1. Introduction
Railways are one of the modes of transport for critical freight and passengers. Wagons and locomotives are connected using specially designed traction devices that maintain a fixed distance between the former and transmit and mitigate the effects of longitudinal (tensile and compressive) forces. Until 1934, screw couplings were used to connect wagons and locomotives. However, screw couplings were associated with multiple risks, including insufficient strength and a hazard to the railway worker who had to crawl between the wagons when coupling and uncoupling them. The coupling process was also slowed down by maneuvering due to the need for precise alignment of the axles of devices. Automatic couplers have eliminated the disadvantages of screw couplings. Since 1935, the Russian-type automatic coupler was adopted across Eastern Europe. Automatic couplers have provided less time-intensive coupling and uncoupling operations and increased freight and passenger train safety (
Figure 1) [
1,
2].
However, with increasing rolling stock power and speed, loads may reach levels where stress values may exceed the proportionality limit of the material in the event of improper operation. This is acceptable if it happens only a few times during the service life. However, in the case of elastic–plastic strain, frequent overloading may cause low cycle fatigue [
3,
4,
5].
With increasing equipment power and speed, the actual stress values occasionally exceed the proportionality limit of the material. Under the action of random intensive loads, equipment elements and structures fail due to fatigue damage of various types. The accumulated damage develops as a result of high-cycle and low-cycle fatigue associated with cyclic overload, which causes plastic strain [
6,
7].
Usually, the stress and strain fields are distributed unevenly in the parts. In the concentration zones, the stresses exceed the proportionality limit of the material. Only an approximate prediction of stress distribution of the unique structures that make up a spatial body is possible using analytical methods. However, inaccuracies of this kind related to responsible parts may lead to accidents, while excessive safety factors increase the weight of the structure and consumption of the material. It is therefore reasonable to use more accurate numerical methods to determine the stress and strain distribution in complex structures [
8].
An automatic coupler of a rolling stock is a typical example of such a loading case. The automatic coupler of a rolling stock is a crucial part of determining passenger, freight, and environmental safety. Material is an important factor in the calculation of the durability of the coupler. Prior to the investigation of the remaining service life of the coupler before the macro-crack initiation, the stress–strain state must be calculated. However, stresses are calculated using analytical formulae, where changes to the geometric shape are evaluated using stress concentration factors. Given the complexity of the design of an automatic coupler, certain calculation errors may be assumed [
9,
10].
The failure statistics for automatic couplers on the railway rolling stock have suggested that the failure of automatic couplers usually tends to occur at the transition between the head and the tail [
11,
12]. The authors of the papers referred to above propose increasing the low-cycle fatigue resistance of the automatic coupler by selecting materials with higher yield strength
or with higher plasticity (by increasing
). This method involves an alteration in the chemical composition of the material, i.e., it is based on the choice of steel grade and heat treatment. One work [
11] proposes a damage accumulation model for an automatic coupler tail using the damage linear summation hypothesis for low-cycle fatigue. For practical damage summation, an equation treating elastic and plastic damage separately is proposed:
Under the respective conditions (heavy cargo, frequent shunting, track unevenness, etc.), the automatic coupler housing develops stresses that exceed the proportionality limit of the material. This is usually caused by random overloading [
13].
It is imperative that historical load data for the automatic coupler is available for the identification of the possible damage to the automatic coupler and determination of the remaining service life. In ref. [
1], researchers use statistical data available for the rolling stock fleets to determine the load levels and frequencies. The force acting on the automatic coupler was measured during the operation. Further calculations are carried out in the studies above for the full range of operating forces developing during the operation of the automatic coupler over a year, as shown in
Table 1 [
1].
In an American-type automatic coupler, the strain is measured at respective points during the carriage of coal on a defined railway section [
14]. Measurements were made for full versus empty rolling stocks. The distribution of stress levels and cycles obtained was generalized as a linear summation was used, not accounting for the effects of history and consistency. Tensile test results for steels used for automatic couplers have already been presented in other works. The mechanical characteristics obtained are yield strength
MPa and strength limit
MPa. Steel properties are determined based on the set of chemical elements, and
Table 2 summarizes the results of the chemical analysis of an automatic coupler [
14].
In ref. [
14], fatigue curves were obtained in the experiment referring to the cycle asymmetry coefficient
and the constant load amplitude. The fatigue damage was calculated using Miner’s linear dependence:
where
Nri was determined using the Goodman diagram [
15] for the corresponding loading case. The Goodman diagram was used to recalculate conditional stresses using an experimental curve with the coefficient of asymmetry
.
The high density of micropores in the material of the automatic coupler housing is considered an important factor. Micropores are mainly distributed at the edges of the cuts, particularly in the defect areas. This microporosity may be a key factor in lower fatigue resistance. In ref. [
16], the defects were quantified using a computer technique. As the pores of the casting are very irregular in shape, it was simplified for the modeling. The aim was to affect the location and size of the pair so that, despite the irregularity of their shape, the pair was idealized into a sphere with an appropriate diameter. The computational results showed that the closer the pair is to the surface of the body, the higher the stress concentration. If the pair crosses the outer surface, it produces the highest stress concentrations. The results also show that the size of the pore has a significant effect on the stress concentration, regardless of how close the pore is to the surface [
16].
Researchers [
17] have demonstrated the influence of the mechanical and cyclic characteristics of different steels on the durability of automatic couplers. The parameters
(see
Section 3) for damage summation were obtained from experimental diagrams of elastic–plastic cyclic deformation (
Table 3). Alteration of the mechanical characteristics of the material is viewed as the key factor for increasing the durability of an automatic coupler. Structural modifications that could reduce stress concentration are not employed in the literature reviewed.
All the steels investigated were found to belong to the class of cyclically stable materials with weakly anisotropic properties in the normal state and to the class of cyclically softening anisotropic materials after quenching and tempering. A comparison of the low-cycle fatigue curves has demonstrated that an increase in the mechanical strength characteristics of steel results in a significant enhancement in durability. The durability of heat-treated (20GL—quenched and tempered) steel specimens increases almost tenfold compared to normalization alone.
One paper [
18] describes a method for assessing the service life of automatic couplers according to the vulnerability deformation criteria of metal structures. The proposed method is based on a combination of software packages for the simulation of longitudinal dynamics and the assessment of static and dynamic stresses—in this case, those occurring in the couplings. The analysis of the coupling life, based on the results of these study phases, was carried out by means of methods and programs for the assessment of fatigue vulnerability and the determination of the safe life.
The study presented in ref. [
19] evaluates the remaining service life of cast steel heavy-duty railway truck couplings with initial defects. A test program was carried out to determine high-cycle fatigue strength, fatigue crack growth rate, threshold, and fracture toughness. A numerical model of the damaged heavy-duty tractor coupling was developed, taking full account of the assembly gap and the complex non-linear contact. The remaining life was then determined using fracture mechanics methods for the actual load spectrum.
In many research papers, the strength and reliability of automatic couplers have been addressed by stress–strain state computations using the finite element method. However, the strength of the automatic coupler is assessed by calculation using a linear damage summation according to the fatigue curve, without distinguishing between the low-cycle quasi-static fatigue as well as high-cycle damage. This kind of calculation fails to account for changes in the stress and strain state or offer a quantitative evaluation of different types of damage. In addition, the investigations reviewed used the Goodman diagram for durability assessment, while the former is only applicable to the high-cycle fatigue region. Hence, the application of the Goodman diagram to the low-cycle fatigue region is questionable, particularly in the presence of quasi-static damage.
The contributions of this paper are presented as follows:
(1) The cyclic properties of the automatic coupling material and the damage behavior that has an effect on the accumulation of damage were determined; (2) a method for automatic coupling damage summation is proposed, using the stationary load dependencies, taking into account quasi-static and low-cycle fatigue damage; (3) the automatic coupler damage to fatigue crack initiation is calculated; (4) a methodology for assessing a single load cycle to assess damage to any sequence of automatic coupling load cycles is proposed.
To carry out this work, the following tasks were performed:
Section 2 describes the methodology for static and low-cycle fatigue experiments and presents the results of these investigations;
Section 3 examines the methodology for the summation of the damage accumulated in the automatic coupler. The low-cycle fatigue and quasi-static damage caused by a single loading cycle are determined in view of the loading level.
The results obtained and conclusions presented are discussed in
Section 4.
2. Materials and Methods
The experimental test rig included a 50 kN UMM 5T low-cycle tension–compression test machine (Kaunas University of Technology, Kaunas, Lithuania). The standard used for fatigue tests was ref. [
20], and the statistical characteristics were calculated according to ref. [
21]. Static and cyclic experiments used cylindrical deformable samples with a length of 23 mm and a diameter of 10 mm.
Figure 2 presents a detailed drawing.
In this work, a low-cycle tensile–compressive load was applied. This loading method differs from other loading methods (torsion, bending), as the first is characterized by the homogeneity of the strain across the entire cross-section of the working part. The results of the properties of the tests fully reflect the material despite the stringent requirements with respect to the centering of the precision of the clamps of the specimen in the loading machine to prevent the specimen from buckling under compression. Furthermore, static tensile loading tests were performed, allowing for an easy comparison of the data provided by these tests with the data obtained from low-cycle fatigue tests. Restraining stresses (stress-controlled loading) lead to the accumulation of strain. Furthermore, the following cyclic properties of the material become evident under load: softening, hardening, or stability.
Low-cycle load charts were recorded for stress-controlled (
) and strain-controlled (
) types of load. The elastic–plastic cyclic strain in the
half-cycle is generally characterized by cyclic stress
, loop width
, and accumulated unilateral plastic strain
. The variation of the accumulated unilateral plastic strain
was recorded during the stress-controlled low-cycle load. During strain-controlled loading, strain was restrained and the variation of cyclic stress
was recorded. Its value fell within and the registration technique was carried out within the same half-cycles
k as in the case of stress-controlled loading (
Figure A1).
For strain-controlled loading, where the constant value is strain amplitude , the values of cyclic stress change with the increase in the number of half-cycles k. The above values were recorded in the following half-cycles: k = 0, 2, 4, 6, 8, 10, 20, 40, 60, 80, 100, 200, 400, 600, 800, 1000, 2000, 4000, 6000, 8000, 10,000, etc. During the elastic plastic loading, the material is subjected to deformation above the limit of proportionality ; i.e., as the plastic strain increases, the low-cycle deformation diagram changes during the loading as well. It is therefore important to have a diagram of the elastic–plastic strain for each half-cycle of the material and to establish a low-cycle fatigue curve.
In the case of stress-controlled loading, the stresses defined by values
and
were restrained. The variation of the strain loop width
influencing the accumulated unilateral plastic strain
was registered. The loading in the initial (
k = 0) half-cycle is characterized by stress
and strain
. Loading in the first half-cycle at a compressive stress exceeding the cyclic limit of proportionality
enables plastic strain. Loading in the second and subsequent half-cycles is accompanied by the formation of elastic–plastic hysteresis loops with varying
values [
6,
7,
22].
Static and Low-Cycle Results for the Automatic Coupler Steel
The recorded static tension curve was used for reference to produce the static strain (tensile) diagram (
Figure 3). The diagram shall be produced considering both the strain
e (
) and stress
σ (
scales.
The mean arithmetic value
, statistical distribution standard deviation
, and coefficient of variation
were calculated for the normal distribution law using the equation below [
21]:
The obtained mechanical characteristics of steel 20GL and the results of the calculations are shown in
Table 4.
Failure is influenced by various metallographic or geometric defects in the structure. The main internal defects and heterogeneities in the microstructure of metals occur during the metallurgical and heat treatment processes. Surface defects (surface roughness, hardening), which occur during the production of the specimens and are of a statistical nature, are also highly important. Some errors are due to non-uniform test conditions. All of the above errors are specific to a single batch of metal. For a metal of the same grade but different batches, the dispersion of properties between batches will be even greater due to the dispersion of the chemical composition and metallurgical process conditions of the different batches. All factors discussed above influence the dispersion of both static and cyclic material characteristics.
The automatic coupler of a rolling stock is subjected to cyclic loading, that is, when the stresses in the cross-section of the part vary periodically from to . Therefore, material tests were also carried out on the specimen under symmetric and asymmetric loads. The low-cycle loading was chosen for the investigation of the cyclic properties of the material since the automatic couplers of a rolling stock are subjected to variable forces and, as shown above, produce stresses that exceed the proportionality limit.
Two types of load cycles were chosen for the low-cycle fatigue study, asymmetric (pulsating cycle, ) and symmetric (reversed cycle ), because the automatic coupler operates under asymmetric load, while the symmetrical load cycle gives a better indication of the cyclic strain parameters of the material, which is needed for the calculation of the damage caused by low-cycle strain.
In this investigation, the strain scale
and the stress scale
were determined for the low-cycle stress-controlled load. For strain-controlled loading, the strain scale
and the stress scale
. Under stress-controlled loading, the strain is unconstrained and free to develop; therefore, the mode of failure depends on the level of loading. The fatigue curves (
Figure 4) show that there were three failure zones.
The quasi-static failure zone is characteristic of high stress levels. The quasi-static failure zone extends up to , where an intense accumulation of unilateral plastic strain takes place and the specimen failure occurs at the neck. The location of the zones is seen more clearly by looking at the variation of reduction of area ψ. The fatigue fracture zone starts with , since the accumulation of unilateral plastic strain is lower in this zone. The transient zone extends from to . Here, the failure is due both to the formation of the neck and to fatigue.
Figure 5 shows that the material tested is cyclically softening, i.e., the loop width is increasing under stress-controlled loading. This is typical for low-carbon alloy steel. The dependence was used to analytically describe the cyclic strain diagrams [
22,
23,
24]:
The cyclic material characteristics are considered in relative coordinates, which are obtained by dividing the stresses by and strain by .
The investigations have shown that the cyclic limit of proportionality and the cyclic strain parameters, characterizing the widths of the plastic strain hysteresis loops of the first and second half-cycles are and , respectively, and the coefficient of cyclic softening, showing the variation of the hysteresis loop depending on the number of loading half-cycles, , is .
The material accumulates residual plastic strain in the direction of initial loading (tension) (
Figure 6) because the hysteresis loop width of the paired half-cycles is greater than the loop width of the adjacent unpaired half-cycles. The theoretical accumulated unilateral plastic strain can then be presented as follows:
Figure 6 shows the calculated curves and the experimental values of the accumulated unilateral plastic strain
. The low-cycle strain test data shown in
Figure 4,
Figure 5,
Figure 6,
Figure 7 and
Figure 8 suggest that the material of the automatic coupler is cyclically softening and accumulates unilateral plastic strain. Therefore, it is clearly undergoing an accumulation of cyclic and quasi-static damage. For this reason, the investigation of durability under strain-controlled loading s with the strain restrictions applied has also been carried out (
Figure 6 and
Figure 7).
Figure 8 shows the calculated curves for the asymmetric cycle and the experimental
values. Investigations have shown that the cyclic strain parameters of the asymmetric cycle characterizing the hysteresis loop widths of the plastic strain of the first and second half-cycles are
and
. In the case of strain-controlled loading, quasi-static damage is eliminated. The shares of damage caused by fatigue and quasi-static damage can be determined by using the strain-controlled and stress-controlled loading durability curves. This is very important for calculating the total low-cycle damage [
22].
The specimens were made from the body of an automatic coupler and were therefore limited in number. Under strain-controlled low-cycle loading, the strain is restrained; hence, no unilateral accumulation and no quasi-static damage have been identified. In this case, the specimen is damaged only by cyclic plastic strain. The linear dependence of the plastic strain on the number of loading cycles
to failure is known to be present under strain-controlled loading in logarithmic coordinates (Coffin’s equation [
24,
25,
26]); therefore, five specimens were allocated for the tests.
4. Discussion and Conclusions
The material of the analyzed automatic coupler is the insignificantly (α = 0.123) cyclically softening steel 20GL. Hence, the variation of the accumulated fatigue and quasi-static damage depending on the number of loading half-cycles has shown that, in the calculation of these types of damage, the cyclic softening of the material can be ignored and the calculations can be performed by using the hysteresis loop width in the durability half-cycle.
The automatic coupling was found to be subject to static, low-cycle, and quasi-static fatigue damage. Furthermore, the load on the automatic coupler varied over time, depending on the weight, the velocity of the rolling stock, and the railway relief. Therefore, low-cycle stationary stress-limited loading dependencies, accounting for low-cycle quasi-static and fatigue damage, were proposed for the calculation of the durability of an automatic coupler. The linear law of summation of the number of loading cycles was proposed for the assessment of low-cycle fatigue damage. The calculation of an automatic coupler required the determination of its load history in each case and the calculation of its duration using the dependencies shown above.
In order to accurately estimate the duration of the initiation phase in an automatic coupling, it is necessary to know the exact loading history of the coupler, i.e., the sequence of loading levels and the number of cycles for each level. These data can be obtained only by recording the variation of forces or strain in the automatic coupler during the specific trip. Hence, the authors of this paper propose conducting the general calculations by using specific levels and the number of cycles within the levels, i.e., the data provided in the literature, by statistically processing the given operational data, not taking into account the historical load data.
The presented calculation results show that static overload of the automatic coupler is highly dangerous as it causes considerable quasi-static damage. Hence, after train accidents, i.e., wagon rollover or derailment, the automatic couplers must be inspected very thoroughly (i.e., the automatic coupler must be checked for any residual strain and cracks).
The methodology proposed in this paper for the calculation of low-cycle damage is applicable to the durability assessment of different parts of the housing under complex loading conditions both in view of loading cycles and forces.
Based on the results obtained in this work, further research may be carried out with the purpose of suggesting the method for automatic coupler damage summation using low-cycle non-stationary load dependencies considering static, low-cycle, quasi-static, and high-cycle fatigue damage.