INVESTIGATION OF LOW- AND HIGH-CYCLE FATIGUE IN AL 2024-T4 ALLOY

The article presents the results of low-(LCF) and high (HCF) fatigue in samples of aluminum alloy 2024-T4, which is used in aircraft construction, mainly for highly loaded structural components, including for plating and fuselage frames and girders rotor blades of helicopters. This alloy is used where it is required a high strength to weight ratio of the product and high resistance to fatigue. Moreover, it is poorly weldable and has a low corrosion resistance. The tests were performed on hourglass and cylindrical samples, with a parallel and perpendicular orientation relative to the "direction of embodiment" or blank sheet rolling direction. Material for the study was collected from the production line design elements PZL-130 Orlik TC-II. There have been a description of the analytical results in the form of Manson-Coffin and Morrow equations.


Introduction
Aluminum alloys are widely applied in civilian and military engineering (Heinz et al. 2000, Petrasek et al. 2013, Problemy badań i eksploatacji… 1993. They are used in the production of the structural components of aircraft, including plating, fuselage frames, stringers and hatches. The EN AW-2024 T4 aluminum alloy is used in highly loaded structural components and plating where a high strength-to-weight ratio and high fatigue resistance are required. However, the alloy is poorly weldable and has low corrosion resistance.
Analyses of the performance of aircraft structures indicate that mechanical strain is the main cause of damage to aviation plating (sieniawski 2002). Plating is damaged due to the initiation and propagation of cracks, and the material's strength is determined by the number of cycles until destruction within a given range of plastic or total strain values (nogueira et al. 2020(nogueira et al. , Polak 1991. Analyses of materials' behavior under variable loads in a small number of cycles provide valuable information and support the identification of cyclic fatigue mechanisms, localization of strain, cracks and failure of structural components (li et al. 2019, Feng, Qian 2018.
Analyses of low-cycle fatigue resistance are also helpful in estimating the service life of structural components. The shape of the hysteresis loop during low-cycle fatigue resistance tests and their stabilized dimensions are determined by the type of material and loading conditions. An extensive analysis of fatigue parameters and changes in the shape of the hysteresis loop under various experimental and operating conditions, and the extent to which changes in the properties of materials subjected to cyclic and variable loading (including overloading) affect fatigue resistance and the shape of the hysteresis loop was presented by (goss 1982(goss , Kłysz 2000. The results of similar studies are found in the literature -however, in order to compare them with each other and apply them to specific analyzes, it is always necessary to take into account the correct composition, mechanical and temperature processing condition of the tested material -which is not always clearly documented. These tests were performed for the purpose of introducing own material characteristics to the FEM strength analyzes of elements made of materials taken directly from the production line of the PZL-130 Orlik TC-II aircraft.
The aim of this study was to describe low-and high-cycle fatigue of hourglass and cylindrical samples of 2024-T4 alloy with the use of Manson-Coffin and Morrow equations. The alloy's fatigue resistance was evaluated in samples with parallel and perpendicular orientation relative to the sheet rolling direction.

Materials and Methods
The experiment involved hourglass and cylindrical samples with a diameter of Ø 6.5 mm (Fig. 1). The samples were obtained from the production line of PZL-130 Orlik TC-II trainer aircraft in the following configuration: -parallel to the rolling direction, (longitudinal samples, T-L orientation), -perpendicular to the rolling direction, (transverse samples, L-T orientation). The chemical composition of 2024-T4 alloy based on standard PN-EN 573-3 is presented in Table 1. The mechanical properties of the analyzed alloy are presented in Table 2 according to Standard PN-EN 485-2, in Table 3 according to the specifications of ASM Aerospace Specification Metals Inc., and in Tables 4 and 5 according to MIL-HDBK-5J specifications.

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* according to the ASM website, these data were provided by Aluminum Association Inc. and are not for design; ** according to the ASM website, these data were provided by Alcoa and are not for design. Source: ASM Aerospace Specification Metals Inc. http://asm.matweb.com. Table 4 Mechanical properties of 2024 T4 alloy (rolled bars) acc. to MIL-HDBK-5J Note: according to (sieniawski 2002), sample T4 is outdated and should not be used in newly designed structures: 1 for rolled bars 3,175-25, 4 mm, 2 for rolled bars 12,7-25,4 mm, 3 for sheets and plates with a thickness of 0.53-6.32 mm, L-T orientation, 4 for sheets and plates with a thickness of 6.35-12.675 mm, L-T orientation, 5 for sheets and plates with a thickness of 12.7-25.4 mm, L-T orientation, 6 for sheets and plates with a thickness of 0.254-6.32 mm, 7 for sheets and plates with a thickness of ≥6.35 mm. Source: MIL-HDBK-5J (2003).

Analysis of low-cycle fatigue
The initial and middle (corresponding to approximately half the number of load cycles to failure) hysteresis loops were determined in each test, and the initial and stabilized values (accounting for the strengthening of the material under cyclic loading) of test parameters were determined for further analyses. Examples of stabilized hysteresis loops for transverse and longitudinal samples are presented in Figure 3. The Manson-Coffin relationship and coefficients were determined with the use of the following equation:

Sylwester Kłysz
where: ε trans = f(N f ), for data corresponding to the first and middle hysteresis loops ( Fig. 4 and Fig. 5), 2N T and ε Τ -coordinates of the point of intersection of lines ε e -2N f and ε pl -2N f .
The least squares method was used for individual components of deformation (elastic and plastic). The applied transverse strain ε trans was converted to longitudinal strain ε long with the use of the following formulas: where ν is Poisson's ratio for stresses within the elastic range.  log       Manson-Coffin relationships and coefficients at ε long = f(N f ) were determined for the data corresponding to the first and middle hysteresis loops ( Fig. 6 and Fig. 7).
Manson-Coffin relationships and coefficients at coordinates ε trans = f(N f ) and ε long = f(N f ) were determined for the data corresponding to the middle hysteresis loops as the lower and upper limits of fatigue relative to the relationships shown in Figures 4b, 5b, 6b and 7b. The width of the fatigue limit was determined based on the standard deviation of each coefficient in the Manson-Coffin equation (Fig. 8 and Fig. 9).

Analysis of high-cycle fatigue
The high-cycle fatigue of the examined samples was analyzed for stress curves σ = f(N ): -The equations and the coefficients were determined with the use of formula (3)  The resulting curves and coefficients are presented in Figure 11. The curves described by equations (3) and (4) are compared in Figure 12.

Conclusions
A comparison of Manson-Coffin curves in low-cycle fatigue analyses demonstrates that transverse samples are characterized by somewhat longer lowcycle fatigue than longitudinal samples. The range of elastic strain components increases, and the range of plastic strain components decreases (coefficients ε f and σ f , respectively) during fatigue tests, which indicates that the rigidity of the examined samples decreases during tests. These changes are estimated at 10%.
The slope of Manson-Coffin curves (exponents a and b) increases with the cyclic stabilization of test conditions, which decreases the number of cycles and increases deformation at the point of curve intersection. These changes are estimated at 25-40%.
The above changes in Manson-Coffin coefficients occur regardless of sample type (longitudinal/transverse) or type of strain (ε trans /ε long ); therefore, stabilized hysteresis loops can be predicted based on the first hysteresis loops. Since only two points are required to plot a line, Manson-Coffin curves can be correctly plotted when the low-cycle fatigue analysis is limited to only two extreme (or randomly selected) loads. However, this procedure requires further experimental verification and analysis.
The stabilized hysteresis loops are characterized by greater divergence than initial hysteresis loops. The above also leads to a greater scatter of fatigue limit values in the tested samples. At A comparison of Morrow curves for high-cycle analyses indicates that longitudinal samples are characterized by significantly longer high-cycle fatigue than transverse samples.
Stress curves σ = f(N) described with equations (3) and (4) can be regarded as equivalent within the range of the experimental data. The relationship presented in formula (3) assumes a more realistic course when fatigue limits are lower or higher than those determined in this experiment.