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Fracture mechanics analysis of a rail-end bolt hole crack
Theoretical and Applied Fracture Mechanics 1 (1984) 51-60 North- Holland
51
FRACTURE M E C H A N I C S ANALYSIS O F A RAIL-END B O L T H O L E CRACK Ronald A. MAYVILLE Peter D. H I L T O N Arthur D. Little. Inc., Cambridge, Massachusetts 02140, USA Submitted to Oscar Orringer June 27, 1983
Analytic and experimental investigations were conducted to establish the cause of a peculiar ridge feature observed on the fracture surface of a railroad rail-end bolt hole fatigue crack. Calculations are performed which indicate that the ridges were caused by the change in stress caused by the thermal expansion of the rails during each day of fatigue. The ridge features were closely reproduced by a novel laboratory experiment on a four-hole compact tension specimen.
1. Introduction The current practice of constructing railroad track is to lay quarter-mile long strings of continuously welded rail (CWR) formed from 11.9 or 23.8 m rail sections (39 or 78 ft.). In the past, rails were always connected in the track with a bolted joint arrangement similar to the one shown in Fig. 1. There are still many bolted joints in service today and new ones are installed for insulated joints, in sharp curves, where there is a need to be able to quickly replace worn rails, and sometimes to connect strings of CWR. A mode of failure in bolted joints is fatigue crack initiation and growth from the bolt holes in the rail end. During the examination of one of these bolt hole cracks we discovered a peculiar feature on the fracture surface. Visible over a few
mrB
centimeters of crack growth were a set of ridges spaced about one millimeter apart, oriented perpendicular to the direction of crack propagation and not very well defined in appearance. The subject of this paper is our attempt to establish the cause of the ridges and the interesting conclusion that they were probably due to the daily variation in temperature at the rail site.
2. Failure description The crack was discovered at a joint in a section of CWR track in Nebraska during the month of August. The rail was 65.4 k g / m (132 l b / y a r d ) standard carbon, joined with 0.91 m (36 in.), sixhole joint bars; that is, each rail end had three bolt holes. Figure 1 shows the geometry and dimen-
mm
o oiioool 910ram Fig. 1. Geometry of the bolted joint. 016%8442/84/$3.00 © 1984, Elsevier Science Publishers B.V. (North-Holland)
i
Field ~ Side
Gage Side
R.A. Mavville, P.D. Hilton / Fracture mechanics analysis of a rail-end boh hole crack
52
sions of the bolted joint. The joint was on a railroad tie, but it is not certain if the joint was centered on the tie. The crack initiated at the first bolt hole of the rail receiving the loaded traffic and grew toward the rail head in a direction away from the rail end. Fig. 2a shows the geometry of the crack and Fig. 2b shows a macro photo of the fracture surface. The angle at which Fig. 2b is oriented is indicated in Fig. 2a. Details of the fracture surface are obscured by corrosion and rubbing between opposite surfaces, but a number of features are visible from Fig. 2. The crack initiated on the field side of the web as a corner crack inclined at approximately 45 ° to the rail axis. Although not shown here, the bolt hole surface was severely gouged from rubbing between the bolt and the bolt hole surface, thus offering many sites for crack initiation. The crack grew as a comer crack until it reached the gage side of the web at which time it began propagating as a through crack. At about the same time the crack changed its orientation to the rail axis to about 25 ° as shown in Fig. 2a. Before its discovery the crack propagated a total of 66 mm (2.6 in.) toward the rail head, and a small crack was formed at the diametrically opposite location of the bolt hole. The crystalline fracture surface shown in the
top of Fig. 2b resulted from breaking open the bolt hole crack after immersing the piece in liquid nitrogen. The ridge feature mentioned in the introduction is visible on the fracture surface about 13 mm (0.5 in.) from the edge of the bolt hole, particularly on the right-hand side, the gage side. The ridges are perpendicular to the direction of crack growth, extend at least 13 mm (0.5 in.) along the fracture surface, and are spaced by about 1 mm (0.04 in.). They are not well defined in appearance and it was necessary to control the direction of lighting to make them observable. The crack was undoubtedly caused by the fatigue loading resulting from the passage of trains. The section of track in which this crack was discovered was subjected to a large amount of unit trains carrying coal. Data supplied to us by the Dept. of Transportation (DOT) showed that an average of 20 loaded trains pulling 100-ton hopper cars passed each day. Furthermore, the consist or make-up of each train was quite regular: there were almost always 100 to 110 hopper cars and three to six engines in each train. The static vertical wheel load was about 147 kN (33 x 103 lb.) for both the engines and the loaded hopper cars.
Figure2b
f
J
----
Head ~ M ~
mm BoltHole
25°
Ridges
Web
Base Bolt-Hole $urfaoe
(al
Fig. 2. Bolt-hole crack description.
(bl
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
3. Analysis
1.0
53
I
I
I
0.9
Fracture mechanics is employed to investigate the fatigue crack growth behavior of the bolt hole crack. The calculation of loads and stress intensity factors are very approximate because the mechanics of the bolted joint are not well understood. Detailed studies to establish these quantities more precisely are currently underway.
0.8
~.
0.7
•-= o
0.6 0.5 0,
i~- 03 0.2
Loads and stresses
0.1 m
o
The loads on a rail can be estimated by using beam-on-elastic foundation analysis in which the rail is the beam and the ties and ballast--the gravel underneath the ties--are the elastic foundation. This type of analysis has been found to be reasonably accurate [1,2]. Following an approach of Talbot [1], it is assumed that the joint has no effect on the overall behavior of the rail; that is, the rail-joint system behaves as a continuous beam. Fig. 3 shows the distribution of the bending moment along the rail for one wheel. The ordinate of this curve is the ratio of the bending moment for a given location to the maximum bending moment, which occurs directly under the wheel and is given by:
Mo =
Ez/64= ]
(1)
where a = dynamic amplification factor W = wheel load E = Young's modulus for the rail I = moment of inertia for the rail cross section u = foundation modulus. The abscissa of Fig. 3 is given in units x / x l , where x~ is the distance from the location of the wheel to the point at which the bending moment is" zero for a single wheel. It is given by x1
=
(,n/4)[4EI/u] ' / ' .
For 65.4 k g / m (132 lb/yard) standard carbon rail: E = 207 x 103 N//mm 2 (30 × 106 l b / i n 2) and I = 3.7 × 107 mm 4 (88.2 in.4). The wheel load is 147 kN (33 x 1031b) and we assume that a = 2 and u = 10.3 N / m m 2 (1500 lb fine), which are representative of the type of rail system under consideration [1,3]. The result is M 0 = 9.6 x 104N-m(8.52 × 105 in-lb),
-0.1
-
-0.2 0 1 2 3 Distance along Rail from Load Point.
4
X/X, Fig. 3. Relative bending moment, M / M o, as a function of distance from load point, x / x l , for a single wheel.
and x~ = 1.03 m(40.5 in.). The maximum bending moment for two or more adjacent wheels is determined by superposing Fig. 3 for each of the wheels with a knowledge of the wheel separation in terms of xl. Fig. 4 is a schematic representation of a typical rail car connection. Superposition for this configuration shows that the bending moment is nearly the same under each of the wheels but is slightly greater under either of the wheels designated 1. The bending moment at wheel 1 is closely approximated by only considering the effect of the closest wheel. The distance between wheels I and 2 is 1.68 m (66
I
i
1.68 m--IP ~ 3 . ( ~
m
Fig. 4. Typical rail car connection.
~
1.68
R..4. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
54
in.) or 1.63 x 1. Therefore, the moment at wheel 1 caused by wheel 2 is, from Fig. 3, - 0 . 1 8 M 0, which gives a total moment at wheel 1 of M = 0.82 M 0 = 7.87 × 104 N-m(6.98 × l0 s in-lb). We assume that the rail joint is subjected to this moment for the passage of each wheel. The rail ends can carry no bending moment so the bending moment at the joint must be carried entirely by the joint bars. The way in which loads are transferred from the joint bars to the rail ends depends very much on the condition of the joint elements. However, Talbot [1] observed that in many cases the loads on the joint bars are distributed over only small segments located near the center and the ends of the joint bars. Therefore, the joint bars behave as though they are subjected to four-point bending. This situation is depicted in Fig. 5. For simplicity, the loads are assumed to be concentrated and located exactly at the center and ends of the joint bar. With this assumption it is a simple matter to compute the value of the concentrated loads, for they must balance the applied bending moment. The magnitude of the concentrated loads, including both joint bars in the calculation, is
V = M / ( I / 2 ) = 172 kN(38.7 X 103 lb), where I is the length of the joint bars, 0.91 m(36in). The magnitude of V is about half of the dynamic wheel load, 293 kN (66 × 103 lb). The concentrated load at the end of each rail is a shear force which causes high shear stresses in the rail web at the bolt holes. This is essentially a shear force applied to the end of the rail. It is assumed that the sum of the shear forces caused b y the wheel load and the forces at the foundation - - t h e tie--is zero. The shear stress in the rail web caused by the concentrated load can be estimated using a mechanics of materials approach so that
= VQ/It,
(2)
hee~
where Q = is the first moment of the area of the cross section above or below the center of the bolt hole; t = web thickness at the bolt hole. For 65.4 k g / m (132 l b / y a r d ) rail, Q -- 2.6 × 105 mm2(16 in 3) and t = 17.1 mm(0.675 in.) which gives ~"= 71.3 MPa (10.3 × 103 Ib/in2). The shear stress calculated from equation (2) is a reasonable approximation to the shear stress in much of the rail web because Q does not very greatly as a consequence of a web section thin in comparison to the head and base.
Stress intensity factor To estimate the magnitude of K ! resulting from the wheel load, the formula for a single crack emanating radially from a circular hole in an infinite plate in shear is used [4], following a suggestion made by A.A. Wells in a private communication to Allen and Morland [5]. Thus,
K, = F ( a / d ) z f ~ ,
(3)
where a is the crack length from the hole surface to the crack tip and d is the hole diameter. The nominal bolt hole diameter is equal to 28.6 mm (1.125 in.). For a crack length of 13 mm (0.5 in.), which corresponds to the approximate length at which the ridges occurred, F ( a / d ) = 1.6 and using the shear stress calculated in the previous section, Kl.,a x = 23 MPav/-m (21 ksi i ~ . ) . The bending moment distribution given in Fig. 3 shows that there is some reversed bending in the rail, which results in a negative R-ratio at the location of the crack. There is also a reversal in shear caused by the passage of the wheel over the bolt hole. The effects of this reversed (compressive) stress on crack growth are neglected in this approximate analysis. Therefore, Klmi. is taken equal to zero so that AK1 -- 23 MPa¢~- (21 ksiqq-ff) for each of the wheels. Fatigue crack growth occurs readily in rail steels for alternating stress intensity factors of this magnitude. In fact, using fatigue crack growth data obtained for a standard carbon rail specimen removed from the web [6], the growth rates can be estimated by the relation
!
0
0
[]
[]
d a / d N = 2.03 × lO-t°(AKt) 4°4 mm/cycle.
o
Thus, for A K t = 2 3
I
'
1
Fi 8. 5. The mode of load transfer assumed for the joint bar.
(4)
MPact-m (21 ksi iv/i-n..), m m / c y c l e (2.5 × 10 -6 in/cycle). Assuming that the average distance be-
d a / d N = 6.4 × 10 -5
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
tween ridges on the fracture surface is 1 mm (0.04 in.), the number of cycles between each ridge is predicted to be, N = 1/6.4 × 10 -5 = 15,600 cycles. The number of cycles per rail corresponding to a typical train which passed over the crack-containing rail is estimated by counting the number of wheels for the train. Each train had approximately 105 hopper cars with four wheels per car per rail. Adding to this the 24 wheels per rail associated with the three engines gives 440 wheels, or load cycles, per rail per train. Therefore, the number of trains passing during the formation of each ridge is predicted to be, 15,600/440 = 35 trains. The average traffic for this section of track was 20 loaded trains per day, about half of that predicted. If one considers that the 35 train estimate can easily be off by a factor of two because of variability in fatigue crack growth rates and the approximations in our stress analysis, then it is possible to conclude that the occurrence of each ridge was a daily event. Thermal stresses
The conclusion that the formation of a ridge was a daily event was important supporting evidence for the hypothesis that the ridges were a result of the daily variation in thermai stress and the accompanying change in crack growth direc-
tion resulting from the addition of an axial stress. The thermal stress for the bolt hole crack under consideration in this investigation would have to be compressive, because the ridges apparently occurred during the summer. The difference in stress states for the absence and presence of a compressive axial stress are illustrated by the Mohr's circle representations shown in Fig. 6. For the case in which the axial stress is absent, the direction of maximum principal stress caused by the concentrated load at the end of the rail is 45 ° to the rail axis. This is consistent with the initial direction of crack growth. For the case in which an axial compressive stress is present the direction of maximum principal stress is at an angle less than 45 o to the rail axis. Furthermore, the magnitude of the maximum principal stress is lower. This might result in lower growth rates. It should be noted that for points not on the neutral axis, there will be either axial compressive or tensile stresses above and below the neutral axis, respectively, which result from bending caused by the concentrated loads at the end of the rail. These stresses will cause the crack to alter its path in an average sense but not on a daily basis. It appears also that the magnitude of the thermal stresses is sufficient to cause a significant and consequently visible change in crack growth direction. Rails are laid at a relatively high temperature: usually around 32°C (90°F). The neutral temperature is defined as the temperature at which
~7
f O
I
27
:
90 ° , ' = 45 °
W i t h o u t A x i a l Thermal Stress
55
27 < 90 ° , 7 < 45 ° With A x i a l Thermal Stress
Fig. 6. Mohr's circle representation of the stress state in the rail web near the bolt-holes.
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
56
the rail is stress free. Initially it corresponds to the laying temperature, but with time and traffic the neutral temperature can drift and when it does it usually drifts down. For purposes of calculation, suppose that the rail neutral temperature is 32°C (90°F). In very hot summer days, when the rails are exposed to direct sunlight, it is not uncommon for the rails to reach a temperature of 66°C (150°F). If it is assumed that the rail ends are in contact at the neutral temperature the compressive thermal stress associated with this increase in temperature is (207 X 103)(11.7 × 10-6)(34)
o, = E a A T =
= 82 M P a ( l l . 9 × 103 lb/in2). The direction of crack growth resulting from the application of an axial thermal stress is estimated using two methods. The first method is based on the assumption that the direction of crack growth coincides with the global direction of maximum principal stress. Using the Mohr's circle representation of Fig. 6 with a shear stress, ~"= 71.3 MPa (10.3 × 103 l b / i n 2) and an axial stress, o = 82 MPa (11.9 × 103 lb/in2), the direction of crack growth is predicted to be 30 ° to the rail axis. This corresponds to a change in crack growth direction, defined as ~, of 15 °. The direction of crack growth can also be estimated using fracture mechanics
Oi
It
i
' "3 ~ N,, Directionof CrackTip ~¢'~~ ~ MaximumPrincipalStress
4
Oi Fig. 7. The fracture mechanics model for the prediction of crack growth direction.
with the assumption that crack growth occurs in the direction of maximum stress at the crack tip. Use of the angled crack problem is then appropriate [7] as shown in Fig. 7. The angle between the direction of applied stress (the global maximum principal stress) and the crack plane is determined from the global, or Mohr's circle, analysis and is equal to ,n/4 + ~. The angle from the crack plane, 0, at which the maximum stress occurs at the crack tip is given by the equation sin 0 + (3 cos 0 - 1) cos fl = 0.
(5)
Substituting into this equation fl = ~r/4 + 30 ° = 75 °, one obtains ~b= 101 = 26.7 ° as the (initial) change in crack growth direction with the application of the axial thermal stress. Thus, it appears that the change in crack growth direction associated with the thermally-induced axial stress can be sufficient to result in observable ridges. To test this hypothesis further, an experiment was conducted in which the direction of maximum principal stress was varied in a manner similar to that which occurs in the rail.
4. Experiments Two experiments were conducted in an effort to reproduce the fracture surface of the bolt hole crack. Both were conducted with compact tension specimens removed from the web of a 65.4 k g / m (132 l b / y a r d ) standard carbon rail with the crack plane oriented along the axis of the rail. In the first test the specimen was subjected to variable amplitude fatigue loading designed to simulate a regular pattern of traffic. It was originally supposed that the ridges were caused by the passage of several loaded trains followed by the passage of several unloaded trains. However, no ridges were produced in a specimen subjected to a similar load history. The second experiment was designed to model a changing direction of maximum principal stress. The compact tension specimen geometry used for this experiment is shown in Fig. 8a. Loads are applied to the set of holes BB or CC shown in Fig. 8b, to obtain the desired change in maximum principal stress direction. The horizontal spacing between the hole centers was equal to 25 mm (1 in.) and the vertical spacing was equal to 47 mm (1.85 in.). Except for the extra two holes, Fig. 8a is
57
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack 12.7 mm Diam. Holes
B
A
C
Chevron Notch 91.4 mm
47 mm
1 C
i
I
[~
A
B Loading Types
76.2 mm
v
Thickness, B = 12.7 mm
Fig. 8. Four-hole compact tension specimen and the loading configurations used to reproduce the ridge feature.
the specimen geometry recommended in ASTM E647 [8]. The change in crack growth direction in switching from holes BB to CC can be predicted by either of the procedures described in the previous section. By assuming that the fatigue crack growth direction is perpendicular to the line of loading, one obtains 4, = 2 tan- ~(25/47) = 56 ° . Fracture mechanics can also be used to estimate the change in crack growth direction for the configuration of Fig. 8. In this case, an alternate form of equation (5) is used for determining the angle 0: sin 0 + K n / K I (3 cos 0 - 1) = 0,
(6)
where K~ and K n are the Mode I and Mode II stress intensity factors. The finite element program PAPST [9] was used to calculate K, and K u for the geometry of Fig. 8 (straight crack) with loading in Other the BB or CC directions. The result for this geometry and loading was K n / K ~ = - 0 . 1 9 6 and from equation (6), 0 = 20.7 °. The change in crack growth direction in switching from loading BB to CC, ~, is equal to 20 or 41.4 °. Both of the values for ~, 56 ° and 41.4 ° , are greater than the values predicted
earlier for the bolt hole crack under consideration. The specimen was tested in an electro/servohydraulic testing machine in load control under ambient conditions. Prior to testing, the specimen was prefatigued a totai of 10 mm under pure Mode I loading so that the final alternating stress intensity factor was 26 MPavrm (24 ksiv~-). During some portions of the test, crack length was measured with a traveling microscope which has an accuracy of 0.001 ram. A special grip had to be machined in order to accommodate the compact tension specimen when testing in the inclined BB or CC positions. The two types of loading applied to the specimen are illustrated in Fig. 9. The solid line represents the way in which one might expect the direction of maximum principal stress to vary with time for the bolt hole crack. One expects a continuous change in the rail temperature and axial stress which increases and decreases slowly during the day. The flat parts of the curve along the abscissa are supposed to correspond to the period during which the rail ends lose contact. The dashed line in Fig. 9 is the first approximation to the solid curve and corresponds to loading the four-hole compact tension specimen between sets BB and CC. The dotted line is a better approximation to
58
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end boh hole crack
I
Loading
SuspectedActual Variation
__.__~-"I
I-i
BB
I g N
i
i ..... ?
!..
!
ii
i
I!
i
I AA
!iJ
v
CC
time
Loading Type : BB, CC, BB, CC, BB I1: BB, AA, CC, AA, BB Fig. 9. Suspected loading variation for the bolt-hole crack and the loading for the four-hole compact tension specimen.
the solid curve. It corresponds to an alternating loading AA, BB, AA, CC, AA .... where the AA set used is the one closest to the front of the specimen. The specimen was switched between the different configurations manually and the load was set to provide a Mode I A K = 26 MPavt-m (24 ksi i ~ . ) for all configurations. The R ratio was maintained at 0.05 and the cyclic frequency was 10 Hz. Crack length was only measured for the first type of loading. The test procedure began with loading the specimen in configuration BB for 4400 cycles, which corresponds to 10 loaded trains or half-a-day of loading. The specimen was then removed from the testing machine, reinserted in configuration CC, cycled 4400 times, removed, reinserted in configuration BB and so on. This was done until the specimen had been loaded eight times in the BB and CC configurations. The crack was then extended about 4 mm under pure Mode I fatigue to generate a mark between the two types of loading. The second type of loading was conducted in the same way as the first except loading in each of the configurations BB, AA, CC, AA and so on was applied for only 2200 cycles. Crack length was not measured during the second type of loading.
6. Results
The results are best illustrated by the four-hole compact tension specimen fracture surface shown in Fig. 10. The ridges in the left part of the figure correspond to the first type of loading and are very sharply defined. The ridges in the fight part of the figure correspond to the loading type which more closely represents what is actually believed to occur in the rail. These ridge features bear a close resemblance to the ridge features observed on the bolt hole fracture surface shown in Fig. 2b. Fig. 11 shows micrographs of sections made through the fracture surfaces of the compact tension specimen for the two loading types and for the bolt hole crack. The sharpness of the ridge features created by the first type of loading is deafly seen in this Crack Growth
Loading:
I
II
lOmm
Fig. 10. Four-hole compact tension specimen fracture surface.
R.A. Mayoille, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
figure. The angle between the directions of crack growth for loading BB and CC obtained from this figure is 48 ° , which is between the value predicted under the assumption that the crack grows perpendicular to the loading direction, 56 ° , and the value predicted using the fracture mechanics approach, 41.4 ° . More interesting is the section for the fracture surface created by the second loading shown in the center of Fig. 11. Contours of the ridges are irregular and similar to the contours of the ridges in the bolt hole crack, shown in the bottom on Fig. 11.
59
7. Summary and conclusions
The results of this investigation provide strong evidence that the thermal stresses induced in the rail by the daily variation in temperature have an influence on the fatigue crack growth behavior of the rail-end bolt hole crack. The key to arriving at this conclusion was the observation of a multiple ridge feature observed on the fracture surface of a cracked piece of rail removed from service. The amount of traffic passing over the cracked rail during the formation of each ridge was estimated by employing an approximate analysis of the stresses in the rail web and the stress intensity , ~ a c t o r for a crack emanating from a bolt hole, • together with laboratory data for fatigue crack Crack Growth growth rates. The result of this calculation was that 35 trains passed over the cracked piece of rail Loldinv during the formation of each ridge. This is about twice as much as the known regular pattern of traffic of 20 trains per day, but considering the approximations of the stress analysis and variability in fatigue crack growth rates, the conclusion, that each ridge was formed during one day seems reasonable. Further evidence to support this conclusion was (a) I lmm I provided by an experiment with a four-hole, modified compact tension specimen. The specimen was designed and loaded to simulate the variation in maximum principal stress which the bolt hole crack is believed to have experienced. The result was a , ~ . v e r y close reproduction of the ridge feature on the ~ bolt hole fracture surface. .:. " ~ • While it has been possible to preclict changes in crack growth direction due to varying thermal stresses, an insufficient amount of data were ob(b) lmm tained to establish whether the crack growth rates I I are significantly affected by the induced axial thermal stresses. This is expected to occur since the magnitude of the global maximum principal stress is changed by the introduction of an axial stress; it is reduced when the stress is compressive (summer) Bolt-Hole and increased when the stress is tensile (winter). Crack This effect needs to be investigated because the rate of crack growth in rails has a direct bearing on the setting of inspection intervals for flaw detection. In this regard, the tension case poses a (c) i 1ram difficult problem because the axial loads are Fig. 11. Metaliographic sections through the fracture surfaces ._~.. transferred to the rail through direct bearing o+f the of the four-hole compact tension specimen (a) and (b) and of ~t bolts on the bolt surface. Further analytic and the bolt-hole crack at the ridge location (c). ~ experimental work on the subject of fatigue crack growth from bolt holes is currently underway.
60
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
Acknowledgements We would like to acknowledge the technical assistance of Oscar Orringer and James Morris of the Transportation Systems Center and the financial support of the Department of Transportation in the performance of this work.
References [1] "Stresses in railroad track--The talbot reports", Reprinted Reports of the Special Committee on Stresses in Railroad Track, 1918-1940, Prof. A.N. Talbot, Chairman, American Railway Engineering Association (1980), 1304 pages. [2] S. Timoshenko and B.F. Langer, "Stresses in railroad track", J. Applied Mechanics, Trans. ASME~ 54 (1932) 277-302.
[3] Private communication with Oscar Orringer. [4] H. Tada, P. Paris and G. Irwin, The Stress Analysis of Cracks Handbook, Del Research Corp. (1973), p. 19.2. [5] R.J. Allen and G.W. Morland, "The significance of defects in B.S.11 rails: Bolt hole failures and tacheovales", Meeting on Rail Steels, Iron and Steel Inst. (Nov. 23, 1972). [6] R.A. Mayville and P.D. Hilton, "Laboratory analysis of rails containing detail fractures", Arthur D. Little, Inc., Report 85662-01 to DOT (March 1983). [7] F. Erdogan and G.C. Sih," On the crack extension in plates under plane loading and transverse shear", J. Basic Engineering, ASME, 85, Ser. D (December 1963)519-527. [8] ASTM E647, "Standard test method for constant-load-amplitude fatigue crack growth rates above 10-8 m/cycle", in: part 10 American Society of Testing and Materials Annual Book of ASTM Standards (1981). [9] P.D. Hilton and D.D. Wilmarth, "PAPST-Revision 2.0", Report to David Taylor Naval Ship R&D Center, Bethesda, MD, Contract N00167-81-C0260, ADL Case No. 87058(August 1982).
51
FRACTURE M E C H A N I C S ANALYSIS O F A RAIL-END B O L T H O L E CRACK Ronald A. MAYVILLE Peter D. H I L T O N Arthur D. Little. Inc., Cambridge, Massachusetts 02140, USA Submitted to Oscar Orringer June 27, 1983
Analytic and experimental investigations were conducted to establish the cause of a peculiar ridge feature observed on the fracture surface of a railroad rail-end bolt hole fatigue crack. Calculations are performed which indicate that the ridges were caused by the change in stress caused by the thermal expansion of the rails during each day of fatigue. The ridge features were closely reproduced by a novel laboratory experiment on a four-hole compact tension specimen.
1. Introduction The current practice of constructing railroad track is to lay quarter-mile long strings of continuously welded rail (CWR) formed from 11.9 or 23.8 m rail sections (39 or 78 ft.). In the past, rails were always connected in the track with a bolted joint arrangement similar to the one shown in Fig. 1. There are still many bolted joints in service today and new ones are installed for insulated joints, in sharp curves, where there is a need to be able to quickly replace worn rails, and sometimes to connect strings of CWR. A mode of failure in bolted joints is fatigue crack initiation and growth from the bolt holes in the rail end. During the examination of one of these bolt hole cracks we discovered a peculiar feature on the fracture surface. Visible over a few
mrB
centimeters of crack growth were a set of ridges spaced about one millimeter apart, oriented perpendicular to the direction of crack propagation and not very well defined in appearance. The subject of this paper is our attempt to establish the cause of the ridges and the interesting conclusion that they were probably due to the daily variation in temperature at the rail site.
2. Failure description The crack was discovered at a joint in a section of CWR track in Nebraska during the month of August. The rail was 65.4 k g / m (132 l b / y a r d ) standard carbon, joined with 0.91 m (36 in.), sixhole joint bars; that is, each rail end had three bolt holes. Figure 1 shows the geometry and dimen-
mm
o oiioool 910ram Fig. 1. Geometry of the bolted joint. 016%8442/84/$3.00 © 1984, Elsevier Science Publishers B.V. (North-Holland)
i
Field ~ Side
Gage Side
R.A. Mavville, P.D. Hilton / Fracture mechanics analysis of a rail-end boh hole crack
52
sions of the bolted joint. The joint was on a railroad tie, but it is not certain if the joint was centered on the tie. The crack initiated at the first bolt hole of the rail receiving the loaded traffic and grew toward the rail head in a direction away from the rail end. Fig. 2a shows the geometry of the crack and Fig. 2b shows a macro photo of the fracture surface. The angle at which Fig. 2b is oriented is indicated in Fig. 2a. Details of the fracture surface are obscured by corrosion and rubbing between opposite surfaces, but a number of features are visible from Fig. 2. The crack initiated on the field side of the web as a corner crack inclined at approximately 45 ° to the rail axis. Although not shown here, the bolt hole surface was severely gouged from rubbing between the bolt and the bolt hole surface, thus offering many sites for crack initiation. The crack grew as a comer crack until it reached the gage side of the web at which time it began propagating as a through crack. At about the same time the crack changed its orientation to the rail axis to about 25 ° as shown in Fig. 2a. Before its discovery the crack propagated a total of 66 mm (2.6 in.) toward the rail head, and a small crack was formed at the diametrically opposite location of the bolt hole. The crystalline fracture surface shown in the
top of Fig. 2b resulted from breaking open the bolt hole crack after immersing the piece in liquid nitrogen. The ridge feature mentioned in the introduction is visible on the fracture surface about 13 mm (0.5 in.) from the edge of the bolt hole, particularly on the right-hand side, the gage side. The ridges are perpendicular to the direction of crack growth, extend at least 13 mm (0.5 in.) along the fracture surface, and are spaced by about 1 mm (0.04 in.). They are not well defined in appearance and it was necessary to control the direction of lighting to make them observable. The crack was undoubtedly caused by the fatigue loading resulting from the passage of trains. The section of track in which this crack was discovered was subjected to a large amount of unit trains carrying coal. Data supplied to us by the Dept. of Transportation (DOT) showed that an average of 20 loaded trains pulling 100-ton hopper cars passed each day. Furthermore, the consist or make-up of each train was quite regular: there were almost always 100 to 110 hopper cars and three to six engines in each train. The static vertical wheel load was about 147 kN (33 x 103 lb.) for both the engines and the loaded hopper cars.
Figure2b
f
J
----
Head ~ M ~
mm BoltHole
25°
Ridges
Web
Base Bolt-Hole $urfaoe
(al
Fig. 2. Bolt-hole crack description.
(bl
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
3. Analysis
1.0
53
I
I
I
0.9
Fracture mechanics is employed to investigate the fatigue crack growth behavior of the bolt hole crack. The calculation of loads and stress intensity factors are very approximate because the mechanics of the bolted joint are not well understood. Detailed studies to establish these quantities more precisely are currently underway.
0.8
~.
0.7
•-= o
0.6 0.5 0,
i~- 03 0.2
Loads and stresses
0.1 m
o
The loads on a rail can be estimated by using beam-on-elastic foundation analysis in which the rail is the beam and the ties and ballast--the gravel underneath the ties--are the elastic foundation. This type of analysis has been found to be reasonably accurate [1,2]. Following an approach of Talbot [1], it is assumed that the joint has no effect on the overall behavior of the rail; that is, the rail-joint system behaves as a continuous beam. Fig. 3 shows the distribution of the bending moment along the rail for one wheel. The ordinate of this curve is the ratio of the bending moment for a given location to the maximum bending moment, which occurs directly under the wheel and is given by:
Mo =
Ez/64= ]
(1)
where a = dynamic amplification factor W = wheel load E = Young's modulus for the rail I = moment of inertia for the rail cross section u = foundation modulus. The abscissa of Fig. 3 is given in units x / x l , where x~ is the distance from the location of the wheel to the point at which the bending moment is" zero for a single wheel. It is given by x1
=
(,n/4)[4EI/u] ' / ' .
For 65.4 k g / m (132 lb/yard) standard carbon rail: E = 207 x 103 N//mm 2 (30 × 106 l b / i n 2) and I = 3.7 × 107 mm 4 (88.2 in.4). The wheel load is 147 kN (33 x 1031b) and we assume that a = 2 and u = 10.3 N / m m 2 (1500 lb fine), which are representative of the type of rail system under consideration [1,3]. The result is M 0 = 9.6 x 104N-m(8.52 × 105 in-lb),
-0.1
-
-0.2 0 1 2 3 Distance along Rail from Load Point.
4
X/X, Fig. 3. Relative bending moment, M / M o, as a function of distance from load point, x / x l , for a single wheel.
and x~ = 1.03 m(40.5 in.). The maximum bending moment for two or more adjacent wheels is determined by superposing Fig. 3 for each of the wheels with a knowledge of the wheel separation in terms of xl. Fig. 4 is a schematic representation of a typical rail car connection. Superposition for this configuration shows that the bending moment is nearly the same under each of the wheels but is slightly greater under either of the wheels designated 1. The bending moment at wheel 1 is closely approximated by only considering the effect of the closest wheel. The distance between wheels I and 2 is 1.68 m (66
I
i
1.68 m--IP ~ 3 . ( ~
m
Fig. 4. Typical rail car connection.
~
1.68
R..4. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
54
in.) or 1.63 x 1. Therefore, the moment at wheel 1 caused by wheel 2 is, from Fig. 3, - 0 . 1 8 M 0, which gives a total moment at wheel 1 of M = 0.82 M 0 = 7.87 × 104 N-m(6.98 × l0 s in-lb). We assume that the rail joint is subjected to this moment for the passage of each wheel. The rail ends can carry no bending moment so the bending moment at the joint must be carried entirely by the joint bars. The way in which loads are transferred from the joint bars to the rail ends depends very much on the condition of the joint elements. However, Talbot [1] observed that in many cases the loads on the joint bars are distributed over only small segments located near the center and the ends of the joint bars. Therefore, the joint bars behave as though they are subjected to four-point bending. This situation is depicted in Fig. 5. For simplicity, the loads are assumed to be concentrated and located exactly at the center and ends of the joint bar. With this assumption it is a simple matter to compute the value of the concentrated loads, for they must balance the applied bending moment. The magnitude of the concentrated loads, including both joint bars in the calculation, is
V = M / ( I / 2 ) = 172 kN(38.7 X 103 lb), where I is the length of the joint bars, 0.91 m(36in). The magnitude of V is about half of the dynamic wheel load, 293 kN (66 × 103 lb). The concentrated load at the end of each rail is a shear force which causes high shear stresses in the rail web at the bolt holes. This is essentially a shear force applied to the end of the rail. It is assumed that the sum of the shear forces caused b y the wheel load and the forces at the foundation - - t h e tie--is zero. The shear stress in the rail web caused by the concentrated load can be estimated using a mechanics of materials approach so that
= VQ/It,
(2)
hee~
where Q = is the first moment of the area of the cross section above or below the center of the bolt hole; t = web thickness at the bolt hole. For 65.4 k g / m (132 l b / y a r d ) rail, Q -- 2.6 × 105 mm2(16 in 3) and t = 17.1 mm(0.675 in.) which gives ~"= 71.3 MPa (10.3 × 103 Ib/in2). The shear stress calculated from equation (2) is a reasonable approximation to the shear stress in much of the rail web because Q does not very greatly as a consequence of a web section thin in comparison to the head and base.
Stress intensity factor To estimate the magnitude of K ! resulting from the wheel load, the formula for a single crack emanating radially from a circular hole in an infinite plate in shear is used [4], following a suggestion made by A.A. Wells in a private communication to Allen and Morland [5]. Thus,
K, = F ( a / d ) z f ~ ,
(3)
where a is the crack length from the hole surface to the crack tip and d is the hole diameter. The nominal bolt hole diameter is equal to 28.6 mm (1.125 in.). For a crack length of 13 mm (0.5 in.), which corresponds to the approximate length at which the ridges occurred, F ( a / d ) = 1.6 and using the shear stress calculated in the previous section, Kl.,a x = 23 MPav/-m (21 ksi i ~ . ) . The bending moment distribution given in Fig. 3 shows that there is some reversed bending in the rail, which results in a negative R-ratio at the location of the crack. There is also a reversal in shear caused by the passage of the wheel over the bolt hole. The effects of this reversed (compressive) stress on crack growth are neglected in this approximate analysis. Therefore, Klmi. is taken equal to zero so that AK1 -- 23 MPa¢~- (21 ksiqq-ff) for each of the wheels. Fatigue crack growth occurs readily in rail steels for alternating stress intensity factors of this magnitude. In fact, using fatigue crack growth data obtained for a standard carbon rail specimen removed from the web [6], the growth rates can be estimated by the relation
!
0
0
[]
[]
d a / d N = 2.03 × lO-t°(AKt) 4°4 mm/cycle.
o
Thus, for A K t = 2 3
I
'
1
Fi 8. 5. The mode of load transfer assumed for the joint bar.
(4)
MPact-m (21 ksi iv/i-n..), m m / c y c l e (2.5 × 10 -6 in/cycle). Assuming that the average distance be-
d a / d N = 6.4 × 10 -5
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
tween ridges on the fracture surface is 1 mm (0.04 in.), the number of cycles between each ridge is predicted to be, N = 1/6.4 × 10 -5 = 15,600 cycles. The number of cycles per rail corresponding to a typical train which passed over the crack-containing rail is estimated by counting the number of wheels for the train. Each train had approximately 105 hopper cars with four wheels per car per rail. Adding to this the 24 wheels per rail associated with the three engines gives 440 wheels, or load cycles, per rail per train. Therefore, the number of trains passing during the formation of each ridge is predicted to be, 15,600/440 = 35 trains. The average traffic for this section of track was 20 loaded trains per day, about half of that predicted. If one considers that the 35 train estimate can easily be off by a factor of two because of variability in fatigue crack growth rates and the approximations in our stress analysis, then it is possible to conclude that the occurrence of each ridge was a daily event. Thermal stresses
The conclusion that the formation of a ridge was a daily event was important supporting evidence for the hypothesis that the ridges were a result of the daily variation in thermai stress and the accompanying change in crack growth direc-
tion resulting from the addition of an axial stress. The thermal stress for the bolt hole crack under consideration in this investigation would have to be compressive, because the ridges apparently occurred during the summer. The difference in stress states for the absence and presence of a compressive axial stress are illustrated by the Mohr's circle representations shown in Fig. 6. For the case in which the axial stress is absent, the direction of maximum principal stress caused by the concentrated load at the end of the rail is 45 ° to the rail axis. This is consistent with the initial direction of crack growth. For the case in which an axial compressive stress is present the direction of maximum principal stress is at an angle less than 45 o to the rail axis. Furthermore, the magnitude of the maximum principal stress is lower. This might result in lower growth rates. It should be noted that for points not on the neutral axis, there will be either axial compressive or tensile stresses above and below the neutral axis, respectively, which result from bending caused by the concentrated loads at the end of the rail. These stresses will cause the crack to alter its path in an average sense but not on a daily basis. It appears also that the magnitude of the thermal stresses is sufficient to cause a significant and consequently visible change in crack growth direction. Rails are laid at a relatively high temperature: usually around 32°C (90°F). The neutral temperature is defined as the temperature at which
~7
f O
I
27
:
90 ° , ' = 45 °
W i t h o u t A x i a l Thermal Stress
55
27 < 90 ° , 7 < 45 ° With A x i a l Thermal Stress
Fig. 6. Mohr's circle representation of the stress state in the rail web near the bolt-holes.
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
56
the rail is stress free. Initially it corresponds to the laying temperature, but with time and traffic the neutral temperature can drift and when it does it usually drifts down. For purposes of calculation, suppose that the rail neutral temperature is 32°C (90°F). In very hot summer days, when the rails are exposed to direct sunlight, it is not uncommon for the rails to reach a temperature of 66°C (150°F). If it is assumed that the rail ends are in contact at the neutral temperature the compressive thermal stress associated with this increase in temperature is (207 X 103)(11.7 × 10-6)(34)
o, = E a A T =
= 82 M P a ( l l . 9 × 103 lb/in2). The direction of crack growth resulting from the application of an axial thermal stress is estimated using two methods. The first method is based on the assumption that the direction of crack growth coincides with the global direction of maximum principal stress. Using the Mohr's circle representation of Fig. 6 with a shear stress, ~"= 71.3 MPa (10.3 × 103 l b / i n 2) and an axial stress, o = 82 MPa (11.9 × 103 lb/in2), the direction of crack growth is predicted to be 30 ° to the rail axis. This corresponds to a change in crack growth direction, defined as ~, of 15 °. The direction of crack growth can also be estimated using fracture mechanics
Oi
It
i
' "3 ~ N,, Directionof CrackTip ~¢'~~ ~ MaximumPrincipalStress
4
Oi Fig. 7. The fracture mechanics model for the prediction of crack growth direction.
with the assumption that crack growth occurs in the direction of maximum stress at the crack tip. Use of the angled crack problem is then appropriate [7] as shown in Fig. 7. The angle between the direction of applied stress (the global maximum principal stress) and the crack plane is determined from the global, or Mohr's circle, analysis and is equal to ,n/4 + ~. The angle from the crack plane, 0, at which the maximum stress occurs at the crack tip is given by the equation sin 0 + (3 cos 0 - 1) cos fl = 0.
(5)
Substituting into this equation fl = ~r/4 + 30 ° = 75 °, one obtains ~b= 101 = 26.7 ° as the (initial) change in crack growth direction with the application of the axial thermal stress. Thus, it appears that the change in crack growth direction associated with the thermally-induced axial stress can be sufficient to result in observable ridges. To test this hypothesis further, an experiment was conducted in which the direction of maximum principal stress was varied in a manner similar to that which occurs in the rail.
4. Experiments Two experiments were conducted in an effort to reproduce the fracture surface of the bolt hole crack. Both were conducted with compact tension specimens removed from the web of a 65.4 k g / m (132 l b / y a r d ) standard carbon rail with the crack plane oriented along the axis of the rail. In the first test the specimen was subjected to variable amplitude fatigue loading designed to simulate a regular pattern of traffic. It was originally supposed that the ridges were caused by the passage of several loaded trains followed by the passage of several unloaded trains. However, no ridges were produced in a specimen subjected to a similar load history. The second experiment was designed to model a changing direction of maximum principal stress. The compact tension specimen geometry used for this experiment is shown in Fig. 8a. Loads are applied to the set of holes BB or CC shown in Fig. 8b, to obtain the desired change in maximum principal stress direction. The horizontal spacing between the hole centers was equal to 25 mm (1 in.) and the vertical spacing was equal to 47 mm (1.85 in.). Except for the extra two holes, Fig. 8a is
57
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack 12.7 mm Diam. Holes
B
A
C
Chevron Notch 91.4 mm
47 mm
1 C
i
I
[~
A
B Loading Types
76.2 mm
v
Thickness, B = 12.7 mm
Fig. 8. Four-hole compact tension specimen and the loading configurations used to reproduce the ridge feature.
the specimen geometry recommended in ASTM E647 [8]. The change in crack growth direction in switching from holes BB to CC can be predicted by either of the procedures described in the previous section. By assuming that the fatigue crack growth direction is perpendicular to the line of loading, one obtains 4, = 2 tan- ~(25/47) = 56 ° . Fracture mechanics can also be used to estimate the change in crack growth direction for the configuration of Fig. 8. In this case, an alternate form of equation (5) is used for determining the angle 0: sin 0 + K n / K I (3 cos 0 - 1) = 0,
(6)
where K~ and K n are the Mode I and Mode II stress intensity factors. The finite element program PAPST [9] was used to calculate K, and K u for the geometry of Fig. 8 (straight crack) with loading in Other the BB or CC directions. The result for this geometry and loading was K n / K ~ = - 0 . 1 9 6 and from equation (6), 0 = 20.7 °. The change in crack growth direction in switching from loading BB to CC, ~, is equal to 20 or 41.4 °. Both of the values for ~, 56 ° and 41.4 ° , are greater than the values predicted
earlier for the bolt hole crack under consideration. The specimen was tested in an electro/servohydraulic testing machine in load control under ambient conditions. Prior to testing, the specimen was prefatigued a totai of 10 mm under pure Mode I loading so that the final alternating stress intensity factor was 26 MPavrm (24 ksiv~-). During some portions of the test, crack length was measured with a traveling microscope which has an accuracy of 0.001 ram. A special grip had to be machined in order to accommodate the compact tension specimen when testing in the inclined BB or CC positions. The two types of loading applied to the specimen are illustrated in Fig. 9. The solid line represents the way in which one might expect the direction of maximum principal stress to vary with time for the bolt hole crack. One expects a continuous change in the rail temperature and axial stress which increases and decreases slowly during the day. The flat parts of the curve along the abscissa are supposed to correspond to the period during which the rail ends lose contact. The dashed line in Fig. 9 is the first approximation to the solid curve and corresponds to loading the four-hole compact tension specimen between sets BB and CC. The dotted line is a better approximation to
58
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end boh hole crack
I
Loading
SuspectedActual Variation
__.__~-"I
I-i
BB
I g N
i
i ..... ?
!..
!
ii
i
I!
i
I AA
!iJ
v
CC
time
Loading Type : BB, CC, BB, CC, BB I1: BB, AA, CC, AA, BB Fig. 9. Suspected loading variation for the bolt-hole crack and the loading for the four-hole compact tension specimen.
the solid curve. It corresponds to an alternating loading AA, BB, AA, CC, AA .... where the AA set used is the one closest to the front of the specimen. The specimen was switched between the different configurations manually and the load was set to provide a Mode I A K = 26 MPavt-m (24 ksi i ~ . ) for all configurations. The R ratio was maintained at 0.05 and the cyclic frequency was 10 Hz. Crack length was only measured for the first type of loading. The test procedure began with loading the specimen in configuration BB for 4400 cycles, which corresponds to 10 loaded trains or half-a-day of loading. The specimen was then removed from the testing machine, reinserted in configuration CC, cycled 4400 times, removed, reinserted in configuration BB and so on. This was done until the specimen had been loaded eight times in the BB and CC configurations. The crack was then extended about 4 mm under pure Mode I fatigue to generate a mark between the two types of loading. The second type of loading was conducted in the same way as the first except loading in each of the configurations BB, AA, CC, AA and so on was applied for only 2200 cycles. Crack length was not measured during the second type of loading.
6. Results
The results are best illustrated by the four-hole compact tension specimen fracture surface shown in Fig. 10. The ridges in the left part of the figure correspond to the first type of loading and are very sharply defined. The ridges in the fight part of the figure correspond to the loading type which more closely represents what is actually believed to occur in the rail. These ridge features bear a close resemblance to the ridge features observed on the bolt hole fracture surface shown in Fig. 2b. Fig. 11 shows micrographs of sections made through the fracture surfaces of the compact tension specimen for the two loading types and for the bolt hole crack. The sharpness of the ridge features created by the first type of loading is deafly seen in this Crack Growth
Loading:
I
II
lOmm
Fig. 10. Four-hole compact tension specimen fracture surface.
R.A. Mayoille, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
figure. The angle between the directions of crack growth for loading BB and CC obtained from this figure is 48 ° , which is between the value predicted under the assumption that the crack grows perpendicular to the loading direction, 56 ° , and the value predicted using the fracture mechanics approach, 41.4 ° . More interesting is the section for the fracture surface created by the second loading shown in the center of Fig. 11. Contours of the ridges are irregular and similar to the contours of the ridges in the bolt hole crack, shown in the bottom on Fig. 11.
59
7. Summary and conclusions
The results of this investigation provide strong evidence that the thermal stresses induced in the rail by the daily variation in temperature have an influence on the fatigue crack growth behavior of the rail-end bolt hole crack. The key to arriving at this conclusion was the observation of a multiple ridge feature observed on the fracture surface of a cracked piece of rail removed from service. The amount of traffic passing over the cracked rail during the formation of each ridge was estimated by employing an approximate analysis of the stresses in the rail web and the stress intensity , ~ a c t o r for a crack emanating from a bolt hole, • together with laboratory data for fatigue crack Crack Growth growth rates. The result of this calculation was that 35 trains passed over the cracked piece of rail Loldinv during the formation of each ridge. This is about twice as much as the known regular pattern of traffic of 20 trains per day, but considering the approximations of the stress analysis and variability in fatigue crack growth rates, the conclusion, that each ridge was formed during one day seems reasonable. Further evidence to support this conclusion was (a) I lmm I provided by an experiment with a four-hole, modified compact tension specimen. The specimen was designed and loaded to simulate the variation in maximum principal stress which the bolt hole crack is believed to have experienced. The result was a , ~ . v e r y close reproduction of the ridge feature on the ~ bolt hole fracture surface. .:. " ~ • While it has been possible to preclict changes in crack growth direction due to varying thermal stresses, an insufficient amount of data were ob(b) lmm tained to establish whether the crack growth rates I I are significantly affected by the induced axial thermal stresses. This is expected to occur since the magnitude of the global maximum principal stress is changed by the introduction of an axial stress; it is reduced when the stress is compressive (summer) Bolt-Hole and increased when the stress is tensile (winter). Crack This effect needs to be investigated because the rate of crack growth in rails has a direct bearing on the setting of inspection intervals for flaw detection. In this regard, the tension case poses a (c) i 1ram difficult problem because the axial loads are Fig. 11. Metaliographic sections through the fracture surfaces ._~.. transferred to the rail through direct bearing o+f the of the four-hole compact tension specimen (a) and (b) and of ~t bolts on the bolt surface. Further analytic and the bolt-hole crack at the ridge location (c). ~ experimental work on the subject of fatigue crack growth from bolt holes is currently underway.
60
R.A. Mayville, P.D. Hilton / Fracture mechanics analysis of a rail-end bolt hole crack
Acknowledgements We would like to acknowledge the technical assistance of Oscar Orringer and James Morris of the Transportation Systems Center and the financial support of the Department of Transportation in the performance of this work.
References [1] "Stresses in railroad track--The talbot reports", Reprinted Reports of the Special Committee on Stresses in Railroad Track, 1918-1940, Prof. A.N. Talbot, Chairman, American Railway Engineering Association (1980), 1304 pages. [2] S. Timoshenko and B.F. Langer, "Stresses in railroad track", J. Applied Mechanics, Trans. ASME~ 54 (1932) 277-302.
[3] Private communication with Oscar Orringer. [4] H. Tada, P. Paris and G. Irwin, The Stress Analysis of Cracks Handbook, Del Research Corp. (1973), p. 19.2. [5] R.J. Allen and G.W. Morland, "The significance of defects in B.S.11 rails: Bolt hole failures and tacheovales", Meeting on Rail Steels, Iron and Steel Inst. (Nov. 23, 1972). [6] R.A. Mayville and P.D. Hilton, "Laboratory analysis of rails containing detail fractures", Arthur D. Little, Inc., Report 85662-01 to DOT (March 1983). [7] F. Erdogan and G.C. Sih," On the crack extension in plates under plane loading and transverse shear", J. Basic Engineering, ASME, 85, Ser. D (December 1963)519-527. [8] ASTM E647, "Standard test method for constant-load-amplitude fatigue crack growth rates above 10-8 m/cycle", in: part 10 American Society of Testing and Materials Annual Book of ASTM Standards (1981). [9] P.D. Hilton and D.D. Wilmarth, "PAPST-Revision 2.0", Report to David Taylor Naval Ship R&D Center, Bethesda, MD, Contract N00167-81-C0260, ADL Case No. 87058(August 1982).