Introduction

Ships are an economically important means of transportation, as they transport cargo of very high tons, reaching 10,000 tons [1]. Given that ships are important from an economic standpoint and in the transportation process, one of the main challenges these ships face is the deterioration of structural materials due to the corrosive marine environment constantly exposed to cyclic loads [2, 3]. Because these plates are constantly exposed to a corrosive marine environment, they are exposed to the occurrence of cracks on the metal surface due to corrosion, which is considered the beginning of the growth of the crack [4, 5]. These cracks. as a result of periodic loads, will experience rapid growth [6]. These cyclic loads result from seawater waves and winds, the acceleration and deceleration of the ship, and the vibrations issued by the ship’s engines [7, 8]. These loads affect the hull plate, leading to fatigue of the metal, a weakening of its strength, a decrease in its life and fatigue limit, and some cases it leads to failure, breakage of the plate, and sinking of the marine ship [9, 10]. Improper loading or unbalanced distribution of cargo and weights can accelerate the onset of fatigue [11, 12].

Research Aim

This research aims to investigate the behavior of C35 carbon steel plates under the influence of cyclic loading and corrosion in the marine environment, which is one of the important matters to avoid failure of the hull of marine ships.

Fatigue Mechanism

Fatigue occurs when cyclic loads of stress or strain are continuously applied to the metal, leading to the metal's eventual failure [13]. An example of this phenomenon is the cyclic load placed on the connecting rod and crankshaft of the engines and turbine blades, leading to their failure [14]. In this research, we will focus on the effect of the fatigue phenomenon on the hull of marine ships resulting from the weight of the cargo as well as the sea waves hitting the hull's surface [15]. Fracture occurs less than the yield stress or less than the tensile stress in some metals [16]. The stages of metal failure resulting from cyclic loads are divided as follows [17]:

  • The stage of fatigue crack initiation, where the crack grows at an angle of 45 degrees with respect to the stress axis.

  • The stage of fatigue crack propagation, where the crack continues to grow at an angle of 90 degrees with respect to the stress axis. This growth continues until it reaches the failure stage.

  • The stage of fatigue final fracture, where the metal failure and breakage.

These stages occur gradually until the metal reaches the stage of failure and collapse [18]. The TecQuipment SM1090 device was used, and the principle of operation of this device is to connect the sample on one end to a rotating motor that rotates the sample, and on the other end, it is a rotating ball bearing through which a load of different weights is applied [19]. That is, the sample is treated as a cantilever, as by rotating this sample and applying the bending load, periodic loads occur that ultimately lead to the failure of the sample. The type of diagram that describes the action of the stresses placed on the sample is a completely reversed stress cycle (see Fig. 1):

Fig. 1
figure 1

Completely reversed stress cycle mechanism where (a) the initial state, (b) the half-turn, (c) the full turn

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In this type of stress, the sample is exposed to tensile stress from the bottom and compressive stress from the top. When the sample rotates a half-cycle, the area that was previously subjected to tensile stress is now exposed to compressive stress. The area that was previously exposed to compressive stress is now exposed to tensile stress, so the value of the maximum stress will be equal to the minimum stress. When the complete cycle occurs, the area of the sample will return to the first case and will be subjected to the same type of stress in the first case. The rotation process continues until the sample reaches failure due to cyclic loads.

Some mathematical relationships have been derived from Fig. 1, Stress Range \(\Delta\updelta\) as in Eq 1 Below [20]:

$$\Delta\updelta ={\updelta }_{{\text{max}}}-{\updelta }_{{\text{min}}}$$
(1)

where the \({\updelta }_{{\text{max}}}\) is the maximum stress, \({\updelta }_{{\text{min}}}\) is the minimum stress.

Stress Amplitude \({\updelta }_{a}\) as in Eq 2 Below:

$${\updelta }_{a}=({\updelta }_{{\text{max}}}-{\updelta }_{{\text{min}}})\backslash 2$$
(2)

Mean Stress \({\updelta }_{m}\) as in Eq 3 Below:

$${\updelta }_{m}=({\updelta }_{{\text{max}}}+{\updelta }_{{\text{min}}})\backslash 2$$
(3)

In completely reversed stresses the \({\updelta }_{{\text{max}}}=-{\updelta }_{{\text{min}}}\), so \({\updelta }_{m}=0\).

Stress Ratio \(R\) as in Eq 4 Below:

$$R={\updelta }_{{\text{max}}}\backslash {\updelta }_{{\text{min}}}$$
(4)

In completely reversed stresses, the \({\updelta }_{{\text{max}}}=-{\updelta }_{{\text{min}}}\), so \(R=-1\).

The relation between endurance limit and stress ratio \({\sigma }_{e}{\prime}\) as in Eq 5 Below:

$${\sigma }_{e}{\prime}={3\upsigma }_{e}\backslash 2-R$$
(5)

A factor of safety is a parameter applied to the calculated fatigue life, providing a safety factor to mitigate the risk of premature failure [21]. Engineers incorporate a safety factor to account for uncertainties in material properties, loading conditions, and potential defects in the structure [22]. This factor prolongs components' structural integrity and durability, contributing to safety and performance in applications ranging from ships, bridges and aircraft to gear parts and various other applications as in Eq 6 Below:

$$F.S=\frac{{\upsigma }_{e}(\mathrm{Endurance\,Limit\,Stress})}{{\upsigma }_{d}(\mathrm{Design\,or\,Working\,Stress})}$$
(6)

Fatigue Curve (S-N Curve)

The fatigue curve is a basic and important concept in materials engineering, which explains the relationship between stress (\({{\varvec{\sigma}}}_{{\varvec{f}}}\)) and the number of cycles to failure (\({\mathbf{N}}_{\mathbf{f}}\)) during cyclic stress applied to the metal [23]. This curve is critical for evaluating the fatigue behavior of the metal [24]. The shape and characteristics of the S-N curve depend on many factors, such as material type, heat treatment, and environmental conditions, providing valuable insights into the fatigue performance of materials in various engineering applications [25]. The S-N curve diagram can be represented by the following mathematical equation: Eq 7 Below:

$${\sigma }_{f}={{\text{AN}}}_{f}^{\alpha }$$
(7)

where \({\sigma }_{f}\) the stress at which failure occurs, \({N}_{f}\) is the number of cycles at which failure occurs, A and \(\alpha\) are constants.

Fatigue life is defined as the extent to which a material can withstand repeated cycles of stress and strain applied to the metal before failure [26]. Understanding fatigue life is essential to ensuring the longevity of structures as it helps prevent unexpected failures that may result from cumulative damage resulting from repeated loading and unloading cycles [27]. Engineers use advanced testing methods and numerous mathematical models to estimate and predict the fatigue life of materials with high accuracy to extend the fatigue life of materials, enhancing safety and durability across various industries [28]. There are two types of methods used in the analysis and design of fatigue life, which are as follows:

  • The stress-life method.

  • The strain-life method.

The first method will be used to design and analyze fatigue life in this current research [29]. The Endurance limit is the highest stress value can be safely applied to the metal without causing failure or breakage for an infinite number of life cycles, usually \({10}^{7}\). This laminate is only used with completely reversed stress [30].

Experimental Procedure

The procedure includes conducting an experiment in terms of preparing DIN 1.0501 C35 steel from the process of purchasing, cutting, cleaning and polishing samples to use them for fatigue testing, then obtaining S-N-curve diagrams and knowing the number of cycles at which fracture occurs to test fatigue for the cases of corroded and non-corroded steel. We will discuss each process in detail.

Material

DIN 1.0501 C35 steel was purchased from Chinese company [31]. The samples were cut according to the dimensions required for the fatigue samples (the large diameter of 8.99 mm, small diameter of 4.05 mm, and length 64 mm) with ten samples, five samples for the corrosion-fatigue case and five samples for the pure fatigue case. The sample and the dimensions required for the testing operations as shown (see Fig. 2) below:

Fig. 2
figure 2

(a) The fatigue sample, (b) The dimensions of fatigue sample

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Mechanical Properties

The purchased fatigue samples are examined in terms of chemical elements and mechanical properties of C35 carbon steel, and the chemical composition data has been measured as shown in Table 1 below:

Table 1 Chemical composition of C35 Carbon Steel Sample.
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The mechanical properties data (ultimate tensile stress, yield stress, elongation and BHN) obtained from the tensile test and hardness test are attached in Table 2 below:

Table 2 Mechanical properties of C35 Carbon Steel for ASTM standard fatigue Sample.
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Mechanical properties are of great importance in fatigue testing, because knowing the value of ultimate strength is considered one of the important parameters in knowing the value of the stress levels applied to samples for fatigue testing.

Samples Preparation

After preparing the samples and cutting them to the required dimensions, the ten samples are prepared and processed for the fatigue process, as shown (see Fig. 3) below:

Fig. 3
figure 3

The C35 carbon steel fatigue samples

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The microstructure of the alloy is clarified and samples are prepared in two stages, as follows:

  1. 1.

    The first stage, which is the mechanical method, is carried out by removing the oxides and corrosion materials remaining on the surface of the metal through the process of polishing and grinding using sandpapers with different degrees of roughness of 120, 240 and 600 sand grits. Starting with rough papers, then smooth papers, and then polishing, the procedures followed are those suggested by ASTM standards that govern surface cleaning [32].

  2. 2.

    The second stage includes washing the samples with distilled water, drying them, cleaning them with organic solvent acetone to remove suspended organic materials, and then rinsing them with distilled water before drying.

Corrosion Test

The corrosion test is carried out by immersing the cylindrical samples in an artificial seawater solution to complete the corrosion process for the five samples prepared for the corrosion-fatigue test. This is to determine the effect of corrosion on the fatigue life and fatigue limit of C35 carbon steel. A glasses pool is prepared and filled with a solution of artificial seawater prepared by mixing 1 liter of distilled water with 35 grams per liter of sodium chloride salt (weight concentration of 3.5%). The corrosion pool with water pump and heater is shown (see Fig. 4) below:

Fig. 4
figure 4

The pool of artificial seawater for corrosion-fatigue test

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The pump was used inside the basin to dissolve the salt only. After the end of the first dissolve, the samples are lowered by total immersion under conditions of flowing water (accelerated corrosion) at a rate of 1500 (liters per hour) in order to simulate the flowing marine environment. This is done for 24 hours of immersion to reach a reasonable level of corrosion. The level of corrosion was based on the immersion time.

Fatigue Test

Fatigue testing is performed by applying 5 different stresses (200.7, 211.5, 220.7, 231.5, 240.7) (MPa). The division of these stress levels was based on the ultimate strength value and the yield stress value that were previously measured from mechanical properties test. Where 0.9 of the yield stress value of 275 (Mpa) is taken as the highest stress value applied to the sample. And take 0.4 of the ultimate strength value of 500 (Mpa) as the minimum stress value applied to the sample [33]. Then we scale the values by 0.8, 0.7, and 0.6 of the yield stress. Five samples will be used for pure fatigue case and 5 samples for corrosion-fatigue case. A fatigue device (TecQuipment SM1090) located in the strength laboratory in the Department of Mechanical Engineering at the University of Baghdad was used. The fatigue device used in this research as shown (see Fig. 5) below:

Fig. 5
figure 5

Rotating Fatigue Machine (TecQuipment SM1090)

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This device is connected to a controller to control the frequency (Hz) and to turn the device on and off, as well as a screen to display the amount of load placed on the sample. The device can be connected to a personal computer to receive the obtained results and draw a curve (S-N) directly by using TecQuipment VDAS Software as shown in Appendix Fig. 13.

Results and Discussion

This research aims to study the fatigue and corrosion-fatigue behavior of C35 carbon steel, which is one of the necessary things for engineers to know this behavior for the sake of design processes especially ship hull design [33]. It is of great importance to know the metal’s resistance to marine conditions because the marine environment is considered one of the most intense and severe environments that engineers take into consideration to ensure the safety of industrial facilities [34].

Corrosion Test

After applying the immersion process to the samples for 24 hours at a temperature of 24 degrees Celsius, the samples are taken out of the solution. The corrosive environment was monitored and regulated precisely during the whole test process, and the corrosion process was constantly observed as shown (see Fig. 6) below:

Fig. 6
figure 6

Corroded samples for corrosion-fatigue test

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From Fig. 6, the surface of the corrosion fatigue sample is covered by a large number of corrosion pits and corrosion products. After completing the corrosion process, samples are prepared for the fatigue process to obtain data on fatigue behavior in the corrosion-fatigue test. The sample is cleaned with distilled water using a brush to remove the materials stuck on it, then the sample is washed with acetone, and then the samples are dried.

Fatigue Test

The fatigue test is performed for fatigue and corrosion-fatigue cases to know the corrosion effect. Samples are taken and installed in the TecQuipment SM1090 device to perform a fatigue test for C35 carbon steel, where the bending load is applied from one end of the sample, and the other end of the sample is installed in the rotating part connected to the motor. The frequency (HZ) is constant and set at 60 Hz to obtain a constant rotation speed. Different stress levels are applied to the samples for each stress level of one sample, and the stress levels are as follows (200.7, 211.5, 220.7, 231.5, 240.7) (Mpa). The fatigue sample goes through three stages: the crack formation stage, the crack growth stage, and finally, the fracture stage. When the sample reaches the fracture stage, the two parts of the sample separate in the form of a cup and cone, which is the way samples break for ductile materials, as shown (see Fig. 7) below:

Fig. 7
figure 7

Ductile fracture (cup and cone) in fractured fatigue sample

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After completing the breaking of all C35 carbon steel samples designated for the corrosion-fatigue and pure fatigue cases, as shown (see Fig. 8) below:

Fig. 8
figure 8

Fractured Fatigue samples (a) after pure fatigue test, (b) after corrosion-fatigue test

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The fatigue life of samples can be obtained directly from computer-recorded cycle numbers taken from the controller. For further analysis, data on the applied load during the tests were collected. Stress is a fundamental mechanical parameter used to study fatigue. The stress applied during the testing process can be understood as an external manifestation of internal damage to the sample. After breaking the samples, three distinct areas are formed in the surface area of the broken area of the carbon steel sample, as shown (see Fig. 9) below:

Fig. 9
figure 9

Fracture failure areas of fatigue sample, (1) fatigue crack initiation zone, (2) fatigue crack propagation zone, (3) final overload zone

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The fatigue fracture of the tested sample is presented in Fig. 9. In this figure, surface cracks may be noticed. The cracks appear mainly on the surface and penetrate inside the material. Such a structure of cracks may result from an excessive material of surface layer deformation during the corrosion process. A degree of too high corrosion causes micro-cracks and flaking on the surface; these cracks increase during fatigue load weakening of the sample. The area of the fatiguing fracture and the immediate fracture can be seen. These areas in the fracture zone of the C35 carbon steel sample indicate different stages of crack propagation. The dark area (area No. 1), where the crack formed and began to grow under repeated loading. This area typically shows micro-cracks and microscopic marks corresponding to each loading cycle. Area (2), represented by the dark areas surrounding the initiation area, shows a mixture of faulting and cleavage features. Cleavage features are areas where the crack propagates along grain boundaries in the metal, resulting in a relatively flat and featureless fracture surface. As for the final light outer area (area No. 3), the crack grew quickly and disastrously until it failed. This area usually shows little or no cracking, and the fracture surface may be rough and ununiformed. The impact of the stress notch on the fatigue strength of such components can be limited by strengthening this area by using appropriate design or technological solutions [35]. Fatigue data for fatigue life and the value of stresses applied to fatigue samples in the corrosion-fatigue and pure Fatigue cases are collected as shown in Table 3 below:

Table 3 Fatigue data for corrosion-fatigue and pure fatigue cases.
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From Table 3 above, we conclude that the fracture of the corroded samples occurred at a low number of cycles as a result of the decrease fatigue resistance of C35 carbon steel, this can be seen in the decreased fatigue life. As for the non-corroded samples, they fractured at a high number of cycles, and the fracture did not occur at the stress of 200.7 (Mpa), as the number of cycles exceeded \({10}^{7}\) without a fracture occurring, i.e. the metal has reached the fatigue limit. After obtaining the necessary data to study fatigue behavior, S-N curve diagrams are drawn from the data obtained from Table 3 for the corrosion-fatigue case, as shown (see Fig. 10) below:

Fig. 10
figure 10

S-N curve diagram for corrosion-fatigue case

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S-N curve diagrams are drawn from the data obtained from Table 3 for the pure fatigue case, as shown (see Fig. 11) below:

Fig. 11
figure 11

S-N curve diagram for pure fatigue case

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We note from the data obtained from the SN curves that the fatigue life decreased in the corrosion-fatigue case compared to the pure fatigue case. This means that steel structures in a corrosion environment are much more at risk than those that are somehow protected from corrosion [36]. It is worth noting that the test set-up for this research were not in a real location, and therefore are not exactly the same results as what a ship's hull would experience in natural seawater. The percentage decrease of fatigue life of C35 carbon steel samples is shown (see Fig. 12) below:

Fig. 12
figure 12

The percentage decrease of fatigue life

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Notice from the figure above that the percentage of decrease was small when applying high loads, but the percentage of decrease gradually increased when applying low loads. This is due to the fact that the samples in the non-corroded case, when low loads are applied to them, require a very high number of cycles in order for the fatigue crack to initiate. However, the fatigue crack had already occurred in the corroded samples, so the failure occurred much faster than the failure of the non-corroded samples. While fatigue cracks initiate when high loads are applied to samples, whether they are corroded or not, they can initiate quickly relative to the high load applied, which is sufficient to cause cracks. Therefore, there was no significant difference in the percentage of fatigue life reduction for the samples compared to the samples under low loads. We can obtain the percentage mean of fatigue life reduction by dividing the sum of the percentages by their number, obtaining a mean that is equivalent to 70.15%.

Fatigue Life Prediction

Predicting the fatigue life is one of the necessary matters that must be considered to know the number of cycles at which failure occurs due to the cyclic stresses applied to the samples. This is necessary to know the corrosion effect of metals, especially the behavior of C35 carbon steel. This is done by deriving a predictive relationship for the fatigue process from Eq 7:

$${\sigma }_{f}={{\text{AN}}}_{f}^{\alpha }$$

We multiply both sides of the equation by the natural logarithm to obtain Eq 8 and my agencies:

$${\mathrm{Log\sigma }}_{{\text{f}}}={\text{logA}}+\mathrm{\alpha log}{{\text{N}}}_{{\text{f}}}$$
(8)

In comparison with the mathematical equation used in the Least Square Curve Fitting method, as in Eq 9, as follows:

$$y=a0+a1x$$
(9)

The final predictive equation obtained for fatigue as in Eq 10, which is as follows:

$${\sigma }_{f}={\text{a}}0{{\text{N}}}_{f}^{a1}$$
(10)

Using the MATLAB 2015 Software and entering the data obtained from Table 2, the MATLAB Code is shown in Appendix Fig. 14. The final predictive equation for the life and fatigue limit for the corrosion-fatigue case as in Eq 11 is as follows:

$${\sigma }_{f}=1048.5{{\text{N}}}_{f}^{-0.12}$$
(11)

The special equation for the pure fatigue case, as in Eq 12, is as follows:

$${\sigma }_{f}=532.75{{\text{N}}}_{f}^{-0.06}$$
(12)

Using the two prediction equations, we can now calculate the fatigue limit of C35 carbon steel for the pure fatigue and corrosion-fatigue cases, by replacing the \({\mathbf{N}}_{\mathbf{f}}\) value with a number of cycles equal to \({10}^{7}\), which is the fatigue limit value for the metal, so, the endurance limit of the pure fatigue test is equal to (202.5 Mpa), and for corrosion-fatigue samples is equal to (151.5 Mpa). Therefore, the fatigue limit decreased by 25.18% due to corrosion, which is a very high percentage, and it is advisable to get solution for the corrosion problem to avoid this rapid failure of the metal. To predict the fatigue life and the number of cycles at which failure occurs depending on the amount of stress applied, the data were mentioned and according to Table 4 shown below for the corrosion-fatigue case and the fatigue case is as follows:

Table 4 Data predicted by MATLAB for the corrosion-fatigue and pure fatigue cases.
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Conclusion

The following was concluded from this research:

  1. 1.

    The fatigue life decreased by (86.25, 73.93, 61.45, 59%) for the corroded samples compared to those not subjected to corrosion depending on the applied load.

  2. 2.

    The fatigue limit decreased, which weakened the metal's ability to resist cyclic loads. The fatigue limit of the corrosion-fatigue test, equal to (151.5 MPa), is greatly decreased compared with the fatigue limit of the pure fatigue test, which is equal to (202.5 MPa).

  3. 3.

    The percentage mean of reduction in fatigue life is 70.15%, while the percentage of reduction in fatigue limit is 25.18% due to the effect of corrosion. These are considered high percentages and must be taken into consideration.

  4. 4.

    The predictive model is economical and saves the cost of many samples, as we only need five samples for each case.