Cyclic Material Behavior of High-Strength Steels Used in the Fatigue Assessment of Welded Crane Structures with a Special Focus on Transient Material Effects.
The development of high-strength steels is a crucial issue for the encouragement of lightweight design of modern steel structures. Within the production process of such structures, major aims arise from demands on technological features, e.g. material efficiency and reduction of weight. The service life of crane structures is characterized by high service loads, e.g. those occurring at the telescopic boom of truck cranes , Figure 1. With regard to fatigue, critical sections are often linked to welded joints. In the case of seam welds, the transition from the weld seam to the base material, which is additionally affected by the heat input due to welding, is a well recognized source of crack initiation.
Fatigue recommendations for the design and analysis of welded structures [2,3] are based on stress analysis and fatigue resistance S-N curves (Wohler curves), irrespective of the steel grade. These recommendations are limited to a yield strength of 960 MPa and describe the low cycle fatigue (LCF) behavior improperly. In the case of highly loaded welded structures, the fatigue strength of critical sections is dominated by plastic strains in the LCF regime. Therefore, a fatigue life assessment by the notch strain concept is based on the evaluation of the local strain at the weld toe or weld root and, rather, includes the cyclic material behavior. The choice of the stress-strain relationship is connected to the cyclic stress-strain curve and a hardening model.
In addition to strain-life curves, cyclic stress-strain curves are part of the results arising from strain-controlled testing. Three main purposes substantiate strain-controlled fatigue testing:
* Characteristic data in terms of the cyclic material behavior (strain-life curve and cyclic stress-strain curve) are obtained
* Damage mechanisms at notches are strain-dominated so that local effects of the stresses and strains in the material become apparent
* Input data for strain-life approaches are obtained
Current research concerns the investigation of modern steels under welded conditions and is directed at the assessment and improvement of their fatigue behavior with respect to the steel grade and welding process. The present paper focuses on the experimental determination of the cyclic material behavior of base material and butt welded specimens of high-strength structural steels.
In comparison to stress-based fatigue life concepts, the life assessment by the notch strain approach, including an elastic-plastic numerical model of welded sections, shows a comparable assessment quality when notch support effects are considered . Neither monotonic (tensile) stress-strain relationships nor stress-strain relationships from data from the literature and which, furthermore, are evaluated for the cyclically stabilized state, can be directly applied for life assessment. In fact, the cyclic material behavior should be supplemented with an analysis of transient effects.
In previous research, it has been found that, for the base material of high-strength steel sheets and butt joints, a cyclic softening occurs in the elastic-plastic range for a total strain amplitude above [[epsilon].sub.a,t] = 0.4 % [4,5]. In the case of butt welded specimens, the reduction of the stress amplitude due to the cyclic loading is also influenced by a combination of the geometrical and metallurgical notch effects.
For the consideration in the fatigue assessment using damage parameters and energy criteria, the amount of cyclic softening and the amount of mean stress relaxation has been estimated empirically . A good assessment quality for sheet metal and flange specimens, using both estimations, has been found. In the context of the further development of notch strain approaches, the analysis of transient effects is extended to high-strength steels and butt welds.
STATE OF THE ART
Fatigue Assessment of Butt Joints Considering Nominal Stress Amplitudes
A standardized fatigue assessment of numerous types of welded joints is given by fatigue classes (FAT) using the nominal stress approach and a survival probability of [P.sub.S] = 97.7 % according to fatigue recommendations [2, 3]. Fatigue test data from the literature are shown in Figure 2. The literature data contain uniaxial test results up to the LCF regime of butt joints with V-, X- and Y-shape manufactured from steels with yield strengths between 355 MPa and 1100 MPa. The stress ratios vary between R = -1 to R = 0.5 and the sheet thickness of the base material is 5 mm to 38 mm . According to the different recommendations, FAT classes differ from each other. Relevant FAT classes for a fatigue assessment of butt joints in the HCF regime of FAT 70, FAT 80 and FAT 90 have been added to Figure 2. These are valid for a maximum yield strength of 960 MPa and a minimum of [10.sup.4] cycles to failure. For stresses above the material's yield strength, fatigue life is strain-dominated and a transition of the S-N curve towards the tensile strength is the consequence. An improvement of the fatigue life assessment by a more realistic implementation of the cyclic (transient) material behavior and local stress-strain hysteresis may therefore be expected.
Conventional Description of the Cyclic Material Behavior
The cyclic material behavior is a set of characteristic fatigue data resulting from strain-controlled tests. A stabilized state is defined at the half number of cycles to crack initiation [N.sub.i], whereas [N.sub.i] is commonly evaluated for a reduction of the stress amplitude of 10 % compared to the stabilized state. Essentially, it comprises the cyclic stress-strain curves and strain-life curves. The strain-life curve, according to Basquin , Coffin-Manson [8, 9] and Morrow , is a summation of the elastic strain [[epsilon].sub.a,e] and the plastic strain [[epsilon].sub.a,p], so that the total strain amplitude [[epsilon].sub.a,t] equates to
[[epsilon].sub.a,t] = [[epsilon].sub.a,e] + [[epsilon].sub.a,P] = [[sigma]'.sub.f]/E * [(2[N.sub.i]).sup.b] + [[epsilon]'.sub.f] * [(2[N.sub.i]).sup.c] (1)
where [[sigma]'.sub.f] is the cyclic strength coefficient, E the Young's modulus, b the cyclic strength exponent, [[epsilon]'.sub.f] the cyclic ductility coefficient and c the cyclic ductility exponent.
The cyclic stress-strain curve of Equation (2) was introduced by Ramberg and Osgood  in the form
[[epsilon].sub.a,t] = [[epsilon].sub.a,e] + [[epsilon].sub.a,p] = ([[sigma].sub.a]/E) + [([[sigma].sub.a]/K').sup.1/n'] (2)
where [[sigma].sub.a] is the stress amplitude, K' the cyclic hardening coefficient and n' the cyclic strain-hardening exponent.
The characteristic parameters of cyclically stabilized stress-strain curves can be derived from strain-life curves using the compatibility conditions of Equations (3) and (4):
n' = b/c(3)
[mathematical expression not reproducible] (4)
Trilinear Approach of the Strain-Life Curve
The strain-life curve according to Equation (1) might not be the best choice for any material to represent the cyclic material behavior from low cycle fatigue to high cycle fatigue and long life fatigue. For the case of aluminum wrought alloys, a trilinear strain-life curve was introduced, which divides the elastic part of the strain-life curve into three sections [12, 13]. A separate strain-life curve is assigned to each section and transition conditions are allocated. In the first section ([[sigma]'.sub.f1], [b.sub.1]), an elastic-plastic material behavior is assumed so that relations according to Ramberg-Osgood and Coffin-Manson [[epsilon]'.sub.f] * [(2[N.sub.i]).sup.c] are valid. Section two ([[sigma]'.sub.f2], [b.sub.2]) is characterized by an elastic-plastic first hysteresis loop. With respect to cyclic hardening, the formation of dislocations results in a hysteresis, which is dominated by elastic strains. For the third section ([[sigma]'.sub.f3], [b.sub.3]), the hysteresis shows macroscopic elastic strains. The trilinear strain-life curve is therefore given by a system of equations. The presentation according to Equation (5) requires the determination of eight parameters.
[mathematical expression not reproducible] (5)
Under consideration of the compatibility conditions for the first section of the trilinear strain-life curve, the cyclic stress-strain curve analogous to Equations (3) and (4) is derived from [[sigma]'.sub.f1], [b.sub.1], [[epsilon]'.sub.f] and c. A more precise description of the cyclic material behavior has been found using this procedure.
A New Methodology for the Consideration of Transient Effects
Transient effects of the stress-strain relationship under cyclic loading, such as cyclic hardening/softening, mean-stress relaxation or ratcheting, may have an influence on the fatigue life. In , a strain-based fatigue assessment using two damage parameters and one energy parameter for the consideration of cyclic softening and mean-stress relaxation, has been evaluated. The cyclic softening of the stress amplitude [[sigma].sub.a] and relaxation of the mean stress [[sigma].sub.m] have been simulated based on experimental data of the cyclic stress evolution. The basic idea is that both parameters can be described by considering their dependence on the strain amplitude and the number of cycles separately (linear independence). The amount of cyclic softening is dependent on the strain amplitude and the number of cycles was observed to reach stabilization. For this reason, the description using exponentially decreasing functions has been chosen.
The amount of cyclic softening [DELTA][[sigma].sub.a], defined as the difference between the maximum amount of softening [DELTA][[sigma].sub.[infinity],max] (occurring at the maximum strain amplitude) and the stress amplitude of the stabilized state, as a function of the strain amplitude [[epsilon].sub.a] for sheet metal specimens, is shown in Figure 3. This value represents the difference between the initial (quasi-static) and cyclically stabilized stress-strain curves. An exponential equation with optimization parameters [k.sub.0] and [[epsilon].sub.0] is used to estimate the amount of cyclic softening. Furthermore, the dependence on the logarithmic number of cycles log(W) has been expressed by another exponential function and optimization parameters [b.sub.0] and [b.sub.1], so that the cyclic softening of the stress amplitude is estimated using Equation (6).
[mathematical expression not reproducible] (6)
Two independent regressions are applied to perform the estimation according to Equation (6). Experimental results and the estimation for sheet metal specimens are shown in Figure 4. The difference in the stress amplitudes between estimation and experimental results is mainly due to the fact that the estimated curves are based on a regression, while experimental data vary due to scatter of a single test. For higher strain amplitudes, the estimations are in good agreement with the experimental results. Comparable results have been found for specimens extracted from flow split flanges.
The set of four optimization parameters results from the two regressions. To provide an impression of the levels of these parameters, Table 1 summarizes the estimated values for both material states, as-received material and flange specimens.
In a similar procedure, the mean stress relaxation is described by an analytical equation using another set of four optimization parameters. The equation is based on the initial mean stress of the first (monotonic) loading. For the two functional relationships, again exponential equations are used. Since mean stress relaxation is out of the scope of this paper, the work of Coffin  and Tomasella  is recommended for further information.
Butt welds of high-strength, fine-grained steels are typical connections widely used in crane structures and adjacent industrial sectors. A manual or partially mechanized welding is the common process. For some time, the water-quenched, fine-grained steel S960QL has been utilized for welded crane structures. In the past few years, the ultra-high-strength steel S1100QL and the thermomechanically rolled steel S960M have become of interest for this application. Knowledge of their fatigue behavior, especially in the welded state, is however incomplete. Within this study, the advantages of GMAW welded butt joints of three high-strength steels - S960M, S960QL and S1100QL - should become apparent.
The experimental studies were performed on steel sheets and butt welds of the high-strength steels S960QL, S960M (from 2 suppliers, abbr.: suppl. 1/suppl. 2) and S1100QL. All specimens were made from sheets with a thickness of t = 8 mm. Butt joints had been prepared with a 22.5[degrees] chamfer on each of the two sheets and were joined together using a filler material of type G 89 6 M Mn4Ni2CrMo (minimum yield strength of 890 MPa) by a manual welding process. The root run was ground in order to fit in the following runs. Afterwards, the sealing run was welded from the back side, finished by the final runs. The transition from the base material (BM) and heat affected zone (HAZ) to the weld metal (WM) can clearly be seen from the microsection of the butt weld in Figure 5. A known phenomenon of GMAW welded high-strength steels is a hardness drop in the HAZ, below 300 HV10 in this particular case.
To evaluate the cyclic material behavior in strain-controlled testing, specimens with the dimensions shown in Figure 6 have been extracted from welded sheets. Strain-controlled tests were performed according to the standardized test conditions of SEP 1240 . The extensometer has a measuring length of 25 mm and is placed in the constant cross section of the specimen, so that, for specimens in the as-welded (AW) state, the entire butt weld is within the measuring length of the extensometer. The test rig for strain-controlled fatigue experiments is driven by hydraulic cylinders with a maximum force of 100 kN. Figure 7 shows the test set-up. The test frequency varies from 0.1 to 4.0 s-1. Nominal stresses are calculated from applied forced for both, base material and as-welded state.
CYCLIC MATERIAL BEHAVIOR
The strain-controlled test results have been analyzed using the trilinear strain-life curve, as introduced previously. A more precise description of the cyclic material behavior in comparison to the conventional strain-life curve or data from the literature, e.g. the uniform material law  for high strength steels , is the result, when compatibility conditions are considered. An improvement of the cyclic stress-strain curve, derived from compatibility conditions based on the trilinear strain-life curve, can be noted for butt-welded high-strength steels. For elastic-plastic loading, the elastic part of the strain-life curve in section 1 is described by the material constants [[sigma]'.sub.f1] and [b.sub.1] according to Equation (5), while K' as well as n' of the cyclic stress-strain curve are calculated by (3) and (4), respectively. When the elastic strain dominates the cyclic material behavior in section 2 and an elementary modification is applied in section 3, the material parameters [[sigma]'.sub.f2] = [[sigma]'.sub.f3] and [b.sub.2] = [b.sub.3] describe the strain-life curve [12, 13]. The evaluated parameters of the cyclic material behavior (Young's modulus at a cyclically stabilized state of E' = 205 GPa) are listed in Table 2.
Furthermore, strain-life and cyclic stress-strain curves characterize the LCF behavior of materials and allow a comparison of the base material (BM) with the as-welded state (AW). The results of the AW-experiments represent an overall, integral behavior of a certain weld feature. As is well known, crack initiation under cyclic loading mainly starts from the notch at the weld toe. In the case of 8mm thick welded sheet specimens, fatigue failure initiates from the notch at the weld toe in about 95% of the experiments, while crack propagation is divided between propagation right across the HAZ and propagation at the transition between WM and HAZ (each ca. 50 %). Even though, crack initiation is linked to the geometrical notch at the weld toe, fracture of ground specimens occurs, in about 40 % of all experiments, at the transition from HAZ to WM and another 40 % within the HAZ . Crack initiation is then dominated by the geometrical notch.
Strain-life curves have been evaluated for a reduction of the stress amplitude of 10 % (crack initiation) with respect to the stabilized state. Comparison of BM with AW for the different steel grades (8 mm thick specimens) is shown by the diagrams in Figure 8. As a combination of the geometrical and metallurgical notch effects, all diagrams visualize a reduction of cycles to crack initiation [N.sub.i] in the AW state in the range of 1-2 decades, compared to the BM.
Cyclic Stress-Strain Curves
Cyclic stress-strain curves, the relation between the total strain amplitude [[epsilon].sub.a,t] and the (nominal) stress amplitude [[sigma].sub.a] shown in the diagrams of Figure 9, have been calculated from trilinear strain-life curves using compatibility equations. The cyclic stress-strain curves of steels with 960 MPa yield strength (Figure 9 a), c) and d)) indicate small differences between the BM and AW states. It can be noted that the curve for S960QL is slightly increased in the plastic region for the AW-experiments. For the ultra-high-strength steel S1100QL, the lower static yield strength of the filler material reduces the stress-strain curve for the AW-experiments (Figure 9 b)) to the same level as those for the 960 MPa steels. The advantages of the base material's high strength are therefore not delivered in the AW state.
ANALYSIS OF TRANSIENT EFFECTS
The basis for the consideration of transient effects is the analysis of changes in the hysteresis loop during cyclic loading. The shape and characteristic as a function of the number of cycles can significantly change. Hysteresis loops of S1100QL base material specimens at [[epsilon].sub.a] = 0.7 % for the specified states of the first loading cycle, the stabilized state and the crack initiation are plotted in Figure 10. Firstly, the shape of the hysteresis between the three states does not seem to change significantly. Secondly, the reduction of the stress amplitude between the initial and cyclically stabilized states causes a rotation of the axis through the reversal points (min-to-max). Thirdly, this specific test shows a mean stress relaxation from the stabilized state to crack initiation, which could not be seen in every test result.
Comparison of the hysteresis loops for the S1100QL base material with the as-welded state of the butt joint (Figure 11, [[epsilon].sub.a] = 0.7 %) shows a bellied shape at a lower stress level for the AW state. A cyclic softening is indicated by the reduction of the maximum and minimum stress amplitudes from the initial and cyclically stabilized states to crack initiation. Again, a rotation of the axis through the reversal points is the result.
The orientation of the axis through the reversal points between minimum and maximum (of the strain amplitude) can be interpreted as a global slope of the hysteresis. This slope [m.sub.glob] can be calculated for each loading cycle according to Equation (7).
[m.sub.glob] = [DELTA][sigma]/[DELTA][epsilon] = ([[sigma].sub.max] - [[sigma].sub.min])/([[epsilon].sub.max] - [[epsilon].sub.min]) (7)
Results for the S1100QL steel at [[epsilon].sub.a] = 0.7 % are shown in Figure 12. The decrease of the global slope indicates the cyclic softening, since [DELTA][epsilon] is constant. There is a moderate decrease in the global slope over the total fatigue life for the base material state, shown in Figure 12a), while, for the as-welded state, the slope drops down rapidly. Higher absolute values for the base material are due to higher stress ranges/amplitudes.
The three main parameters describing the transient material behavior are the strain amplitude, the stress amplitude and the number of cycles. The stress amplitude has a major influence on the fatigue failure, while mean stress analysis of welded joints is usually connected to residual stresses occurring during welding.
The course of the stress amplitude during a single test confirms the cyclic softening for the BM, Figure 13, as well as in the AW state, Figure 14. Significant cyclic softening can be observed for total strain amplitudes of 0.6 % and higher. Tests with a strain amplitude of 0.2 % produce runouts at a constant stress amplitude (no cyclic softening is observed at all). Analysis for the four investigated steel grades shows, for strain amplitudes of 0.6 % to 0.8 %, that the stress amplitude at the cyclically stabilized state is reduced to about 80 % to 90% of the initial stress value for the BM and to approximately 85 % to 95 % for AW.
The amount of cyclic softening is calculated from the difference between the initial and the cyclically stabilized stress-strain curves. In the case of a continuously increasing amount of cyclic softening converging towards a threshold, an estimation, using an exponential equation with optimization parameters [k.sub.0] and [[epsilon].sub.0] according to Equation (6), can be applied. It has been found that this is a good approximation for the S960QL and S1100QL base material states, shown in Figure 15. For S960M steels, this estimation is not as accurate as for S960QL and S1100QL, since the amount of cyclic softening shows no distinctive saturation. Comparison of the initial and cyclic stress-strain curves of butt welds show that there is no continuously increasing cyclic softening to a certain threshold value. On the contrary, especially in the range of strain amplitudes from 0.2 % to 0.6 %, cyclic hardening can occur (Figure 9c) and d)).
Estimations for the amount of cyclic softening by a pure exponential equation do not seem accurate in such cases. However, the procedure is able to estimate the amount of cyclic softening (or hardening), if it is first increasing and finally saturating (towards a threshold).
SUMMARY AND CONCLUSIONS
The cyclic material behavior of high-strength structural steels has been analyzed for the base material specimens extracted from sheet metal and for butt-joints in the as-welded state. Strain-controlled tests characterize the cyclic material behavior in terms of trilinear strain-life as well as cyclic stress-strain curves and aim to extend local fatigue approaches to welded details of high-strength steels in the LCF regime. The combination of the geometrical and metallurgical notches at the weld results in a reduction of the fatigue life in the range of 1-2 decades compared to strain-life curves of the base material. Cyclic stress-strain curves for S960 materials have small variations between base material and as-welded state. As can be seen from the reduced cyclic stress-strain curves, the advantages of the ultra-high-strength steel base material (S1100QL) disappear in the as-welded state.
Lower strain amplitudes ([[epsilon].sub.a] [approximately equal to] 0.2 %) result in an early stabilization and do not show a fracture. This can be directly seen from the course of the stress amplitude with the number of cycles. Stress-strain hystereses for the initial (monotonic) state, for the cyclically stabilized state and for crack initiation are suggestive of the transient material behavior. The global slope, i.e. the orientation of the axis between reversal points, is a measure for the change of the stress-strain hysteresis and cyclic softening, which has been observed for the base material and butt welds at high strain amplitudes ([[epsilon].sub.a] [greater than or equal to] 0.6 %). A continuously increasing amount of cyclic softening, which saturates towards a threshold, can be estimated using exponential functions. for S960QL and S1100QL base material, an accurate estimation has been found. If the amount of cyclic softening (or hardening) shows more complex courses, a (slightly) different functional relationship, possibly including additional variables, has to be found.
An improvement of the fatigue life assessment using notch-based concepts, especially the notch strain approach, is expected if the local, transient stress-strain state is considered. Neither a monotonic (tensile) nor cyclically stabilized stress-strain curve nor purely literature-derived data can be used in an accurate fatigue assessment procedure with a focus on the LCF regime of high-strength steels. For the implementation of stress-strain relationships into analytical or numerical models, the transient effects should be included. In the case of the investigated high-strength steels and butt welds, attention has to be paid to cyclic softening.
Within a fatigue assessment, the shape of stress-strain hystereses will be characterized in detail to account for transient effects of high-strength steels and welds. Future work will therefore focus on damage and energy parameters. Furthermore, the influence of variable amplitude loading has not been considered, so that an experimental analysis is planned to investigate service-relevant Gaussian load spectra.
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Fraunhofer Institute for Structural Durability and System Reliability
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This work is part of the research project " Erweiterung des ortlichen Konzeptes zur Bemessung von LCF-beanspruchten geschweiBten Kranstrukturen aus hochfesten Stahlen", IGF-project-no. 17102 N, of the Research Association for Steel Application (FOSTA - Forschungsvereinigung Stahlanwendung e.V.), which was funded by the AiF as part of the program for "Joint Industrial Research (IGF)" by the German Federal Ministry of Economic Affairs and Energy (BMWi) by decision of the German Bundestag.
AW - As-welded (state)
BM - Base material
FAT - Fatigue class
GMAW - Gas metal arc welding
HAZ - Heat affected zone
LCF - Low cycle fatigue
WM - Weld metal
This is a work of a Government and is not subject to copyright protection. Foreign copyrights may apply. The Government under which this paper was written assumes no liability or responsibility for the contents of this paper or the use of this paper, nor is it endorsing any manufacturers, products, or services cited herein and any trade name that may appear in the paper has been included only because it is essential to the contents of the paper.
Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE International. The author is solely responsible for the content of the paper.
Benjamin Moller, Alessio Tomasella, Rainer Wagener, and Tobias Melz Fraunhofer LBF
Table 1. Estimated parameters for the cyclic softening of the sheet metal and flange specimens for HC340LA . Parameter [k.sub.0] [[epsilon].sub.0] [b.sub.0] [b.sub.1] Sheet metal -1084 0.0015 -0.5883 1.2125 Flange specimens -171.7 0.0016 -0.3367 2.2650 Table 2. Parameters of the cyclic material parameters for high-strength steels in base material (BM) and as-welded (AW) states using a trilinear approach. Parameter S960QL S1100QL BM AW BM AW Exp. 12 12 12 12 E [GPa] 205 205 205 205 [[sigma]'.sub.f1] [MPa] 1099 952 2175 1086 [[epsilon]'.sub.f] [m/m] 0.931 0.017 1.904 0.056 [b.sub.1] -0.049 -0.037 -0.099 -0.051 c -0.805 -0.430 -0.922 -0.609 [[sigma]'.sub.f2] [MPa] 1873 1717 3562 15362 [b.sub.2] -0.105 -0.157 -0.157 -0.386 K' 1103 1355 2030 1384 n' 0.060 0.086 0.107 0.084 [R'.sub.p0,2] [MPa] 759 793 1041 820 [R'.sub.p0,2AW]/ 1.045 0.788 0.959 1.024 [R'.sub.p0,2BM] Parameter S960M S960M (suppl. 1) (suppl. 2) BM AW BM AW Exp. 12 12 10 13 E [GPa] 205 205 205 205 [[sigma]'.sub.f1] [MPa] 1310 1141 1124 1570 [[epsilon]'.sub.f] [m/m] 1.766 0.106 3.704 0.138 [b.sub.1] -0.067 -0.082 -0.048 -0.121 c -0.854 -0.750 -0.991 -0.761 [[sigma]'.sub.f2] [MPa] 2942 2360 2631 6936 [b.sub.2] -0.153 -0.182 -0.145 -0.319 K' 1254 1458 1055 2152 n' 0.078 0.109 0.049 0.159 [R'.sub.p0,2] [MPa] 772 740 781 800 [R'.sub.p0,2AW] /[R'.sub.p0,2BM]
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|Author:||Moller, Benjamin; Tomasella, Alessio; Wagener, Rainer; Melz, Tobias|
|Publication:||SAE International Journal of Engines|
|Date:||Apr 1, 2017|
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