledge of the stress fields is 
needed. 
1.3. ElTects of residual stresses on web fracture 
A steady-state energy release rate analysis was performed [1.6) to find the stress 
intensity on a web crack due to partial release of the longitudinal residual stress. Values 
of calculated stress intensities K I were of the order of the fracture toughness K IC , 
implying that the longitudinal stresses present in roller-straightened rail can be 
sufficient to drive web fracture, especially in alloy rails with low fracture toughness. 
The other components of residual stress were also considered, but their effects on web 
fracture were found to be negligible. The calculated stress intensities due to 
longitudinal residual stress ranged from 36 to 47 MPa"r,;:;(33 to 43 ksiJin). The range 
of fracture toughness K IC for carbon and alloy rail is 27 to 55 MPa"r,;:; (25 to 50 
ksiJin) [1.8), with the values of K IC for high-strength alloy rails near the bottom of 
this range. Even with uncertainty in the residual stress data leading to the above values 
of K I , they are sufficiently close to K IC to indicate a danger of spontaneous web 
fracture, especially in alloy rail with low fracture toughness. 
4 Chapter 1 
J 
SAWCUT--====~~~~~==~============~ 
Figure 1.2. The saw-cut rail. 
1.4. A saw-cutting test to quantify severity of residual stresses 
An estimate of the stress intensity K I due to residual stresses, and tending to grow 
a web crack, can be made from a saw-cutting test (Figure 1.2). In such a test, the rail 
web is saw-cut longitudinally and the change in curvature of the split ends due to partial 
residual stress relief is measured. That the curvature change, rather than the opening 
displacement or shortening, is needed for a K I estimate is based on the following 
argument [1.6]. Unstable fracture of a web crack due to residual stresses should depend 
on Mode I energy release rate, since Mode II would tend to produce a change in crack 
direction. Release of the longitudinal stresses present in roller-straightened rail would 
make a web crack tend towards mid-web, where there is zero K II and maximum 
K I • The total energy release rate from the change in curvature of the split ends due 
to moment release is then concentrated into Mode I. If the resulting K I is above 
the critical value K I C for the rail steel, therail is capable of unstable web fracture 
driven by residual stresses. K I must be less than K IC by some finite amount to 
avoid undue risk of fracture. 
Some previous work has been done in saw-cutting the rail web to estimate residual 
stresses. Lempitskiy and Kazarnovskiy [1.4] attempted to correlate saw-cut openings 
with measured residual stresses. Orringer and Tong [1.9] mention work done at the 
Association of American Railroads (AAR) in which the rail web was saw-cut and 
displacements of the cut openings measured. Indeed, it was these test results that 
Joerms [1.10] used in his finite element work mentioned below, assuming uniform radii 
of curvature for the split ends to estimate the residual stresses in a rail end. However, 
Residual stresses and web fracture in roller-straightened rail 5 
none of these tests relates the curvature change of the split rail ends to the stress 
intensity K 1 • 
The saw-cutting test described below seems particularly attractive for the following 
reasons. First, it allows a simple estimate of the stress intensity K 1 , requiring only 
the measurement of rail curvatures and an algebraic calculation. Second, it is a static 
test, allowing isolation of residual stress effects from dynamic effects that are present 
in the drop-weight impact ("whom per") test described by Orringer and Tong [1.9]. 
Procedure 
Table 1.1 summarizes the procedure for estimating K 1 from the curvature change 
of the saw-cut ends. The residual stresses are assumed to be nearly uniform along the 
cut rail, i.e., the wavelength of any residual stress variation is greater than several rail 
heights. The presence of non-uniform residual stresses would be indicated, after 
cutting, by fluctuations in rail curvatures and resulting stress intensities along a short 
length of rail. Also, it is assumed that the cut is in a location where the effects of K 11 
are negligible (typically mid-web). Unequal lengths of the cut ends would indicate the 
presence of K lion a crack at the saw-cut location, and therefore a value of K 1 less 
than the maximum. 
Table 1.1. Summary of procedure for estimating 
stress intensity from saw-cutting test. 
1 Measure local radius of curvature R before and after saw cutting, for upper 
and lower split sections, at same distances from rail end. 
Saw-cut length should be greater than or equal to measuring length (of at least 
100 mm) plus 2 split section heights at start and end of cut. 
2 Calculate the stress intensity K 1 : 
1 ----- +1 -----[ ( 1 1)2 (1 1)2 ] 
H R alrer R be/or:e H B R oller R be/ore B 
where 
E = elastic modulus of rail steel 
v = Poisson's ratio 
t web = web thickness at saw-cut 
I H, I B = moments of inertia of head and base split sections 
R H be/ore' R H after = radii of curvature, head split section, 
before and after cutting 
R B be/ore' R B after = radii of curvature, base split section, 
before and after cutting 
6 Chapter 1 
Saw-cutting and curvature change measurement 
The rail web must be cut longitudinally into two split sections. The saw-cut must be 
long enough to provide a region for measuring curvatures away from stress transition 
regions at the start and end of the cut. These transition regions are estimated from 
Saint Venant's principle to be at most 2 split-section heights (about 200 mm, or 8 
inches) from a free split end or from the tip of the saw-cut. 
Since the stress intensity K I is a function of the residual stress relieved by saw-cutting 
or cracking, what is actually of interest is the change in curvature due to cutting. 
Therefore, the curvature of the rail head and base should be measured both before 
and after cutting. 
The radius of curvature at a point on the rail can be estimated in several ways. A 
plot of the rail profile could be made by running a dial gauge referenced to a flat surface 
along the head or base of each split rail section. Local curvatures could then be 
estimated by, say, fitting a parabola to three evenly spaced points along the rail. This 
was done for the AAR rail specimens discussed below. The simplest means of curvature 
measurement, however, seems to be a device consisting of a dial gauge centrally 
mounted on a bar, with guides for alignment. An average local curvature is found 
directly from the difference in displacement between the dial gauge and feet at each 
end of the bar. In terms of the dial gage deflection 0 and the half-length L between 
the dial gauge and feet at either end of the bar, 
R (1.4 ) 
Calculation of stress intensity K I 
The formula for stress intensity K I is found by relating the changes in curvature of 
the split ends to the bending moment released by the saw cut. This moment release 
is related to the strain energy release, which can in turn be related to the stress intensity 
K I that would act on a web crack at the saw-cut location. This formula was derived 
in detail by Wineman and McClintock [1.11]. The final expression is given in terms of 
the radii of curvature, R, before and after saw-cutting, of the head (H) and base (B) 
split sections, the centroidal moments of inertia I H and I B of the split sections, the 
web thickness t wab at the saw-cut, and the elastic modulus E and Poisson's ratio 
V: 
Residual stresses and web fracture in roller-straightened rail 7 
[1 (_I __ I )2+1 (_I __ I )2J 
H R after R be/ore H B R alter R be/ore B 
KI=--~--~~~~~====~~----~~ 
~2tweb(1-V2) 
E 
( 1.5) 
Application of procedure to AAR data 
Plots of the deflection of three roller-straightened rails split by the AAR were used to 
estimate stress intensities along the rails. Figure 1.3 is a plot of calculated stress 
intensities along the rail for one of the three rail specimens. The rails were assumed 
straight before cutting 1 / R be! ore = O. 
Error bars represent estimated uncertainty in the value of K I , due to estimated 
uncertainties in measuring local radii of curvature of the split sections. Uncertainties 
UK I / K I are typically 20% or less for 95% of such measurements, and were 
calculated from estimated uncertainties in dial gauge deflections [1.11]. The exact rail 
dimensions were not known, so typical dimensions were assumed. Differences between 
these and the actual dimensions will change the vertical scale of the entire plot slightly 
rather than affecting the error bars for individual measurements. 
ENDEFFECfS ENDEFFECfS 
oL-~~~--~~~~~ __ ~~~~~~~J-~~ __ 
o 10 20 30 
DISTANCE ALONG RAIL. IN. (SPEC. 1. NOT CLAMPED) 
Figure 1.3. Calculated stress intensity K I 
versus position along the rail for Specimen 1. 
(E"or bars represent estimated uncertainty in 
K I due to measurements for local curvature.) 
8 Chapter J 
Stress transition regions, shown on the plots by dotted lines, are estimated to be 2 
split section heights, or approximately 200 mm (8 inches), from the free split end or 
from the tip of the saw-cut. Calculated stress intensities in the middle portion of the 
specimens are: 
Specimen 1 
K 1= 33 to 55 MPar;:;i(3O to 50 ksi~) shown in Figure 1.3. 
Specimen 2 
K I = 66 to 88 MPar;:;i (60 to 80 ksi~) with one point at approximately 22 
MPar;:;i (20 ksi~). 
Specimen 3 
K I = 33 to 55 MPar;:;i (30 to 50 ksi~) with one point at approximately 93 
MPar;:;i (85 ksi~). 
The low value for Specimen 2 occurs at a relatively flat spot on the deflection plot, and 
the high value for Specimen 3 occurs at a sharp bend of the deflection curve. 
The fracture toughness K IC for these rails, or even the type of rail, was not known 
for the AAR specimens. However, the fracture toughness K IC for carbon and alloy 
rail ranges from about 27 to 55 MPar;:;i (25 to 50 ksi~), with typical values for carbon 
rail of 38 MPar;:;i (35 ksi~) [1.8] and for chromium-vanadium (CrV) rail of 31 
MPar;:;i(28 ksi~) [1.12]. Therefore, there is danger of spontaneous cracking in these 
rails tested by the AAR. 
Usefulness of this test and other methods of residual stress quantification 
Thesaw-cutting test can give a quantitative estimate of the stress intensity K I acting 
on a web crack at the saw-cut location. Therefore, it is a more useful and direct test 
for tendency to web fracture than the drop-weight impact ("whom per") test or a 
saw-cutting test where the cut opening only is measured, both of which give at best 
only a qualitative indication of the residual stresses present in the rail. Also, the 
saw-cutting test is simple to perform, requiring a longitudinal saw cut, curvature 
measurements, and an algebraic calculation. The test is further simplified by using a 
device we have made consisting of a dial gauge mounted on a bar with aligning guides. 
A calculator has been programmed to accept input data and calculate K I . 
Another promising method of residual stress measurement uses the Debro ultrasonic 
stress meter (see Volume I, Chapter 11). This device can measure the near-surface 
Residual stresses and web fracture in roller-straightened rail 9 
longitudinal residual stresses around the periphery of the rail and provides a quick, 
nondestructive method of residual stress measurement useful for production quality 
control. However, it does not measure residual stresses within the head and base, 
which also contribute to K I • 
1.5. Stress transients and short cracks at rail ends 
The energy release rate analysis to estimate K I was based on release of the mid-rail 
longitudinal residual stress field. However, at a rail end, where a crack is most likely 
to initiate, the longitudinal residual stress must drop to zero. At the same time, there 
may be increases in other stress components. In particular, a tensile vertical residual 
stress (which tends to drive a web crack) develops at the end of the rail in mid-web. 
Analytical and finite element models were compared [1.13] to determine the maximum 
vertical residual stress (J yy in mid-web at a cut rail end and the distance L 55 from 
the end to achieve 95% of the mid-rail residual stress field. 
The results of the models discussed below are in agreement with those of the finite 
element work of Joerms [1.10]. He reconstructed the residual stresses at the cut end 
of a roller-straightened rail by modeling the deformed rail resulting from longitudinal 
saw-cutting of the web, then forcing the displacements at the saw-cut location back to 
zero. The resulting length to develop 95% of the mid-rail longitudinal residual stress 
was between 0.8 and 1.1 rail heights. The maximum vertical residual stress at the end 
was 0.96 of the maximum magnitude of longitudinal residual stress developed in 
mid-rail. 
Allalyticalmodels 
Three analytical models were used to estimate the distance from a cut end needed to 
develop 95% of the mid-rail residual stress field. Two of these, the beam-on-elastic-
foundation model [1.14] and the elasticity solution of Horvay [1.15], can also be used 
to estimate the maximum vertical stress developed at the end. 
Beam 011 elastic foundatioll 
Modeling the rail head as a beam on the web as an elastic foundation can give an 
estimate of the length to reach the mid-rail residual stress and also of the maximum 
vertical residual stress at the rail end. Several different models were compared, using 
different definitions for the "beam" and "foundation". Both a free rail end and one 
whose base is restrained in the vertical direction were modeled. The best agreement 
with the finite element results was obtained, for a free rail end, by modeling the rail 
head plus half the web as the beam on half the web as the foundation, and for a rail 
with fixed base, by modeling the head plus half the web as the beam on the whole web 
10 Chapter 1 
as the foundation. In these models, the web or part of the web behaves as both beam 
and foundation. The results of these two-dimensional models are discussed below. 
It should be kept in mind that real cases of cut rail ends will never have a base which 
is rigidly constrained, since the spiking of the base to the ties is intermittent and there 
will always be some compliance in the ties and roadbed. However, the fIxed- and 
free-base boundary conditions are still useful for estimates. 
The length of stress transients at a cut rail end can be found from the characteristic 
length 1 / A of the differential equation for displacement of the beam [1.14]. For 
rail, the stiffness k of the elastic foundation can be written in terms of the web thickness 
t web, the height of web used as the foundation h found, and the elastic modulus E 
[1.16]: 
k 
t web E 
h found 
(1.6 ) 
Dominance by the exponential in the solution for beam displacement means that the 
length L ss to reach 95% of the mid-rail residual stress fIeld is three times the char-
acteristic length: 
_ 3 _ [4£1 yyJ1/4 _ [ 4hfound l yyJ1/4 
L ---3 -- -3 
ss A k t web 
( 1.7) 
Here, I yy is the centroidal moment of inertia of the part of the rail modeling the 
beam. The maximum vertical residual stress in the web at a cut end can be estimated 
from the vertical deflection W at the end of a semi-infinite beam subject to an end 
moment M 0 [1.14]: 
w(z = 0) [ J1/2 _ M 0 h found 
£ t web I yy 
( 1.8) 
The moment M 0 was taken to be that acting above the rail centroid for a fourth-order, 
self-equilibrating polynomial stress distribution representing the longitudinal mid-rail 
Residual stresses and web fracture in roller-straightened rail 11 
stress. 
The vertical stress a yy in the web at the end is then related to the dimensions and 
residual moment by 
a (Z=O)=EE <>;E[W(Z=O)]=r===-=M=o== 
yy yy h found ~ t w.b h found I yy 
( 1.9) 
Shear lag model 
A shear-lag model derived in [1.13] predicts the length to attain the mid-rail residual 
stress field by idealizing the rail as a composite of a web and two equal flanges, with 
transition regions between the web and flanges. Web, flange, and transition-region 
displacements are idealized so that the web and flanges are in a state of longitudinal 
compression and tension, respectively, and the transition regions are mostly in shear. 
Equilibrium for differential elements in the web and one flange, in terms of changes 
in stress and displacement from the mid-rail field, gives a differential equation with 
characteristic length L and, therefore, an estimate of the length L ss of stress 
transients [1.13]. 
Saint Venant (Horvay) model 
Saint Venant's principle suggests that for a uniform-thickness bar, 95% of the 
steady-state residual stress field will be attained one or two bar heights away from the 
cut end. Horvay [1.15] has solved a problem for stresses near a self-equilibrated, 
parabolic distribution of end loads on a uniform-thickness, semi-infinite rectangular 
strip. From superposition, the stress changes should be the same for end stresses going 
to zero in mid-strip as for mid-strip stresses going to zero at a free end. For the rail, 
these stress transients will be changed somewhat by the non-uniform thickness but will 
still be useful as a comparison. Horvay's solution gives both the length L ss of stress 
transients and the vertical residual stress a yy at the end. 
Finite element models 
To obtain a more detailed description of stress transients at the rail end, a plane-stress 
finite element model with elements of different thickness for the head, web, and base 
was run using the finite element program ABAQUS [1.17]. The curvature of the stress 
contours over several elements was measured, and the final element size was chosen 
so that the difference between these curved stress distributions and linearly varying 
12 Chapter 1 
I I 
I I 
L._ .. ___ ' 
I I 
I I 
I I 
I I 
I I 
I I 
I I 
I I 
r---- J -'-----, 
I I 
L. ___________ ~ 
hraiJ = 
185mm 
-.L 
-0- Ozz 
, , 
, 
" " 
, - -. 
~ 
~~ 
~ rj 
.... 1 .. ------ 610 mm -------I.~I 
Figure 1.4. Finite element model of the rail end. 
element stress was less than 5% of the maximum longitudinal residualstress. The final 
mesh of 8-node elements (Figure 1.4) represented a 610 mm (24 in) long section of 
rail. At one end, the longitudinal displacements of all nodes and the vertical dis-
placement ofthe node nearest to the centroid were constrained to simulate attachment 
to the rest of the rail. For the case imitating a rail spiked to fixed ties, the bottom 
nodes were also constrained. Constraining the base nodes vertically only, or con-
straining them both vertically and longitudinally, gave similar results. Residual stresses 
were introduced by specifying a self-equilibrating initial stress distribution in the form 
of a fourth-order polynomial with maximum values of :t 138 MPa (:t 20 ksi), and letting 
the program bring this to equilibrium. 
Singularities at thickness transitions 
In a rail model with discontinuities in thickness, singularities in stress exist at the rail 
end at the thickness transitions. The strength of such singularities can be found by 
modeling the different thicknesses as different shear moduli: G 1 / G 2 '" t I / t 2 , and 
using Bogy's solution [1.18] for two elastic quarter-planes with different moduli [1.13]. 
This singularity is very weak. For example, suppose the singularity is in effect 10 mm 
(0.4 in) from the rail end. Then the stress will not double due to the singularity until 
0.1 mm (0.004 in) from the end for the web-base region, and not until 0,01 mm (0.0004 
in) from the end for the head-web region. These lengths to double are negligible 
compared to an 18 mm (0.7 in) web thickness. Fillets with radii of the order of 20 to 
Residual stresses and web fracture in roller-straightened rail 13 
25 mm (approximately 3/4 to 1 inch) at the head-web and web-base intersections 
smooth the thickness transitions and would practically eliminate the effects of stress 
singularities. 
Discussion of model predictions 
Contour plots from the finite element model for a free rail end (Figures 1.5 and 1.6) 
give a general picture of stress components a zz and a yy near the rail end. There 
is also a buildup of shear stress a yz near, but not at, the end, but the magnitude of 
this stress is small and is not important for web fracture. Stresses in Figures 1.5 and 
1.6 have been plotted separately for the head, web, and base to avoid smoothing across 
the thickness transitions. Although there should be no visible singularities in stress at 
the rail ends near the thickness transitions, the plot of longitudinal stress shows small 
perturbations there, probably from approximating the actual stress fields using ele-
ments with linearly varying stresses. As a confirmation of the finite element modeling, 
a uniform-thickness finite element model was applied to Horvay's problem, giving 
results within 10% for a parabolic stress distribution. Use of a fourth-order distribution 
did not affect the length of transients appreciably but increased the maximum vertical 
stress from 0.7 to 1.0 times the maximum value of a zz • 
Length of stress transients 
Table 1.2 summarizes the predictions from various models of the length L ss to reach 
95% of the mid-rail residual stress distribution, normalized by a rail height of 185 mm 
(7.3 in). For a free rail end, values of the length L ss range from 0.69 to 1.22 times 
the rail height, with the highest value coming from the beam-on-elastic-foundation 
model and the lowest value coming from the shear lag model. The finite element 
predictions for free and fixed rail ends are 1.10 and 1.12 rail heights, respectively, while 
the beam-on-elastic-foundation model predictions are at most 30% higher. 
Maximum vertical stress 
Table 1.2 also summarizes the analytical and finite element predictions of maximum 
vertical residual stress a yy at the rail end near mid-web, normalized by the maximum 
value of mid-rail longitudinal residual stress a zz = 138 MPa (20 ksi). For a free rail 
end, values of maximum vertical residual stress range from 0.7 to 1.35 times the 
maximum a zz. The finite element predictions for free and fixed rail ends are 1.35 
and 1.10, respectively, while the beam-on-elastic-foundation model predictions are at 
most 30% lower. 
14 
I-- 8in.--I (ksi) 
~; : 
a z;: 
(ksi) 
z (in.) 
O,'~_~ ___ ~ 
2 4 6 8 10 
-10 
- 20 - 138 MPa 
Figure 1.5. Contours of constant longitudinal residual stress 
a zz from the finite element model for a free rail end. 
(hrail = 7.3 in.) 
\' 8 in. .\ 
• r===-",([/======::::J-'-9 I HEAD 
cr yy r,-,--+-----------------~1 (ksi) I 
FREE 
END 
30 
186 MPa ___ 
(1.35 cr u mnx ) 20 
10 
(kSI) 
- 10 
-------0--
f-L1L-L-++--------1 1 
WEB 
DISCONTINUITY BASE 
6 8 
z (in.) 
Chapter 1 
Figure 1.6. Contours of constant vertical residual stress a yy for the 
first 8 in. (200 mm) from the finite element model for a free rail end. 
Residual stresses and web fracture in roller-straightened rail 15 
It can be concluded, then, that appropriately chosen beam-on-elastic-foundation 
models, requiring only algebraic calculations, can give estimates of stress transients at 
a cut rail end that are within 30% of the 2D finite element results. 
Table 1.2. Length L 55 to reach 95% of the mid-rail residual stresses. * 
Model 
Finite element 
Joerms [10] (free end) 
free end 
base spiked to fIXed ties 
Analytical models 
Beam on elastic foundation 
free end 
base spiked to fIXed ties 
Shear lag 
Uniform strip solution (Horvay [15]) 
h 
cr zz 
0.8-Ll 0.96 
1.10 1.35 
1.12 1.10 
1.22 1.11 
1.45 0.79 
0.69 
0.72 0.70 
*Length normalized by a rail height h of 185 mm (7.3 in.); maximum vertical 
residual stress cr yy at the rail end normalized by the maximum mid-raillongitudi-
nal residual stress, cJ %% of 138 MPa (20 ksi). 
Stress intensity on short end cracks 
The worst location for a crack is at the cut rail end, near mid-web where the vertical 
residual stress is a maximum. The stress intensity K I was estimated for a short 
horizontal crack in the mid-web (uncracked) vertical stress field from the finite element 
analysis of a free rail end. Point load K I solutions [1.19, 1.20] were superposed to 
represent the effect of the non-uniform distribution of vertical residual stress near the 
end. The resulting values of K I versus crack length are shown in Figure 1.7 by a 
solid line: the stress intensity reaches approximately 22 MPa,Jrn (20 ksiji;) for cracks 
13 mm (0.5 in) long. A region bounded by light lines, representing the probable 
behavior, connects the stress intensity K I for short cracks with K I for long running 
cracks of 36-47 MPa,Jrn (33-43 ksiji;) from the energy release rate analysis in [1.6]. 
These stress intensity values are comparable to the range offracture toughnesses K Ie 
mentioned earlier (see Section 1.4). 
Longitudinal displacements at the free rail end 
For roller-straightened rail, when a short length is cut from mid-rail, for example, to 
use in the Meier technique of residual stress measurement [1.7], the flanges of the 
16 
Stress 
intensity 
K, 
(ksiv'in) 
50 - - - - - - - - - - -
40 
30 
20 
10 
0 
K 
I 
mid-rail 
"- POINT LOAD SUPERPOSITION 
0 2 3 4 5 6 7 8 
Crack length (in) 
Figure 1.7. Variation of stress intensity K 1 with 
crack length for a horizontal crack in mid-web. 
Chapter 1 
carbon 
and 
alloy 
·rail 
~ 
Meier length will be shorter and the web longer than the average length of the section. 
From the finite element model, this difference in displacement is as much as 0.1 mm 
(0.004 in). Failure to correct for these differences during initial cutting could result in 
an underestimate of the magnitude of the longitudinal residual stress of as much as 48 
MPa (7 ksi) on a 460 mm (18 in) Meier length. This is significant compared to typical 
residual stress maxima of138 MPa (20 ksi) for roller-straightened rail. Thus, the length 
changes at various locations around the rail periphery should be measured and used 
in calculating residual stress, as is done in practice.A further, smaller effect is due to 
the variation of longitudinal stress across the head from surface to interior. 
1.6. Creation of residual stresses: analyzing the roUer-straightener 
Work is in progress to analyze the roller straightener itself. The objectives of this work 
are to develop a model for residual stress formation during roller straightening and to 
determine the effects of process parameters on the severity of residual stress for 
eventual process improvement. Several unusual aspects of the roller-straightening 
problem make its analysis especially challenging. Because each roll leaves a wake of 
Residual stresses and web fracture in roller-straightened rail 17 
residual stress which is modified by subsequent rolls, the straightener is not equivalent 
to a series of stationary deformations. The local deformation and spreading near the 
rolls precludes idealization as beam bending (also, stationary beam bending does not 
give the observed V-shaped pattern oflongitudinal residual stress: it gives a Z-shaped 
pattern). Decreasing roll loads through the straightener mean that each adjacent 
section of the straightener has different boundary conditions and cannot be treated as 
a repeating periodic section. Non-proportional loading under the rolls means that 
simple isotropic and kinematic hardening material behavior may be insufficient for a 
model of residual stress creation. Nevertheless, kinematic hardening behavior is 
assumed as a first approximation. Material properties are assumed to be those of 
room-temperature rails. 
A schematic of the roller-straightener showing the boundary conditions on the rail 
is given in Figure 1.8. This straightener, which is typical of German-made roller 
straighteners, consists of four fixed upper rolls, which drive the rail through the 
straightener, and five lower rolls. The center three lower rolls apply vertical forces 
whose magnitudes decrease from the first to the third central roll. The outer lower 
rolls are displaced upwards. In some mills the outer lower rolls are not used. 
A key observation guiding the analysis of the roller straightener is the following. The 
dimensional changes of the rails after straightening are a shortening of the overall rail 
length, a widening of the flanges, and a shortening of the overall rail height. This 
suggests that the dominant mechanism in residual stress formation is that a small 
element in the head or base near the roll becomes shorter in length, shorter in height, 
and wider (Figure 1.9). This leads to a mismatch in length between the flanges and 
web that gives the V -shaped longitudinal residual stress distribution. 
A plane stress model using a half-roll-spacing long section of rail, with end conditions 
representing the rest of the straightener and kinematic hardening material behavior, 
gives longitudinal residual stresses similar to those observed. However the problem 
is actually three dimensional, with conditions approaching plane strain near the 
centerline of the rail near the roll. A "macro-dislocation" model (Figure 1.10) can be 
postulated to show that the process is not plane strain rolling contact, either, and to 
qualitatively describe the dimensional changes occurring under the rolls. The plane 
strain slip-line field for rolling of a rigid cylinder is shown in Figure 1.10a. In this field, 
a "macro-dislocation" (the resultant of many dislocations in the material) in the triangle 
under the roll will be forced downwards and left behind. This dislocation can be 
decomposed into two edge dislocations which correspond to an increase in overall 
length and an increase in rail height. There is also a compressive residual stress left 
behind the roll. These dimensional changes are the opposite of what occurs in roller 
straightening. Putting in a longitudinal stress due to bending under the roll in addition 
to the vertical roll stress (as happens in the straightener) gives the desired dislocations 
(Figure 1.10b). Such a dislocation pattern would give the desired shortening of the 
length and height and leave tension in the flange. Figure 1.10c shows a "macro-
18 
~I 
Figure 1.8. Schematic of the roller-straightener, showing 
idealized force and displacement boundary conditions. 
O/WII 
U! -- ----- -- (j ". (BENDING) - ----. ~ 
ttt 
LfJ ---~ @ 
Chapter 1 
Figure 1.9. Deformation of a small element in the flange as it passes beneath 
the roll, resulting in a decrease in length and height and an increase in width. 
Residual stresses and web fracture ill roller-straightened rail 
Longitudinal compression 
and forward tilt of material 
relative to roll 
(a) slip-line field for a rigid cylinder rolling on a rigid-perfectly-plastic 
half-space [1.21], with corresponding "macro-dislocation" model 
Longitudinal tension and 
backward tilt of material 
relative to roll 
A T 
-I 
(b) "macro-dislocation" model with addition of bending, corresponding 
to dimensional changes occurring in the roller-straightener 
-j 
-I 
-I 
Shortening of height and 
spreading of width 
19 
(c) cross-section of flange and "macro-dislocation" model with addition of bending. 
Figure 1.10. "Macro-dislocation" model. 
20 Chapter 1 
dislocation" picture of the out-of-plane spreading of the flanges. 
The above arguments suggest that the roller-straightening process is neither plane 
stress nor plane strain. Work continues on three-dimensional finite element modeling 
of the straightener for comparison with the two-dimensional, plane stress and plane 
strain models. 
1.7. Conclusions 
Checks of local and global equilibrium for existing residual stress data suggest that the 
data are only accurate within a factor of two. This uncertainty still allows predictions 
of the effects on web fracture, but probably does not allow predictions of the transition 
of longitudinal fatigue cracks (shells) to transverse cracks (detail fractures), where 
accurate knowledge of the stress fields is needed. 
A steady-state energy release rate analysis shows that longitudinal residual stress is 
the key stress component affecting web fracture of roller-straightened rail. Calculated 
Mode I stress intensities from this analysis were found to be of the same order as the 
range of typical fracture toughness values for rail steel. Therefore, even with a factor 
of two uncertainty in the residual stress data, there is danger of spontaneous web 
fracture, especially for alloy rails with low fracture toughness. 
A saw-cutting test can give a quantitative estimate of the Mode I stress intensity 
acting on a web crack at the saw-cut location. The test is simple, requiring a longitudinal 
saw cut of the web, measurement of the curvature changes of the split ends, and an 
algebraic calculation. 
Stress transients at a cut end of roller-straightened rail consist of a decrease to zero 
of longitudinal stress at the end and a vertical tensile residual stress in the web at the 
end. Finite element models for both a free end and an end with a fixed base gave the 
lengths to reach 95% of the mid-rail stress field to be 1.10 and 1.12 rail heights, 
respectively. The maximum vertical stresses at the end were 1.35 and 1.10 times the 
maximum value of mid-rail longitudinal residual stress. Beam-on-elastic-foundation 
models give algebraic estimates of such stress transients agreeing within 30% of the 
finite element results. 
An estimate of the Mode I stress intensity on a short web crack at the rail end, in 
the (uncracked) vertical residual stress field there, gives K I increasing with crack 
length and reaching approximately 2/3 of the typical rail steel fracture toughness for 
cracks 13 mm (0.5 in) long. Although K I on a short crack may not be sufficient in 
itself to drive a web crack, in the presence of service loads the risk of fracture is greatly 
increased. 
When a length of roller-straightened rail is taken from mid-rail, the changes inlongitudinal displacements can be large enough to affect subsequent residual stress 
measurements. For example, if the uneven length changes on cutting a 460 mm (18 
in) Meier section are not accounted for, there may be an underestimate of the mag-
Residual stresses and web fracture in roller-straightened rail 21 
nitude of measured longitudinal residual stress of as much as 48 MPa (7 ksi), a sig-
nificant amount compared to typical maxima of 138 MPa (20 ksi) for roller-straightened 
rail. This further suggests that measuring length changes around the rail periphery, 
as is done in practice, is necessary for accurate residual stress measurement. 
Analyzing the roller-straightener is a challenging problem requiring consideration 
of a three-dimensional stress state, local deformation under the roll as well as bending, 
non-periodic boundary conditions, and non-proportional loading under the rolls. A 
plane stress, kinematic hardening model gives longitudinal residual stresses similar to 
those observed. However, the real process is neither plane stress nor plane strain. 
Work continues on three-dimensional finite element modeling for comparison with 
and selection of appropriate two-dimensional models. 
Acknowledgements 
We wish to thank Dr. Oscar Orringer of the US DOT Transportation Systems Center 
for guidance on this project and Mr. R.c. Rice of the Battelle Columbus Laboratories 
for several helpful comments. Financial support from the US DOT, Transportation 
Systems Center, Contract DTRS-57-88-C-00078, is gratefully acknowledged. All word 
processing and graphics were performed on a Data General MVlOOOO computer 
donated to MIT by the Data General Corporation. 
References 
[Ll] 
[1.2] 
[1.3] 
[1.4] 
[1.5] 
[1.6] 
[1.7] 
[1.8] 
Anon., "Factors influencing the fracture resistance of rails in the unused 
condition", in: Possibilities of Improving the Service Characteristics of Rails by 
Metallurgical Means, Report No.1, Office for Research and Experiments of 
the International Union of Railways (ORE/IUR), Utrecht (1984). 
Deroche, R.Y. et ai., "Stress releasing and straightening of rails by stretching", 
Paper no. 82-HH-17, Proc. Second International Heavy Haul Railway Con-
ference, Colorado Springs, CO, 1982. 
Konyukhov, A.D., Reikhart, VA., and Kaportsev, V.N., "Comparison of two 
methods for assessing residual stresses in rails", Zavodskaya Laboratoriya 39 
(1),87-89 (1973). 
Lempitskiy, V.V. and Kazarnovskiy, D.S., "Improving the service life and 
reliability of railroad rails", Russian Metallurgy 1,111-117 (1973). 
Masumoto, H. et al., "Production and properties of a rail of high serviceability", 
Proc. 61st Transportation Research BoardAnnual Meeting, Washington, D.C., 
1982. 
"Rail web fracture in the presence of residual stresses", 77leoret. Appl. Fracture 
Mech. 8, 87-99 (1987). 
Groom, J.J., "Determination of residual stresses in rails", Battelle Columbus 
Laboratories, Columbus, OH, report no. FRA/ORD-83/05, 1983. 
Orr inger, 0., Morris, J.M., and Steele, R.K., "Applied research on rail fatigue 
and fracture in the United States·, 77woret. Appl. Fracture Mecl!. 1, 23-49 
(1984). 
22 
[1.9] 
[1.10] 
[1.11] 
[1.12] 
[1.13] 
[1.14] 
[1.15] 
[1.16] 
[1.17] 
[1.18] 
[1.19] 
[1.20] 
[1.21] 
[1.22] 
Chapter 1 
Orringer, o. and Tong, P. "Investigation of catastrophic failure of a 
premium-alloy railroad rail", Fracture Problems in the Transportation Industry, 
Proc. ASCE Conference, Detroit, MI 1985. 
Joerms, M.W., "Calculation of residual stresses in railroad rails and wheels 
from sawcut displacement", Residual Stress - in Design, Process and Material 
Selection (W.B. Young, ed.), American Society of Metals, 1987, p. 205. 
Wineman, SJ. and McClintock, F A., "A saw-cutting test for estimating stress 
intensity at a rail web crack due to residual stresses", Theoret. Appl. Fracture 
Mech. 13,21-27 (1990). 
Jones, OJ. and Rice, R.C., "Determination ofKIC fracture toughness for alloy 
rail steel", final report to DOT Transportation Systems Center, Cambridge, 
MA,1985. 
Wineman, SJ. and McClintock, FA., "Residual stresses near a rail end", 
Theoret. Appl. Fracture Mech. 13,29-37 (1990). 
Hetenyi, M., "Beams on elastic foundation", in: Handbook of Engineering 
Mechanics (W. Flllgge, ed.), McGraw-Hill, New York, 1962. 
Horvay, G., "Some aspects of Saint Venant's principle",!. Mech. Phys. Solids 
5,77-94 (1957). 
Orringer, 0., Morris, J.M., and Jeong, D.Y., "Detail fracture growth in rails: 
test results", Theoret. Appl. Fractllre Mech. 5,63-95 (1986). 
ABAQUS, A general-purpose finite element code with emphasis on nonlinear 
applications, version 4.5, Hibbitt, Karlsson, and Sorensen Inc., Providence, 
RI,1985. 
Bogy, D.B., "On the problem of edge-bonded elastic quarter-planes loaded at 
the boundary", Int. J. Solids Stmctllres 6, 1287-1313 (1970). 
Hartranft, R.J. and Sih, G.c., "Alternating method applied to edge and surface 
crack problems", in Methods of Analysis and Solutions of Crack Problems: Vol. 
I - Mechanics of Fracture (G.c. Sih ed.), Noordhoff International Publishing 
(now Martinus Nijhoff Publishers), Netherlands, 1973, pp. 179-238. 
Murakami, Y. (ed.), Stress Intensity Factors Handbook, Pergamon, 
Oxford,1987, p. 108. 
Mandel,J., "Resistance au roulement d'un cylindre indeformable sur un massif 
pa rfaitement plastique", in Le Frottcmcnt & l'Usllre, Paris: GAMI, 1967, p. 
25. 
Johnson, K.L., Contact Mechanics, Cambridge University Press, 1985, p. 297. 
T.N. FARRIS, Y. XU, and L.M. KEER 
Some factors influencing the transition 
from shelling to detail fracture 
2.1. Introduction 
The railroad industry perpetually increases the wheel loads used by freight traffic to 
enhance cost effectiveness. One drawback of the increase in wheel loads is the sub-
sequent increase in the quantity of fatigue defects induced near the top surface of the 
rail in the region known as the railhead. In particular, the occurrence of horizontal 
cracks located about 6 to 7 mm (1/4 inch) below the surface of the rail has increased. 
The horizontal cracks are referred to as shell defects or shells. Shells grow in fatigue 
driven by the live contact shear stress that occurs at this depth as well as vertical residual 
stresses that are tensile at this depth. The shells are considered benign in nature since 
they do not directly cause rail failure. However, the shells may grow out of the horizontal 
plane to form vertical detail fractures that can lead to rail failure. The initiation of 
detail fractures is of interest because they are potentially failure causing whereas 
shelling is comparatively benign. The schematic of wheel/rail contact in Figure 2.1 
describes the location of shells and detail fractures [2.1]. 
The live stresses that drive the shell growth are calculated by modeling the rail as a 
semi-infinite elastic body and are shown in Figure 2.2. Manufacture and service induced 
residual stresses are known to reach significant magnitudes near the location of shell 
occurrence [2.2 - 2.4]. The residual stresses present at the location of the shell are 
included in the calculations using superposition. These residual stresses usually include 
a tensile stress oriented normal to the rail surface that serves to open the shell. The 
live compressive stress opposes the residual stress and closes the shell. The live shear 
stress causes the faces of the shell to move tangentially relative to each other in a sliding 
motion. 
The opening of the shell is called Mode I deformation while the relative sliding of 
the shell faces is called Mode II deformation. This chapter investigates some aspects 
23 
O. Orringer el al. (eds.). Residual Slress in Rails. Vol.ll. 23-44. 
© 1992 Kluwer Academic Publishers. 
24 
GAUGE 
SIDE 
DETAIL 
FRACTURE 
SHELLING 
Figure 2.1. Schematic of wheel/rail contact [2.1]. 
Chapter 2 
of the growth of the shell caused by the combined or mixed mode loading. The next 
three sectionsconcentrate on the following aspects of mixed mode crack growth 
respectively: a review of previous work concerning a stability analysis of the in-plane 
growth of the statically growing shell; the effect of crack velocity on the in-plane stability 
for dynamically growing cracks; and the effect of crack-face friction on the fatigue crack 
growth rates of shell defects. 
2.2. Crack path stability of statically growing shells 
A stability model that predicts the tendency of a statically growing shell to grow out-
of-plane to form a detail fracture was developed by Farris, Keer, and Steele [2.5]. The 
details of this stability analysis are omitted here, since they are similar to those described 
in the next section for the dynamic stability analysis. The stability analysis predicts 
that the leading edge of a short shell, that edge which 'sees' the wheel first, grows out 
of plane in a manner that initiates a detail fracture under unidirectional train traffic. 
However, the trailing edge of the shell branches up towards the surface. When train 
traffic is reversed, the trailing edge becomes the leading edge, and the direction of the 
Some factors influencing the transition from shelling to detail fracture 
400 tress (O"yy,O"xy, MPa) 
200 O"xy 
o 
-200 
-400 
-600 
-800 
-30 -15 o 
Position (mm) 
15 
Figure 2.2. The live stresses that drive the growth 
of a shell located 7mm below the surface. 
30 
(The maximum contact pressure is Po = 1000 MPa, the contact half-length 
is C = 7 mm, and the running sUrface friction coefficient is f = 0.1.) 
25 
out of plane growth at each tip is reversed. Therefore, the small out-of-plane growth 
associated with different loading directions causes a wavy crack path and traffic 
reversals tend to cause short shells to grow in a stable in-plane manner. 
The effect of the residual stresses, shell depth and length, and coefficient of friction 
at the wheel/rail contact on the shell path stability were predicted. These predictions 
can be summarized as follows [2.6]: 
1) Greater longitudinal residual tensile stress tends to increase the 
tendency for the shell to turn downward and increases the shell length in 
which this can occur. 
2) Increased vertical residual tensile stress reduces the tendency for the 
shell to turn downward and reduces the shell length in which this can 
occur. 
3) Increased running surface friction coefficient increases the length of 
shell in which downward turning is possible. 
4) Greater shell depth diminishes the downward turning tendency but 
may increase very slightly the length of shell over which downward turning 
is possible. 
26 Chapter 2 
.05 Aid 
.OOr-----+-----~~~~----~----~ 
1. 4. tid 5. 
-.05 
-.10 y 
i 
c x/ es =10 ksi 
-.15 _____ /P~x 
------t-------h-
Figure 2.3. Extent of out-of-plane growth as a function of normalized length. 
( hid = 0.05, die = 1, f = 0.1; see Figure 2.7.) 
The amount of out -of-plane growth is estimated by the magnitude of the parameter 
A., defmed as the vertical excursion in a crack-length increment of horizontal 
dimension h (Figure 2.3). The sign of A. indicates the direction of out-of-plane 
growth with positive A. being up towards the surface of the rail and negative A. being 
downward to form a potential detail fracture. The stability model [2.5] predicts A. I d 
as a function of II d ,where l is the current length of the shell and d is its depth 
below the surface. The example results in Figure 2.3 illustrate the points 1) and 2) 
above. 
The main conclusion from this analytical prediction is that relatively short shells have 
a strong tendency to form detail fractures while long shells will tend to grow in a stable 
in-plane manner. The sign of A. reverses for increased incremental length ( h ) for 
the longer shells that initially turn upward so that they will not tend to break the surface. 
That is, the shell would grow in and out-of-plane in a wave-like pattern. This is 
sometimes observed as evidenced by the occurrence ofJong shells without an associated 
Some factors influencing the transition from shelling to detail fracture 27 
detail fracture. One may question how a shell could grow through the length at which 
it has a high tendency to tum downward to form a detail fracture without doing so. A 
possible explanation for this could be that it grows past this length during the summer 
when high temperatures induce compressive longitudinal stresses in the rail. 
More recent analyses are the subject of the next two sections. The next section 
concentrates on the effect of the propagation velocity on the in-plane stability of a 
rapidly growing crack SUbjected to mixed mode loading. This effect could be important 
to the understanding of rapid growth of a shell caused by wheel/rail impact. Section 
2.4 outlines a procedure for including the effect of crack-face friction on the growth 
rate of a shell. Previous fatigue crack growth calculations which ignored crack-face 
friction predicted that the shell reached the fast fatigue crack growth regime at a length 
shorter than that observed under test track conditions. 
2.3. Dynamic crack curving 
The analysis uses perturbation techniques to calculate stress intensity factors at the tip 
of a crack growing with constant speed with a slight deviation out of its plane of growth. 
This is a preliminary investigation of the effect of crack velocity on crack path stability, 
as the fmite geometry corresponding to the rail is not included here, and it is assumed 
that the original crack must be growing with a steady velocity. The analysis should be 
viewed as a first step towards determining the velocity dependence of the stability of 
a running crack. 
Review of previous literature 
The quasi-static crack path under different load conditions was investigated nearly two 
decades ago by Goldstein and Salganik [2.7]. Cotterell and Rice [2.8] used Muskhe-
Iishvili's complex potentials [2.9] to derive the first order expression for the stress 
intensity factors to examine the crack growth path in an infinitely extended domain. 
Karihaloo et al. [2.10] obtained the second order solution for the kinked and curved 
extension of a crack in an unbounded medium. Sumi, Nemat-Nasser, and Keer [2.11, 
2.12] considered the effects of the finite geometry and boundary conditions in an 
iterative manner and found that the geometrical effects due to the crack extension are 
proportional to the length of the crack extension. 
This analysis considers inertial effects on the dynamic fracture path problem. As 
Nilsson [2.13] has described, the angular distribution of the near tip field singular 
stresses is only dependent on the instantaneous crack-tip velocity. Therefore, at the 
tip, the stress and displacement fields of a running crack can be characterized as 
28 Chapter 2 
y 
o( i) It 
/.4..' = N(h) 
x 
Figure 2.4. Straight crack moving with a curved extension. 
steady-state fields. The stress and displacement components can be expressed in terms 
of two analytic functions of two complex variables as shown by Rado~ [2.14]. The ratios 
between the real and imaginary parts of these two functions are constants whose values 
are related to the loading conditions. 
Basic fonnulation 
Consider a semi-infinite straight running crack in a homogeneous linearly elastic brittle 
solid as shown in Figure 4. The original coordinate system is x I - Y I and the 
coordinate system X - Y IS attached to the crack tip such that 
x = x I - a ( t) , Y = Y I . The instantaneous crack speed, V = ci ( t) . The shape 
of the crack extension can be approximated by: 
A(X) = ax + f3x3/2 (2.1 ) 
where higher order terms are disregarded. The shape parameters of crack extension 
are a and f3. The a term corresponds to the initial kink angle observed by cracks 
Some/actors influencing the transitionjrom shelling to detail/racture 29 
subjected to mixed mode loading. The f3 term includes the stress