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Structural integrity assessment in the transportation sector
Theoretical and Applied Fracture Mechanics 6 (1986) 63-74 North-Holland
63
S T R U C T U R A L I N T E G R I T Y A S S E S S M E N T IN T H E T R A N S P O R T A T I O N S E C T O R O. O R R I N G E R u.s. DOT Transportation Systems Center, Cambridge, M,4 02142, U.S.A.
Pressures for increased transportation efficiencyoften lead to structural weight reduction campaigns; some designers reduce weight by selecting high strength materials and increasing allowable stresses. However, material strength improvements are not generally accompanied by better fracture toughness or better resistance to fatigue crack growth. Pressures for increased transportation economy sometimes cause operators to extend vehicle life rather than to incur major capital costs for new equipment. However, aging structures may experience widespread cracking, a situation that has not been fully considered even for some structures that were designed in accordance with a damage tolerance philosophy. Design for high performance or extension of service life thus have the potential to put the integrity of the affected structure at risk. One deals'with such situations either by reducing fracture mechanics principles to practice or by assessing a service failure after the fact. Both reactions require methods of engineering calculation that are well defined, easy to apply, and reasonably conservative. These criteria often conflict with the standards of accuracy demanded for basic research in the mechanics of fracture. A sacrifice of such standards can be worthwhile, however, provided that the engineering method captures the service environment's principal effects on crack growth and that the method is ultimately based on good research results. How the results of fracture research are reduced to practice depends on material properties, attachment details, the mission of the structure, and its service environment. Three examples are presented to illustrate how the foregoing factors affect the reduction of research to practice. The damage tolerance concept originally developed for airframes is first discussed. The concept can be generalized, but its application implicity relies on the methods used to design, manufacture, and inspect airframes. The other examples cover structures which differ from airframes in one or more basic respects.
1. Introduction T h e ability of a sharp crack to limit the strength of a brittle material was first recognized in the 1920's a n d 1930's [1,2] a n d was formalized in terms of the elastic stress intensity factor a n d extended to metals with low ductility in the 1940's [3,4]. By the early 1950's the ductility transition p h e n o m e n o n in steel alloys was empirically u n d e r stood, C h a r p y tests were being .routinely performed to d e t e r m i n e the n o t c h sensitivities of metals, a n d basic investigations of ductile fracture m e c h a n i s m s had b e e n started. By the mid-1960's linear elastic fracture mechanics was an established basic discipline, the compact tension specim e n and other precracked specimen tests were s u p p l e m e n t i n g the C h a r p y test, a n d research engineers were b e g i n n i n g to use the stress intensity factor to correlate fatigue crack growth rate data. Structures engineers first b e g a n to address the p r o b l e m of tolerance to fatigue crack growth in the 1970's. The 40 year evolution from fracture science to fracture engineering is similar to the progress from solid mechanics to engineering stress
analysis in the 19th a n d early 20th centuries [5]; the slow pace reflects an i m p o r t a n t difference between research a n d engineering practice. I n basic research, the investigator uses experim e n t s a n d m a t h e m a t i c a l models to isolate specific elements of a problem. This isolation makes it possible to correlate experiments with models, while meeting high standards of accuracy in m a t h e m a t i c a l formulation, experiment control, a n d m e a s u r e m e n t error analysis. The end result is a precise description of a p h e n o m e n o n that can be reproduced b y m e a n s of an i n d e p e n d e n t experiment, i.e., a scientific result. Engineers m a y find the description useful as an idealization. Conversely, the engineer begins with a piece of hardware a n d must consider all factors that might affect its performance. Typically some b u t n o t all factors have scientific descriptions. The process of c o m p a r i n g basic research results with hardware p e r f o r m a n c e experience gradually evolves a n engineering practice, viz: a well defined a n d reasonably conservative calculation procedure that can be followed b y a n engineer who is n o t necessarily well versed in the u n d e r l y i n g science. Simplicity is
0167-8442/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
O. Orringer / Structural integrity assessment in the transportation sector
64
also a desirable but not essential attribute of an engineering practice. Fatigue crack nucleation provides a simple example of the difference between basic research and engineering practice. Railroad axle fatigue was recognized and was the subject of experiments over a century ago [6]. Subsequent experiments led to the S-N curve,
(1)
SPAN = C,
as a description of the number of cycles, N, required to nucleate a crack at constant stress amplitude, SA, and zero mean stress, where P and C must be fitted to describe the experimental results for a specific material. The results can be reproduced to within a factor of two to ten, depending on the precision of the experiment protocol. Engineers use these basic research results to predict the fatigue lives of structures for which the service environment generally includes many different combinations of stress amplitude and mean stress. The starting point for such predictions is the Palmgren-Miner rule [7,8], which states that the crack nucleation life is determined by the damage sum /7 i
L
~,~ = 1,
(2)
i=l where L is the life in (say) hours, n i is the number of service cycles per hour of the i th stress amplitude, and N, is the number of cycles to nucleate a crack under the ith stress alone. Implicit in this rule are the ideas that damage can be measured by counting stress cycles, that the ith stress causes damage linearly proportional to the number of cycles applied (n~), and that the damage fraction
n,/N~ has the same physical meaning for all stress amplitudes. The Palmgren-Miner rule has no scientific basis, but engineers have used it for over thirty years in numerous applications. Equation (2) certainly provides a simple and well defined calculation procedure. Conservatism, the other essential of engineering practice, has been achieved by means of various empirical modifications. Examples of such modifications are designed to L ) 2 ( n / N ) = 0.25 (an airframe design practice in the 1950's) and the modified Goodman diagram (Fig. 1) to account for the effects of mean tensile stress. Many such fatigue design practices have been developed for automotive and rail vehicles, rotating machinery, aircraft, and spacecraft [9]; they owe their success to feedback from full-scale fatigue tests and service experience. A similar situation prevails with respect to fracture engineering and mechanics of fracture. Since a mechanics model of crack propagation is easier to defend than a crack nucleation model, however, scientific description has tended to mask the role of reduction to practice in fracture.
2. Airframe damage tolerance The need to assess a structure's ability to tolerate established fatigue cracks was brought to light by a 1969 in-flight airframe failure and loss of an F-111 at Nellis AFB, Nevada. Investigation revealed that a fracture of the lower (tension) skin in the wing carry-through box had caused the failure when the airplane had accumulated only 105 flight hours, although the airframe fatigue life was estimated to be about 8000 flight hours. The dark semi-oval area on the fracture surface (Fig. 2) is an oxidized forging crack that existed when
SAI ~,,./,.u.~u,u-~,,eConstant-life lines SA2 N I~ ' ~ N I
Ni =Zer°-mean life at SAi Su=UItimate tensile strength
SU Fig. 1. Modified G o o d m a n diagram.
Mean stress, SM
O. Orringer / Structural integrity assessment in the transportation sector
during the next flight. These terms cannot be precisely defined. Research involving blind experiments With cracked components inserted in shop inspection lines has been performed to characterize NDI methods [14], and counting accelerometers have been used to gather data on airplane dynamic load factors [15]. However, the research results are only probability descriptions (Fig. 3). To reduce such results to practice requires judgements based on experience, generally leading to selection of a specific initial crack size and a specific maximum load factor for a given situation. The efficacy of the practice depends strongly on the choice of initial size because crack growth life is sensitive to this parameter. Crack growth life is much less sensitive to the choice of critical crack size, which is generally based on an extreme load (e.g. the expected once per flight load). Critical crack sizes are based on plane strain fracture toughness for thick sections, thickness-dependent empirical values of fracture toughness for thin sections, or net section plastic rupture calculations for thin sections of highly ductile materials. The calculation of crack growth life is based on the stress intensity factor of linear elastic fracture mechanics (LEFM)
Fig. 2. F-111 lower skin fracture surface.
the airplane entered service. The lighter narrow band surrounding the oval is the fatigue crack growth region; it is apparent that the initial crack drastically shortened the fatigue life of this component. Although an undetected initial crack this large is an extremely rare event, the consequences show that long crack nucleation life does not guarantee tolerance to crack propagation damage. In the light of the F-111 accident, the US Air Force conducted thorough structural integrity assessments of its existing aircraft fleets [10] and issued damage tolerance specifications for new airframes [11]. The Federal Aviation Administration later issued similar regulations for transport category commercial airplanes [12] and developed special inspection programs for the older jet fleets [13]. For the first time the standards [11,12] included requirements to establish safe intervals for nondestructive inspection (NDI) based on service time for a crack to grow from initial to critical size. 'Initial size' refers to a crack that one N D I might fail to detect. 'Critical size' refers to a crack that would be expected to fracture imminently, as determined by the maximum load encountered Crack detection p r o b a b i l i t y , PD I
K
=
SG(a)v~
A K = Kmax - Kmin=( Smax - Smin)G( a)y/a
= ASG(a)v'~. nz = o z / g
\
a z = Vertical acceleration
\
of centerof moss g = Acceleration of g r a v i t y
0.5
O Crack surface length, 2c
Fig. 3. Probabilistic descriptions of NDI and dynamic load.
(3)
for a crack length, a, subjected to a remote stress magnitude, S, where G(a) incorporates the effects of crack shape, free surfaces, and the shape of the remote stress distribution. The crack length increment per fatigue cycle, da/dn, is correlated with the stress intensity factor range:
Exceedonces per f l i g h t hour
. . . . . . . . . . . . . . . . . . . . . . . . . .
65
Airplane load factor, n z
(4)
66
O. Orringer / Structural integrity assessment in the transportation sector
Foctor
Crock growth rote, /.~/. ( do/dn )
._~ ,~
~
~ . '
I
] 1 ~ I~Experiment; [i[[ii R= 0.50
,. ~ ,',,,%.X~'" :,..,~:,, ~-
rl
~
~
I
KC
KTH
R = 0.05
--
Equotion(5)
.....
Equotion (6) Stress intensity ronge, ~ ( ~ K )
Fig.4.Characterizationofcrackgrowthrate. A correlation with ( A K ) 4 w a s first proposed on theoretical grounds by Paris [16]. Crack growth rates at constant AK or constant AS have since been obtained from basic research experiments which have also shown effects of mean stress. The results for many alloys are available [17] in the form shown in Fig. 4 and can be described by empirical rate equations of the form
da
C(AK) P
dn
(1 - R ) 0 ,
(5)
da
dn
[(1-R)K
c-AK]
Q '
(6)
(1 - R)KTH < A K < (1 - R ) K c, where the stress ratio R = S m i n / S m a x incorporates the mean stress effect, and where C, P, Q, K T H , and K c are empirical parameters. The growth rates generally lie within a factor of two for nominally identical conditions and are consistent for test specimens with different L E F M stress intensity factors. The simplest practices for estimating service crack growth life assume that the crack length increment per cycle is affected only by the stresses in the same cycle, i.e., d a / d n is summed for groups of n, cycles (AS~, Ri) per flight hour until the number of flight hours is such that the crack has grown from initial size a I to critical size a 2. The assumption in r e m i n i s c e n t of the Palmgren-Miner rule for crack nucleation life. In
the case of crack growth, it turns out that the integrated form of eq. (5) is exactly equivalent to the Palmgren-Miner rule if N~ in eq. (1) is interpreted as crack growth life for the single cycle combination (ASi, Ri); strictly speaking, eq. (6) should be summed to obtain the proper stress sequence effects, but the Palmgren-Miner rule is found to give reasonable approximations for typical service histories in which the different stress combinations are well mixed [18]. The accumulated effects of plastic zone stress must be accounted for in some cases. The increased crack-tip plastic zone size created by an overstress cycle can decrease the rate of crack propagation in succeeding nominal stress cycles [19]. Linear summations for crack growth life under variable-amplitude ('spectrum') loading based on constant-amplitude crack growth rates do not reflect this retardation effect. Elber's crack closure model [20] accounts for retardation but requires either cycle-by-cycle calculations or linear summation coupled with an update of the crack-opening stress intensity factor Kop at intervals of tens to hundreds of cycles. In practice, specimen crack growth tests are performed to assess the amount of retardation associated with a given material and type of load spectrum. In many cases Kop attains a steady state value within a few spectrum blocks and linear summation can be applied by replacing g m i n with Kop in eq. (4). Elber's model is then useful for calculating Kop for similar spectra by analyzing a few blocks. The major U.S. airframe manufacturers have
O. Orringer / Structural integrity assessment in the transportation sector
Airplane weight and balance Performance
weight I ~ ~_~ Airframe MateriaI selection
Aerodynamics Flight controls Engine characteristics
Detail stress checks
Flight ?
Nominal
loads
stresses
67
H Crockgrowth life Inspectability
Damage tolerance
Fig. 5. Organization of airframe design.
reduced the foregoing damage tolerance concepts to procedures compatible with their existing practices for detail design. The simplified schematic in Fig. 5 illustrates the interaction between the structures department and the other design departments. Computer models and data bases for the entire airplane constitute the medium through which the different design departments communicate; among the models are airframe finiteelement models from which nominal stresses are obtained. Engineers who perform detail stress checks use these nominal stresses in conjunction with company handbooks to design part thicknesses and evaluate stresses at attachments. These calculations are recorded on stress-check forms to facilitate supervisory review and uniform engineering work standards. The detail design engineers also evaluate damage tolerance by means of a similar system of handbooks and check forms. A structures technology group within the department keeps track of advances in basic research and integrates them into the company's detail stress check procedures. For example, some technology groups devise crack growth calculation programs tailored to the company's experience with load spectra and materials; the detail design engineers can then be trained to use these programs in conjunction with the damage tolerance check form. This type of procedure is well suited to the iterative process of aircraft design.
3. Rail integrity The U.S. Department of Transportation has begun to apply damage tolerance concepts to the problem of inspecting the rails in the nation's
track. U.S. railroads carry primarily freight over a privately owned network that includes about 180000 miles of mainline track. Existing regulations require annual NDI of about 70000 to 100000 miles of this track, and most railroads exceed the requirement. Rail NDI has been performed by means of continuous search for over fifty years, starting with magnetic induction equipment mounted on rail-bound vehicles in the 1930's. Ultrasonic flaw detection systems were introduced and the inspection fleet was augmented with railable road vehicles in the 1960's [21]. The railroads presently schedule rail NDI based on empirical experience. The goal of the current DOT program is to apply knowledge of crack behavior to improve the N D I schedules [22]. The use of continuous search for rail NDI reflects an important difference between the rail and airframe inspection problems, viz: the volume of material that must be inspected. The total structural weight of a typical medium jet transport fleet of 500 planes is of the order of 104-105 tons, and only a fraction of this material requires NDI because airframe fatigue cracks tend to develop at the Stress raisers created by attachment details. Conversely, the weight of rail in the inspected part of the U.S. track net is of the order of 107-108 tons, and rail fatigue cracks can occur anywhere in the rail length. Continuous search methods optimized for detection of specific defect categories and tolerant of variations in rail section and condition thus constitute the only practical approach to rail NDI. Studies of rail defect reports have been shown that three types of fatigue crack account for 70%-95% of the cracks in U.S. rail and that the remaining flaws are divided between mill defects
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O. Orringer / Structural integrity assessment in the transportation sector
Detail fracture (DF)
Locations of VSH and DF with respect to the rail cross section
I
Vertical split head (V
Field side
~ ~ - ~
/
Gage side /
/
J
t /
/
/
1 /
t¢"
~ f l
/
/~
/ / ~
f
~"
1 t /
I
/ 1
/ /
/
/
/
/
/ /
/
/
/
t
t
t
/
" B o l t hole crock
Rail-end bolt hole (bolted joint track)
Fig. 6. Major types of rail fatigue cracks.
and other types of fatigue cracks [23]. The focus of the DOT rail integrity program is on the behavior of the three major fatigue crack types, which are illustrated in Fig. 6. Detail fracture behavior has been investigated by means of laboratory experiments, simulated service tests of rails placed in a test track at the U.S. Transportation Test Center (TTC), and limited observations on revenue tracks [24]. Laboratory tests have been performed on simulated bolt hole cracks [25], some field investigations have been made, and naturally developed samples are currently being observed at the TTC. Only preliminary metallurgical investigations have been completed on vertical split heads. A detail fracture or a vertical split head can occur anywhere in the rail length. These crack types each account for about 25% of the rail defect population but the proportion of detail fractures is expected to increase as more of the U.S. track network is upgraded from bolted joint to continuous welded rail. Test and analysis have shown that detail fracture growth cannot be explained without reference to the residual stress field which develops in the rail head as the result
of repeated wheel-rail contact loads [24], and residual stresses may also influence the growth of vertical split heads. Bolt hole cracks currently comprise about 50% of the defect population. Bolt hole cracks grow in a region where the residual stresses are known to be small, but they are constantly subject to the dynamic effects of wheels pounding on rail-end gaps. The laboratory experiments have suggested that the stress-raising effect of the bolt hole makes the stress intensity factor nearly independent of bolt hole crack length in the detectable to critical crack length range [25]. Thus, it appears that first-passage statistics of rail-end train load spectra, rather than the conventional slow crack growth approach, might be the proper basis for estimating safe inspection intervals for bolt hole cracks. The detail fracture is the best understood of the three major flaw types, and its behavior is consistent with the slow crack growth concept of damage tolerance. Sufficient information is now available for construction of representative stress spectra in terms of trains and gross tonnage [24], the rail analogs of flights and flight hours for airframes. When the axial residual and thermal
O. Orringer / Structural integrity assessment in the transportation sector
stresses in a rail are properly accounted for, it appears possible to obtain reasonable estimates of detail fracture life by means of linear summation. Recent laboratory experiments on rail steels subjected to a typical train load spectrum in real sequence order have revealed the existence of moderate underload acceleration (the opposite of overload retardation), i.e., linear summation predicts a somewhat longer crack growth life than the life obtained in the experiment [26]. A similar trend appears when linear summation calculations are compared with the test track experiments. The acceleration changed to retardation, however, when the laboratory test was performed with a decreasing m a x i m u m load (DMS) spectrum. DMS or other artificially ordered spectra are often used for convenience in both calculations and laboratory specimen tests. The results of the detail fracture experiments suggest that some tests should always be performed in real sequence order when retardation or acceleration is expected. The application of fracture mechanics to protection of rail against failures from detail fractures is similar to the transport category airframe damage tolerance application in that the fundamental inspection interval can be estimated from average conditions (expectations of load spectra, average crack growth rates, etc.). Both systems also implicitly rely on independent and continuous means of protection. Transport wing and fuselage structures are highly redundant and continue to function even if a large crack causes a loss of fuel or cabin pressure. Such losses give an immediate warning of an unsafe situation, allowing the flight crew to reduce maneuvering loads and land the airplane before the structure fails. The automatic signal circuits on mainline track run small electrical currents through the rails; a service break from a detail fracture interrupts the current and sets the signal to red. One train can generally traverse the break without incident, should the break occur under the train on tangent track, and following traffic will be held by the signal until the break is found and repaired. There are also important differences. A fleet of aircraft consists of nominally identical articles that tend to accumulate flights and flight hours at generally similar rates. The airframe manufacturer is therefore able to target the fleet inspection program to specific locations by compiling crack occurrence statistics from the airframe fatigue test
69
and from service defect reports. Conversely, the inventory of rail in U.S. mainline track has a wide range of accumulated gross tonnage, and crack occurrences depend not only on the rail age but also on the track curvature, grade, foundation modulus, weather conditions, and other operational or construction factors. The railroads do gather crack reports, but the occurrence patterns are highly specific to individual lines [23]. These statistics can be used to target supplemental actions (special inspections, operational changes, or trackwork) but have no bearing on the continuous search N D I program. This difference is also reflected in the treatment of extreme cases. For example, military airplanes fly a variety of different missions with different degrees of severity; it is generally possible to divide the fleet into two or three severity categories based on individual aircraft tracking, and inspection intervals can be established for each category. Conversely, the service extremes for rail are associated with the inventory and environment variations and are better dealt with by means of supplemental actions. When the variety of inventory and lack of redundancy in the rail per se are viewed in the light of the inherent imperfection of N D I , it becomes logical to consider the calculated safe inspection interval as a baseline and to inspect more often if the exposure of trains to rail defects increases. Comparison of defect occurrence statistics with derailment statistics has shown that a trend toward more derailments is associated with increased exposure (in terms of defects per track mile per inspection), although no quantitative relation was found [23]. A recent study has also shown that the expected life cycle cost of inspection, repair, and derailment decreases if the inspection interval is adjusted to reflect the exposure rate [27]. However, the translation of expected life cycle cost calculations into guidelines for inspection interval adjustment on revenue track must ultimately rely on practical judgement. Perhaps the most important technical difference is that the damage tolerance concept cannot be applied to rail without considering longterm consequences in the light of the entire railroad operating system. The U.S. railroads have historically increased productivity, among other means, by increasing freight car axle loads. Freight traffic presently consists of a mixture of vehicles with 70 or 100 ton cargo capacities, and unit trains com-
70
O. Orringer / Structural integrity assessment in the transportation sector
prised of 100-ton cars operate regularly on many lines. Consideration is currently being given to increasing the maximum allowed capacity from 100 to 110 or 125 tons. If adopted, such a change would result in the imposition of static freight car wheel loads up to 40 kips (versus the present allowance of 33 kips) on the existing rail network. Increased residual stress is expected and will affect both exposure and the crack growth life. The effect on inspection interval must be estimated before revenue track experience is available. Current research on this question is aimed at the development of a stress analysis method for predicting shakedown residual stresses (or the absence of a shakedown state) in the rail head [28]. In contrast to airframe damage tolerance design practice, the principal focus for rail integrity practice is the operating framework (Fig. 7). Although the NDI is periodic, the inspection frequency varies from annual (the regulatory requirement) to six or seven times per year. Railroads set inspection frequencies empirically, using annual gross tonnage, knowledge of their track, and defect report statistics as guides. The use of defect reports is an implicit recognition of the importance of the rate of exposure of trains to potential service breaks in the rails. 4. Girth welds in pipelines Large-diameter gas and oil pipelines are assembled in the field by means of automated girth welding machines that join pipe sections. The
Rail section and specifications
designs
Rail
maker I
J
Railroad
!-]_1
--I E h
Defect rote
I
Fig. 7. System for rail integrity assurance.
I
multipass welding process can sometimes generate crack-like surface defects from bead root undercuts or internal defects from partially missed passes (Fig. 8). Such defects become fatigue cracks within a few load cycles, if left in the pipeline. Pipeline welding practice in the U.S. is currently governed by workmanship standards, and radiography is also used to check each girth weld for defects. Rejection criteria based on radiographs have traditionally been set in accordance with porosity standards because porosity is the most prevalent type of pipeline welding defect. A pipeline wall can tolerate an area of porosity much larger than an area of early cracking without danger of nucleating a crack during service life. Construction of the Trans-Alaskan Pipeline System (TAPS) in the 1970's brought fracture mechanics into conflict with these practices when the radiography revealed a large number of defects that would have been considered acceptable as porosity. The DOT required the TAPS defects to be assessed as cracks because of the potential environmental consequences of a large oil spill on the arctic permafrost. The initial assessment, based on linear elastic fracture mechanics, would have rejected almost all the defects and required a major rebuild. Linear elastic fracture mechanics is unnecessarily conservative, however, when applied to extremely ductile materials such as line pipe steels. The TAPS case was eventually resolved by additional assessments and judgement, but the controversy generated by the wide range of critical
Calendar
u'; hr'r
I.o,,.oo0o
1 independent
Damage tolerance requirements
NDT technology
O. Orringer / Structural integrity assessment in the transportation sector
Z ~
71
"~ Girthweld
• ono.od,oo,
;
Fig. 8. Pipeline girth weld defects. crack size estimates stimulated government and industry research on the problem of ductile fracture mechanics. The government program investigated the stability mechanics of ductile girth cracks [29], while an industry committee independently worked to develop an alternate girth weld acceptance criterion based on ductile fracture [30]. Similar criteria were concurrently developed in the United Kingdom and Canada [31,32]. The general approach is to make a conservative allowance for the crack length increment expected during one service life and to increase the initial crack size accordingly; the defect is then accepted or rejected on the basis of a residual strength estimate. The so-called COD design curve is the basis for the residual strength estimate. The COD design curve is the empirical relation:
8 = 2,~ya*
• t (~/,,)2,
,/e, ~ 0.5,
(c/or-
c/cy > 0.5,
0.25,
for the allowable crack opening displacement 8 of a wide center-cracked panel with half crack length a* and yield strain ~y when subjected to uniform tensile strain c in Mode I loading. Equation (7) incorporates a safety factor of two on 8 with respect to the COD for unstable crack propagation in the elastic range, C/Cy ~< 0.5, and experience suggests that the safety factor is also close to two for strains up to the plastic collapse limit [33]. To apply the COD design curve to pipeline girth weld defect tolerance assessment requires two steps. First, the weld ductility must be characterized in terms of COD. Notched three-point bend bar specimens taken from sample welds (Fig. 9) are used for this purpose, and ~ is calculated in accordance with a British Standards Institution specification [34]. This procedure determines the allowable COD for the weld material. Second, the applied COD must be estimated for the girth weld defect and the maximum service
(7)
Pipe section
O \\
j
Fig. 9. COD specimen and test.
- Zest specimeo
I
----
I
O. Orringer / Structural integrity assessment in the transportation sector
72
Additional tests are planned and are expected to lead to acceptable engineering specifications for assessment of girth weld defect tolerance in pipelines. Such specifications focus on fabrication quality control, as shown in Fig. 11.
/./"
Fig. 10. Significantgeometricalparameters for girth weld crack.
5. Concluding remarks
loading. This requires a fracture mechanics calculation to account for the actual crack geometry, which differs from that of the center-cracked panel (Fig. 10). The common approach is to derive curves that relate the actual crack geometry to an equivalent panel center crack a* by equating the COD values based on linear elastic fracture mechanics. In U.S. practice, the allowable defect dimensions are plotted as functions of material COD and applied strain [30]. The COD measurement and design curve constitute a scientific result as far as concerns the specimen behavior per se. However, the translation of strain into applied COD or the converse derivation of allowable defect dimensions for pipeline girth weld defects is an engineering result subjected to variations that were noted in a recent study [35]. The major variations involve the treatment of the welding residual strain contribution to applied strain, the method of limiting defect length E to avoid cracks that might suffer unstable propagation at loads less than the plastic collapse limit of the pipe, and the effects of plastic constraint conditions on allowable COD as a function of pipe radius R and crack aspect ratio a/f. Corrections for some of these effects have been developed from comparisons of failure strain with calculated allowable strain for full-scale pipe section tests, but the test data available thus far are for materials less ductile (lower allowable COD) than the minimum COD specified in some of the proposed criteria [35].
Three examples have been presented to show how the mechanics of fracture can be reduced to practice. Fracture mechanics provides the foundation for fracture control practice but is only the starting point. Material, design, and operation are generally the main determinants of practice. The airframe industry, recognizing the limits of fabrication quality in complex fastened and highly stressed structures, reacted by grafting damage tolerance assessment methods onto existing systems for management of the airplane detail design process and by adding fracture toughness to the list of properties considered for material selection. Airframe design stress levels are generally low enough so that linear elastic fracture mechanics can be used. Airframe manufacturers have accordingly applied the stress intensity factor approach by combining the basic theory with component tests to develop empirical handbook data on stress intensity factors for generic attachment details in airframes. These handbooks supplement earlier handbooks that deal with plain stress and fatigue analysis. Fleet experience will continue to be fed back to improve design system. For example, the problem of designing for tolerance to adjacent panel cracking (a characteristic of aging airframes) will likely be addressed in the near future [13]. The railroad industry, recognizing the tendency of rail defects to break rails and derail trains, reacted by developing and fielding equipment to search for all types of defects. Inspection schedules were empirically developed in reaction to
I Pipeline ~ . ~ Radiographic construction inspection
i
l Sample ~.~ girth welds
Allowable COD
Fig. 11. System for girth weld quality control.
~ ..~Actual defect size ~_ ~ " Allowable defect size
~. Accept or reject each defective girth weld
O. Orringer / Structural integrity assessment in the transportation sector
defect occurrence and derailment rates. Only recently has attention been paid to the fact that fatigue cracks comprise most of the rail defect population and the idea that the inspection schedules might be further improved by adjustment based on fatigue crack growth rates. It appears that linear elastic fracture mechanics can be applied to rail fatigue cracks, but the correlation of theory with experiment remains to be completed. Empirical adjustment of periodic rail inspection will undoubtedly continue, but fracture mechanics will likely play an increasing role if axle loads increase in the future. Fracture mechanics is also beginning to be applied to develop guidelines for the manufacture of modern high-strength rail [36,37]. The pipeline industry, recognizing an economic need to avoid excessive rejection of field welds found to contain crack-like defects, reacted by seeking a defect acceptance criterion based on the mechanics of ductile fracture to take full advantage of line pipe steel resistance to crack propagation. The goal of codifying the research results in the form of allowable defect size curves reflects the need for quality control guidelines that can be applied on site in real time to avoid costly construction delays. Once this goal has been attained for current line pipe steels, additional research along the same lines will likely be required to derive similar criteria for new steels that have a higher ratio of yield to tensile strength. The foregoing examples involve situations in which reactions to immediate problems have progressed to or are approaching the point at which fracture mechanics is reduced to engineering practice. The government role in these cases has included specification development, review and approval of specifications proposed by the industry, and conduct or support of both basic and applied research. The government also has the unique role of maintaining a capability to quickly apply fracture mechanics technology to assessments of unexpected structural integrity problems that pose threats to transportation safety [10,13,36,38,39]. One must hope that such ad hoc reactions will eventually lead to other engineering practices for better control of fracture in design, quality assurance, and operations.
73
References [1] A.A. Griffith, "The phenomena of rupture and flow in solids", Philos. Trans. Royal Soc. London A221, 163-198 (1920). [2] E. Orowan, "The mechanical strength properties and the real structure of crystals", Zeitschrift der Kristallographie 89, 327-343 (1934). [3] I.N. Sneddon, "The distribution of stress in the neighbourhood of a crack in an elastic solid", Proc. Royal Soc. London, A187, 229-260 (1946). [4] E. Orowan, "Fracture and strength of solids", Rep. Prog. Phys. 12, 185-232 (1948). [5] S.P. Timoshenko, History of the Strength of Materials, McGraw-Hill, New York (1953). [6] A. Wt~hler, Zeitschrift ]fir Bauwesen: 8, 641-652 (1858); 10, 583-616 (1860); 16, 67-84 (1866); 20, 73-106 (1870). [7] A. Palmgren, "Die Lebensdauer von Kugellagern", Z.V.D.I. 68, 339-341 (1924). [8] M.A. Miner, "Cumulative damage in fatigue", J. Appl. Mech. 12, A159-A164 (1945). [9] C.C. Osgood, Fatigue Design, McGraw-Hill, New York (1969). [10] J.F. McCarthy Jr., C.F. Tiffany and O. Orringer, "Application of fracture mechanics to decisions on structural modifications of existing aircraft fleets", in: T.P. Rich and D.J. Cartwright, eds. Case Studies in Fracture Mechanics, U.S. Army Materials and Mechanics Research Center, Watertown, MA, AMMRC MS 77-5, June 1977. [11] Military Specification, "Airplane damage tolerance requirements", MIL-A-83444 (USAF) (1972). [12] Code of Federal Regulations, Title 14, Aeronautics and Space, Part 25.571, "Damage tolerance and fatigue evaluation of structure" (1978). [13] T. Swift, "Damage tolerance assessment of commercial airframes", in: P. Tong and O. Orringer, eds. Fracture Problems in the Transportation Industry, American Society of Civil Engineers, New York, NY, 97-138 (1985). [14] W.H. Lewis et al., "Reliability of nondestructive inspections", Lockheed Georgia Company, Marietta, GA, final report to USAF San Antonio Air Logistics Center, Kelly AFB, TX, SA-ALC/MME 76-6-38-1 (1978). [15] J.E. Holpp and M.A. Landy, "The development of fatigue/crack growth analysis loading spectra", NATO Advisory Group for Aerospace Research and Development, Report No. 640 (1976). [16] P.C. Paris, "The fracture mechanics approach to fatigue", in: J.J. Burke, N.L. Reed, and V. Weiss, eds., Fatigue: An Interdisciplinary Approach, Syracuse University Press, 107-132 (1964). [17] J.E. Campbell et al., "Damage tolerant design handbook", Battelle Columbus Laboratories, Columbus, OH, MCICHB-01 (1975). [18] O. Orringer, "Rapid estimation of spectrum crack-growth life based on the Palmgren-Miner rule", Computers and Structures 19, 149-153, (1984). [19] J. Schijve, "Observations on the prediction of fatigue crack growth propagation under variable-amplitude loading", in: Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, 3-23 (1976).
74
O. Orringer / Structural integrity assessment in the transportation sector
[20] W. Elber, "Equivalent constant-amplitude concept for crack growth under spectrum loading", in: Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, 236-250 (1976). [21] O. Orringer and H.L. Ceccon, "Detection of rail defects and prevention of rail fracture", in: T.R. Shives and W.A. Willard, eds. Failure Prevention in Ground Transportation Systems, Special Publication 621, National Bureau of Standards, Gaithersburg, MD, 69-90 (1982). [22] O. Orringer, J.M. Morris and R.K. Steele, "Applied research on rail fatigue and fracture in the United States", Theoret. Appl. Fracture Mech. 1, 23-49 (1984). [23] O. Orringer and M.W. Bush, "Applying modern fracture mechanics to improve the control of rail fatigue defects in track", Amer. Railway Engng. Assoc. Bull. 689 84, 19-53 (1983). [24] O. Orringer, J.M. Morris and D.Y. Jeong, "Detail fracture growth in rails: test results", Theoret. Appl. Fracture Mech. 5, 63-95 (1986). [25] R.A. Mayville and P.D. Hilton, "Fracture mechanics analysis of a rail-end bolt hole crack", Theoret. AppZ Fracture Mech. 1, 51-60 (1984). [26] B.G. Journet, "Fatigue crack propagation under complex loading," PhD thesis, Department of Materials Science and Engineering, MIT, Cambridge, MA (1986). [27] D.D: Davis, M.J. Joerms, O. Orringer and R.K. Steele, "The economic consequences of rail integrity", Proc. Third Internat. Heavy Haul Railway Conf., Vancouver, BC, Canada (1986), to appear. [28] J. Orkisz, A.B. Perlman, A. Harris, P. Tong and O. Orringer, "Recent progress in the development of a rail residual stress calculation method", Proc. Second Internat. Symposium on Contact Mechanics and Wear of Rail/Wheel Systems, University of Rhode Island, Kingston, RI (1986), to appear. [29] F. Erdogan, "Theoretical and experimental study of fracture in pipelines containing circumferential flaws", Lehigh University, Bethlehem, PA, DOT-RSPA-DMA-50/83/3 (1982). [30] Anon., API 1104, 16th ed., Appendix A, "Alternative
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
standards of acceptability for girth welds", American Petroleum Institute, Washington, DC (1983). Anon., BS 4515, Appendix H, "A proposed appendix for BS 4515 containing defect tolerance criteria for girth welds based on fracture mechanics approach", British Standards Institution, London, UK (1982). Anon., CSA Z184, Appendix K (draft), "Proposed changes to CSA A184 to accommodate alternative standards of acceptibility", Canadian Standards Association, Toronto, Canada (1984). M.G. Dawes and M.S. Karnath, "The crack opening displacement (COD) design curve approach to crack tolerance", Proc. Conf. on the Significance of Flaws in Pressurized Components, Institution of Mechanical Engineers, London, UK (1978). Anon., BS 5762, "Methods for crack opening displacement testing", Britisch Standards Institution, London, UK (1979). P.D. Hilton and R.A. Mayville, "Girth weld defect tolerance criteria", in: P. Tong and O. Orringer, eds. Fracture Problems in the Transportation Industry, American Society of Civil Engineers, New York, NY, 80-96 (1985). R.R. John et al., "Task force report: rail failure evaluation", DOT Transportation Systems Center, Cambridge, MA (1984). M. Gence et al., "Possibilities of Improving the Service Characteristics of Rails by Metallurgical Means, Report No. 1, Factors Influencing the Fracture Resistance of Rails in the Unused Condition," D 156 Committee, Office for Research and Experiments of the International Union of Railways, Utrecht, the Netherlands (1984). O. Orringer, "Failure mechanics: damage evaluation of structural components", in: G.C. Sih and L. Faria, eds. Fracture Mechanics Methodology: Evaluation of Structural Components Integrity, Martinus Nijhoff, the Hague, The Netherlands (1984). P. Tong et al., "Task force report: D O T - 1 0 5 / l l l / 112/114 tank cars shell cracking and structural integrity assessment", DOT Transportation Systems Center, Cambridge, MA (1986).
63
S T R U C T U R A L I N T E G R I T Y A S S E S S M E N T IN T H E T R A N S P O R T A T I O N S E C T O R O. O R R I N G E R u.s. DOT Transportation Systems Center, Cambridge, M,4 02142, U.S.A.
Pressures for increased transportation efficiencyoften lead to structural weight reduction campaigns; some designers reduce weight by selecting high strength materials and increasing allowable stresses. However, material strength improvements are not generally accompanied by better fracture toughness or better resistance to fatigue crack growth. Pressures for increased transportation economy sometimes cause operators to extend vehicle life rather than to incur major capital costs for new equipment. However, aging structures may experience widespread cracking, a situation that has not been fully considered even for some structures that were designed in accordance with a damage tolerance philosophy. Design for high performance or extension of service life thus have the potential to put the integrity of the affected structure at risk. One deals'with such situations either by reducing fracture mechanics principles to practice or by assessing a service failure after the fact. Both reactions require methods of engineering calculation that are well defined, easy to apply, and reasonably conservative. These criteria often conflict with the standards of accuracy demanded for basic research in the mechanics of fracture. A sacrifice of such standards can be worthwhile, however, provided that the engineering method captures the service environment's principal effects on crack growth and that the method is ultimately based on good research results. How the results of fracture research are reduced to practice depends on material properties, attachment details, the mission of the structure, and its service environment. Three examples are presented to illustrate how the foregoing factors affect the reduction of research to practice. The damage tolerance concept originally developed for airframes is first discussed. The concept can be generalized, but its application implicity relies on the methods used to design, manufacture, and inspect airframes. The other examples cover structures which differ from airframes in one or more basic respects.
1. Introduction T h e ability of a sharp crack to limit the strength of a brittle material was first recognized in the 1920's a n d 1930's [1,2] a n d was formalized in terms of the elastic stress intensity factor a n d extended to metals with low ductility in the 1940's [3,4]. By the early 1950's the ductility transition p h e n o m e n o n in steel alloys was empirically u n d e r stood, C h a r p y tests were being .routinely performed to d e t e r m i n e the n o t c h sensitivities of metals, a n d basic investigations of ductile fracture m e c h a n i s m s had b e e n started. By the mid-1960's linear elastic fracture mechanics was an established basic discipline, the compact tension specim e n and other precracked specimen tests were s u p p l e m e n t i n g the C h a r p y test, a n d research engineers were b e g i n n i n g to use the stress intensity factor to correlate fatigue crack growth rate data. Structures engineers first b e g a n to address the p r o b l e m of tolerance to fatigue crack growth in the 1970's. The 40 year evolution from fracture science to fracture engineering is similar to the progress from solid mechanics to engineering stress
analysis in the 19th a n d early 20th centuries [5]; the slow pace reflects an i m p o r t a n t difference between research a n d engineering practice. I n basic research, the investigator uses experim e n t s a n d m a t h e m a t i c a l models to isolate specific elements of a problem. This isolation makes it possible to correlate experiments with models, while meeting high standards of accuracy in m a t h e m a t i c a l formulation, experiment control, a n d m e a s u r e m e n t error analysis. The end result is a precise description of a p h e n o m e n o n that can be reproduced b y m e a n s of an i n d e p e n d e n t experiment, i.e., a scientific result. Engineers m a y find the description useful as an idealization. Conversely, the engineer begins with a piece of hardware a n d must consider all factors that might affect its performance. Typically some b u t n o t all factors have scientific descriptions. The process of c o m p a r i n g basic research results with hardware p e r f o r m a n c e experience gradually evolves a n engineering practice, viz: a well defined a n d reasonably conservative calculation procedure that can be followed b y a n engineer who is n o t necessarily well versed in the u n d e r l y i n g science. Simplicity is
0167-8442/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
O. Orringer / Structural integrity assessment in the transportation sector
64
also a desirable but not essential attribute of an engineering practice. Fatigue crack nucleation provides a simple example of the difference between basic research and engineering practice. Railroad axle fatigue was recognized and was the subject of experiments over a century ago [6]. Subsequent experiments led to the S-N curve,
(1)
SPAN = C,
as a description of the number of cycles, N, required to nucleate a crack at constant stress amplitude, SA, and zero mean stress, where P and C must be fitted to describe the experimental results for a specific material. The results can be reproduced to within a factor of two to ten, depending on the precision of the experiment protocol. Engineers use these basic research results to predict the fatigue lives of structures for which the service environment generally includes many different combinations of stress amplitude and mean stress. The starting point for such predictions is the Palmgren-Miner rule [7,8], which states that the crack nucleation life is determined by the damage sum /7 i
L
~,~ = 1,
(2)
i=l where L is the life in (say) hours, n i is the number of service cycles per hour of the i th stress amplitude, and N, is the number of cycles to nucleate a crack under the ith stress alone. Implicit in this rule are the ideas that damage can be measured by counting stress cycles, that the ith stress causes damage linearly proportional to the number of cycles applied (n~), and that the damage fraction
n,/N~ has the same physical meaning for all stress amplitudes. The Palmgren-Miner rule has no scientific basis, but engineers have used it for over thirty years in numerous applications. Equation (2) certainly provides a simple and well defined calculation procedure. Conservatism, the other essential of engineering practice, has been achieved by means of various empirical modifications. Examples of such modifications are designed to L ) 2 ( n / N ) = 0.25 (an airframe design practice in the 1950's) and the modified Goodman diagram (Fig. 1) to account for the effects of mean tensile stress. Many such fatigue design practices have been developed for automotive and rail vehicles, rotating machinery, aircraft, and spacecraft [9]; they owe their success to feedback from full-scale fatigue tests and service experience. A similar situation prevails with respect to fracture engineering and mechanics of fracture. Since a mechanics model of crack propagation is easier to defend than a crack nucleation model, however, scientific description has tended to mask the role of reduction to practice in fracture.
2. Airframe damage tolerance The need to assess a structure's ability to tolerate established fatigue cracks was brought to light by a 1969 in-flight airframe failure and loss of an F-111 at Nellis AFB, Nevada. Investigation revealed that a fracture of the lower (tension) skin in the wing carry-through box had caused the failure when the airplane had accumulated only 105 flight hours, although the airframe fatigue life was estimated to be about 8000 flight hours. The dark semi-oval area on the fracture surface (Fig. 2) is an oxidized forging crack that existed when
SAI ~,,./,.u.~u,u-~,,eConstant-life lines SA2 N I~ ' ~ N I
Ni =Zer°-mean life at SAi Su=UItimate tensile strength
SU Fig. 1. Modified G o o d m a n diagram.
Mean stress, SM
O. Orringer / Structural integrity assessment in the transportation sector
during the next flight. These terms cannot be precisely defined. Research involving blind experiments With cracked components inserted in shop inspection lines has been performed to characterize NDI methods [14], and counting accelerometers have been used to gather data on airplane dynamic load factors [15]. However, the research results are only probability descriptions (Fig. 3). To reduce such results to practice requires judgements based on experience, generally leading to selection of a specific initial crack size and a specific maximum load factor for a given situation. The efficacy of the practice depends strongly on the choice of initial size because crack growth life is sensitive to this parameter. Crack growth life is much less sensitive to the choice of critical crack size, which is generally based on an extreme load (e.g. the expected once per flight load). Critical crack sizes are based on plane strain fracture toughness for thick sections, thickness-dependent empirical values of fracture toughness for thin sections, or net section plastic rupture calculations for thin sections of highly ductile materials. The calculation of crack growth life is based on the stress intensity factor of linear elastic fracture mechanics (LEFM)
Fig. 2. F-111 lower skin fracture surface.
the airplane entered service. The lighter narrow band surrounding the oval is the fatigue crack growth region; it is apparent that the initial crack drastically shortened the fatigue life of this component. Although an undetected initial crack this large is an extremely rare event, the consequences show that long crack nucleation life does not guarantee tolerance to crack propagation damage. In the light of the F-111 accident, the US Air Force conducted thorough structural integrity assessments of its existing aircraft fleets [10] and issued damage tolerance specifications for new airframes [11]. The Federal Aviation Administration later issued similar regulations for transport category commercial airplanes [12] and developed special inspection programs for the older jet fleets [13]. For the first time the standards [11,12] included requirements to establish safe intervals for nondestructive inspection (NDI) based on service time for a crack to grow from initial to critical size. 'Initial size' refers to a crack that one N D I might fail to detect. 'Critical size' refers to a crack that would be expected to fracture imminently, as determined by the maximum load encountered Crack detection p r o b a b i l i t y , PD I
K
=
SG(a)v~
A K = Kmax - Kmin=( Smax - Smin)G( a)y/a
= ASG(a)v'~. nz = o z / g
\
a z = Vertical acceleration
\
of centerof moss g = Acceleration of g r a v i t y
0.5
O Crack surface length, 2c
Fig. 3. Probabilistic descriptions of NDI and dynamic load.
(3)
for a crack length, a, subjected to a remote stress magnitude, S, where G(a) incorporates the effects of crack shape, free surfaces, and the shape of the remote stress distribution. The crack length increment per fatigue cycle, da/dn, is correlated with the stress intensity factor range:
Exceedonces per f l i g h t hour
. . . . . . . . . . . . . . . . . . . . . . . . . .
65
Airplane load factor, n z
(4)
66
O. Orringer / Structural integrity assessment in the transportation sector
Foctor
Crock growth rote, /.~/. ( do/dn )
._~ ,~
~
~ . '
I
] 1 ~ I~Experiment; [i[[ii R= 0.50
,. ~ ,',,,%.X~'" :,..,~:,, ~-
rl
~
~
I
KC
KTH
R = 0.05
--
Equotion(5)
.....
Equotion (6) Stress intensity ronge, ~ ( ~ K )
Fig.4.Characterizationofcrackgrowthrate. A correlation with ( A K ) 4 w a s first proposed on theoretical grounds by Paris [16]. Crack growth rates at constant AK or constant AS have since been obtained from basic research experiments which have also shown effects of mean stress. The results for many alloys are available [17] in the form shown in Fig. 4 and can be described by empirical rate equations of the form
da
C(AK) P
dn
(1 - R ) 0 ,
(5)
da
dn
[(1-R)K
c-AK]
Q '
(6)
(1 - R)KTH < A K < (1 - R ) K c, where the stress ratio R = S m i n / S m a x incorporates the mean stress effect, and where C, P, Q, K T H , and K c are empirical parameters. The growth rates generally lie within a factor of two for nominally identical conditions and are consistent for test specimens with different L E F M stress intensity factors. The simplest practices for estimating service crack growth life assume that the crack length increment per cycle is affected only by the stresses in the same cycle, i.e., d a / d n is summed for groups of n, cycles (AS~, Ri) per flight hour until the number of flight hours is such that the crack has grown from initial size a I to critical size a 2. The assumption in r e m i n i s c e n t of the Palmgren-Miner rule for crack nucleation life. In
the case of crack growth, it turns out that the integrated form of eq. (5) is exactly equivalent to the Palmgren-Miner rule if N~ in eq. (1) is interpreted as crack growth life for the single cycle combination (ASi, Ri); strictly speaking, eq. (6) should be summed to obtain the proper stress sequence effects, but the Palmgren-Miner rule is found to give reasonable approximations for typical service histories in which the different stress combinations are well mixed [18]. The accumulated effects of plastic zone stress must be accounted for in some cases. The increased crack-tip plastic zone size created by an overstress cycle can decrease the rate of crack propagation in succeeding nominal stress cycles [19]. Linear summations for crack growth life under variable-amplitude ('spectrum') loading based on constant-amplitude crack growth rates do not reflect this retardation effect. Elber's crack closure model [20] accounts for retardation but requires either cycle-by-cycle calculations or linear summation coupled with an update of the crack-opening stress intensity factor Kop at intervals of tens to hundreds of cycles. In practice, specimen crack growth tests are performed to assess the amount of retardation associated with a given material and type of load spectrum. In many cases Kop attains a steady state value within a few spectrum blocks and linear summation can be applied by replacing g m i n with Kop in eq. (4). Elber's model is then useful for calculating Kop for similar spectra by analyzing a few blocks. The major U.S. airframe manufacturers have
O. Orringer / Structural integrity assessment in the transportation sector
Airplane weight and balance Performance
weight I ~ ~_~ Airframe MateriaI selection
Aerodynamics Flight controls Engine characteristics
Detail stress checks
Flight ?
Nominal
loads
stresses
67
H Crockgrowth life Inspectability
Damage tolerance
Fig. 5. Organization of airframe design.
reduced the foregoing damage tolerance concepts to procedures compatible with their existing practices for detail design. The simplified schematic in Fig. 5 illustrates the interaction between the structures department and the other design departments. Computer models and data bases for the entire airplane constitute the medium through which the different design departments communicate; among the models are airframe finiteelement models from which nominal stresses are obtained. Engineers who perform detail stress checks use these nominal stresses in conjunction with company handbooks to design part thicknesses and evaluate stresses at attachments. These calculations are recorded on stress-check forms to facilitate supervisory review and uniform engineering work standards. The detail design engineers also evaluate damage tolerance by means of a similar system of handbooks and check forms. A structures technology group within the department keeps track of advances in basic research and integrates them into the company's detail stress check procedures. For example, some technology groups devise crack growth calculation programs tailored to the company's experience with load spectra and materials; the detail design engineers can then be trained to use these programs in conjunction with the damage tolerance check form. This type of procedure is well suited to the iterative process of aircraft design.
3. Rail integrity The U.S. Department of Transportation has begun to apply damage tolerance concepts to the problem of inspecting the rails in the nation's
track. U.S. railroads carry primarily freight over a privately owned network that includes about 180000 miles of mainline track. Existing regulations require annual NDI of about 70000 to 100000 miles of this track, and most railroads exceed the requirement. Rail NDI has been performed by means of continuous search for over fifty years, starting with magnetic induction equipment mounted on rail-bound vehicles in the 1930's. Ultrasonic flaw detection systems were introduced and the inspection fleet was augmented with railable road vehicles in the 1960's [21]. The railroads presently schedule rail NDI based on empirical experience. The goal of the current DOT program is to apply knowledge of crack behavior to improve the N D I schedules [22]. The use of continuous search for rail NDI reflects an important difference between the rail and airframe inspection problems, viz: the volume of material that must be inspected. The total structural weight of a typical medium jet transport fleet of 500 planes is of the order of 104-105 tons, and only a fraction of this material requires NDI because airframe fatigue cracks tend to develop at the Stress raisers created by attachment details. Conversely, the weight of rail in the inspected part of the U.S. track net is of the order of 107-108 tons, and rail fatigue cracks can occur anywhere in the rail length. Continuous search methods optimized for detection of specific defect categories and tolerant of variations in rail section and condition thus constitute the only practical approach to rail NDI. Studies of rail defect reports have been shown that three types of fatigue crack account for 70%-95% of the cracks in U.S. rail and that the remaining flaws are divided between mill defects
68
O. Orringer / Structural integrity assessment in the transportation sector
Detail fracture (DF)
Locations of VSH and DF with respect to the rail cross section
I
Vertical split head (V
Field side
~ ~ - ~
/
Gage side /
/
J
t /
/
/
1 /
t¢"
~ f l
/
/~
/ / ~
f
~"
1 t /
I
/ 1
/ /
/
/
/
/
/ /
/
/
/
t
t
t
/
" B o l t hole crock
Rail-end bolt hole (bolted joint track)
Fig. 6. Major types of rail fatigue cracks.
and other types of fatigue cracks [23]. The focus of the DOT rail integrity program is on the behavior of the three major fatigue crack types, which are illustrated in Fig. 6. Detail fracture behavior has been investigated by means of laboratory experiments, simulated service tests of rails placed in a test track at the U.S. Transportation Test Center (TTC), and limited observations on revenue tracks [24]. Laboratory tests have been performed on simulated bolt hole cracks [25], some field investigations have been made, and naturally developed samples are currently being observed at the TTC. Only preliminary metallurgical investigations have been completed on vertical split heads. A detail fracture or a vertical split head can occur anywhere in the rail length. These crack types each account for about 25% of the rail defect population but the proportion of detail fractures is expected to increase as more of the U.S. track network is upgraded from bolted joint to continuous welded rail. Test and analysis have shown that detail fracture growth cannot be explained without reference to the residual stress field which develops in the rail head as the result
of repeated wheel-rail contact loads [24], and residual stresses may also influence the growth of vertical split heads. Bolt hole cracks currently comprise about 50% of the defect population. Bolt hole cracks grow in a region where the residual stresses are known to be small, but they are constantly subject to the dynamic effects of wheels pounding on rail-end gaps. The laboratory experiments have suggested that the stress-raising effect of the bolt hole makes the stress intensity factor nearly independent of bolt hole crack length in the detectable to critical crack length range [25]. Thus, it appears that first-passage statistics of rail-end train load spectra, rather than the conventional slow crack growth approach, might be the proper basis for estimating safe inspection intervals for bolt hole cracks. The detail fracture is the best understood of the three major flaw types, and its behavior is consistent with the slow crack growth concept of damage tolerance. Sufficient information is now available for construction of representative stress spectra in terms of trains and gross tonnage [24], the rail analogs of flights and flight hours for airframes. When the axial residual and thermal
O. Orringer / Structural integrity assessment in the transportation sector
stresses in a rail are properly accounted for, it appears possible to obtain reasonable estimates of detail fracture life by means of linear summation. Recent laboratory experiments on rail steels subjected to a typical train load spectrum in real sequence order have revealed the existence of moderate underload acceleration (the opposite of overload retardation), i.e., linear summation predicts a somewhat longer crack growth life than the life obtained in the experiment [26]. A similar trend appears when linear summation calculations are compared with the test track experiments. The acceleration changed to retardation, however, when the laboratory test was performed with a decreasing m a x i m u m load (DMS) spectrum. DMS or other artificially ordered spectra are often used for convenience in both calculations and laboratory specimen tests. The results of the detail fracture experiments suggest that some tests should always be performed in real sequence order when retardation or acceleration is expected. The application of fracture mechanics to protection of rail against failures from detail fractures is similar to the transport category airframe damage tolerance application in that the fundamental inspection interval can be estimated from average conditions (expectations of load spectra, average crack growth rates, etc.). Both systems also implicitly rely on independent and continuous means of protection. Transport wing and fuselage structures are highly redundant and continue to function even if a large crack causes a loss of fuel or cabin pressure. Such losses give an immediate warning of an unsafe situation, allowing the flight crew to reduce maneuvering loads and land the airplane before the structure fails. The automatic signal circuits on mainline track run small electrical currents through the rails; a service break from a detail fracture interrupts the current and sets the signal to red. One train can generally traverse the break without incident, should the break occur under the train on tangent track, and following traffic will be held by the signal until the break is found and repaired. There are also important differences. A fleet of aircraft consists of nominally identical articles that tend to accumulate flights and flight hours at generally similar rates. The airframe manufacturer is therefore able to target the fleet inspection program to specific locations by compiling crack occurrence statistics from the airframe fatigue test
69
and from service defect reports. Conversely, the inventory of rail in U.S. mainline track has a wide range of accumulated gross tonnage, and crack occurrences depend not only on the rail age but also on the track curvature, grade, foundation modulus, weather conditions, and other operational or construction factors. The railroads do gather crack reports, but the occurrence patterns are highly specific to individual lines [23]. These statistics can be used to target supplemental actions (special inspections, operational changes, or trackwork) but have no bearing on the continuous search N D I program. This difference is also reflected in the treatment of extreme cases. For example, military airplanes fly a variety of different missions with different degrees of severity; it is generally possible to divide the fleet into two or three severity categories based on individual aircraft tracking, and inspection intervals can be established for each category. Conversely, the service extremes for rail are associated with the inventory and environment variations and are better dealt with by means of supplemental actions. When the variety of inventory and lack of redundancy in the rail per se are viewed in the light of the inherent imperfection of N D I , it becomes logical to consider the calculated safe inspection interval as a baseline and to inspect more often if the exposure of trains to rail defects increases. Comparison of defect occurrence statistics with derailment statistics has shown that a trend toward more derailments is associated with increased exposure (in terms of defects per track mile per inspection), although no quantitative relation was found [23]. A recent study has also shown that the expected life cycle cost of inspection, repair, and derailment decreases if the inspection interval is adjusted to reflect the exposure rate [27]. However, the translation of expected life cycle cost calculations into guidelines for inspection interval adjustment on revenue track must ultimately rely on practical judgement. Perhaps the most important technical difference is that the damage tolerance concept cannot be applied to rail without considering longterm consequences in the light of the entire railroad operating system. The U.S. railroads have historically increased productivity, among other means, by increasing freight car axle loads. Freight traffic presently consists of a mixture of vehicles with 70 or 100 ton cargo capacities, and unit trains com-
70
O. Orringer / Structural integrity assessment in the transportation sector
prised of 100-ton cars operate regularly on many lines. Consideration is currently being given to increasing the maximum allowed capacity from 100 to 110 or 125 tons. If adopted, such a change would result in the imposition of static freight car wheel loads up to 40 kips (versus the present allowance of 33 kips) on the existing rail network. Increased residual stress is expected and will affect both exposure and the crack growth life. The effect on inspection interval must be estimated before revenue track experience is available. Current research on this question is aimed at the development of a stress analysis method for predicting shakedown residual stresses (or the absence of a shakedown state) in the rail head [28]. In contrast to airframe damage tolerance design practice, the principal focus for rail integrity practice is the operating framework (Fig. 7). Although the NDI is periodic, the inspection frequency varies from annual (the regulatory requirement) to six or seven times per year. Railroads set inspection frequencies empirically, using annual gross tonnage, knowledge of their track, and defect report statistics as guides. The use of defect reports is an implicit recognition of the importance of the rate of exposure of trains to potential service breaks in the rails. 4. Girth welds in pipelines Large-diameter gas and oil pipelines are assembled in the field by means of automated girth welding machines that join pipe sections. The
Rail section and specifications
designs
Rail
maker I
J
Railroad
!-]_1
--I E h
Defect rote
I
Fig. 7. System for rail integrity assurance.
I
multipass welding process can sometimes generate crack-like surface defects from bead root undercuts or internal defects from partially missed passes (Fig. 8). Such defects become fatigue cracks within a few load cycles, if left in the pipeline. Pipeline welding practice in the U.S. is currently governed by workmanship standards, and radiography is also used to check each girth weld for defects. Rejection criteria based on radiographs have traditionally been set in accordance with porosity standards because porosity is the most prevalent type of pipeline welding defect. A pipeline wall can tolerate an area of porosity much larger than an area of early cracking without danger of nucleating a crack during service life. Construction of the Trans-Alaskan Pipeline System (TAPS) in the 1970's brought fracture mechanics into conflict with these practices when the radiography revealed a large number of defects that would have been considered acceptable as porosity. The DOT required the TAPS defects to be assessed as cracks because of the potential environmental consequences of a large oil spill on the arctic permafrost. The initial assessment, based on linear elastic fracture mechanics, would have rejected almost all the defects and required a major rebuild. Linear elastic fracture mechanics is unnecessarily conservative, however, when applied to extremely ductile materials such as line pipe steels. The TAPS case was eventually resolved by additional assessments and judgement, but the controversy generated by the wide range of critical
Calendar
u'; hr'r
I.o,,.oo0o
1 independent
Damage tolerance requirements
NDT technology
O. Orringer / Structural integrity assessment in the transportation sector
Z ~
71
"~ Girthweld
• ono.od,oo,
;
Fig. 8. Pipeline girth weld defects. crack size estimates stimulated government and industry research on the problem of ductile fracture mechanics. The government program investigated the stability mechanics of ductile girth cracks [29], while an industry committee independently worked to develop an alternate girth weld acceptance criterion based on ductile fracture [30]. Similar criteria were concurrently developed in the United Kingdom and Canada [31,32]. The general approach is to make a conservative allowance for the crack length increment expected during one service life and to increase the initial crack size accordingly; the defect is then accepted or rejected on the basis of a residual strength estimate. The so-called COD design curve is the basis for the residual strength estimate. The COD design curve is the empirical relation:
8 = 2,~ya*
• t (~/,,)2,
,/e, ~ 0.5,
(c/or-
c/cy > 0.5,
0.25,
for the allowable crack opening displacement 8 of a wide center-cracked panel with half crack length a* and yield strain ~y when subjected to uniform tensile strain c in Mode I loading. Equation (7) incorporates a safety factor of two on 8 with respect to the COD for unstable crack propagation in the elastic range, C/Cy ~< 0.5, and experience suggests that the safety factor is also close to two for strains up to the plastic collapse limit [33]. To apply the COD design curve to pipeline girth weld defect tolerance assessment requires two steps. First, the weld ductility must be characterized in terms of COD. Notched three-point bend bar specimens taken from sample welds (Fig. 9) are used for this purpose, and ~ is calculated in accordance with a British Standards Institution specification [34]. This procedure determines the allowable COD for the weld material. Second, the applied COD must be estimated for the girth weld defect and the maximum service
(7)
Pipe section
O \\
j
Fig. 9. COD specimen and test.
- Zest specimeo
I
----
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O. Orringer / Structural integrity assessment in the transportation sector
72
Additional tests are planned and are expected to lead to acceptable engineering specifications for assessment of girth weld defect tolerance in pipelines. Such specifications focus on fabrication quality control, as shown in Fig. 11.
/./"
Fig. 10. Significantgeometricalparameters for girth weld crack.
5. Concluding remarks
loading. This requires a fracture mechanics calculation to account for the actual crack geometry, which differs from that of the center-cracked panel (Fig. 10). The common approach is to derive curves that relate the actual crack geometry to an equivalent panel center crack a* by equating the COD values based on linear elastic fracture mechanics. In U.S. practice, the allowable defect dimensions are plotted as functions of material COD and applied strain [30]. The COD measurement and design curve constitute a scientific result as far as concerns the specimen behavior per se. However, the translation of strain into applied COD or the converse derivation of allowable defect dimensions for pipeline girth weld defects is an engineering result subjected to variations that were noted in a recent study [35]. The major variations involve the treatment of the welding residual strain contribution to applied strain, the method of limiting defect length E to avoid cracks that might suffer unstable propagation at loads less than the plastic collapse limit of the pipe, and the effects of plastic constraint conditions on allowable COD as a function of pipe radius R and crack aspect ratio a/f. Corrections for some of these effects have been developed from comparisons of failure strain with calculated allowable strain for full-scale pipe section tests, but the test data available thus far are for materials less ductile (lower allowable COD) than the minimum COD specified in some of the proposed criteria [35].
Three examples have been presented to show how the mechanics of fracture can be reduced to practice. Fracture mechanics provides the foundation for fracture control practice but is only the starting point. Material, design, and operation are generally the main determinants of practice. The airframe industry, recognizing the limits of fabrication quality in complex fastened and highly stressed structures, reacted by grafting damage tolerance assessment methods onto existing systems for management of the airplane detail design process and by adding fracture toughness to the list of properties considered for material selection. Airframe design stress levels are generally low enough so that linear elastic fracture mechanics can be used. Airframe manufacturers have accordingly applied the stress intensity factor approach by combining the basic theory with component tests to develop empirical handbook data on stress intensity factors for generic attachment details in airframes. These handbooks supplement earlier handbooks that deal with plain stress and fatigue analysis. Fleet experience will continue to be fed back to improve design system. For example, the problem of designing for tolerance to adjacent panel cracking (a characteristic of aging airframes) will likely be addressed in the near future [13]. The railroad industry, recognizing the tendency of rail defects to break rails and derail trains, reacted by developing and fielding equipment to search for all types of defects. Inspection schedules were empirically developed in reaction to
I Pipeline ~ . ~ Radiographic construction inspection
i
l Sample ~.~ girth welds
Allowable COD
Fig. 11. System for girth weld quality control.
~ ..~Actual defect size ~_ ~ " Allowable defect size
~. Accept or reject each defective girth weld
O. Orringer / Structural integrity assessment in the transportation sector
defect occurrence and derailment rates. Only recently has attention been paid to the fact that fatigue cracks comprise most of the rail defect population and the idea that the inspection schedules might be further improved by adjustment based on fatigue crack growth rates. It appears that linear elastic fracture mechanics can be applied to rail fatigue cracks, but the correlation of theory with experiment remains to be completed. Empirical adjustment of periodic rail inspection will undoubtedly continue, but fracture mechanics will likely play an increasing role if axle loads increase in the future. Fracture mechanics is also beginning to be applied to develop guidelines for the manufacture of modern high-strength rail [36,37]. The pipeline industry, recognizing an economic need to avoid excessive rejection of field welds found to contain crack-like defects, reacted by seeking a defect acceptance criterion based on the mechanics of ductile fracture to take full advantage of line pipe steel resistance to crack propagation. The goal of codifying the research results in the form of allowable defect size curves reflects the need for quality control guidelines that can be applied on site in real time to avoid costly construction delays. Once this goal has been attained for current line pipe steels, additional research along the same lines will likely be required to derive similar criteria for new steels that have a higher ratio of yield to tensile strength. The foregoing examples involve situations in which reactions to immediate problems have progressed to or are approaching the point at which fracture mechanics is reduced to engineering practice. The government role in these cases has included specification development, review and approval of specifications proposed by the industry, and conduct or support of both basic and applied research. The government also has the unique role of maintaining a capability to quickly apply fracture mechanics technology to assessments of unexpected structural integrity problems that pose threats to transportation safety [10,13,36,38,39]. One must hope that such ad hoc reactions will eventually lead to other engineering practices for better control of fracture in design, quality assurance, and operations.
73
References [1] A.A. Griffith, "The phenomena of rupture and flow in solids", Philos. Trans. Royal Soc. London A221, 163-198 (1920). [2] E. Orowan, "The mechanical strength properties and the real structure of crystals", Zeitschrift der Kristallographie 89, 327-343 (1934). [3] I.N. Sneddon, "The distribution of stress in the neighbourhood of a crack in an elastic solid", Proc. Royal Soc. London, A187, 229-260 (1946). [4] E. Orowan, "Fracture and strength of solids", Rep. Prog. Phys. 12, 185-232 (1948). [5] S.P. Timoshenko, History of the Strength of Materials, McGraw-Hill, New York (1953). [6] A. Wt~hler, Zeitschrift ]fir Bauwesen: 8, 641-652 (1858); 10, 583-616 (1860); 16, 67-84 (1866); 20, 73-106 (1870). [7] A. Palmgren, "Die Lebensdauer von Kugellagern", Z.V.D.I. 68, 339-341 (1924). [8] M.A. Miner, "Cumulative damage in fatigue", J. Appl. Mech. 12, A159-A164 (1945). [9] C.C. Osgood, Fatigue Design, McGraw-Hill, New York (1969). [10] J.F. McCarthy Jr., C.F. Tiffany and O. Orringer, "Application of fracture mechanics to decisions on structural modifications of existing aircraft fleets", in: T.P. Rich and D.J. Cartwright, eds. Case Studies in Fracture Mechanics, U.S. Army Materials and Mechanics Research Center, Watertown, MA, AMMRC MS 77-5, June 1977. [11] Military Specification, "Airplane damage tolerance requirements", MIL-A-83444 (USAF) (1972). [12] Code of Federal Regulations, Title 14, Aeronautics and Space, Part 25.571, "Damage tolerance and fatigue evaluation of structure" (1978). [13] T. Swift, "Damage tolerance assessment of commercial airframes", in: P. Tong and O. Orringer, eds. Fracture Problems in the Transportation Industry, American Society of Civil Engineers, New York, NY, 97-138 (1985). [14] W.H. Lewis et al., "Reliability of nondestructive inspections", Lockheed Georgia Company, Marietta, GA, final report to USAF San Antonio Air Logistics Center, Kelly AFB, TX, SA-ALC/MME 76-6-38-1 (1978). [15] J.E. Holpp and M.A. Landy, "The development of fatigue/crack growth analysis loading spectra", NATO Advisory Group for Aerospace Research and Development, Report No. 640 (1976). [16] P.C. Paris, "The fracture mechanics approach to fatigue", in: J.J. Burke, N.L. Reed, and V. Weiss, eds., Fatigue: An Interdisciplinary Approach, Syracuse University Press, 107-132 (1964). [17] J.E. Campbell et al., "Damage tolerant design handbook", Battelle Columbus Laboratories, Columbus, OH, MCICHB-01 (1975). [18] O. Orringer, "Rapid estimation of spectrum crack-growth life based on the Palmgren-Miner rule", Computers and Structures 19, 149-153, (1984). [19] J. Schijve, "Observations on the prediction of fatigue crack growth propagation under variable-amplitude loading", in: Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, 3-23 (1976).
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O. Orringer / Structural integrity assessment in the transportation sector
[20] W. Elber, "Equivalent constant-amplitude concept for crack growth under spectrum loading", in: Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, 236-250 (1976). [21] O. Orringer and H.L. Ceccon, "Detection of rail defects and prevention of rail fracture", in: T.R. Shives and W.A. Willard, eds. Failure Prevention in Ground Transportation Systems, Special Publication 621, National Bureau of Standards, Gaithersburg, MD, 69-90 (1982). [22] O. Orringer, J.M. Morris and R.K. Steele, "Applied research on rail fatigue and fracture in the United States", Theoret. Appl. Fracture Mech. 1, 23-49 (1984). [23] O. Orringer and M.W. Bush, "Applying modern fracture mechanics to improve the control of rail fatigue defects in track", Amer. Railway Engng. Assoc. Bull. 689 84, 19-53 (1983). [24] O. Orringer, J.M. Morris and D.Y. Jeong, "Detail fracture growth in rails: test results", Theoret. Appl. Fracture Mech. 5, 63-95 (1986). [25] R.A. Mayville and P.D. Hilton, "Fracture mechanics analysis of a rail-end bolt hole crack", Theoret. AppZ Fracture Mech. 1, 51-60 (1984). [26] B.G. Journet, "Fatigue crack propagation under complex loading," PhD thesis, Department of Materials Science and Engineering, MIT, Cambridge, MA (1986). [27] D.D: Davis, M.J. Joerms, O. Orringer and R.K. Steele, "The economic consequences of rail integrity", Proc. Third Internat. Heavy Haul Railway Conf., Vancouver, BC, Canada (1986), to appear. [28] J. Orkisz, A.B. Perlman, A. Harris, P. Tong and O. Orringer, "Recent progress in the development of a rail residual stress calculation method", Proc. Second Internat. Symposium on Contact Mechanics and Wear of Rail/Wheel Systems, University of Rhode Island, Kingston, RI (1986), to appear. [29] F. Erdogan, "Theoretical and experimental study of fracture in pipelines containing circumferential flaws", Lehigh University, Bethlehem, PA, DOT-RSPA-DMA-50/83/3 (1982). [30] Anon., API 1104, 16th ed., Appendix A, "Alternative
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
standards of acceptability for girth welds", American Petroleum Institute, Washington, DC (1983). Anon., BS 4515, Appendix H, "A proposed appendix for BS 4515 containing defect tolerance criteria for girth welds based on fracture mechanics approach", British Standards Institution, London, UK (1982). Anon., CSA Z184, Appendix K (draft), "Proposed changes to CSA A184 to accommodate alternative standards of acceptibility", Canadian Standards Association, Toronto, Canada (1984). M.G. Dawes and M.S. Karnath, "The crack opening displacement (COD) design curve approach to crack tolerance", Proc. Conf. on the Significance of Flaws in Pressurized Components, Institution of Mechanical Engineers, London, UK (1978). Anon., BS 5762, "Methods for crack opening displacement testing", Britisch Standards Institution, London, UK (1979). P.D. Hilton and R.A. Mayville, "Girth weld defect tolerance criteria", in: P. Tong and O. Orringer, eds. Fracture Problems in the Transportation Industry, American Society of Civil Engineers, New York, NY, 80-96 (1985). R.R. John et al., "Task force report: rail failure evaluation", DOT Transportation Systems Center, Cambridge, MA (1984). M. Gence et al., "Possibilities of Improving the Service Characteristics of Rails by Metallurgical Means, Report No. 1, Factors Influencing the Fracture Resistance of Rails in the Unused Condition," D 156 Committee, Office for Research and Experiments of the International Union of Railways, Utrecht, the Netherlands (1984). O. Orringer, "Failure mechanics: damage evaluation of structural components", in: G.C. Sih and L. Faria, eds. Fracture Mechanics Methodology: Evaluation of Structural Components Integrity, Martinus Nijhoff, the Hague, The Netherlands (1984). P. Tong et al., "Task force report: D O T - 1 0 5 / l l l / 112/114 tank cars shell cracking and structural integrity assessment", DOT Transportation Systems Center, Cambridge, MA (1986).