Abstract
The test results on hourglass specimens of steel under repetitive sine loads provide graphs that indicate the stress range in terms of the number of cycles to failure and are known as S-N curves. Using this curve, it is determined that if the applied stress is less than a certain level, failure will not occur as the number of load cycles increases. The S-N curve can be affected by several factors such as yield stress, temperature, surface properties, and corrosion. In this research, the S-N curve has been investigated for two types of high-strength steels, S690 and S460, as well as two types of mild-strength steels, S235 and S355, at 25°C, and S355 with corrosion. The numbers of samples used for S235 and S460 steels were 45 each while S355 and S690 steels were 36 each and for S355 with corrosion was 15 with the high cycle fatigue curve obtained for them. To investigate the effect of plate thickness on the high cycle fatigue of the samples, four sets of 24-piece S235 steel samples, being 96 samples in total, were made of plates with different thicknesses of 8, 12, 15, and 20 mm and tested. Finally, a four-story three-span steel moment frame was designed, and under the Northridge earthquake record, the high cycle fatigue was investigated. It was observed that the high cycle fatigue was not effective for the mentioned structure under the Northridge earthquake record, but in the corroded structure, damage from high cycle fatigue occurs under this record.
1. Introduction
The term fatigue was first used by a French mathematician named Punklet in his book in French in 1841 [1]. In 1850, Wohler first systematically examined the fatigue behavior of steel [2]. Since the concept of metal fatigue was unknown at the time, the microscopic and mechanical aspects of the fatigue data were not well understood, and therefore, Wohler’s aim was to obtain rail fatigue data for which the fatigue characteristics were not considered up to that time. Attempts for obtaining fatigue parameters for different materials have continued to this day since Wohler introduced railroad design for safe design [3]. Fatigue in microstructure scale is a complex process of formation and cracking which depends on microstructural features [4–9].
Ultralow cycle, low cycle, and high cycle fatigue are all types of fatigue [10]. In ultralow cycle fatigue, failure will be malleable due to strain greater than the yield stress in the structure, which is characterized by high plastic strain amplitudes (several plastic strains) and a very small number of load cycles (typically about 10–20 cycles) [11–14]. When a structure experiences low cycle fatigue, which has cycles between 102 and 104, the strain is less than the yield strain, causing brittle failure [15]. High cycle fatigue is characterized by a high number of cycles (more than 104 cycles) and, like low-cycle fatigue, a brittle failure with a strain less than the yield strain at the time of failure [16].
Considering alloy design, conditions that contribute to nucleation resistance and growth of microcracks under fatigue load may not help resist the growth of large macrocracks, and vice versa. For example, fine grain tends to resist more nucleation and microcracks growth, and in this case, the grain boundaries act as deflectors or stoppers of microcracks, thus reducing the growth rate of microcracks of fatigue. However, as the crack grows and the length of cracks increases, fine-grained flatter the crack path and elevate the crack growth rate. In contrast, coarse-grained materials tend to create a rougher crack path for macrocracks, and due to crack closure and the crack tip deflection mechanism, the rougher the crack path, the greater the resistance to the growth of large cracks. As mentioned, many variables are involved in fatigue, so it is best to do the test to consider all of factors.
In the hot rolling process, the thickness of steel slabs diminishes by passing through two rollers, while the direction of the slab is opposite to the direction of rotating of the rollers, and if the width of the slab is constant, its length rises [17]. The general hot rolling process is displayed in Figure 1.
The processes involved in hot rolling are as follows: Reheating: the slab is heated to a temperature of 1200–1250°C in a furnace to remove dendrites from casting as well as to combine most of the alloying elements. Rough rolling: before rolling, the scale created during the heating stage is removed by spraying high-pressure water in the descaling box. The slab then moves to the roughing mill. At this step, the thickness of the slab is reduced between 270 mm and 50 mm by passing through the roller. Also, its width is altered using vertical rollers installed on the sides. After shaping, it is transferred to the next stage using the transfer table. Finish rolling: the final forming stage consists of five to seven rollers. The slab enters this part, with temperature and thickness measured by sensors for the final mill at this stage and the temperature adjusted using the speed of the rollers. Cooling: after rolling, the strip is cooled by a water flow. Coiling: in the last step, the strip temperature is measured and the strip is coiled by the coiler.
Due to the difference in the cooling rate of the sample, for example, in the cooling stage, the size of the grain changes with the thickness of the steel, and near the surface, the steel grain will have a finer structure than the center of the strip because it cools faster (the surface of the metal cools quickly, and the crystals on the surface do not get a chance to grow, but in the center of the section, due to the fact that the cooling speed is lower than the surface, the crystals can grow). As mentioned, the finer the steel grain, the slower the crack nucleation rate, but the higher the crack growth rate, and if the grain is coarse, the higher the crack nucleation rate but the slower the growth rate.
The estimated annual cost of corrosion in the United States of America is about 30 billion dollars, which shows a huge economic loss. Wherever there is metal, corrosion occurs with different degrees and intensities. When protective coatings and cathodic protection systems are either absent or ineffective, steel structures exposed to harsh environments such as urban, industrial, and marine environments, such as transmission towers, steel bridges, industrial buildings, and offshore platforms, show signs of surface corrosion [18, 19].
Significant degradation in the strength and ductility of corroded steel plates, as well as a large decrease in the energy dissipation capability of corroded H-shaped steel columns with an increase in the percentage of corrosion, were observed using the tensile test [20, 21].
Corroded steel members are more likely to experience damage and failure when a strong earthquake occurs, for example, the Wen Chuan earthquake in China, the Osaka earthquake in Japan [22], the Northridge earthquake in 1994 [23], and the Alaska earthquake in 1964, where corroded structures experienced more damage and failure than other structures.
To study cyclic fatigue in this paper, S-N curves are used, in which the vertical axis is the stress applied to the structure (σ) and the horizontal axis is the number of cycles that can be tolerated by the structure at the stress applied to the structure. In order for the structure not to be damaged under high cycle fatigue, the amount of stress applied in each cycle should be lower than the corresponding amount of stress that cycle which is obtained from the S-N diagram for the desired material.
Unfortunately, a one S-N diagram cannot be used for all metals, and each metal has its own S-N curve, which changes under factors such as corrosion, surface finishing, and treatments. [24], where S-N diagram requires a large number of tests at different stress intensities and a large number of cycles, which requires considerable time to perform the test. In this study, the Wohler method was used to perform the cyclic fatigue test. In the Wohler method, or the same method of the four-point bending test, which is very common, one half of the sample is under tensile stress at all times, while the other half, which is symmetrical to the first half, is under compressive stress, and thus, in a complete cycle, the average received stress (Sm) is zero (see Figure 2). The mean stress, Sm, can have a substantial influence on fatigue behavior. In general, tensile mean stresses are detrimental, and compressive mean stresses are beneficial. Substantial investigation of tensile mean stress influence on long-life fatigue strength has been made [24].
is equal to the applied stress and also is equal to −1 called the “fully reversed” condition, and the loading frequency is 120 Hz selected. Mean, Sm, maximum, , minimum, , and range, , of applied stress are shown in the following equations and also are displayed in Figure 3.
The samples to be tested for cyclic fatigue must have polished surfaces so that the surface roughness of the samples does not interfere with the results. Figure 4 displays the details of fatigue sample as well as a number of samples before and after failure. To report the amount of applied stress, the stress range or the stress amplitude Sa = S/2 is used. In this research, all applied stresses are in the form of Sa.
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Another parameter that affects the S-N curve is corrosion. In the following, explanations are given regarding the classification of corrosive environments and the amount of consumption for different years.
This research investigates high cycle fatigue in common steels in civil engineering, which include high-strength steels (S690 and S460) and mild-strength steels (S235 and S355) used in the construction industry, and also investigates the effect of thickness on the fatigue limit. Since steel is prone to corrosion in environments and atmospheric corrosion is one of the most common types of corrosion in steel structures, at the end of this research, the effect of corrosion on the fatigue of steel structures is investigated. The process of research is shown in Figure 5.
In the following, explanations are given regarding the classification of corrosive environments and the amount of consumption for different years.
2. Corrosion
Corrosion is defined as the destruction or corruption of a material as a result of reaction with the environment in which it is located. Some authorities insist that corrosion is limited to metals, but in a comprehensive classification, even nonmetallic materials such as plastic and ceramics are destroyed and corroded in the vicinity of chemicals and even sunlight [26].
If the environments that cause corrosion are divided, they can be divided into three general areas: corrosion in the atmospheric environment, corrosion in seawater, and corrosion in soil. In this research, atmospheric corrosion has been investigated. Atmospheric corrosion is mainly due to moisture and oxygen, but the problem becomes more critical with impurities such as sulfur compounds and sodium chloride.
The ISO 9223 standard examines the corrosion rate in the first year in different atmospheric environments. This standard divides atmospheric corrosive environments into 6 categories, which are shown in Table 1.
By using the ISO 9224 standard, which is an annex to the ISO 9223 standard, the amount of corrosion can be obtained for different years based on the category of the corrosive environment (Table 2).
The corrosion rate considered for this article corresponds to 20 years of corrosion in a corrosive environment with the CX category, which is related to the subtropical region with high humidity and high SO2 pollution (SO2 more than 250 mg/m3).
3. The Method of Creating Corrosion
It is clear that it can in some way create the corrosion that occurs in natural conditions in the samples with the necessary instructions, with the difference that the time when the corrosion occurs in the samples should be much shorter than the time when the corrosion occurs in the real area, and it should be able to be implemented with the same accuracy. ASTM G60-1 standard is used to simulate corrosion; this standard specifies the conditions of simulation corrosion for atmospheric conditions [29].
The specimens should be humidity cycle three times per day, as shown in Figure 6, and a dip cycle once a day.
The temperature of the air in the test chamber is 52 ± 1°C. The range of relative humidity can be extended by adding a drying period to the humidity cycle. The minimum relative humidity shall be ≤20%, and the maximum relative humidity shall be ≥95% for each cycle.
The dip solution should be prepared by dissolving 1% sodium chloride (NaCl), 1% calcium chloride (CaCl2), and 0.1% sulfuric acid (H2SO4) by solution weight in water (See Figure 7). The solution volume to specimen surface area ratio should be a minimum of 250 mL/cm2.
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One dip cycle shall consist of three 5 min immersion periods. The dip solution is drained from the test chamber for a 1 min period between each immersion period. The samples before corrosion and after 5 months of exposure in the corrosion simulator environment can be seen in Figures 8(a) and 8(c). The two ends of the sample, which are placed in the clamp of the fatigue testing machine, are coated with epoxy to prevent the corrosion of these two areas.
The amount of corrosion in the samples is equal to 10%. For a column with S355 material with a total depth of 400, a flange width of 250, a flange thickness of 20, and a web thickness of 10 mm, the amount of corrosion corresponding to 20 years in environmental conditions CX (see Table 1), which is the weather conditions in an industrial area, is equal to 10%.
The choice of 20 years when the structure is exposed to a corrosion environment is because the protective coating of the structures to prevent corrosion usually disappears after 5 years, and after the end of this time, the main structure undergoes corrosion [30]. Considering that the life of a structure is assessed to be 30 years, an estimate of the capacity of a structure that undergoes corrosion, during this period and still has 5 years of its life remaining, is necessary.
4. Stress-Strain Diagrams of S235, S355, S460, and S690 Steels
The chemical composition of S235, S355, S460, and S690 steels is given in Table 3. The strain-stress diagram of the steels used in this study to test the high cyclic fatigue is shown in Figure 9. It can be seen that as the strength of the steel rises, its ductility decreases. For example, the ultimate strength of S690 steel is one and a half times that of S235 steel, but its ductility is 0.3 times that of S235 steel.
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5. Sensitivity of S-N Diagram to Plate Thickness
According to the thickness of the plates produced in hot rolling mills in Iran, to investigate the effect of plate thickness in high cycle fatigue, four plates with thicknesses of 8, 12, 15, and 20 mm were selected and from each plate, 24 hourglass samples have been made for high cycle fatigue testing (see Figure 10).
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The samples are placed in a rotating bending fatigue testing machine. The shape of the rotating bending fatigue testing machine used in this research is depicted in Figure 11.
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The results of the high cycle fatigue test for the S235 sample made from different palates are reported in Table 4. Note that in this table, the results of each sample are the average of the results of the three samples at the same level of stress.
If the applied stress is plotted against the corresponding number of cycles, the S-N diagram of the selected steel is obtained. In this figure, a horizontal line is marked in red with a dashed line which indicates the fatigue limit (see Figure 12).
Because of the flattening of the S-N curve and the independence of fatigue life from stress cycles, this region is fatigue limit and is the region of infinite life, at least for ferrous alloys and titanium. A load can be applied indefinitely many times below this limit without experiencing failure.
Five different results are likely to be obtained from the same traction or fatigue test if five specimens of the same material, size, and surface finish are used. Ten different results are probably to be expected if there were ten test pieces. Increasing the number of specimens will not change this general outcome but will probably yield some new lower or higher value, as well [24]. In this research, the average of three data at each stress level is used to draw the S-N diagram.
Fatigue limit is the stress that, if the applied stress is equal to or less than it, the fatigue failure will never occur in the material, regardless of the number of loading cycles. As a result, in various industries such as aerospace engineering and civil engineering, for the design of structures, design based on the fatigue limit obtained from the S-N curve in such a way that the size of the section and the amount of stress applied to the member, always below the fatigue stress limit and in this way, the long life of the member is guaranteed.
Thus, in designing for parts where access is not possible to replace the part or the replacement cost is high, it is tried to observe the fatigue limit for that member so that the member does not get influenced by failure due to high cycle fatigue.
The S-N diagram of S235 sample made from plates with thicknesses 8, 12, 15, and 20 mm is shown in Figure 13.
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As displayed in Figure 13, for samples made of steel plate with thicknesses of 8, 12, 15, and 20 mm, respectively, at stresses of 150 MPa, 145 MPa, 135 MPa, and 115 MPa, they become insensitive to cycle loads. The diagram can be divided into two parts according to Figure 14: one part of the diagram that changes with changing stress (area 1) and the other part that is not sensitive to stress change (area 2).
Fitted diagram S235 sample made from plates with thicknesses of 8, 12, 15, and 20 mm is presented in Figure 15. At the top of each diagram, the equation of the fitted lines corresponding to the different parts of the diagram is written. The correlation coefficient for fitted diagram S235 from plates with thicknesses of 8, 12, 15, and 20 mm is, respectively, equal to 0.98, 0.92, 0.94, and 0.99.
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To evaluate the sensitivity of the S-N diagram to the thickness of the selected plate for producing the sample, the first part of the diagram for different thicknesses is drawn in Figure 16 and the second part of the diagram, which reveals the fatigue limit, is drawn in Figure 17. Observing Figure 16, it is concluded that if the sample made from plate with 8 mm thickness is considered as a basis, the maximum diagram changes in the first region compared to increasing the plate thickness to 20 mm are equal to 25%, suggesting that the fatigue strength of the sample made from plate with 20 mm thickness is about 25% less than the plate with 8 mm thickness.
For the second region of the S-N diagram (see Figure 17), the fatigue limit for S235 samples made of steel plate with a thickness of 20 mm is about 24% lower than the fatigue limit ratio of the sample made of steel plate with a thickness of 8 mm. The reason for this difference, as stated, is due to the different cooling rates in plates with different thicknesses in the production process and the size effect strongly depends on the average number of defects and inclusions in the material, which increases with thickness [24].
It can be seen that the size of the diameter is affecting the S-N curve of the material. A size factor that reduces the fatigue limit of the material as the specimen diameter increases. One of the most common and rather conservative formulas is that proposed by Shigley and Mitchell (equation (4)) [31].where d is the diameter of the specimen or component. Being empirical in nature, equation (4) can be used only in the range of diameters considered, i.e., 8–250 mm.
If the sample with a diameter of 8 mm is set as a reference, according to equation (4), the fatigue limits 140, 137, and 133 are obtained for samples with a diameter of 12, 15, and 20 mm, respectively.
Another formula for fatigue limit for specimens with different diameters is proposed by Weibull (equation (5)) [24]. In this formula, l is the length of the specimen.
If the sample with a diameter of 8 mm is set as a reference and the factor m is taken for steel 25, according to equation (5), the fatigue limits 147, 146, and 144 are obtained for samples with a diameter of 12, 15, and 20 mm, respectively. Table 5 shows the experimental values and the corresponding values obtained from equations (4) and (5)
Equation (6) was proposed by the authors for size factor in the fatigue limit for S235 specimens made of different plate thicknesses. The correlation coefficient for this equation is 0.97 and to use this formula, the fatigue limit must be in MPa.
6. High Cycle Fatigue Diagram of S235, S355, S460, and S690 Steels
The following are the fatigue diagrams for S235, S355, S460, and S690 steels, each containing 36, 45, 36, and 45 samples made of plates with a thickness of 10 mm, respectively. Table 6 lists the data related to the S235 steel high cycle fatigue test and Figure 18 depicts the diagram as well as the line fitted for it. The correlation coefficient for fitted diagram for the sample S235 is equal to 0.99.
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The data for the S355 high cycle fatigue test are shown in Table 7 as well as the line fitted for its fatigue diagram in Figure 19. The correlation coefficient for fitted diagram for the sample S355 is equal to 0.99.
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Table 8 relates to the high cycle fatigue test data of S460 steel and a fitted line is also drawn for it in Figure 20. The correlation coefficient for fitted diagram for the sample S460 is equal to 0.99.
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Table 9 reports the data for the S690 high cycle fatigue test, as shown in Figure 21, as well as the line fitted for it. The correlation coefficient for fitted diagram S690 is equal to 0.99.
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7. High Cycle Fatigue Diagram of S355 with Corrosion
S355 samples after being placed in the corrosion simulator with the process explained in Section 3 to simulate atmospheric corrosion with a corrosion rate of 10% (it should be mentioned that it took five months to create this amount of corrosion with the described process for the creation of corrosion), were subjected to the high cycle fatigue test, and the S-N diagram for it is shown in Figure 22(a). The S-N diagram of S355 with 10% corrosion and without corrosion is shown in Figure 22(b). As can be seen in Figure 22(b), the fatigue limit in the case of the sample with corrosion has decreased by 39%. In the area before the fatigue limit, the stress reduction is equal to 25%.
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The reason for reducing the fatigue limit is explained below. Corrosion created using the ASTM G60-1 standard cause’s uniform corrosion on the surface of the member, but due to the presence of materials such as calcium chloride and sodium chloride in solution, along with uniform corrosion, it causes pits on the surface of the member (Figure 23). These pits are caused by the concentration of stress in the member, and if the amount of stress concentration in the same area increases due to the singularity of stress in different cycles, it causes cracks to spread and causes the overall failure of the member.
8. Modeled Steel Moment Frame to Check High Cycle Fatigue
As stated in the Introduction section, there are three types of fatigue include ultralow cycle, low cycle, and high cycle. Ultralow cycle fatigue is strain-dependent, but in the case of high cycle and low cycle fatigue, it is stress-dependent. When a strong earthquake occurs, in such a way that the structure enters the nonlinear domain under the effect of this earthquake and the amount of strains in the structure exceeds the elastic strain limit, ultralow cycle fatigue becomes important. If the structure under earthquake record does not enter the nonlinear domain, high cycle and low cycle fatigue become important.
The important point is that this low-intensity earthquake that does not enter the whole structure into the nonlinear domain may happen many times in a certain period, which can be mentioned as an example; the Wenchuan earthquake occurred on May 12, 2008, by September 8, 2008, and there had been 42,719 total earthquakes [32].
Or as mentioned in the Introduction section, the Northridge earthquake in 1994, and the Alaska earthquake in 1964 where corroded structures experienced more damage and failure than other structures [23].
To investigate the high cyclic fatigue, a four-story three-span steel moment frame with a story height of 3 meters and a span length of 6 meters, as well as a load span of 6 meters perpendicular to the frame beams, according to ASCE/SEI 7–22 and AISC 360−22 for dead load 750 and live loads 200 kg/m2 and soil type II design and is shown in Figure 24. The Northridge earthquake record of Canyon Country—W Lost Cany earthquake station in 1994 (see Figure 25) is introduced into the structure and then the history of stress carried out for the bottom of the column is specified in the figure in which the highest amount of stress is applied to this area due to the Northridge earthquake record.
The frame was once modeled with S235 material and again with S355 material. The cross-section of the column for S235 material is as a column with a total depth of 500 and a flange width of 300 and web thickness of 20 and flange thickness of 10 mm, and for a column with S355 material a total depth of 400 and a flange width of 250 and a flange thickness of 20 and a web thickness of 10 mm. The stress history on the column for S235 and S355 materials is depicted in Figure 26.
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The number of cycles for different stresses calculated by the rainflow algorithm [3]; this is the most common and most accurate way to count cycles. The rules of rainflow are as follows:(1)Rearranging the stress-time diagram of the events so that the highest peak or the deepest valley comes first.(2)Starting from the highest peak (or the lowest valley), go down to the next reversal. The rainflow runs down and continues unless either the magnitude of the following peak (or the following valley, if we started from the lowest valley) is equal to or larger than the peak (or valley) from which it initiated, or a previous rainfiow is encountered.(3)For the following reversal, follow the same procedure, and so on until the end.(4)For all ranges and parts of a range that were not used in the previous steps, repeat the procedure.
The result of rainflow is shown in Figure 27. As can be seen from Figure 26, high cyclic fatigue does not matter for the Northridge earthquake record for building with materials S235 and S355 but in the building with corrosion, this record has caused damage to the structure. In fact, in the steel structure with S355 , some lines of the stress, pass through the red area in the figure diagram, which means crossing the fatigue tolerance threshold.
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9. Conclusion
In this study, high cycle fatigue was investigated for S235, S355, S460, and S690 materials. The number of samples used for S460 and S235 was 45 each and S690 and S355 was 36 and for S355 with corrosion was 15. Then, to investigate the effect of the selected plate thickness on cyclic fatigue, four sets of samples, each containing 24 pieces, were made and tested from plates with different thicknesses of 8, 12, 15, and 20 mm. The results of this study for the fatigue limit of the abovementioned materials are as follows:(i)By changing the thickness of the plates from which the high cycle fatigue samples were made, the fatigue limit was changed about 25%. The reason for this difference is due to the different cooling rates in plates with different thicknesses in the production process and the size effect strongly depends on the average number of defects and inclusions in the material, which increases with thickness.(ii)The S-N curve has been investigated for two types of high-strength steels, S690 and S460, as well as two types of mild-strength steels, S235 and S355, at 25°C.(iii)For S355 steel, the ASTM G60-1 standard was used to simulate atmospheric corrosion and by using the ISO 9224 standard, which is an annex to the ISO 9223 standard, the amount of corrosion for 20 years was obtained and the fatigue limit in the case of the sample with corrosion has decreased by 39%.
Then, high cyclic fatigue was calculated for a four-story, three-span frame, once with S235 and again with S355, which inputted the Northridge earthquake record of Canyon Country—W Lost Cany earthquake station in 1994; high cyclic fatigue does not matter for the Northridge earthquake record for building with materials S235 and S355 without crossing but in the building with corrosion, this record has caused damage to the structure.
Data Availability
The data used to support the study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.