Conference Proceedings

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1 CzechTourism.com VAL rd International conference on material and component performance under variable amplitude loading Conference Proceedings March 23 26, 2015 Prague, Czech Republic

2 ISBN

3 Contents Fatigue crack growth approach for fleet monitoring Bastien Bayart Load interaction effects in propagation lifetime of railway axles Stefano Beretta A method for quantitative fatigue fracture surface analysis Philippe Feraud Calculations of fatigue life of different materials under loadings with variable amplitudes Melanie Fiedler Investigations on the cumulative fatigue life for an austenitic stainless steel AISI 304L used for Pressure Water Reactors: application of a double linear damage rule Antoine Fissolo AFGROW crack growth life prediction software James A. Harter Development of fatigue damage estimation to gearbox shafts Jan Křepela Fatigue life under multiaxial fatigue spectrum Yves Nadot Butt-joints of helicopters tail-boom in-service fatigue cracking under variable loading amplitude Andrey Shanyavskiy Why variable amplitude loading? A key for lightweight-structural durability design Cetin Morris Sonsino

4 3 rd International Conference on Material and Component Performance under Variable Amplitude Loading, VAL 2015 Fatigue crack growth approach for fleet monitoring Bastien Bayart a 1, Joseph Despujols a, Pierre Madelpech a a DGA Aeronautical Systems, 47 rue Saint Jean - BP Balma Cedex, France Abstract Military aircraft are subject to unpredictable variable amplitude loadings. Fighter aircraft structures are essentially sized by operational loads, which vary widely according to the missions flown by the aircraft. For safety reasons, it is necessary to be able to estimate each aircraft's actual fatigue "consumption" relative to its potential. For this purpose, most French military aircraft are equipped with load monitoring systems (flight parameter recorder or g-counters). These systems give direct or indirect access to the service loads. The data is processed for each aircraft throughout its lifetime. The cumulative fatigue damage is calculated at various points of the structure pointed out as being critical, notably during full-scale fatigue tests. This information enables the Armed Forces to optimize the fleet management in terms of structure potential. Also, for fleet life-extension purposes and usage predictions, the use of more precise damage and crack growth prediction models is a major concern. However, the fatigue consumption is up to now controlled by initiation models while during the fatigue life test and the operational life later, fatigue cracks are usually detected. The initiation models are yet insufficient to cover the entire lifetime. Studies are conducted concerning the use of both initiation and propagation models to control the fatigue consumption. For the aircraft equipped with g-counters with no temporal data, only initiation models can be used to control the crack propagation. The prediction qualities of this method are analyzed. Furthermore, propagation models are investigated for the fleet providing temporal data. Experiments are carried out on CT samples for further analyses on the use of propagation models to predict crack growth The Authors. Keywords: Crack growth, propagation models, fleet monitoring 1. Introduction Aircraft, and especially military ones, are subject to unpredictable variable amplitude loadings. Fighter aircraft structures are essentially sized by operational loads, which vary widely according to the missions flown by the aircraft (combat, cruising, training, airshow display). For safety reasons, it is necessary to be able to estimate each aircraft's actual fatigue "consumption" relative to its potential. For this purpose, most French military aircraft are equipped with load monitoring systems (flight parameter recorder, g-counters and others acquisition systems). These systems give direct or indirect access to the service loads. The data is regularly processed for each aircraft throughout its lifetime. The cumulative fatigue damage is calculated at various points of the structure pointed out as being critical, notably during full-scale fatigue tests. This information enables the Armed Forces to optimize the fleet management in terms of structure potential. Also, for fleet life-extension purposes and usage predictions, the use of more precise damage and crack growth prediction models is a major concern. Military aircraft were historically designed with a safe life philosophy, that is to say designed to demonstrate their entire lifetime with no damage. However, during the fatigue life test and the operational life later, fatigue cracks are usually detected. The initiation models are yet insufficient to cover the entire lifetime. In order to maintain the 1 Corresponding author. address: bastien.bayart@intradef.gouv.fr VAL 2015 Conference proceedings

5 design safety margin, the technical authority introduced the damage tolerance philosophy: cracks are allowed below a given size provided propagation process is well known. This change of philosophy opens prospects in terms of crack propagation control. Indeed, new and more effective monitoring methods are developed. Systems currently in operation on the French Air Force Mirage 2000D and Rafale enable the acquisition of large number of parameters and thus advanced monitoring methods. The use of this information gives access to continuous parameters such as g-accelerations, roll, pitch... This data associated with crack growth models such as PREFFAS or ONERA provide information about the propagation phase. The fatigue potential consumption during the operational life can thus be estimated by combining initiation and propagation models. Studies are conducted concerning the use of both initiation and propagation models to control the fatigue consumption. For the aircraft equipped with g-counters with no temporal data, only initiation models can be used to control the crack propagation. The prediction qualities of this method are analyzed. Furthermore, propagation models are investigated for the fleet providing temporal data. At this stage, experiments are carried out on CT samples. In the future, experiments will be carried out on a more realistic geometry close to the spar one. 2. Tests Tests were made on standardized compact tensile specimens CT40 B18 made of 2024A-T351 aluminum alloy. First tests are necessary to determine the material parameters of propagation models and then, complex spectrum are applied to test the models. These kinds of spectrum are the well-known FALSTAFF SC, minitwist, or more specific ALPHAJET inspired from the full-scale fatigue test or a combination of g-acceleration inspired from real M2000 flights. The mechanical properties of 2024A-T351 represent the mean value from three tests on standardized tensile specimens. Table 1 : Mechanical properties of the sheet materials Yield stress Ultimate strength Elongation Material S0.2, MPa Su, MPa e, % 2024A-T Propagation model: PREFASS PREFFAS (PREvision de la Fissuration en Fatigue Aérospatiale) was developed by A.Davy, D.Aliaga, and H.Schaff in 1985 and published in the ASTM in 1988 [1]. This model is based on the crack closure model developed by Elber which realizes a sequential calculation of the crack growth. Each cycle from the load sequence is defined as a stress intensity factor constraint couple (,,, ) corresponding to the minimum and the maximum stresses.,,, Where and are material parameters The main point of this model is the evaluation of the opening point, of each cycle. Its value takes into account the load history. As a consequence, it depends on the overloads and underloads in the load sequence which can create large plastic zone at the crack tip and increase its value or conduct to the reversed plasticity effect, and decrease it. Plus, the original load-time history is used with the original load sequence, but the PREFFAS model doesn t realize a cycle by cycle counting but a rainflow counting Identification of parameters There are 4 parameters to determine in the PREFASS model:,,, which can be found with two tests and the approximation that the Elber parameters and satisfy the equation 1. The first test is a constant amplitude loading with a stress ration of R=0.1 and the second test uses the same stress ratio with an overload (factor =1.7) every 1000 cycles. In Figure 1 are reported tests performed on specimens.

6 1,00E-01 Crack growth rate ( mm / Cycle ) 1,00E-02 1,00E-03 1,00E-04 1,00E-05 1,00E-06 R=0.1 R=0.1 + overload 1000 cycles 3 K ( MPa.m ) 30 Figure 1: Crack growth rate for constant amplitude (CA) loading and CA loading + overload Parameters are obtained from linear regressions with the hypothesis that the two straight lines are parallel. They are presented in Table 2. Table 2 : Linear regressions m C / Area of validity Correlation R= C0.1=3.21 E -8 9 < < R=0.1+ surcharge C0.1+s= 3.65 E < < Delay effect is defined with the ratio below : Yet, So, Which implies : b=0.602,, ,91 1,6 1 1, ,6 1 1,7 0,7.. By definition,..

7 Finally, the PREFASS parameters are: (with CT40B18 Samples of 2024A T351 Aluminium) Table 3 : PREFASS parameters for 2024A T351, 18 mm thickness a b / m E Initiation model Initiation models enable to control the processing damage. In the case of aircraft with temporal flight parameters recorders, the initiation model is based on a unit damage matrix. In practice, the monitoring systems data are treated to know the real load sequence applied to the critical structural points. This load sequence is then used to make a rainflow count. The result gives a matrix which has to be multiplied by the unit damage matrix to determine the damage. Thus, the cumulative damage law is linear. As a consequence, the damage law is linear too. In the case of aircraft equipped with g-counters (with no temporal data), the cumulative damage law is linear too but it is necessary to build an acceleration usage spectrum with the cumulative number of occurrence vs g- level, then to extrapolate and to discretize it. The discretization gives elementary damage by referencing to Wöhler curves or abacus. The total damage is then obtained by cumulating all elementary damage multiplied by the number of cycles. 3. Results 3.1. Results processing For each load listed above, three results are obtained: The damage calculation at a critical point for each sequence; A theoretical crack propagation curve calculated with the PREFASS model; A real crack propagation curve given by the test on the CT sample. The Figure 2 shows results obtained with the FALSTAFF SC and with Mirage 2000 flights loads Crack size (mm) PREFASS test Flights number Crack size (mm) PREFASS Experiment Flights number Figure 2: Propagation curves, PREFASS vs Experiment (Left: FALSTAFF SC Load, Fmax = N) (Right: M2000 Load, Fmax = N) The damage calculation is the basis of the creation of the fatigue index (FI) which is used to control the fatigue life. FI is calculated as follow: 100 _

8 Where E is the classical cumulative damage value calculated at a critical point. The value is found with a rainflow cycle counting multiplied by an elementary damage matrix obtained from Wohler s curve. First, these results let to check the efficiency of the crack propagation model compared to the real one. Then, in practice, the crack propagation is mastered by the use of a propagation index (PI), which represents the severity of the aircraft use. A reference load is defined and crack propagation is calculated with the propagation model. Then, when the temporal data are available, the crack propagation is calculated with the real load and compared to the reference curve. It means PI is not a cumulative index but a comparative one. PI is calculated as follow: 100 _ Where - is the critical number of flights corresponding to the crack critical size minus the detectable crack size; - is the current number of flights read on the reference curve so that. In this study, since the reference curve doesn t exist, it is assumed that the theoretical crack propagation curve represents the reference curve. Values concerning the critical crack size and the detectable crack size are derived from typical structure closed to a spar. Its dimensions are in Figure 3. The critical crack length is about 50 mm and the detectable crack length is about 26 mm. Figure 3: Typical damage on spars The characteristic crack sizes and the corresponding IP values are indicated on the curves below: Figure 4: PI calculation

9 To compare the different indexes, since propagation tests are not carried out with the same maximal value, the same ratio between the maximum value for the crack propagation test and the maximum for the damage calculation is used. Table 4: Maximum values propagation test on CTs (N) for damage calculation (MPa) Alphajet Falstaff SC M M2000_severe MiniTwist The treatment of these values enables to draw the graphs below: Crack length (mm) Alphajet Falstaff sc M2000 M2000_severe MiniTwist FI Figure 5: Crack Length versus FI Crack length (mm) Alphajet Falstaff sc M2000 M2000_severe MiniTwist SC PI Figure 6: Crack Length versus PI

10 The Table 5 summarizes the Figures 5 and 6: Table 5: and for each load from a= 26mm to a=50mm from a= 26mm to a=50mm Alphajet Falstaff SC M M2000_severe MiniTwist Mean Standard deviation Analysis From the results, it can be introduced the inspections frequency of the maintenance scheme to control the crack process. If we want to control the crack propagation with the initiation models, and so the FI indicator, it is necessary to define an FI inspection frequency. Therefore, FI inspection is calculated with the Alphajet full scale fatigue test. In that case, the inspection frequency is: By using the Alphajet full scale fatigue test, In the same way, to control the crack propagation with propagation models, the PI indicator is used. The way PI is defined decrees to have 100/3 33. From these inspection values reported in Figure 7, it seems that IP is more suitable for controlling the crack propagation process. Indeed, crack size dispersion appears when it is controlled with the FI indicator Crack length (mm) Alphajet Falstaff sc M2000 M2000_severe MiniTwist Crack length (mm) Alphajet Falstaff sc M2000 M2000_severe MiniTwist SC FI PI Figure 7: Frequency of inspections, with FI or PI

11 From the Figure 7, it can be noted the values below: Table 6: Crack length inspections, FI versus PI control Crack length (mm) FI inspection Crack length (mm) PI inspection Alphajet Falstaff SC Failure 29.3 M M2000_severe MiniTwist Failure 30.5 Mean Standard deviation Conclusion It has been shown that the use of propagation models is predictive and enables to create an indicator on which it is possible to build a maintenance scheme. The issue still exists concerning the fleet with no temporal data. Therefore, the main goal is to build an equivalent IP to control the crack propagation process. The PREFFAS model, as widely experienced, is well predictive and most of the time conservative in this kind of tests. It is moreover relatively easy to determine the material parameters. Besides, if the use of a fatigue index is essential to follow the structure damaging of a military aircraft by analyzing the real loading spectrum, it has been shown that it is not necessary relevant to predict the propagation time. It can be explained by several reasons: The fatigue index is computed on the uncracked structure. Any dependence of the crack length is not taken into account; The propagation reference is based on the spectrum of the full scale fatigue test. Any effect due to real spectrum is taken into account. No retardation is considered; The initiation physics and the propagation law are not the same and do not follow the same relationship compared to the loads. The exponent in the respective law are not the same (~3 for propagation versus ~4.5 for initiation) It has been shown that the use of PI and so of propagation models are predictive and enable to create an indicator on which it possible to build a reliable maintenance scheme. Considering the differences of the encountered spectra, we can conclude that for this purpose to, the use of monitoring for air-fighter remains a necessity to cover the huge scattering in the usage. The next step will be to propose something for the fleet with no temporal data, but only g-counter and regular computations. To build an equivalent PI, and thus monitor the crack propagation process, the approach will be to make regular computation with partial exceedance numbers. The right period will be determined as a compromise between not too long period to have temporal data but long enough to minimize the influence of extrapolation and spectrum closure. It has been shown that the inspection based on FI are definitively not conservative when the load level is low, compared to the one applied during full scale fatigue test. One mitigation action could be to use as reference a representative spectrum of the current use of the fleet. One study will also be to develop this kind of spectrum from the monitoring data. References [1] A. Davy, D. Aliaga et H. Schaff, «A simple crack closure model for predicting fatigue crack growth under flight simulation loading,» ASTM STP, vol. 982, pp , [2] W. Elber, «The significance of fatigue crack closure,» ASTM STP, vol. 486, pp , 1971.

12 [3] O. Wheeler, «Spectrum loading and crack growth,» Journal Basic Engineering, vol. 94, n 13, pp , [4] P. Watson et B. Dabell, «Statistical aspects of fatigue testing: cycle counting and fatigue damage,» Symposium of the Society of environmental engineers, [5] N. Dowling, «Fatigue failure predictions for complicated stress-strain stories,» University of Illinois, [6] J. Schijve, «The significance of flight-simulation fatigue tests,» 1985.

13 3 rd International Conference on Material and Component Performance under Variable Amplitude Loading, VAL 2015 Load Interaction Effects in Propagation Lifetime of Railway Axles Stefano Beretta a1, Michele Carboni a, Daniele Regazzi b a Dept. Mechanical Engineering, Politecnico di Milano, Via La Masa 1, Milano, Italy b Lucchini RS Spa, Via Paglia 45, Lovere (BG), Italy Abstract As well known, an interaction effect arises, on crack propagation, when a specimen or a component is subjected to variable amplitude fatigue loading. Depending on the applied load sequence, a certain amount of retardation or acceleration can then be observed, on the fatigue crack growth rate, with respect to the constant amplitude case. In the case of structural ductile materials, the interaction phenomenon is mainly addressed by the local plasticity at the crack tip and can be explained, from a global point of view, by adopting the crack closure concept. In the present research, load interaction effects in a medium strength steel for railway axles are experimentally analyzed by small-scale, companion and full-scale specimens. The experimental outcomes were then modeled adopting both a simple no-interaction approach and a Strip-Yield model in order to quantify the possible interaction effects. The modeling was carried out considering different experimental techniques for deriving the crack growth and threshold behaviors of the material, i.e. the traditional K-decreasing technique and the compression pre-cracking one The Authors. Keywords: crack propagation; variable amplitude loading; EA4T steel; compression pre-cracking; railway axles 1. Introduction Railway axles are usually designed against fatigue limit [1-2], but, due to their very long service life (30 years or even more on European lines) and to in-service damage like corrosion or ballast impacts, the approach has moved to damage tolerance [3-5]. From this point of view, the presence of cracks in axles is accepted and they must be periodically inspected using non-destructive techniques. The problem so moves to the determination of the appropriate maintenance inspection intervals, based on crack growth life predictions and the adopted nondestructive testing technique [6]. Considering the former aspect of inspection intervals, it is well known from the literature that an interaction effect on crack propagation arises when a specimen or a component is subjected to variable amplitude (VA) fatigue loading, like railway axles. Depending on the applied load sequence, a certain amount of retardation or acceleration in fatigue crack growth rate can then be observed if compared to the constant amplitude (CA) case. In the case of structural ductile materials, this interaction phenomenon is mainly addressed by the local plasticity at the crack tip and can be explained, from a global point of view, by adopting the plasticity-induced crack closure concept [7-8]. For example, a good correlation between crack growth interaction effects under variable amplitude loading and the amount of plasticity-induced crack closure has been previously derived by the authors [9], relatively to the standardized European EA1N steel (a normalized C40 grade) for railway axles [10]. A second critical aspect of crack growth predictions deals with the proper experimental procedure for generating threshold stress intensity factor (SIF) ranges. In particular, the traditional procedures are reported in the ASTM E standard [11] and are known as K-decreasing and constant K max. Such procedures have been 1 Corresponding author. Tel.: ; fax: address: stefano.beretta@polimi.it VAL 2015 Conference proceedings

14 challenged ([12-13]) because it seems they influence the experimental results they generate. In order to fix these problems, mainly related to the application of a load reduction technique, a different experimental procedure [12] is being increasingly adopted. It is based first on the pre-cracking of fracture mechanics specimens under cyclic compression [14], then on a stabilization step of crack growth. Finally, specimens are tested adopting proper load programs able to generate threshold values in condition where load interaction effects are minimized. In order to check which is the correct experimental approach for the EA1N steel, the authors compared [15] the K th data generated using different procedures ([15-16]) with the results obtained from fatigue limit experiments on small defects and arranged in terms of the so called Kitagawa-Takahashi diagram (derived in [17] for the EA1N steel). As could be clearly seen, the correct estimation of the crack growth threshold seems to be, at least for the considered steel, the threshold SIF range obtained by compression pre-cracking techniques. Another important topic regards the capability of traditional small-scale fracture mechanics specimens to describe crack propagation in full-scale axles. Also this subject has been studied by the authors, who defined [18] a modified thick version of the SE(T) specimen characterized by the same constraint found at the crack tip in axles and, consequently, able to compensate for the scale effect and to provide the same crack growth curves. Indeed, such a modified SE(T) specimen can be adopted as a companion specimen for full-scale axles. The present paper deals with the other standardized European steel for railway axles: the medium strength EA4T [10], a quenched and tempered 25CrMo4 grade. Two batches of this steel grade were adopted, named respectively batch A and batch B. Firstly, a CA loading experimental campaign, applying compression pre-cracking experimental methodologies, was carried out, on EA4T batch B, using traditional small-scale SE(B) specimens, to compare the obtained data to existing K-decreasing results [19] and to calibrate the parameters of Forman-Mettu equations [20]. Then, VA tests were performed on SE(T) companion specimens from the two batches. Crack propagation was experimentally measured considering the original in-service load time history and different equivalent block loading sequences defined from it. This kind of analysis is particularly useful because the typical fatigue benches used for testing full-scale axles are not able to apply complex load time histories, but only block load sequences, and the impact of this simplification should be known. In addition, a mean stress was eventually superimposed to the block load sequence, in order to simulate the presence of a wheel press-fitted onto the railway axle and the consequent variation of the applied stress ratio from the typical R=-1 to higher values. An experimental full-scale test was carried out, as well. Finally, crack growth predictions, using both a simple no-interaction algorithm and a Strip-Yield model [21], were carried out for small-scale and full-scale specimens and compared to the experimental evidence. 2. Characterization of the crack propagation behavior of EA4T steel A dedicated experimental campaign was carried out, for each batch, in order to investigate the crack propagation behavior of the EA4T grade at constant amplitude loading. The near-threshold region was particularly investigated, because, typically, the life of a railway axle is mostly spent within such a region. The details about this campaign are reported in [22], while a summary is provided in the following. Eight traditional SE(B) specimens from batch A and twelve from batch B, having a 12x24 mm 2 cross section and an 8 mm initial notch length obtained by electro-discharge machining (EDM), were tested. Each specimen was pre-cracked under compression. Crack propagation tests onto SE(B) specimens were then carried out using a Rumul Craktronic resonant plane bending facility having a capacity equal to 160 Nm and working at a frequency of about 130 Hz. Crack length was measured, on either side of the crack, using 10 mm crack-gages and a dedicated control unit, by the potential drop technique. The specimens were tested at different stress ratios ranging from R=0.7 to R=-2.5. Figure 1a shows the experimental crack growth curves obtained from each batch, along with their interpolation carried out applying the maximum likelihood method to the Forman-Mettu equation for crack growth rates [20]: p Kth n 1 da 1 f K C K q dn 1 R (1) K max 1 Kcrit where C, n, p and q are the empirical constants, K th is the threshold SIF range, K max and K crit are the maximum and the critical SIF values, respectively, R is the stress ratio and f=s op /S max is the Newman s closure function [21] describing the plasticity-induced crack closure phenomenon. Data were normalized due to their proprietary nature. In spite of the big differences, between the experimental approaches considered in the threshold region, the two data sets, from the two experimental methodologies for batch B steel grade, are in good agreement in the linear region of the da/dn- K diagram, as was shown by the authors [19].

15 (a) (b) Fig. 1. Constant amplitude crack growth characterization of the considered EA4T steel: a) crack growth curves; b) trend of thresholds with R. Figure 1b shows (normalized again) the trend of thresholds with stress ratio R, as derived from the current experimental campaigns, and compares it to data available in the literature [15] and obtained by the K-decreasing technique (batch B only). The figure also shows the interpolation of experimental data, applying again the maximum likelihood method, by the Forman-Mettu equation for thresholds [20]: a 1 f Kth Ko / aao 1Ao1R 1CthR (2) where A o is a constant in the formulation of f, K 0 is the threshold value at R=0, C th is an empirical constant, a is the crack length and a o is the El-Haddad parameter [23]. The dependence of K th with R is controlled through the C th parameter: different values of C th (namely C th+ and C th- ) have to be considered for positives and negatives R-values. The empirical parameters determined by interpolating experimental data were then K 0, C th+ and C th- : it is evident that the compression pre-cracking technique results in lower thresholds when compared to the traditional approach, especially considering the lowest stress ratios. This is in accordance to what was found for the EA1N steel [15]. The threshold trend line of EA4T batch A is higher over the whole stress ratio R range, as in Figure 1b. Since it was not possible to carry out threshold experiments on EA4T batch A steel grade adopting the ΔK-decreasing methodology, the increase of ΔK th at R=-1, for prospective crack growth simulations adopting the threshold trend from ΔK-decreasing, was estimated to be approximately 15%, as for EA4T batch B data. 3. Variable amplitude loading experiments on companion specimens A new type [18] of SE(T) specimen (width equal to 50 mm, thickness equal to 20 mm and initial notch length equal to 6 mm), having the same crack tip constraint of cracks in real axles, was adopted for the variable amplitude loading experiments as companion specimen for full-scale axles. Tests were then performed by a monoaxial servo-hydraulic Schenck facility with 250 kn maximum load. First, the specimens were pre-cracked under compression, in order to obtain, similar to small-scale SE(B) specimens, a non-propagating and naturally arrested fatigue crack characterized by no closure effects. After compression pre-cracking, each specimen was instrumented by two 20 mm crack-gages, one on either side, for the real-time crack length monitoring by a potential drop technique. Moreover, before starting each test, eight strain gages were glued on each specimen in order to verify the correct alignment of the load axis. The first two SE(T) specimens (EA4T batch B steel grade) were tested with the aim to check the crack propagation behavior of the material subjected to a load-time history and to an equivalent block load sequence derived from the time history itself.

16 (a) (b) Fig. 2. Normalized VA loadings derived from in-line service: a) equivalent block load spectrum (R=-1); b) adopted Gassner block load sequences (R -1): long blocks (upper figure) against short blocks (lower figure). (a) (b) (c) (d) Fig. 3. Experimental results and numerical simulations of the tests carried out onto EA4T companion specimens: a) Specimen A4T2- SE(T)#4; b) Specimen A4T2-SE(T)#5; c) Specimen A4T-SE(T)#1; b) Specimen A4T-SE(T)#2. These experiments were also performed because the typical fatigue benches used for testing full-scale axles are not able to apply load time histories, but only block load sequences and the possible differences in the response could be checked. The applied load-time history is representative of km of service and was derived by inline measurements onto a high-speed train. Figure 2a shows the load spectrum of the load-time history and compares it to its equivalent block loads: the blocks were rearranged according to a Gassner sequence [24] typically adopted by some European railway operators for the homologation of axles and defined as long blocks (Fig. 2b). The amplitudes of both the load-time history and the block load sequence were applied to specimens after being scaled so that their maximum K max at the beginning of each test was the same of the one at the tip of a 2.5 mm deep crack located in the most stressed section along the groove of a real axle. Figures 3a and 3b directly compare

17 the crack advance a registered during the two tests. As can be seen, they seem comparable, at least over the initial propagation of the crack. Regarding the tests onto EA4T batch A steel grade, the load spectrum was amplified, compared to specimens from batch B, by 25%, and the mean stress of Figure 2a was also considered. This mean stress value was added to each block of the load spectrum, then rearranged in the already adopted Gassner sequence, obtaining the block load sequence shown, again normalized, in Figure 2b. It is worth noticing that, due to the superposition of the constant stress value onto the load spectrum, the resulting stress ratio moves from the typical value R=-1 (pure rotating bending), to less negative values. The acting stress ratios are between zero and minus one. Since the aim of this research was to understand the effect of the block length onto crack propagation, two different block s lengths were adopted: the longer one (upper plot in Figure 2b), composed of about 5 million cycles, and a shorter one, obtained dividing each block by seven (lower plot in Figure 2b). Specimen A4T-SE(T)#1 was tested applying the longer block sequence, while specimen A4T-SE(T)#2 was tested using the shorter one. Results of crack propagation on the two tested specimens, both from batch A, are shown in Figures 3c and 3d. As can be seen, both experiments lasted about 25 million cycles and crack propagation curves match very well. As for EA4T batch B steel grade, there is no additional retardation effect due to the length of the blocks for the considered material. 4. Variable amplitude loading experiments on full-scale axles Based on the observations of the previous Section, a full-scale railway axle was tested using a block load sequence. The railway axle specimen, shown in Figure 4a and made of EA4T batch B steel grade, was tested under three point rotating bending on a dedicated test bench, available at the Dept. Mechanical Engineering Politecnico di Milano, having a capacity of 250 knm and a rotating at a speed of about 9 Hz. The static scheme of the test bench is shown in Figure 4b. Two artificial notches were machined at the section highlighted in Figure 4a by EDM, at 180 from each other, in order not to interfere during crack propagation. The notches had a semi-elliptical shape, with depth a 0 = 1.5 mm and shape a/c = The full-scale specimen was first subjected to 10 repetitions of the long blocks sequence scaled to a maximum SIF value equal to the one applied to SE(T) specimens, in order to nucleate a sharp crack out of the artificial notches. Then, other 90 repetitions were applied and, finally, since no significant crack advance was measured, to another 77 repetitions increasing the load levels by 25%. Results of crack propagation onto the full-scale specimen are shown in Figure 5. About 16 repetitions of the block load sequence were required for crack closure stabilization, as clearly visible from the initial behavior of the experimental curve, and a small amount of crack propagation was measured during the whole experiment. (a) (b) Fig. 4. Experimental setup for testing full-scale railway axles: a) drawing of the specimen; b) scheme of the three point rotating bending facility. 5. Crack growth simulations Crack growth simulations were initially carried out using a simple no-interaction model, adopting both compression pre-cracking and ΔK-decreasing thresholds, in order to quantify how much the experimental methodology for the definition of the thresholds can affect predictions. Then, a more refined attempt to match lifetime predictions to the experiments consisted in the use of the Strip-Yield model, as implemented in the commercial software Nasgro [24]. By the Strip-Yield model, it is possible to take into account for interaction effects, during propagation, due to crack tip plasticity and the consequent crack closure. The experimental effective crack growth curve (conventionally taken at R=0.7) of each batch of EA4T steel grade, derived from the compression pre-cracking experimental methodology, was provided as input for material modeling.

18 A first result, clearly appearing in Figures 4 and 5, is that, for all the tested specimens, including the full-scale one, the experiments always lie in between the no-interaction simulations performed by compression pre-cracking and ΔK-decreasing methodologies. In particular, adopting compression pre-cracking parameters, simulations always result in conservative predictions, while, on the contrary, they result in non-conservative predictions when adopting ΔK-decreasing parameters. This is true for both EA4T batches, for both specimen s geometries (SE(T) and full-scale) and for each shape of the applied load program. This indication also confirms the validity of SE(T) specimens as companion of full-scale ones. Regarding the simulations by the Strip-Yield model, the constraint factor values for strip yield simulations were set, for both batches, to α = 2.5, according to Nasgro user s manual [24]. This assumption was first verified by CA crack growth simulations at stress ratio R=-1, returning in a good description of crack growth curves onto SE(T) specimens [22, 26], confirming the validity of the chosen value. The evidence, regarding the tests under variable amplitude loading, is that a slight retardation appears, due to the interaction between load levels, and this can be well represented by the Strip-Yield model. Anyway, it is worth remarking that the amount of retardation does not depend on the applied load sequence. The same conclusions can be drawn observing the simulations of the fullscale test (Fig. 5), where the SY model, calibrated again using α = 2.5, provides the best description of experimental evidence, remaining a bit conservative. It is important to annotate that a significant retardation has been also observed by Madler [27] in VA crack growth tests on A4T axles. The conclusion that can be drawn is that, even if the experiments on SET and axles show that 'no interaction' calculations are too conservative, the present validation of the SY simulations opens the possibility to incorporate load interaction into the estimation of inspection interval under service conditions. Fig. 5. Experimental results and numerical simulations of the tests carried out onto the full-scale specimen. 6. Concluding remarks Load interaction effects in propagation lifetime of railway axles made of EA4T steel grade were studied and analyzed both experimentally and numerically. Main results can be summarized: the two bathes of EA4T material resulted in different thresholds, with batch A showing results higher (up to 10 15%) than batch B, while the linear portion of the Paris diagrams are nearly identical; thresholds obtained by compression pre-cracking and ΔK-decreasing methodologies resulted to be quite different for the EA4T batch B grade, with compression pre-cracking being lower, of about 15%, at stress ratio R=-1; no evidence of an interaction effect arose in terms of the shape of the applied VA loading, for both batches: results derived applying a load-time history versus an equivalent block load sequence, or long blocks versus short ones, are always in good agreement; this allows the application of load sequences to full-scale specimens (where it is not feasible to apply a load- time history) without affecting the results; the experimental evidence is always in between the no-interaction simulations considering thresholds from compression pre-cracking (conservative predictions) and ΔK-decreasing (non-conservative predictions); an evident retardation effect clearly appears, with respect to no-interaction predictions adopting compression pre-cracking thresholds; such retardation effect was justified and quantified by the performed strip yield simulations.

19 the same results, obtained by companion specimens, were observed from a full-scale axle subjected to the same block load sequence and the simulations of the full-scale test. References [1] EN 13103: Railway Applications Wheelset and Bogies Non-powered axles Design Method, European Committee for Standardization, Technical Committee CEN/TC 25, [2] EN 13104: Railway Applications Wheelset and Bogies Powered axles Design Method, European Committee for Standardization, Technical Committee CEN/TC 25, April [3] A. F. Jr.Grandt, Fundamentals of Structural Integrity, John Wiley & Sons, Hoboken, NJ, [4] U. Zerbst, R. Lunden, K.-O. Edel, RA. Smith, Introduction to the damage tolerance behavior of railway rails a review. Eng Fracture Mech 76 (2009) [5] S. Cantini, S. Beretta (Editors), Structural reliability assessment of railway axles, LRS-Techno Series 4, Lovere, [6] S. Cantini, S. Beretta, M. Carboni, POD and Inspection Intervals of High Speed Railway Axles, 15th International Wheelset Congress, Prague, Czech Republic, [7] J. Schijve, Fatigue crack propagation in light alloy sheet materials and structures, Pergamon Press, 1961, [8] J.L. Handrock, J.A. Bannantine, J.J. Comer, Fundamentals of metal fatigue analysis. Prentice Hall, US, [9] S. Beretta, M. Carboni, Variable amplitude fatigue crack growth in a mild steel for railway axles: experiments and predictive models, Eng. Fract. Mech. 78 (2011) [10] EN 13261: Railway Application Wheelsets and Bogies Axles Product Requirements, European Committee for Standardization, Technical Committee CEN/TC 25, [11] ASTM E647-05: Standard Test Method for Measurement of Fatigue Crack Growth Rates, Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, [12] R. Pippan, H.P. Stüwe, K. Golos, A comparison of different methods to determine the threshold of fatigue crack propagation, Fatigue 16 (1994) [13] S.C., Forth, J. Newman Jr., R.G. Forman, On generating fatigue crack growth thresholds, Int. J. Fatigue 25 (2003) [14] R. Pippan, The growth of short cracks under cyclic compression, Fatigue Fract. Engng Mater. Struct. 9 (1987) [15] M. Carboni, L. Patriarca, D. Regazzi, Determination of K th by compression pre-cracking in a structural steel, J. ASTM International 6 (2009), [16] S. Beretta, M. Carboni, S. Cantini, A. Ghidini, Application of fatigue crack growth algorithms to railway axles and comparison of two steel grades. Journal of Rail and Rapid Transit 218 (2004) [17] S. Beretta, M. Carboni, A. Lo Conte, E. Palermo, An investigation of the effects of corrosion on the fatigue strength of A1N axle steel. Journal of Rail and Rapid Transit 222 (2008) [18] M. Carboni, S. Beretta, M. Madia, Analysis of crack growth at R=-1 under variable amplitude loading on a steel for railway axles, J. ASTM Int. 5 (2008) [19] M. Carboni, D. Regazzi, Effect of the experimental technique onto R dependence of K th, Procedia Engineering, 10 (2011) [20] R.G. Forman, S.R. Mettu, ASTM STP 1131, pp , [21] J. Newman Jr., A crack opening stress equation for fatigue crack growth, Int. J. Fract. 24 (1984) R131-R135. [22] S. Beretta, M. Carboni, D. Regazzi, Load Interaction Effects in a Medium Strength Steel for Railway Axles, Mat. Perf. Charact. 4 (2015) [23] M.H. El-Haddad, K.N. Smith, T.H. Topper, Fatigue crack propagation of short cracks, J. Eng. Mater. Tech. ASME Trans. 101 (1979) [24] E. Gaßner, 1941, Auswirkung betriebs ahnlicher belastungsfolgen auf die festigkeit von flugzeugbauteilen, Jahrbuch Deutsch Luftfahrtforschung, 1941, [25] Nasgro, N.J.S.C., Fatigue crack growth computer program Nasgro version 4.2-reference manual, [26] D. Regazzi, Advances in life prediction and durability of railway axles, Ph.D. Thesis, Politecnico di Milano, Milano, [27] K. Madler, T. Geburtig, D. Ullrich, An experimental approach to determining the residual lifetimes of wheelset axles on a full-scale wheelrail roller test rig, Proc. 17th Wheelset Congress, Kiev, 2013.

20 3 rd International Conference on Material and Component Performance under Variable Amplitude Loading, VAL 2015 A method for quantitative fatigue fracture surface analysis A. Rattier a, b 1, P. Feraud a, F. Chalon b, N. Ranganathan b, P. Lallet a a SNCF Agence d essais ferroviaires, 21 Avenue du Président Allende, Vitry-sur-Seine, France b Laboratoire de Mécanique et rhéologie, Université François Rabelais de Tours, 7 Avenue Marcel Dassault, Tours, France Abstract When fatigue failure occurs, it is important to identify the cause of failure. In terms of fracture mechanics, the ideal method is the one that permits the determination of maximum stress intensity factor Kmax and the load ratio R from a fracture analysis. Different techniques have been developed and have met with limited success. Such techniques include evaluation of roughness, fractal analysis or measurement of hardness. The authors have developed a method based on the determination of the areal coverage of significant fractographic features on the fracture surface. In this paper, after a brief presentation of the method, results obtained on a structural steel are highlighted and discussed. XRD measurements on fracture surfaces are also presented, with a view to couple them with method explained before The Authors. Keywords: Fatigue failure ; variable amplitude loading ; quantitative fractography ; X-Ray Diffraction ; FWHM 1. Introduction In the case of fatigue crack propagation in polycrystalline metallic materials, the evolution of fractographic features from near threshold to high growth rates near failure have been qualitatively identified ever since the advent of scanning electron microscopy. Such quantitative analysis permits the identification of crack growth mechanisms. In the case of service failures, it is important to identify causes of failure in terms of fracture mechanics parameters, such as the maximum stress intensity factor K max and the load ratio R. Different methods have been developed to this end which have met with limited success: Nomenclature R K max K loading ratio maximum stress intensity factor stress intensity factor range FWHM Full Width at Half Maximum of the diffraction peak SEM XRD da/dn Scanning Electron Microscope R-ray Diffraction propagation speed 1 Corresponding author. Tel.: +33 (0) ; fax: +33 (0) address: alexis.ratier@sncf.fr VAL 2015 Conference proceedings

21 a) Striation topography [1], b) Texture analysis [2] or c) Fractal analysis [3] The above references are given as examples and the list is not complete. One of the reasons for the lack of success for such techniques is that fatigue fracture surfaces reflect the local fracture mechanisms and sometimes it is difficult to identify the mechanisms involved by automated techniques. The authors have developed a quantitative fractographic analysis technique which permits the estimation of the maximum stress intensity factor K max and an equivalent load ratio that lead to the fatigue failure [4]. This method is based on the hypothesis that all the grains across the crack front do not undergo the same mechanical loading as that determined by the remote loading. This phenomenon is related to microstructure and differences in grain orientation across the crack front. This aspect is schematically illustrated in figure 1. Fig.1. Grain orientation changes across a surface - grains with the same color have similar orientations. The method was first developed in the case of an aluminium alloy [4]. The salient features of the method are now presented. In aluminium alloys, the fractographic features observed are: - Crystallographic facets. These ones have been identified to occur on (111) planes, by etch-pitting techniques [5]. When such crack propagation occurs, the crack path can be quite tortuous. - Pseudo-cleavage facets. Such features have been identified by Lynch [6] as crack propagation occurring simultaneously along two [110] directions and lying on a (100) plane. In this plane, the crack profile can follow slip lines. - Striations. Two kinds can be identified: classical ductile striations, according to the mechanism identified by Laird [7], and fragile striations. In such cases the crack path is quite straight. - Dimples: two kinds can be identified small circular dimples and elongated ones, the crack path can be slightly tortuous as the crack may follow local inclusions. - Secondary cracks. In this case, the crack may follow the grain boundaries, if there is an environmental effect associated. As schematized in figure 1, the grain orientations can change along the crack front and one can expect a mixed distribution of the different fractographic features described above. In the original study [4], it was shown that the spatial distribution of significant fractographic features such as striations, pseudo-cleavage facets, secondary crack length and dimples can lead to the determination of K max and R under constant amplitude loading conditions. Some results of this study, obtained in the 2024 T351 alloy, are succinctly presented below:

22 Fig. 2. Spatial coverage striations Fig. 3. Spatial coverage striations VA tests It can be seen in figure 2, that the spatial distribution of striations reflects the K level and the load ratio R. For example, for K=12MPa m, one finds the presence of 50% striated areas at R=0.1, while this feature occupies only 30% at R=0.7. The results for a variable amplitude test can be found in figure 3. This test is a block load test with five different load amplitudes [9]. The analysis based on quantitative fracture analysis permits the determination of an equivalent K max and R ratio. Details are given in [10]. To complete this study and improve results obtained with the method presented above [4], first results of X-ray diffraction (XRD) measurements are presented. The aim of these measurements is to decrease uncertainties, coupling the two methods. The use of XRD to determine the K max and K values is presented in [11]. For passengers safety, the French railway company has the responsibility to identify the crack speed in view of the frequency inspections in maintenance, for all the parts in the train.we have decided to further develop these techniques in first to a safety component. By the important feed-back and studies on the axles we have chosen the EA4T steel for starting. 2. Experimental protocol, material and specimen Tables 1 and 2 show the composition and nominal properties of the studied material, a railway axle s steel (bainitic). Table 1. Chemical composition of the steel EA4T Nuance C Si Mn P S Cr Cu Mo Ni V EA4T Table 2.Nominal properties Yield stress (MPa) Ultimate tensile stress (MPa) Elongation (%) Constant amplitude tests, using middle-crack tension (M(t)) specimens were carried out at three load ratios of -1, 0 and 0.4, to determine calibration curves for the fracture analysis. A variable amplitude spectrum, from the SNCF database, was also carried out to determine the variability of the technique. Figure 4 shows a sample of the loading spectrum for an axle under rotating bending. This loading is similar to a constant amplitude one with R=-1.