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Characterisation of equivalent initial flaw sizes in 7050 aluminium alloy
Abstract
This paper summarises a collation of crack growth related data from a significant number of fatigue tests on commercial quality 7050-series aluminium alloy tested under various F/A-18 aircraft spectra. The data presented consist of quantitative fractography measurements of the fracture surfaces including effective initiating defect size and type (mechanical, environmental or chemical). Three different surface conditions were considered: chemically etched, glass bead peened and machined. The purpose of providing these data was to facilitate analyses on the parameters governing the propagation of fatigue cracks in the 7050-series aluminium alloy. Here an investigation to determine whether surface finish or applied stress and spectra have any bearing on the initial defect size or the damage type is summarised. Based on this investigation, it appears that the applied stress and spectra have no correlation to the size of the equivalent initiating flaw; however, the surface finish appears to influence the various crack-initiating mechanisms and to govern the formation of the damage type.
... The terms pre-IVD and pre-Type 1C shall be used henceforth to describe the surface preparation steps during which the etching occurs prior to the application of either the anodized or IVD layers ( Figure 5). Separate studies for both AA7050 [24], [32] and AA7085 [36] confirm the pitting of interest occurs during these preparatory etching phases and not during the final coating step. To isolate the 'crack-like-effectiveness' of etch pitting from either production surface finish treatment, the average EPS of all nucleating discontinuities was calculated. ...
... The geometric mean and 95% confidence interval of the measured initial discontinuity depths and EPS were calculated. It was assumed the data population had a lognormal distribution per previous AA7050 EPS studies [32]. This data is shown in Table 1 and plotted in a bar chart at Figure 16. ...
... All values below 0.001mm have been rounded up to this value. Since EPS is also a spectrum independent characteristic [32], only the peak spectrum stress (σ) multiplied by the specimen stress concentration (Kt) or 'Ktσ' was used to distinguish between different FCG specimens pooled for this study. ...
Aluminium alloy 7085 forgings are a suitable replacement for 7050 thick-plate material in large, thick airframe parts such as bulkheads. In this paper two factors in small fatigue crack growth rates are contrasted for these two materials – microstructure and fatigue crack nucleation from etch pitting, an unavoidable artefact of aircraft production surface finishes for high strength aluminium alloys.
Evidence of the complex interactions between small fatigue cracks and the microstructure of AA7085-T7452 is presented at a sub-grain level to explain scatter in small fatigue crack growth rates below 1x10⁻⁹ m/cycle and ΔK = 1.2 MPa√m. Above this level, small fatigue crack growth rate data is presented that demonstrates that growth rates are relatively insensitive to grain size in this material.
Equivalent pre-crack size data is presented for several AA7085 and AA7050 specimens, in different material directions, and treated with pre-Type 1C anodising and pre-ion vapour deposition etching processes. The measured mean depths of the etch pits produced in both materials was found to be similar yet etch pitting in AA7085 was shown to be less effective in nucleating small fatigue cracks. The etching pre-processes associated with ion vapour deposition coatings were also found to lead to more effective fatigue crack nucleation than pre-anodizing treatments.
... For pitting-induced fatigue cracks, it has been observed that the effective cracklike pit depth (EPS = equivalent pre-crack size) is a defining fatigue crack growth metric [6,[13][14][15][29][30][31][32][33][34][35][36][37][38][39]. Coupling this result with a well-proven crack growth model, such as that used in the lead crack framework [40], could enable predicting the impact with time of service-detected corrosion pitting on airframe or individual component structural integrities. ...
... Back-extrapolation of these equations to time zero yields EPS values of 10.4, 6.3 and 3.9 µm for the cracks C1, C2 and C3. (EPS is used to distinguish this method from the more commonly used EIFS (equivalent initial flaw size; see [35,36]. EPS values are based on QF measurements encompassing very small crack sizes (approximately 10-100 µm). ...
... Back-extrapolation of these equations to time zero yields EPS values of 10.4, 6.3 and 3.9 m for the cracks C1, C2 and C3. (EPS is used to distinguish this method from the more commonly used EIFS (equivalent initial flaw size; see [35,36). EPS values are based on QF measurements encompassing very small crack sizes (approximately 10-100 μm). ...
Corrosion-induced maintenance is a significant cost driver and availability degrader for aircraft structures. Although well-established analyses enable assessing the corrosion impact on structural integrity, this is not the case for fatigue nucleation and crack growth. This forces fleet managers to directly address detected corrosion to maintain flight safety. Corrosion damage occurs despite protection systems, which inevitably degrade. In particular, pitting corrosion is a common potential source of fatigue. Corrosion pits are discontinuities whose metrics can be used to predict the impact on the fatigue lives of structural components. However, a damage tolerance (DT) approach would be more useful and flexible. A potential hindrance to DT has been the assumption that corrosion-induced fatigue nucleation transitions to corrosion fatigue, about which little is known for service environments. Fortunately, several sources indicate that corrosion fatigue is rare for aircraft, and corrosion is largely confined to ground situations because aircraft generally fly at altitudes with low temperature and humidity Thus, it is reasonable to propose the decoupling of corrosion from the in-flight dynamic (fatigue) loading. This paper presents information to support this proposition, and provides an example of how a DT approach can allow deferring corrosion maintenance to a more opportune time.
... This framework builds on the observation that (near) exponential (i.e., log crack size versus linear cycles) FCG is a common occurrence for naturally nucleating lead cracks (i.e. those leading first to failure) in test specimens, components and airframe structures subjected to variable amplitude load histories (6,(11)(12)(13)(14)(15)(16)(17)(18) . ...
... where a = Crack depth (or length) a 0 = Initial crack size (or EPS) (11)(12)(13)(14)(15) λ = Growth rate parameter that includes the finite geometry factor β t = Fatigue life in terms of Cycles/Number of Load Blocks/Simulated Flight Hours (SFH) 3. A significant portion of their lives is spent in the physically short crack regime (i.e. at depths less than approximately 1mm). 4. They grow in an optimum manner generally unaffected by such factors as crack-closure or material grain size, etc. 5. The fastest possible lead crack is more likely to be revealed in a larger component than in a small coupon (i.e. the area or volume effect). ...
... For a given material, spectrum, peak stress level and structural detail, the λ parameter of the exponential equation, e.g. the slope of the FCG curve shown in Fig. 1, is approximately a constant. 7. The mean EPS for a 7050-T7451 aluminium alloy (AA) plate is approximately equivalent to a 0.01 mm deep (semi-circular) surface fatigue crack (6,7,(11)(12)(13)(14) . In other words, in this material, a 0.01 mm deep crack is a good starting point for estimating the average fatigue life using the lead crack framework, see Fig. 1. ...
Aircraft full-scale fatigue tests are expensive and time-consuming to conduct but are a critical item on the certification path of any aircraft design or modification. This paper outlines a proposal that trades cycling hours for increased detail in the teardown of a metallic test article. A method for determining the equivalent demonstrated crack size (and crack growth curve) at the mandated test life utilising the lead crack framework is demonstrated. It is considered that the test duration can be significantly reduced, whilst still achieving all the desired outcomes of a certification program.
... Despite pre-testing inspection that identified many occurrences of dents and scratches that were induced during service or CB removal, the fatigue cracking associated with mechanical damage was restricted to that induced at fastener holes as the result of manufacture [11,12] and the mechanical damage found at these sites was assessed as typical of the as-manufactured quality of modern aircraft. There were a limited number of cracks from in-service induced corrosion pitting found, e.g. ...
... The EPS can be derived by back-extrapolating measured crack growth data to the beginning of the fatigue life using an exponential crack growth model (see Fig. 13). Since numerous such calculations were possible with the many cracks investigated, the average EPS for the pre-etched aluminium alloy of the CB bulkheads was calculated and was found to be approximately equivalent to a 0.01 mm deep crack [9,11,12,[28][29][30]. The average EPS for other discontinuity types may be larger or smaller than 0.01 mm. ...
... For cases when the crack origin had been damaged (e.g. by rubbing of the fracture surfaces during testing) or was missing altogether (e.g. excision of the fracture site from test article or modification of the area during test or service had caused the crack origin's removal), then a typical EPS of 0.01 mm depth was assumed [9,11,12,[28][29][30]. Also, in cases where no QF data was available, but the crack depth at another time in the crack's life was (e.g. at the end of fatigue testing), an EPS of 0.01 mm deep was assumed to allow the derivation of an approximate fatigue crack growth curve. ...
This paper summarises some of the significant outcomes of a fatigue test program for ex-service aircraft structure. Seventeen F/A-18 Hornet aircraft aluminium alloy 7050-T7451 centre fuselages (referred to as centre barrels (CBs)) were tested, torn down and inspected in this program. Significant results of the test program included the demonstration of the repeatability of service fatigue cracking locations, the collection of data to characterise the types of defects that typically nucleate fatigue cracks in aircraft components and a more accurate assessment of the safe operating life of this structure. The results of the program also enhanced the existing understanding of fatigue cracking in aluminium alloy 7050-T7451. Furthermore, the improved understanding of the fatigue cracking that occurred in service F/A-18 CBs and the damage tolerance of this structure allowed increased aircraft availability and reduced maintenance costs in the Royal Australian Air Force (RAAF) F/A-18 fleet.
... 6 This etching produced small pits all over the bulkheads, which are the predominant crack initiation site in these bulkheads, although other initiation sources have been found and are also considered (e.g. porosity) [21][22][23][24]. The corrosion protection layer on the bulkheads is applied using the Ion Vapour Deposition (IVD) technique. ...
... In other cases the estimates were not so consistent, due to the limited accuracy of the assumption on which the method was based. Specifically, some discontinuities are either more effective or less effective at growing a crack than a crack of the same depth [20][21][22]24], which caused some uncertainty in the estimated shows an example of the slowing of the crack growth acceleration rate that occurred for many of the cracks at this location. This particular case is for a crack that grew from the aft hole on the LHS of CB3 (note the significant slowing that can be seen near the very end was caused by the failure of the Y470.5 bulkhead). ...
... The SD of log 10 fatigue lives calculated for the sample without the LHS of CB4 was 0.099, 20 while it was 0.088 when CB4 was excluded entirely. 21 Fig . 9 shows normal probability plots for the log 10 fatigue lives at the Y453 bulkhead upper duct flange location. ...
This paper describes an investigation to determine the scatter in fatigue performance of aluminium alloy 7050-T7451 plate as used in a fighter aircraft. The results for two failure locations on eight full-scale fatigue tests of near identical modern monolithic airframe sections, as well as over 150 low stress concentration fatigue coupons that were tested at a number of stress levels were considered. Fatigue scatter was quantified in terms of the standard deviation of log10 fatigue lives. It appears that even for monolithic aircraft structures, the level of fatigue scatter is location dependent. Also, the results of the investigation indicated that the fatigue lives at mirrored locations on monolithic parts may not be independent of one another.
... Within the bounds of these conditions, observations from the DSTO about the formation, growth, and failure of lead cracks have led to various deductions (Molent, Barter and Wanhill, 2011), including: • For a given material, spectrum and item, the λ parameter of the exponential equation, i.e. the slope of the crack growth curve shown in Fig. 1, is approximately a constant. • Typical initial discontinuity sizes of AA7050-T7451 are approximately equivalent to a 0.01 mm deep fatigue crack (Molent, Sun and Green, 2006;Molent and Barter, 2007). ...
... This value is below the smallest initial flaw/crack size -the equivalent initial flaw size (EIFS)usually assumed in the damage tolerant method (USAF, 1974). • The metallic materials used in highly stressed areas of a high-performance aircraft have typical critical crack depths of about 10 mm (Molent, Sun and Green, 2006;Molent and Barter, 2007). ...
... Th e EPS is a recent development, and its values for some defect types are approximations to a physical measurement of the initiating fl aw or discontinuity derived via back projection to time zero from experimental FCG data. Th erefore, it should not be compared to the more traditional EIFS concept (Molent, Sun and Green, 2006). Th e fatigue life variation of any given region of metallic structure appears to correlate primarily to the distribution of the EPS of these fatigue initiators for a given material, spectrum, and stress level (Pell, Molent and Green, 2004). ...
http://dx.doi.org/10.5028/jatm.v5i2.219
The lead crack concept is adopted as the basis for a new fatigue lifing method using the safe life philosophy. As part of its management strategy, a full-scale fatigue test is conducted to identify high-risk locations in the airframe, and for each item the time for retirement or structural repair is dictated by the safe life limit. A scatter factor is defined to account for the scatter in the material fatigue performance. The fatigue life variation of any given region of aircraft metallic structures is assumed to primarily correlate to the distribution of the equivalent pre-crack size of the fatigue crack initiators. By assuming that the sizes of these crack initiators are independent from each other, the present paper estimates the scatter factor by calculating safe life limit based on known growth characteristics of critical cracks.
... This framework builds on the observation that (near) exponential FCG is a common occurrence for naturally-initiating lead cracks (i.e. those leading to first failure) in test specimens, components and airframe structures subjected to variable amplitude load histories [8][9][10][11][12][13][14][15][16][17][18]. ...
... where: a = Crack depth a 0 = Initial crack size (or equivalent pre-crack size (EPS) 4 [10][11][12][13][14][15]) k = Growth rate parameter that includes the finite geometrical factor b t = Cycles/No. of Load Blocks/Simulated Flight Hours (3) A significant portion of their lives is spent in the short crack regime (i.e. at depths less than approximately 1 mm). ...
... plate is approximately equivalent to a 0.01 mm deep (semicircular) surface fatigue crack [8][9][10][11][12][13][14]. In other words a 0.01 mm deep crack is a good starting point for assessing the average fatigue life using the lead crack framework, see Fig. 1. ...
... For fatigue cracks that originate from pitting corrosion it has been found that the effective crack-like pit depth is a defining fatigue crack growth characteristic [3,8,9,[15][16][17][18][19] (excluding at end grains). Coupling these findings with a robust crack growth model, such as the lead crack framework [19], provides a means of predicting the impact of pitting corrosion on the structural integrity of an airframe. ...
... The three cracks coalesced to form the crack front shown in Fig. 2 which was examined with QF. Each had initiated from pitting caused by the chemical etching of the AA7050-T7451 (see [15]) which is conducted as a precursor to the Ion Vapour Deposited (IVD) aluminium corrosion preventative scheme. The measured IVD pit depths for C1, C2 and C3 were 12, 6.2 and 8.4 lm respectively. ...
... The Equivalent Pre-crack Size (EPS) , 4 defined as the back-projection to time zero from the QF derived crack growth curve (see [15,16] for more details), from Fig. 6 for C1, C2 and C3 were 10.4, 6.3 and 3.9 lm respectively, which compared favourably with the measured etch pit depths in this case, 12, 6.2 and 8.4 lm (see more examples for etch pits in [9]). ...
Despite corrosion prevention or protection schemes/treatments and corrosion prevention and control plans, in-service corrosion does occur and has the potential to impact the structural integrity of aircraft. Whilst the fatigue management of the aircraft is generally well understood as reflected in typical Aircraft Structural Integrity Management Plans (ASIMP), which in some cases contain environmental degradation plans, limited provision beyond find and fix exists for corrosion repair. Thus the repair of corrosion can be a major through life cost driver as well as an aircraft availability degrader. This find and fix policy exists largely because tools are currently considered too immature to accurately assess the structural significance of corrosion when it is detected.
In this paper a process is described which should allow an alternative to the current find (corrosion) and fix philosophy for pitting corrosion. The method is intended to maintain a probability of failure consistent with ASIMP structural certification requirements for fatigue cracks initiating from corrosion pits for a specific period. Unanticipated maintenance costs significantly more than planned maintenance. Thus delaying the repair of pitting corrosion until the next scheduled maintenance, should save considerable resources and improve aircraft availability. The development of analytical tools capable of accurately assessing the effect of corrosion on the durability of a structure would be considered a major advance for the ASIMP.
... (a) For a given material, spectrum and geometry, the k parameter of the exponential equation, i.e., the slope of the crack growth curve shown in Fig. 1, is approximately a constant for given stress level. (b) A mean EPS for AA7050-T7451 and the manufacturing processes used for the F/A-18 is approximately equivalent to a 0.01 mm deep (semi-elliptical) fatigue crack [15,16,18] 4 Note that variations in aircraft usage will also lead to significant scatter in fatigue lives. This is one reason why most military agile aircraft are fatigue usage monitored, see [5]. 5 Some aspects of item 1 (e.g. ...
... This mean EPS is consistent with those reported in [19,20] for other aluminium alloy airframe materials. (c) The metallic materials used in highly stressed areas of high performance aircraft, where load shedding does not tend to occur, typically have critical crack depths of the order of 10 mm, see [6,10,15,16,18]. ...
... EPS), which is related to their size and type. As such the primary metric defining the fatigue-like characteristic for the discontinuities are their EPS, see [6,15,16,18]. ...
The safe-life method is widely used to ensure that airframes have an acceptably low probability of structural failure. This method uses a scatter factor to account for the variability in a metal's fatigue performance to maintain a probability of failure below acceptable levels. However, given the empirical nature of scatter factors, the method does not enable the influence of the various factors that contribute to this scatter to be individually assessed. This paper compares alternative methods for determining the safe life of monolithic 7050-T7451 aluminium alloy structures with the traditional approach used to life fighter/attack aircraft. These methods are designed to protect the fleet by maintaining a cumulative probability of failure below 1/1000, as required by a certification structural design standard. The alternative methods are based on estimating the distribution of the most significant factor affecting the scatter noted in fatigue test results, namely the sizes of the fatigue initiating material discontinuities. Crown Copyright
... 1 This paper summarises the analyses of these cracks 2 and updates previous work. 3 The analyses include the equivalent pre-crack size (EPS) derived for many of these fatigue cracks. The EPS values are an estimate of the effective size (of an equivalent fatigue crack size) of pre-existing initial discontinuities/flaws in a material that grow fatigue cracks. ...
... (1) description of EPS data samples; (2) is EPS sensitive to varying stress levels? (3) probability distribution of the EPS data; and (4) correlation of EPS and measured initial discontinuities/ flaw size. ...
... In general, the early exponential crack growth is back-projected to time zero (assuming a negligible initiation period 4,7 ). (Note that the EPS values quoted in the body of this paper were obtained using a more sophisticated method of regression to determine a best fit EPS; see Ref. [3] for more details.) From Fig. 1, an EPS = 0.0148 mm was derived, compared with an EIQM value of 0.0277 mm. ...
This paper reviews some analyses of quantitative fractography measurements of the fatigue fracture surfaces of 7050 aluminium alloy specimens along with relevant fatigue crack information including crack initiating discontinuity size and type. These data were used to assess whether surface finish or applied stress level has any effect on the estimated effective crack initiating discontinuity size, namely the equivalent pre-crack size (EPS). The statistical distributions for the EPSs of the following initiating discontinuity types were examined: chemically etched pits, glass bead peening damage, mechanical damage, inclusions and porosity. The EPSs at various percentile levels for these types were determined on the basis of the samples considered. Finally, the correlation between measured initiating discontinuity depth and EPS was investigated, and good correlation was found in the case of mechanical damage. The purpose of conducting these analyses was to gain a better understanding of the parameters governing the fatigue crack-like effect of discontinuities to facilitate the better prediction of fatigue lives.
... Paris' law) can be used. Many methods have been used to establish the EIFS, these include back-extrapolation [6][7][8][9][10][11], equivalent pre-crack sizes (EPS) [5,10,11], and the Kitagawa-Takahashi diagram [12][13][14]. Statistical approaches, involving the use of Bayesian updating and MLE have also been undertaken [15][16][17]. ...
... Paris' law) can be used. Many methods have been used to establish the EIFS, these include back-extrapolation [6][7][8][9][10][11], equivalent pre-crack sizes (EPS) [5,10,11], and the Kitagawa-Takahashi diagram [12][13][14]. Statistical approaches, involving the use of Bayesian updating and MLE have also been undertaken [15][16][17]. ...
A method is proposed in this work for the inference of the Equivalent Initial Flaw Size (EIFS) distribution using the Boundary Element Method (BEM). The EIFS distribution for a cracked stiffened panel is determined using Maximum Likelihood Estimation (MLE). Various sources of uncertainty are considered, such as uncertainty in loading conditions, measurement of crack size during inspections, and in fatigue crack growth model parameters. Results suggest that MLE is effective at estimating the statistics of an EIFS distribution in the absence of prior information.
... This EIFS distribution can then be used to estimate the fatigue life of the structure. A common method used to determine EIFS is the back-extrapolation method [5][6][7][8][9][10]. In this method, the initial crack that best matches the load history and inspection data of a structure is determined using an iterative procedure. ...
... One disadvantage of this approach is that the resulting EIFS will be dependent on the loading history [5]. Another approach involves the equivalent pre-crack size (EPS) [9][10][11]. The Kitagawa-Takahashi diagram has also been employed [12][13][14]. ...
In this work, a method for determining the Equivalent Initial Flaw Size (EIFS) distribution using the Boundary Element Method (BEM) is proposed. Maximum Likelihood Estimation (MLE) is used to infer the EIFS distribution of a cracked stiffened panel under multiple sources of uncertainty, including uncertainty in loading, fatigue crack growth model parameters, and in the measurement of crack size found from routine inspections. Results suggest that MLE is an effective tool for estimating the parameters of an EIFS distribution when no prior knowledge is available regarding the EIFS distribution or its parameters.
... This EIFS distribution can then be used to estimate the fatigue life of the structure. A common method used to determine EIFS is the back-extrapolation method [5][6][7][8][9][10]. In this method, the initial crack that best matches the load history and inspection data of a structure is determined using an iterative procedure. ...
... One disadvantage of this approach is that the resulting EIFS will be dependent on the loading history [5]. Another approach involves the equivalent pre-crack size (EPS) [9][10][11]. The Kitagawa-Takahashi diagram has also been employed [12][13][14]. ...
In this work, a method for determining the Equivalent Initial Flaw Size (EIFS) distribution using the Boundary Element Method (BEM) is proposed. Maximum Likelihood Estimation (MLE) is used to infer the EIFS distribution of a cracked stiffened panel under multiple sources of uncertainty, including uncertainty in the loading conditions, fatigue crack growth model parameters, and in the measurement of crack size found from routine inspections. Results suggest that MLE is an effective tool for estimating the parameters of an EIFS distribution when no prior knowledge is available regarding the EIFS distribution or its parameters.
... Paris' law) can be used. Many methods have been used to establish the EIFS, these include back-extrapolation [6][7][8][9][10][11], equivalent pre-crack sizes (EPS) [5,10,11], and the Kitagawa-Takahashi diagram [12][13][14]. Statistical approaches, involving the use of Bayesian updating and MLE have also been undertaken [15][16][17]. ...
... Paris' law) can be used. Many methods have been used to establish the EIFS, these include back-extrapolation [6][7][8][9][10][11], equivalent pre-crack sizes (EPS) [5,10,11], and the Kitagawa-Takahashi diagram [12][13][14]. Statistical approaches, involving the use of Bayesian updating and MLE have also been undertaken [15][16][17]. ...
A method is proposed in this work for the inference of the Equivalent Initial Flaw Size (EIFS) distribution using the Boundary Element Method (BEM). The EIFS distribution for a cracked stiffened panel is determined using Maximum Likelihood Estimation (MLE). Various sources of uncertainty are considered, such as uncertainty in loading conditions, measurement of crack size during inspections, and in fatigue crack growth model parameters. Results suggest that MLE is effective at estimating the statistics of an EIFS distribution in the absence of prior information.
... Main problem of this method is the complexity of small crack theory. However, life prediction based on EIFS concept is an applicable method, which has been considered by numerous researchers [7][8][9]. Riveted lap joints are susceptible to cracks due to fatigue and fretting [1]. Multiple site damage (MSD) (sometimes called widespread fatigue damage (WFD)) is an important problem associated with aging aircraft, which was started to be studied by Aloha accident in 1988 [10]. ...
... The cyclic shear strains caused crack initiation, whereas cyclic normal strains caused crack propagation [26]. Therefore, they suggested Eq. (8) for the life estimation of structures. ...
... These origins were grouped at the surface near the middle of each of the cracks. The fatigue cracking had initiated from numerous closely spaced etch pits that had been produced by chemical etching of the AA7050-T7451 [10]. The pitting had occurred to the bulkhead when it was cleaned prior to being coated with a layer of almost pure aluminium that was applied as a corrosion preventative scheme. ...
... The subject aircraft was a trainer and therefore it is reasonable to assume a repetitive syllabus. 7 EPS is used to differentiate this method from the more commonly used EIFS (equivalent initial flaw size), see [10]. EPS values are derived based on QF data which are available down to very small crack sizes (i.e. ...
It has been postulated that for combat aircraft corrosion generally occurs whilst the aircraft is on the ground, while fatigue damage in the form of cracking (if any) grows as result of operational loading which mainly occurs in flight where the conditions are cold and dry and the loading rates are high. This would suggest that (in general) for combat aircraft the effects of the environmental degradation and any fatigue crack growth are decoupled. From a damage prediction viewpoint, this will significantly simplify assessment of such problems (i.e. the growth of fatigue cracks in these aircraft types is not environmentally assisted). This paper presents a supporting case study that examines fatigue cracks that were detected in an F/A-18 Hornet bulkhead during post-service testing and teardown. The in-service phase of the cracking had significant evidence of oxidation on their surfaces which indicated an exposure to a mildly corrosive environment. Both the service and laboratory phases of the cracking were the subject of quantitative fractography and estimates of the crack growth rates were made. A comparison of the in-service and the in-test phases of crack growth indicated that no notable effect on the service part of the fatigue crack could be attributed to its exposure to the service environment. Crown Copyright
... The dimensions of these intermetallic particles were greater than any surface scratches or machining marks and so they provided ideal crack initiation sites. The typical sizes of these discontinuities (as well as other types) are provided in [2]. Many specimens contained several cracks on the primary fracture surface. ...
... As can be noted from Fig. 3, there is some variation in the lives and crack growth rates for coupons tested under the same conditions. Assuming that the variation in fatigue life is log-normally distributed [2], then the probability density function is given by: ...
DSTO conducted a comprehensive series of fatigue coupon tests as part of the fatigue life substantiation of the RAAF F/A-18 Hornet. The study employed five spectra which were applied to flat aluminium alloy 7050-T7451 coupons to determine the effects of manufacturing discontinuities and stress magnitude on the fatigue nucleation and crack growth behavior. Crack growth behavior was established using optical microscopy and scanning electron fractography, measuring crack sizes greater than approximately 0.05 mm. This paper reports the fraction of life to failure as well as the probability of occurrence of a crack with a defined size.
... This method uses fatigue crack growth analysis and assumes that the initial crack geometry and size match the material failure data (stress life). The initial crack size is obtained by repeated tests, which is called EIFS [27]. It is desirable to regard EIFS as a material property that indicates the initial mass of the material and is independent of the applied stress level [28,29]. ...
Corrosion fatigue is identified as the main failure mechanism for structures working in severe corrosive medium subjected to cyclic rotating bending fatigue, for example crude oil storage tank (COST). Emphasis is placed on the study of corrosion pit formation and the development of cracks from pits. An improved equivalent initial flaw size (I-EIFS) is proposed for corrosion fatigue life prediction. Based on the concept of equivalent initial flaw size (EIFS), pitting corrosion and small crack growth are equivalent to a part of long crack growth process in corrosion fatigue process. Pitting and crack propagation are quantified throughout the fatigue loading thereby allowing a model to be developed that included the stages of pit development, pit-to-crack transition and crack growth in order to predict the fatigue life. A corrosion fatigue life prediction case is adopted to demonstrate the effectiveness of the proposed model. Based on the proposed model, failure analysis and stress calculation are performed to predict the corrosion fatigue life of COST, which provides a method for the life prediction of COST. The validity of proposed method is verified by comparing the service life of COST.
... The EIFS provides a helpful starting point for determining the fatigue life of the structure, and of other similar structures under similar conditions. One of the most common techniques that has been used in the past to determine EIFS is backextrapolation [6][7][8][9][10][11][12][13][14][15][16], which involves extrapolating inspected cracks backwards to some initial time through the use of a crack growth model. However, its application is limited due to the large amount of fatigue crack growth data needed and the required use of fractography techniques to ensure a high degree of accuracy. ...
A new methodology for the statistical inference of the Equivalent Initial Flaw Size Distribution (EIFSD) using the Dual Boundary Element Method (DBEM) is proposed. As part of the inference, Bayesian updating is used to calibrate the EIFS based on data obtained from simulated routine inspections of a structural component from a fleet of aircraft. An incremental crack growth procedure making use of the DBEM is employed for the modelling of the simultaneous growth of cracks in the structure due to fatigue. Multi-fidelity modelling, in the form of Co-Kriging, is used to create surrogate models that act in place of the DBEM model for the expensive Monte Carlo sampling procedure required for the statistical inference of the EIFSD. The proposed methodology is applied to a numerical example featuring a long fuselage lap joint splice in the presence of Multiple Site Damage (MSD). Results show that the EIFSD can be accurately estimated within 10% error with data from just 50 inspections. The employed Co-Kriging models proved to be effective substitutes for the DBEM model, providing significant reductions in the computational cost associated with the implementation of the proposed statistical inference methodology.
... see Refs. [31,32], with significant portions of the FCG lives spent in the so-called short crack regime (crack sizes less than about 0.5-1 mm). This is most important, since the case study crack had maximum dimensions < 1 mm, see Fig. 4. ...
Quantitative Fractography of Fatigue and an Illustrative Case Study
N.T. Goldsmith1, R.J.H. Wanhill2 and L. Molent1
1Aerospace Division, Defence Science and Technology (DST) Group, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia. 2Emmeloord, the Netherlands.
Abstract: Quantitative fractography (QF) may be used for measuring service- and test-induced fatigue crack growth (FCG) in metallic components and structures. The QF compares progression and striation markings on fatigue fracture surfaces with known occurrences in the components’ load histories. This paper concisely surveys fatigue-related QF, followed by a case study for a crack in a component from a maritime patrol aircraft. The case study illustrates how a FCG versus time history can be estimated. This was achieved using (i) knowledge of when the crack was detected, (ii) a reconstruction of the aircraft usage history from counting accelerometer (g-meter) data, (iii) an exponential FCG model of how cracking could have progressed, and (iv) QF of progression markings. Comparison of the reconstructed usage data and the QF information showed that the model provided a useful correlation.
Keywords: Quantitative fractography; Fatigue cracks; Aircraft; Load exceedances
... A full description of each sequence is found in the previous works. 8,[19][20][21][22] A brief description of each spectrum follows: Aircraft 1 -a high damage sequence from a dual seat aircraft; Aircraft 2 -a low damage sequence from a single seat aircraft; APOL -Australian post-LEX fence baseline sequence; FT55 -centre fuselage sequence for the FT55 fatigue test; ST16 -US Navy sequence for the ST16 fatigue test; FT245mb -a version of the FT245 wing test sequence with low levels of truncation and containing marker band loads; FT55mb -a version of the FT55 sequence with marker band loads; Mini-TWIST -a standardised transport aircraft sequence that includes a number of small cycles that represent gust loading. 23 The coupons used in these tests were generally designed to simulate a detail on an aircraft's, for instance, wing carry-through bulkhead using a hourglass type geometry, as shown in Figure 1 and detailed in Table 2. ...
The need and benefits of individual aircraft fatigue monitoring are now well established. There are broadly two fatigue damage methods employed for this purpose, namely, crack growth and stress (or strain)-life. The crack growth methods tend to provide a relative comparison between an aircraft’s usage and a baseline usage, while the strain-life methods provide a measure of the amount of fatigue life consumed against that (generally) demonstrated through a fatigue test. In this article, a new crack growth–based tracking method is described that also includes a measure of the certified fatigue life consumed. The damage model is compared against the results of an extensive coupon fatigue test programme for aluminium alloy 7050-T7451.
... This approach has been successfully extended to establish corrosion modified-EIFS (CM-EIFS) values for various aerospace Al alloys. 9,10,18,29 The CM-EIFS approach shows the potential to be a useful engineering tool that would capture the deleterious effect of the corroded surface on the fatigue behaviour via a single 'corroded materials property' parameter. However, it would remain burdensome to establish this property for the wide range of corrosion morphologies (e.g. ...
For ageing airframe structures, a critical challenge for next generation linear elastic fracture mechanics (LEFM) modelling is to predict the effect of corrosion damage on the remaining fatigue life and structural integrity of components. This effort aims to extend a previously developed LEFM modelling approach to field corroded specimens and variable amplitude loading. Iterations of LEFM modelling were performed with different initial flaw sizes and crack growth rate laws and compared to detailed experimental measurements of crack formation and small crack growth. Conservative LEFM-based lifetime predictions of corroded components were achieved using a corrosion modified-equivalent initial flaw size along with crack growth rates from a constant Kmax-decreasing ΔK protocol. The source of the error in each of the LEFM iterations is critiqued to identify the bounds for engineering application.
... Reference [2] used a probabilistic fracture approach to derive the equivalent precrack size (EPS), which is also based on the backextrapolation method. Reference [3] used a back projection of the experimental crack growth curve to time zero to derive the EPS for Al 7050. The major problem using the backextrapolation method is that the obtained EIFS seems to be dependent on stress level [4]. ...
... Initially, certain researchers used empirical crack lengths between 0.25 mm and 1 mm for metals (JSSG, 1998;Gallagher et al., 1984;Merati et al., 2007). Later, several researchers (Yang, 1980;Moreira et al., 2000;Fawaz, 2000;White et al., 2005;Molent et al., 2006) used back-extrapolation techniques to estimate the value for equivalent initial flaw size. Recently, Liu and Mahadevan (2008) proposed a methodology based on the Kitagawa-Takahashi diagram (Kitagawa and Takahashi, 1976) and the El-Haddad Model (Haddad et al., 1979) to derive an analytical expression for the equivalent initial flaw size. ...
This paper presents a methodology to quantify the uncertainty in fatigue crack growth prognosis, applied to structures with complicated geometry and subjected to variable amplitude multi-axial loading. Finite element analysis is used to address the complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. Crack growth under variable amplitude loading is modeled using a modified Paris law that includes retardation effects. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis. The effect of different types of uncertainty - physical variability, data uncertainty and modeling errors - on crack growth prediction is investigated. The various sources of uncertainty include, but not limited to, variability in loading conditions, material parameters, experimental data, model uncertainty, etc. Three different types of modeling errors - crack growth model error, discretization error and surrogate model error - are included in analysis. The different types of uncertainty are incorporated into the crack growth prediction methodology to predict the probability distribution of crack size as a function of number of load cycles. The proposed method is illustrated using an application problem, surface cracking in a cylindrical structure.
... where a i is the initial defect size, which as shown by Molent et al. [32], for 7050-T7451 aluminium has a mean value of ∼10 microns and a f is the crack size at failure. ...
Fatigue considerations play a major role in the design of optimised flight vehicles, and the ability to accurately design against the possibility of fatigue failure is paramount. However, recent studies have shown that, in the Paris Region, cracking in high-strength aerospace quality steels and Mil Annealed Ti–6AL–4 V titanium is essentially R ratio independent. As a result, the crack closure and Willenborg algorithm’s available within commercial crack growth codes are inappropriate for predicting/assessing cracking under operational loading in these materials. To help overcome this shortcoming, this chapter presents an alternative engineering approach that can be used to predict the growth of small near-micron-size defects under representative operational load spectra and reveal how it is linked to a prior law developed by the Boeing Commercial Aircraft Company. A simple method for estimating the S–N response of 7050-T7451 aluminium is then presented.
... However, subsequent observation of the condition of aircraft can be used to improve the accuracy of the initial assumptions used in the risk analysis. The input data shown to have high variability is the equivalent pre-crack size (EPS) [1] which is based on the extrapolation of fractographic measurements or even greater variability when using the equivalent initial flaw size (EIFS) which is obtained by back-extrapolating a calculated crack growth curve to an equivalent flaw at time zero. Information obtained during a scheduled aircraft inspection can be used to improve the accuracy of the EIFS distribution in risk analysis. ...
This paper illustrates a technique that may be used to evaluate the risk of structural failure of each aircraft in a fleet when a crack has been detected in a particular member aircraft, or the risk of failure for that member has become too high. When a crack is detected, the calculated risk of failure for other aircraft in the fleet will increase significantly, and the aircraft operators need to decide which aircraft should be temporarily grounded for unscheduled inspection and which ones be allowed to fly. The proposed method applies the Bayesian inference to update the risk assessment by updating the equivalent initial flaw size distribution, which is one of the key inputs for risk analysis. To illustrate the method, a hypothetical fleet aircraft is considered and the single flight probability of failure of each aircraft in the fleet is revised after the occurrence of a failure in one fleet aircraft.
... The estimation of the SFPOF requires knowledge of the crack size, service stress, material properties, and the stress intensity factor for the geometry of interest. The crack sizes for a pristine structure are modeled using the concept of Equivalent Initial Flaw Size (EIFS) [6] which uses past inspection data to determine the Probability Density Function (PDF) of the damage state introduced in the manufacturing process. This initial damage is then evolved based on the curve and the loading history, both of which are random. ...
... In other cases where FT55 locations had no QF data, an initial flaw size of 0.01 mm (0.0004 inch) was assumed, since this value has been found to be a good representative size for the starting size of average cracks in CB bulkheads [9]. The pseudo critical crack size of these was conservatively estimated, typically by using a depth equivalent to the amount of material removed during the FT55 modification that removed the suspected crack. ...
Aircraft Airworthiness and Sustainment (Australia), Brisbane Qld, 26-28 July As tactical military aircraft age, and in particular enter into the last third of their life, sustainment issues become much more important. The expense of structural refurbishment and the cost required to maintain the aircraft's capability can become prohibitive at a time when the RAAF's attention is usually focused on new capability, so ways must be found to maintain the current capability while minimising or reducing costs whilst still maintaining an acceptable level of risk from structural failure. To this end, DSTO is undertaking a series of structural integrity tests aimed at reducing the cost of maintaining the RAAF F/A-18 A/B Hornet fleet to the required planned withdrawal date. These tests cover, among others, three major areas of the aircraft: the Centre Barrel (CB) that acts as the wing attachment structure, the outer wings including attached missile launchers, and the horizontal stabilators. While aspects of the CB test program (Flaw IdeNtification through the Application of Loading: FINAL) is well documented and has already provided significant savings, work continues on related aspects of the CB's fatigue life. The outer wing program (Hornet Outer Wing StAtic Test: HOWSAT) concentrates on reducing the costs of outer wing inspections and the costs of launcher replacements (LAU-7 lifE Extension Program: LEEP). Finally, the horizontal stabilators and other flight control surface (Canadian/Australian Flight control surface Evaluation: CAFÉ) collaborative program with the Canadians is aimed at reducing the rejection rate of control surfaces due to service damage so as to allow currently rejected items to return to service and existing in-service items to remain in-service longer. This paper presents a brief description of each of these test programs and summarises the gains that have been or are likely to be achieved. This work is aimed at satisfying the intent of Defence's Strategic Reform Program (SRP) whilst ensuring the safe operation of the aircraft is not compromised.
... White et al. (2005) used a probabilistic fracture approach to derive the equivalent pre-crack size (EPS), which is also based on the back-extrapolation method. Molent et al. (2006) used a back projection of the experimental crack growth curve to time zero to derive the EPS for Al 7050. The major problem using the back-extrapolation method is that the obtained EIFS seems to be dependent on stress level (Moreira et al. 2005). ...
The loss of strength in a structure as a result of cyclic loads over a period of life time is an important phenomenon for the life-cycle analysis. Service loads are accentuated at the areas of stress concentration, mainly at the connection of components. Structural components unavoidably are affected by defects such as surface scratches, surface roughness and weld defects of random sizes, which usually occur during the manufacturing and handling process. These defects are shown to have an important effect on the fatigue life of the structural components by promoting crack initiation sites. The value of equivalent initial flaw size (EIFS) is calculated by using the back extrapolation technique and the Paris law of fatigue crack growth from results of fatigue tests. We try to analyze the effect of EIFS distribution in a multiple site damage (MSD) specimen by using the extended finite element method (XFEM). For the analysis, fatigue tests were conducted on the centrally-cracked specimens and MSD specimens.
A unified model based on CTOD is proposed to calculate the growth rate of physically small crack (PSC) and long crack (LC). Firstly, an in-situ SEM testing under the single overload condition is performed to reveal that CTOD could be the unique driving parameter for fatigue crack growth (FCG). Then, a unified FCG model is established based on the modified CTOD formula which considers the main physical mechanisms of small crack effect. Additionally, a theoretical equation of the transition crack length from PSC to LC is given. Finally, several datasets of different materials are used to validate the model.
Management of corrosion, and repair and restoration of corrosion‐affected structures pose a daunting challenge to the aircraft industry. This paper presents analytical studies to examine and quantify the effects of corrosion of Al-alloys on the fatigue life of aircraft structures. Two scenarios are considered: (i) fatigue of a pre-corroded material and (ii) fatigue in a corrosive environment. The corrosion damage is idealized using standard crack models, and cycle-by-cycle fatigue crack growth analysis is carried out for an aircraft horizontal stabilizer under spectrum loading conditions. A few aircraft operational scenarios are considered, and fatigue life calculations presented. The zone which experiences 18% lower stress than the maximum stress zone is shown to turn fatigue critical if vulnerable to corrosion. The results point to the risk posed by corroded zones if missed while focusing attention on high stress zones. The computations indicate that an exposure of even 25% of operational life to corrosive environment can reduce life by 40-55%. The study quantifies the significance of corrosion while arriving at design safe life, remaining useful life and maintenance intervals.
The lifting lug is one of the most important structures of aerial bomb, which mainly bears the variable amplitude cyclic loading during the working process. In this paper, the failure analysis of several lifting lugs which failed in fatigue test was carried out. Firstly, through the mechanical analysis, fatigue cumulative damage analysis and fracture surface analysis of the lifting lug structure, it was determined that the fracture failure was not caused by the issue of structural design, but by the Al2O3 inclusion defect in the casting process. Next, the crack source defect was equivalent to the initial crack, and the fatigue full-life was predicted by the method of fatigue crack growth (FCG). The FCG process was divided into two stages: small crack growth stage and long crack growth stage for life prediction respectively. Finally, the validity of this method was verified by comparing with the experimental results, and it was suggested to adopt advanced lifting lug casting and detection technology to prevent similar faults.
Strength reduction in structures like aircraft could be resulted in cyclic loads over a period of time and is an important factor for structural life prediction. Service loads are emphasized at the regions of stress concentration, mostly at the connection of components. The initial flaw prompting the service life was expected by using the equivalent initial flaw size (EIFS) which has been recognized as a powerful design tool for life prediction of engineering structures. This method was introduced 30 years ago in an attempt to study the initial quality of structural details. In this paper, the prediction of life based on fracture mechanics in riveted joints has been addressed through the concept of EIFS. For estimation of initial crack length by EIFS, an extrapolation method has been used. The EIFS value is estimated using the coefficient of cyclic intensity (ΔK) and using the cyclic integral (ΔJ), and the results are compared with each other. The simulation results show that if the coefficient of tension has been used in the EIFS estimation, which is based on the Paris law, the EIFS value will be dependent on the loading domain, while the use of the J-cyclic integral in the EIFS decreases its dependence on the load domain dramatically.
The National Research Council of Canada (NRC) is currently reviewing and assessing the airframe digital twin (ADT) framework being developed by the United States Air Force (USAF). The goal is to investigate the adaptability and potential application of the ADT for reducing maintenance cost and maximize availability of the existing and future fleets of the Royal Canadian Air Force (RCAF). The USAF ADT framework is based on a probabilistic and prognostic individual aircraft tracking approach, which intends to improve the current individual aircraft tracking (IAT) program by quantifying and updating the uncertainties of some IAT parameters in airframe fatigue life assessment. This paper presents the results from recent work at NRC, including: (1) a review and evaluation of the digital twin and digital thread concepts, especially the USAF ADT framework, methods/tool, (2) a brief survey of structural lifing methods and IAT systems of selected RCAF aircraft, (3) a feasibility and adaptability study of the ADT to RCAF aircraft, and (4) the development of NRC ADT technologies, including Bayesian updating algorithms and a demonstration case being developed based on a CF-188 full-scale component test. In conclusion, the NRC review and assessment show that the USAF ADT framework can be adapted to support the RCAF fleets that are managed using IAT-based programs. The NRC models and tools developed from previous projects can be expanded to serve as the core of an ADT framework that can be implemented for RCAF fleets. Some short-term and long-term benefits are identified and discussed in this paper for future research and application.
The airframe digital twin (ADT) framework is a potential game-changing fleet management concept recently proposed by the United States Air Force to allow proactive and cost-effective decisions on an individual aircraft basis. The National Research Council of Canada is currently demonstrating the ADT framework using a CF–188 full-scale component test to assess the adaptability of this approach for Royal Canadian Air Force (RCAF) fleets. An in-house analysis tool is being developed to perform quantitative risk assessment (QRA) based on the Bayesian inference method using individual aircraft tracking and non-destructive inspection data. The modular components of the ADT tool, currently being validated, include load and crack size distribution updating, material initial discontinuity state, residual stress effects, load transfer functions, crack tip stress intensity factor calculations, and crack growth predictions. Test cases analysed to verify and validate these modules showed the benefits of the Bayesian updating approach for performing QRA with inputs that are initially scarce and become less uncertain throughout the service life of the aircraft. Short-term benefits expected from the application of the ADT approach in the RCAF fleet management include a better use of the IAT data and an improvement in fatigue life estimation. In the longer term, a higher return on investment is foreseen in terms of improved life cycle management, increased fleet availability, and reduced total fleet ownership costs.
Fatigue strength and crack propagation behavior of fine particle peened A7075 aluminum alloy was investigated. Residual stress due to fine particle peening treatment was about -350 MPa at the surface and gradually declined inside and disappears at about 80 μm from the surface. The fatigue strength at 10⁷ cycles of the fine particle peened specimen was 1.3 times larger than that of the unpeened specimen. The crack propagation behavior was also investigated under three kinds of stress ratios. The displacement distribution around the crack tip was measured in detail by the digital image correlation method to determine the effective stress intensity factor range and crack tip opening stress. Fine particle peeing contributes to suppressing the crack opening especially when the crack length is small. It was also clarified that the retardation effect of crack propagation by the fine particle peening treatment is remarkable when the stress ratio is small. If the crack starts to open, the crack opening ratio is almost the same as the unpeened condition and this means that the effective stress intensity factor range can be calculated from the crack opening displacement. When the crack propagation rates are arranged by the effective stress intensity factor range, all data collapse into a single narrow scatter band. Therefore, the effective stress intensity factor range dominates the surface crack propagation rate, even when the material is subjected to fine particle peening treatment.
When the linear elastic fracture mechanics-based approaches are used to predict the fatigue life of welded joints, initial crack size is a key point, which eventually affects the accuracy of total fatigue life prediction. Meanwhile, the life prediction process under random loading is complicated. In this paper, a novel method is proposed to determine the initial crack size, which is based on the results of back-extrapolation approach. The proposed method expresses the stress intensity factor, and the boundary between crack initiation and propagation period is taken into consideration. Based on the proposed method, deterministic total fatigue life can be obtained with fewer tests and less cost. In addition, the concept of equivalent crack size and its calculation model are proposed to reduce the complexity of the calculation process of fatigue life prediction under random loading, and model uncertainty is included into the prediction model of probabilistic fatigue life based on equivalent crack size. It is feasible, which has been verified, to take the influence of stress level into account when determining the initial crack size. Meanwhile, the proposal of equivalent crack size simplifies the calculation process of probabilistic fatigue life, and the consideration of model uncertainty is more conducive to assess the safety and reliability of the materials or structures.
This constitutes the lecture notes for the subject "Damage Tolerance and Airworthiness". It focuses on metal rather than comp[osite airframes
Soft multilayer structures have broad applications in transient electronics. Strain-mismatch-induced fracture is key in achieving physical transiency. Here, swelling-mismatch-induced fragmentation of physically transient electrodes is studied. The fragment size of the electrode layer as a function of initial defect distribution is investigated. The average fragment size is predicted and verified by a combination of experimental and FEM analysis. It is found that only large defects initiate fragmentation; this concept can be used to control disintegration of physically transient electronics by means of materials and design, and can be extended to study transiency of soft multilayer structures.
A probabilistic approach for predicting the economic life of an aircraft fleet is proposed with variation in load spectrum and structural property taken into account. Specimens of TA15M titanium alloy were fatigue tested under three individual load spectra of different damage severities. By using the fatigue test results, a generic equivalent-initial-flaw-size distribution was obtained, and a stochastic crack growth model was developed including the load spectrum variation and the material crack resistant variation. With the number of cracks exceeding the economic repair limit as the economic life criteria, a simple expression was derived for the probability of crack exceedance.
Updated version of the MAE4408 Lecture Notes covering topic in Damage Tolerance, Fatigue crack growth, composite repairs, cubic rule, fracture mechanics, etc
Flaw tolerance design absorbs the characteristics of helicopter and is applied in the design of it. The methods to get the flaw tolerance value are not definite; thus, this paper presented its testing methods. The values of three defects were tested by fatigue limit method and computed by finite element method and Y. Murakami function. The results show that the flaw tolerance values of three defects are essentially the same and lower than that of the threshold of long crack. That means it is relatively dangerous to use the value of threshold of long crack. The flaw tolerance values calculated by the two methods are similar, and the values computed by Y. Murakami function are slightly lower than that by finite element method.
This paper presents a nonlinear stability analysis of piles under bilateral contact constraints imposed by a geological medium (soil or rock). To solve this contact problem, the paper proposes a general numerical methodology, based on the finite element method (FEM). In this context, a geometrically nonlinear beam-column element is used to model the pile while the geological medium can be idealized as discrete (spring) or continuum (Winkler and Pas-ternak) foundation elements. Foundation elements are supposed to react under tension and compression, so during the deformation process the structural elements are subjected to bilateral contact constraints. The errors along the equilibrium paths are minimized and the convoluted nonlinear equilibrium paths are made traceable through the use of an updated Lagrangian formulation and a Newton-Raphson scheme working with the generalized displacement technique. The study offers stability analyses of three problems involving piles under bilateral contact constraints. The analyses show that in the evaluation of critical loads a great influence is wielded by the instability modes. Also, the structural system stiffness can be highly influenced by the representative model of the soil.
The text introduces the topic of fracture mechanics and fatigue crack growth and discusses the different tools needed for design and aircraft sustainment.
Fatigue management is generally well understood as reflected in Aircraft Structural Integrity Management Plans, which in some cases considers environmental degradation prevention, however limited provision beyond find and fix exists for corrosion repair. Thus the repair of corrosion can be a major through life cost driver and an aircraft availability degrader. This find and fix approach exists largely because tools are too immature to accurately assess the structural significance of corrosion when it is detected. This work aims to provide a crack growth basis for the justification of allowing detected pitting corrosion to remain in service for a limited period.
How to assess initial fatigue quality and crack growth rate rapidly and economically is the key of durability investigation.At present,experimentation is used to assess durability,which is very costly and time-consuming.Performance degradation curve includes a lot of information about fatigue failure.Based on the tests for specimens with one rivet hole respectirely,a new method of determining initial fatigue quality and crack growth rate with performance degradation curves of specimens are presented in the paper.According to the test results and theoretical derivation,the relationship of crack length with loading cycle is established.Then,the equivalent initial flaw size(EIFS)values are calculated and fatigue crack growth rates are estimated by using exponential fitting technique.The applicability and validity of the method are verified with theoretical computation of fracture limit finally.
Quantitative fractography techniques have been in use at the Aeronautical Research Laboratory (ARL), Melbourne, Australia, for more than 15 years, and they have been developed into a specialized facility for deriving crack growth histories from fracture surfaces. This paper describes current ARL activities in the use and further development of quantitative fractographic techniques and the specialized facilities employed to derive and process data from fracture surfaces observed by both scanning electron microscopy and optical microscopy. The results obtained are illustrated by reference to case histories of defects in components from service aircraft, from full-scale component tests, and from laboratory test samples. Procedures for minimizing or overcoming some of the difficulties associated with interpretation of fracture surface markings are discussed. The paper also describes the way in which fracture mechanics concepts need to be used in conjunction with fracture surface analysis to achieve a correct understanding of the crack growth history.
The cold-expansion of fastener holes is now used widely in aerospace manufacturing to introduce beneficial residual stresses around the hole circumference, retarding the growth of fatigue cracks which form at the hole, and providing substantial benefits in terms of fatigue life extension. A research program at ARL recently investigated the growth of fatigue cracks from cold-worked holes in thick-section aluminium alloy aircraft components, and the effect of having pre-existing cracks at the time of cold expansion. This paper summarises the results of this program, particularly the determination of fatigue crack growth rates using fracture surface marking analysis (quantitative fractography). The paper also describes a model developed to predict the residual stresses and their influence on crack growth rate; comparison of the theoretical and experimental results demonstrates that the model provides useful predictions of critical crack length for cracks from cold-expanded holes, and correctly predicts the crack growth rate characteristics observed. It also permits the asymmetric crack shapes observed at cold-worked fastener holes to be better understood.
During the inspection of the FT488/2 Bare Bulkhead FatigueTest specimen after 79 blocks of applied loading, cracking was found in several wing-attachment hole aft edges. Each of the cracked regions of the holes was cut from the bulkhead, sixteen of the cracks were broken open and the exposed crack surfaces were analysed. This analysis revealed several interesting aspects of fatigue crack growth in this bulkhead. These included the nature of the most (in this case) significant initiating flaws, the type (compared to thick thick 7050 plate material) and effect of the microstructure on the growth of these cracks and the relative growth rates of these cracks including estimates of the number of programs to failure. DGTA
Preface 1. Introduction and overview Part I. Cyclic Deformation and Fatigue Crack Initiation: 2. Cyclic deformation in ductile single crystals 3. Cyclic deformation in polycrystalline ductile solids 4. Fatigue crack initiation in ductile solids 5. Cyclic deformation and crack initiation in brittle solids 6. Cyclic deformation and crack initiation in noncrystalline solids Part II. Total-Life Approaches: 7. Stress-life approach 8. Strain-life approach Part III. Damage-Tolerant Approach: 9. Fracture mechanics and its implications for fatigue 10. Fatigue crack growth in ductile solids 11. Fatigue crack growth in brittle solids 12. Fatigue crack growth in noncrystalline solids Part IV. Advanced Topics: 13. Contact fatigue: sliding, rolling and fretting 14. Retardation and transients in fatigue crack growth 15. Small fatigue cracks 16. Environmental interactions: corrosion-fatigue and creep-fatigue Appendix References Indexes.
This paper describes a method, the Equivalent Initial Quality Method, of quantifying the quality of fastener holes. This quantification is accomplished by representing the imperfections that are either inherent in a material or introduced during the mmanufacturing of a structural component with a fatigue crack of a particular size and shape. This initial quality representation can be used in a crack-propagation analysis to determine the life of the structural component. The potential applications (e. g. , determination of required inspection intervals and maintenance and modification schedules, use in design, assessment of quality of manufacturing procedures, etc. ), as well as the possible limitations (e. g. , sensitivity of method to stress level, material, etc. ), of the Equivalent Initial Quality Method are discussed.
A statistical investigation of the fatigue crack propagation process was conducted. Sixty-eight replicate constant amplitude crack propagation tests were conducted on 2024-T3 aluminum alloy. The following distributions were considered: two-parameter normal distribution, three-parameter log-normal distribution, three-parameter Weibull distribution, two-parameter gamma distribution, three-parameter gamma distribution, the generalized three- parameter gamma distribution, and the generalized four-parameter gamma distribution. From the experimental data, the distribution of N as a function of crack length was best represented by the three-parameter log-normal distribution. Six growth rate calculation methods were investigated and the method which introduced the least amount of error into the growth rate data was found to be a modified secant method. Based on the distribution of da/dN, which varied moderately as a function of crack length, replicate a vs. N data were predicted. This predicted data reproduced the mean behavior but not the variant behavior of the actual a vs. N data.
The equivalent initial flaw size (EIFS) concept was developed nearly 30 years ago in an attempt to account for the initial quality, both manufacturing and material properties, of a structural detail prone to fatigue cracking. Widespread use of this concept has been limited due to the large amount of test data required to develop a reliable EIFS distribution. In this effort, an EIFS distribution was determined for four types of flat, production like transport aircraft fuselage skin joints loaded by remote tension. Two crack growth prediction codes, AFGROW and FASTRAN, were used to not only develop the EIFS but also to compare the crack growth algorithms in each code. The EIFS calculations are prone to compounding errors in the crack growth analysis due to the changing stress intensity factor solutions and stress fields as the crack gets longer. Thus, only including EIFS calculations for mechanically small cracks, crack lengths less than 1.27 mm, results in a mean EIFS of 18.0 μm with a standard deviation of 3.78 μm.
Abstract— Metal and glass-bead peening treatments, widely used throughout the aircraft industry to enhance the fatigue performance of many steels and titanium alloys, are now being routinely applied to high-strength aluminium-alloy components. This paper describes the effects of peening on the fatigue life of 7050 aluminium alloy material, which is representative of alloys used for many components in modern military aircraft. Using simulated service loading, two proposed peening/re-peening procedures were evaluated and compared with both the original peened surface and a simple hand-polished surface. The results show that optimisation of peening parameters to reduce surface damage can provide a substantial improvement in fatigue life over both the original peening treatment and the polished surface treatment, however, poor control of peening procedures, or unnecessary “overpeening” can lead to a relatively poor fatigue life. For re-peened surfaces, a procedure incorporating a polishing step, designed to repair any damage from the severe peening applied initially, gave the best fatigue performance. Results are discussed in relation to the stability of the residual surface stresses under fatigue loading, the surface roughness, and the number and types of defects introduced by the peening treatments.
The Australian Defence Science and Technology Organisation (DSTO) is currently assessing the fatigue life of the F/A-18 aircraft amongst other activities. Projects include full-scale testing as well as coupon test programs.One of the coupon test programs recently completed at DSTO was undertaken to evaluate fatigue performance under a variety of aircraft operational flight profiles. The program consisted of six test phases representing four different reference stress levels with the fifth phase designed to evaluate the effect of overload spikes on fatigue life and the sixth phase designed to evaluate material batch effects. While six loading sequences or spectra were evaluated in the test program only two were tested in all five phases.The coupons were manufactured from the aluminium alloy 7050-T7451 and were representative of the material and geometry of a typical fatigue critical part of the F/A-18 aircraft structure. A minimum of five specimens were tested for at least the two spectra in each of the first four phases. A minimum of three specimens was used in phases five and six. Consequently, more than 120 specimens in total were tested and 50 examined fractographically in this test program.This paper presents a summary of both the total life results as well as the crack growth rates for these specimens. Other aspects considered include the influence of the surface finish of the coupons and the identification of the nature of the crack initiation. This test program allowed two quite different spectra to be compared at several reference stress levels to determine the relative severity of each. Also sufficient numbers of specimens were tested to allow trends and scatter in the data to be fully evaluated.
Fatigue tests have been carried out on mild steel, aluminium alloy and copper sheet specimens containing a small central slit. Measurements of the growth of the fatigue cracks initiated by the slit were made as the test proceeded. In some of the mild steel specimens a plastic zone was visible around the growing crack. Measurements of the plastic zone were made whenever possible and these showed that a state of geometrical similarity existed between the crack length and plastic zone dimensions.For low stresses the crack growth was sometimes erratic, but while the growth was steady and the overall crack length less than about one eighth of the specimen width it was found that the rate of growth was proportional to the current crack length. The effect of mean stress is discussed.
The foundation for the structural airworthiness of many military aircraft is an airframe fatigue test conducted using representative loading. Traditionally, the results from the fatigue test are scaled by empirical scatter factors to derive a safe economic life of the airframe aligned to an acceptable probability of structural failure. This paper illustrates a relatively novel approach to the estimation of the life of the fleet, utilising a probabilistic approach, and considering the wing attachment bulkheads of a specific fighter aircraft. Probabilistic fracture mechanics is used as the basis of the analysis and where possible, all relevant data, including crack growth and its variability, have been collected directly from the aircraft's fatigue test supplemented by laboratory coupon data. The example uses available initial crack size data and associated crack growth rates to estimate the stress levels at critical locations. The benefit and accuracy of the fleet aircraft fatigue monitoring system is also considered. The analysis attempts to include and quantify the effect of all parameters that significantly influence the growth of cracks in metallic airframes, and illustrates the derivation of a probability of failure versus flight hours. The paper also identifies deficiencies in the data required to fully populate the model, and describes current test and teardown activities which are intended to provide information about the defect types which might affect failure of fleet aircraft.
This paper examines the fatigue crack growth histories of a range of test specimens and service loaded components and concludes that in all cases, the crack growth shows, as a first approximation a linear relationship between the log of the crack length or depth and the service history (number of cycles). These cracks have grown from; semi- and quarter elliptical surface cuts, holes, pits and inherent material discontinuities in test specimens, fuselage lap joints, welded butt joints, and complex tubular jointed specimens and include cracks grown under uniaxial and biaxial loading. The implications of this exponential growth are discussed.
This paper describes a model developed for predicting residual stresses and crack growth in residual stress fields, and the application of the model to crack growth from cold-worked fastener holes in thick section aircraft components. Comparison with experimental results demonstrates that the model can provide useful predictions of critical crack length, and a capability for correctly predicting the maxima and minima in the crack growth rate for cracks from cold-expanded holes. It also permits the observed asymmetry in cracking from cold-worked fastener holes to be better understood.
AVD research into material factors likely to affect F/A-18 fatigue life has highlighted the critical role played by surface condition in determining the service fatigue life of aircraft structure. This report presents the results of a fatigue coupon test program. The primary purpose was to obtain results from coupons with a glass bead peened surface condition typical of some regions of the critical structure of the F/A-18 aircraft. Another surface condition that could possibly initiate critical cracks was compared to these results. These specimens were loaded with a representative wing root-bending spectrum derived from the F/A-18 FT488/2 centre barrel bulkhead fatigue test. Several peak stress levels were used. The coupons were representative of the material and geometry typical of a structural detail that has been found to be fatigue-critical in the 7050T7451 high strength aluminium alloy wing carry through bulkheads. The spectrum used had additional marker loads added to aid quantitative fractography. These marker loads are briefly discussed. Following the tests, quantitative fractography was used to produce crack growth curves for each of the fatigue specimens. This allowed a detailed interpretation of the crack growth to be made, including a measure of the severity of the flaws from which the fatigue cracks initiated. In addition to an examination of the effect of the flaws, it was found that the peening produced a retarding effect on the early part of the crack growth. The extent of this effect was examined by comparison to previously examined etched specimens. These comparisons are reported. This report presents the results of a fatigue coupon test program whose primary purpose was to obtain results from coupons treated with a glass bead peened surfaces typical of some regions of critical F/A-18 aircraft structure. A spectrum representative of RAAF's F/A-18 fleet fatigue usage was used. The coupons were representative of the material and geometry of a structural detail that has been found to be fatiguecritical in the 7050T7451 high strength aluminium alloy wing carry through bulkheads. Following the tests, quantitative fractography was used to produce crack growth curves for each of the fatigued specimens. This report describes the surface condition being examined, test spectrum, test methods, test results and examines ways of interpreting the crack growth curves to establish a measure of the severity of the flaws from which the fatigue cracks initiated. ASI
This report presents the results of a fatigue coupon test program. The primary purpose was to obtain results from coupons with a surface condition typical of some Ion Vapour Deposited Aluminium alloy (IVD) coated regions of the critical structure of the F/A-18 aircraft. Other surface conditions that could possibly initiate critical cracks are not considered here. Air Vehicles Division (AVD) research into material factors likely to affect F/A-18 fatigue life has highlighted the critical role played by surface condition in determining the service fatigue life of aircraft structure. This report addresses the etched surface finish likely to be found beneath IVD coated F/A-18 aluminium alloy 7050T7451 components: etched surfaces typical of those which have been observed on OEM IVD coated components. These specimens were loaded with a representative wing root-bending spectrum derived from the F/A-18 FT488/2 wing carry through bulkhead fatigue test. Several peak stress levels were used. The coupons were representative of the material and geometry typical of a structural detail that has been found to be fatigue-critical in the 7050T7451 high strength aluminium alloy wing carry through bulkheads. The spectrum used had additional marker loads to aid quantitative fractography. These marker loads are discussed. Following the tests, quantitative fractography was used to produce crack growth curves for each of the fatigue specimens and to examine ways of interpreting the crack growth curves to establish a measure of the severity of the flaws from which the fatigue cracks initiated. This presents presents the results of a fatigue coupon test program. The primary purpose was to obtain results from coupons with a surface condition typical of some regions of the critical structure of the F/A-18 aircraft. A spectrum representative of RAAF.s F/A-18 fleet fatigue usage was used. The coupons were representative of the material and geometry of a structural detail that has been found to be fatigue-critical in the 7050T7451 high strength aluminium alloy wing carry through bulkheads. Following the tests, quantitative fractography was used to produce crack growth curves for each of the fatigue specimens. This describes the surface condition being examined, test spectra, test methods, test results and examines ways of interpreting the crack growth curves to establish a measure of the severity of the flaws from which the fatigue cracks initiated. ASI
DSTO research into material factors likely to affect F/A-18 fatigue life has highlighted a number of concerns about the fatigue variability of the 7050 thick section plate and the effect that the surface condition has on service fatigue crack initiation. This report presents the results of a fatigue coupon test program, which tested samples cut from three different 7050 plates. The test coupons were drawn from two previously tested Y488 bulkheads that had the original aircraft manufacturers surface finish intact, and from one plate that had been purchased for coupon testing by DSTO. The surfaces of the coupons made from the DSTO plate were etched to simulate the surface on the two Y488 bulkheads, which was preserved on the coupons cut from these bulkheads. All specimens were loaded with a representative wing root-bending spectrum derived from the F/A-18 FT488/2 bulkhead fatigue test. Several peak stress levels were used to test the low Kt coupons cut from the Y488 bulkheads, and a single stress level was tested with specimens from another DSTO plate. The spectrum used had additional marker loads added to aid quantitative fractography. These marker loads are briefly discussed. Following the tests, quantitative fractography was used to produce crack growth curves for each of the fatigued specimens. This allowed a detailed interpretation of the crack growth to be made, including a measure of the severity of the flaws from which the fatigue cracks initiated. Comparisons between a previously tested 7050 plate, the plate purchased for the coupon testing for this report, and the coupons cut from the two Y488 bulkheads were made. It was found that the crack growth rates and the discontinuities from which the cracking initiated were very similar and they could be characterised by the way that cracking grew from them. This is the third in a series of papers that examine material factors likely to influence the fatigue life of F/A-18 structure. Work leading up to these papers has highlighted a number of concerns about the fatigue variability of the 7050 aluminium alloy thick section plate and the effect that the surface condition of finished components has on service fatigue crack initiation and life. This examines examines a series of fatigue test specimens that were cut from three different 7050 plates, including two aircraft manufacturer.s plates. Following the tests, quantitative fractography was used to produce crack growth curves for each fatigue specimen allowing a detailed interpretation of the crack growth to be made, including a measure of the severity of the flaws from which the main fatigue cracks initiated. Comparisons between previously tested 7050 plate, and the three plates tested here were made, with the finding that the crack growth rates and the flaws from which the cracking initiated were very similar to those previously examined. DGTA
Probabilistic fracture prediction based on aircraft specific fatigue test data
- P White
- S Barter
- L Molent
White, P., Barter, S. and Molent, L. (2002) Probabilistic
fracture prediction based on aircraft specific fatigue test data.
Proc. 6 th Joint FAA/DoD/NASA Aging Aircraft
conference-San Diego. Sept 16-19, 2002.
The Canadian and Australian F/A-18 international follow-on structural test project Final report for the component fatigue test Fractographic analysis in support of a structural life assessment Modelling of residual stresses and fatigue crack growth at cold-worked fastener holes
- D L Simpson
- N Landry
- J Roussel
- L Molent
- A D Graham
- N N Schmidt
- S A Barter
- D D Bohret
- A J Green
- M I Houston
- M G N Stimson
- R Bayles
- M Roth
- E Ferko
Simpson, D. L., Landry, N., Roussel, J., Molent, L., Graham, A. D. and Schmidt, N. (2002) The Canadian and Australian F/A-18 international follow-on structural test project. Proc. ICAS 2002 Congress, Toronto, Canada. 26 Athiniotis, N., Barter, S. A., Bohret, D. D., Green, A. J., Houston, M. I. and Stimson, M. G. (2003) Final report for the component fatigue test of a F/A-18 centre fuselage FS488 bulkhead -FT488/2. DSTO-TR-0948, Melbourne, Australia. 27 Goldsmith, N., Bayles, R., Roth, M. and Ferko, E. (2004) Fractographic analysis in support of a structural life assessment. Institute of Materials Engineering Australasia Ltd. Int. Conf. on Failure Analysis and Maintenance Technologies, Brisbane, Australia. 28 Clark, G. (1991) Modelling of residual stresses and fatigue crack growth at cold-worked fastener holes. Fatigue Fract. Eng. Mater. 14, 579–589.
Flaw identification through the application of loads: teardown of the centre barrel from CF-18 188747. DSTO-TR-1660 The F/A-18 fatigue crack growth data compendium. DSTO-TR-1677
- B Dixon
- L Molent
- S A Barter
- V L Mau
- Q Sun
- A J Green
Dixon, B., Molent, L., Barter, S. A. and Mau, V. (2004) Flaw identification through the application of loads: teardown of the centre barrel from CF-18 188747. DSTO-TR-1660, Melbourne, Australia. 23 Molent, L., Sun, Q. and Green, A. J. (2005) The F/A-18 fatigue crack growth data compendium. DSTO-TR-1677, Melbourne, Australia. 24 Laub, W. F., Jr. (2000) White paper ST16 fatigue test—detailed spectra description. Boeing Informal Memo E0098-F18-152-QR, Boeing, St. Louis, USA.
Overview of the F/A-18 Bft fuselage combined manoeuvre and dynamic buffet fatigue and residual strength testing
- S Barter
- L Molent
- N Landry
- P Klose
- P White
Barter, S., Molent, L., Landry, N., Klose, P. and White, P.
(2003) Overview of the F/A-18 Bft fuselage combined
manoeuvre and dynamic buffet fatigue and residual strength
testing. Proc. Australian International Aerospace Congress, Brisbane
Aust., July 29-1 Aug 2003.
Comparison of two F/A-18 aluminium alloy 7050-T7451 bulkhead coupon fatigue tests
- L Molent
- S A Barter
- A J Green
Molent, L., Barter, S. A. and Green, A. J. (2004) Comparison of
two F/A-18 aluminium alloy 7050-T7451 bulkhead coupon
fatigue tests. DSTO-TR-1646, Melbourne, Australia.
Flaw identification through the application of loads: teardown of the centre barrel from CF-18 188747
- B Dixon
- L Molent
- S A Barter
- V Mau
Dixon, B., Molent, L., Barter, S. A. and Mau, V. (2004) Flaw
identification through the application of loads: teardown of the
centre barrel from CF-18 188747. DSTO-TR-1660,
Melbourne, Australia.
The F/A-18 fatigue crack growth data compendium
- L Molent
- Q Sun
- A J Green
Molent, L., Sun, Q. and Green, A. J. (2005) The F/A-18 fatigue
crack growth data compendium. DSTO-TR-1677, Melbourne,
Australia.
The fractographical comparison of F/A-18 aluminium alloy 7050-T7451 bulkhead representative coupons tested under two service spectra and two stress levels
- R A Pell
- L Molent
- A J Green
Pell, R. A., Molent, L. and Green, A. J. (2004) The
fractographical comparison of F/A-18 aluminium alloy
7050-T7451 bulkhead representative coupons tested under two
service spectra and two stress levels. DSTO-TR-1629,
Melbourne, Australia.
F/A-18 FS488 bulkhead fatigue coupon test program-Part 2
- L Molent
- R Pell
- A Mills
Molent, L., Pell, R. and Mills, A. (2003) F/A-18 FS488
bulkhead fatigue coupon test program-Part 2.
DSTO-TR-1464, Melbourne, Australia.
White paper ST16 fatigue test-detailed spectra description. Boeing Informal Memo E0098-F18-152-QR
- W F Laub
- Jr
Laub, W. F., Jr. (2000) White paper ST16 fatigue test-detailed
spectra description. Boeing Informal Memo
E0098-F18-152-QR, Boeing, St. Louis, USA.
Final report for the component fatigue test of a F/A-18 centre fuselage FS488 bulkhead - FT488/2
- N Athiniotis
- S A Barter
- D D Bohret
- A J Green
- M I Houston
- M G Stimson
Athiniotis, N., Barter, S. A., Bohret, D. D., Green, A. J.,
Houston, M. I. and Stimson, M. G. (2003) Final report for the
component fatigue test of a F/A-18 centre fuselage FS488
bulkhead -FT488/2. DSTO-TR-0948, Melbourne,
Australia.
Fractographic analysis in support of a structural life assessment
- N Goldsmith
- R Bayles
- M Roth
- E Ferko
Goldsmith, N., Bayles, R., Roth, M. and Ferko, E. (2004)
Fractographic analysis in support of a structural life assessment.
Institute of Materials Engineering Australasia Ltd. Int. Conf. on
Failure Analysis and Maintenance Technologies, Brisbane, Australia.
FS488 bulkhead fracture surface preliminary fractographic examination. DSTO Defect assessment and failure analysis Report M45/90
- S A Barter
Barter, S. A. (1990) FS488 bulkhead fracture surface preliminary
fractographic examination. DSTO Defect assessment and
failure analysis Report M45/90, Melbourne, Australia.
The Canadian and Australian F/A-18 international follow-on structural test project
- D L Simpson
- N Landry
- J Roussel
- L Molent
- A D Graham
- N Schmidt
Simpson, D. L., Landry, N., Roussel, J., Molent, L., Graham,
A. D. and Schmidt, N. (2002) The Canadian and Australian
F/A-18 international follow-on structural test project. Proc.
ICAS 2002 Congress, Toronto, Canada.
White paper ST16 fatigue test-detailed spectra description
- W F Laub