The Deterioration of Low-Cycle Fatigue Properties and the Fatigue Life Model of Reinforcing Steel Bars Subjected to Corrosion

Abstract

Thousands of coastal reinforced concrete structures using HRB400 bars have served for over three decades in China. Their reinforcement simultaneously endures chloride corrosion and seismic action, yet studies on performance degradation remain limited. This paper investigates the low-cycle fatigue (LCF) behavior of HRB400 bars under various strain amplitudes, systematically analyzing corrosion morphology, cyclic stress–strain response, fatigue life, and underlying mechanisms. Corrosion is induced by an adjusted accelerated method that replicates field conditions. Observations reveal that corrosion pits act as primary crack initiation sites. Crack paths and fracture surfaces progressively follow the local pit geometry as strain and corrosion grow. The detrimental effect of corrosion on LCF life is more pronounced for smaller bars. At a γ of around 8%, 20 mm bars lose 60.7% of the half cycles to failure at ε = ±1.5%, but only 37.5% at ε = ±5.0%. Predictive corrosion-inclusive strain amplitude (ε_a)–fatigue life models are proposed, yielding R² = 0.952 (16 mm) and 0.928 (20 mm). A unified LCF predictive model, calibrated on a database of 310 corroded/uncorroded bar tests, is established. The final model comprehensively considers the characteristics of rebars, seismic action, and corrosion damage, improving the conventional relationship between LCF life and seismic loading. This work contributes to the understanding of the fatigue behavior of HRB400 bars and provides support for time-dependent seismic reliability analysis of aging reinforced concrete structures in corrosive environments.

1. Introduction

The steel bars in coastal reinforced concrete (RC) structures under severe marine climates are likely to prematurely corrode [1]. Reinforcing steel corrosion is the main culprit behind the premature degradation of RC structures in chloride-contaminated environments. Most of the time, these coastal zones lie within the seismic belt, exposing structures to cyclic earthquake loads. Decades of research have documented how corrosion diminishes bar cross-sections and degrades monotonic strength and ductility [2,3,4,5,6,7,8]. Performance-based design mandates that RC structures endure moderate-to-large earthquakes with limited damage. Large inelastic deformations developed in plastic hinges, imposing severe tension–compression reversals on longitudinal bars. Those reversals precipitate low-cycle fatigue (LCF) fracture that can trigger premature member failure and progressive structural collapse. The conceptual diagram of the synergy of corrosion and earthquakes on RC structures is shown in Figure 1.

Different types of uncorroded rebar have been investigated experimentally [9,10,11,12,13] to describe the LCF performance of reinforcing steel bars. Several LCF material models have been proposed [14,15,16,17,18], most of which are based on the well-known Coffin–Manson equation, which links plastic strain amplitude (ε_p) to fatigue life. As the performance and durability of aged RC structures has gained more and more research attention, subsequent LCF studies have transitioned to the investigation of the corrosion effects on LCF behaviors. Representative work includes Apostolopoulos’s research group [19,20,21,22], Hawileh et al. [23], Caprili and Salvatore [24], and Kashani et al. [25]. These studies investigated the effect of corrosion on low-cycle fatigue life of reinforcing bars with and without the effect of inelastic buckling. The results show that the synergy of corrosion and inelastic buckling has a significant impact on the early fracture of rebars under cyclic loading. A systematic study has been conducted in a European research project [26] which presents the results of a wide experimental test campaign on uncorroded and corroded bars. Previous work noted considerable degradation in mechanical property as corrosion advanced. The level of corrosion also significantly affected the LCF behavior of the steel bars. The corroded rebar showed a gradual reduction in load-bearing ability as well as energy dissipation capacity.

Owing to the scarcity of naturally corroded bars extracted from aged structures [27], most studies have relied on laboratory accelerated corrosion methods. Salt spray or fog (5.0 wt.% NaCl solution) tests were applied to 10 mm and 12 mm bare rebars in Apostolopoulos’s group [20,21,28] and Caprili’s study [24], whereas strong acids (10% H₂SO₄/HNO₃) were used by Hawileh et al. [23]. Alternatively, 12 mm bars embedded in concrete were accelerated-corroded by impressed current, and the entire concrete specimen was immersed in NaCl solution [25]. It should be noted that some studies [29,30] have emphasized that the specimens embedded in concrete present more severe superficial localized pitting corrosion in contrast to the bare rebars. Generally, salt spray tests represent conditions for more uniform corrosion, while pitting corrosion can be simulated by current density control. Those two methods remain the dominant laboratory protocols in current research.

The presented studies underscore three critical gaps: (i) most tested diameters (≤12 mm) fall short of practical longitudinal reinforcement (≥16 mm); (ii) the induced corrosion in experiments is closer to uniform, under-representing the pitting corrosion; and (iii) predictive models for LCF of corroded bars are scarce. Apostolopoulos and Michalopoulos [21] suggested that the fatigue life and total dissipated energy were fitted by an exponential decay curve. Kashani et al. [31] adapted Brown et al.’s model [10] for intact rebars by introducing a mass loss parameter calibrated against Apostolopoulos’s data [20]. These studies have taken a valuable step forward in exploring rebar models involving corrosion, but these models still lack the precision required for seismic performance assessment.

Since the late 1990s, HRB400 (hot-rolled ribbed bar featuring a minimum yield strength of 400 MPa) steel bars have dominated China’s RC construction, and a large stock of these structures is now approaching three decades in service. Over the years, corrosion coupled with seismic cyclic loading has progressively damaged the reinforcement. Yet most current studies on reinforcing steel still prioritize the performance of newly developed materials, leaving the degradation problem of HRB400 bars unexplored.

This study addresses that gap by examining how corrosion alters LCF behavior of 16 mm and 20 mm HRB400 bars under constant strain amplitude. Realistic chloride-induced corrosion of embedded bars was reproduced using an adjusted impressed-current accelerated technique. Using the LCF test data from corroded bars, a mass loss integrated LCF life model was established. The obtained prediction model correlates strongly with experimental data (R² = 0.952 for 16 mm and 0.928 for 20 mm). The experimental results were merged with test data in the literature to create an expanded LCF database for corroded bars. Based on this database, a unified LCF predictive model considering the characteristics of rebars, seismic action, and corrosion damage was established. Although the model’s accuracy is moderate, it represents a clear advance over the aforementioned models. The outcomes furnish reliable experimental evidence and deterioration laws for seismic assessment of aging HRB400 structures in corrosive regions. This model can be applied to time-dependent seismic fragility analysis to support remaining-life assessment and retrofit decisions for coastal RC structures in long-term service.

2. Experimental Program

Note that under normal circumstances, the steel bars are embedded in concrete, which provides protection to the rebar. The corrosion process within the concrete cover is a slow and complex procedure. The surface morphology of corroded steel bars depends on the inhomogeneity of both concrete and steel, the microstructure of concrete, and environmental conditions, etc. Only if the corrosion is sufficiently serious will the concrete cover crack and spall due to the volume increase of corrosion products. This finally leaves the steel bars exposed to the environment. In order to realistically simulate the actual engineering condition, steel bars embedded in concrete were chosen instead of bare rebars.

2.1. Specimen Design and Preparation

Most published experiments have addressed bars ≤12 mm, whereas longitudinal reinforcement in RC structures is typically ≥14 mm. This study targets larger diameters; however, owing to loading capacity limits, only unmachined HRB400 steel bars with diameters of 16 mm and 20 mm were used. The chemical composition of the steel bars used is shown in

Table 1. Chemical composition of the steel bars.

Type	C (%)	Si (%)	P (%)	Mn (%)	S (%)	Ceq (%)
HRB400	0.25	0.8	0.045	1.6	0.045	0.54

. A total of 38 pieces of steel bars including 6 uncorroded and 32 corroded steel bars were prepared and tested. The middle portion of each specimen was set at six times the nominal diameter as the gauge length, and 200 mm on each end was used for gripping on the servo-hydraulic test system. Each steel bar was first cleaned with 12% hydrochloric acid to remove surface rust layers. After rinsing with clean water, the steel bars were immersed in whitewash for 72 h to neutralize residual acid and form a passivating film on the surface to prevent the steel bars from quickly corroding. After pickling, the weight of the cleaned steel bar was measured with an accuracy of 0.1 g. To limit fracturing of the rebar within the gauge length during LCF tests, two gripped ends were protected in epoxy coating, and the middle portion was subjected to corrosion. A copper wire was welded at one end of the bar and connected to the external power supply in accelerated corrosion tests.

Nine small RC slabs were cast. Each specimen incorporated four steel bars with the same nominal diameter, and the depth of concrete cover was 25 mm, as shown in Figure 2. The concrete mix was designed to have a mean compressive strength of 30 MPa at 28 days with a maximum aggregate size of 15 mm.

2.2. Accelerated Corrosion Procedure

In experimental studies, the selection of the accelerated corrosion procedure was based on the practical and efficiency requirements. The salt spray chamber, governed by ASTM/ISO 9227, is a standardized method for corroding bare bars. However, studies by Novak et al. [32] and Caprili et al. [33] show that it cannot reproduce the “natural” chloride-induced corrosion experienced by rebars embedded in concrete. The method is unable to capture the ensuing effects on bar performance, member response, or bar–concrete interaction. The application of direct current was eventually chosen as the corrosion method in the present study. The concept of using external currents is simple and consists of forming an electrochemical circuit using an external power supply. The most significant difference between this study and the conventional method was that the concrete slabs were not immersed (fully or half) in the electrolyte solution. The wet salty sand was used to connect positive and negative electrodes of the cell.

Traditional full- or half-immersion methods accelerate corrosion effectively and yield stable mass loss estimates. However, in full immersion, the concrete specimens are fully saturated: corrosion products are leached away due to capillarity, and no expansive pressure develops. Submerged bars get little oxygen, so the corrosion products’ chemistry differs from natural rust. As the electrolyte solution is uniform, it eliminates chloride concentration gradients on the bar surface, producing uniform corrosion with negligible pitting. Half immersion places the bars above the solution, and capillary action completes the electrolytic path. This improves oxygen supply and yields corrosion products closer to natural rust. Yet the circuit is unstable—concrete resistivity fluctuates with moisture, current distribution is unpredictable, and corrosion tends to be localized to the bar surface adjacent to the solution.

The selection of wet salty sand in this paper is based on the following consideration: the concrete will not always maintain water saturation, which will impair the effect of material inhomogeneity on the corrosion process; the large porosity of coarse sand will ensure adequate oxygen supply, and the composition of corrosion products are more similar to those in practical situations; and the internal expansion stress will not significantly decrease due to the loss of corrosion products caused by the capillary action of pore water. These adjustments were made to balance the direct impact on the final appearance of the corroded rebar and accelerate the corrosion process.

After air curing at room temperature for 28 days, all the concrete slabs were completely immersed in a 5.0 wt.% NaCl solution [29] for one week to ensure chloride penetration to the bars. Then, they were transferred to a rectangular concrete pool with a shelter at the top and drains at the bottom, as shown in Figure 3a, for the accelerated corrosion. The target corrosion level in this study ranged from 0% to 15% mass loss. The period required to obtain the desired corrosion level was estimated using Faraday’s 2nd Law of Electrolysis. In accordance with Maaddawy and Soudki’s study [34], the current density over 0.2 mA/cm² resulted significant changes in final corrosion morphology. Meanwhile, higher densities are frequently adopted in the literature to shorten the test duration. In order to balance the corrosion representativeness and time efficiency, the current density was maintained between 0.15 and 0.2 mA/cm² in the present study. The current density was measured and adjusted every 8 h to keep it as stable as possible. The precise control of the corrosion rate was not a target in the present study, and the different periods were estimated to obtain specimens with corrosion gradients. It took a total of three months to achieve the specimens with the highest corrosion level. Key details of the accelerated corrosion procedure are summarized in

Table 2. Key information for the accelerated corrosion procedure.

Solution	Concentration	Current Density (mA/cm2)	Current Detection Interval
NaCl	5.0 wt.%	0.15~0.2	8 h

.

As illustrated in Figure 3b, the steel bar connected to the positive terminal served as an anode in the cell. A piece of copper plate linked to the negative terminal served as a cathode. The specimens were placed side by side, and the space between them as well as the top and bottom spaces were filled with coarse sand. To create a corrosive environment, 5.0 wt.% NaCl solution was sprayed approximately every 2 days on the sand to provide moisture and chloride ions. To reduce the humidity fluctuations, the top of the specimens was covered by a moist sponge pad to reduce the excessive drying of the sand due to evaporation. In the meantime, a separation layer was set at the bottom to drain the excess moisture using gravity.

After reaching an expected corrosion mass loss, the concrete specimens were broken open, and the corroded bars were carefully removed. Mechanical cleaning was carried out using a bristle brush to ensure that the concrete debris and oxidation products adhering to the corroded steel bars were completely removed. Then, the rebars were successively washed with acid, whitewash, and tap water. The cleaned steel bars were then oven-dried and weighed. The actual mean mass loss ratio γ was selected as the corrosion indicator for simplicity [35], which can be defined as follows:

$$\gamma ={\displaystyle \frac{m_0-m_{\mathrm{r}}}{m_0}}\times 100\%$$

(1)

where m₀ is the mass of the test section from uncorroded specimen, and m_r is the residual mass of the test section from corroded specimen after cleaning. The epoxy coating on the bar surface also exhibits mass changes during the experiment procedure. Consequently, the bar mass loss cannot be taken as the simple difference before and after the test. Instead, once the LCF tests were completed, the central gauge length of each bar was cut out and weighed to determine the true mass loss.

All the specimens are identified by “CS/S-XX-YY-ZZ”, where “CS” refers to corroded steel and “S” refers to intact steel; “XX” represents the diameter of the rebar (16 or 20 mm); “YY” represents the loading strain amplitude, e.g., 15 indicates ±1.5%; “ZZ” represents the serial number of the corroded pieces sorted according to the mass loss rate from small to large, and the intact steel bar is numbered “0”.

2.3. Test Setup and Loading Protocol

Previous studies have demonstrated that the free length of the longitudinal reinforcing bars strongly influences the experimental results. Unexpected premature failures of bars occur due to buckling phenomena under compression axial loads. Mander et al. [9] reported a “critical value” for buckling: for the gauge length greater than six times the nominal diameter of the bar, rebars exhibited a progressive reduction in compressive strength and the reversal of the curvature due to inelastic buckling. In addition, the spacing of adjacent stirrups in compression members in high-risk seismic areas is likely to be smaller than 6d₀ (d₀ is the nominal diameter of the intact bar). Consequently, the gauge length of all specimens was selected as 6d₀, and 6 is called “the span-to-diameter ratio” as a dimensionless measure of the gauge length.

LCF tests were executed in displacement control on a 630 kN servo-hydraulic frame. A sinusoidal waveform of constant amplitude was applied until fracture. Two swaged grips connected to the frame and hydraulic actuator were used for mounting steel bars. A 50 mm extensometer with a maximum stroke of ±5 mm was used to measure the average axial strain in the reinforcement over the linear range (Figure 4). As the extensometer could not capture the post-buckling behavior, the displacement transducer integrated into the testing machine (at bottom grip) was used to measure rebar deformation. The average strain across the entire gauge length between grips was calculated based on the readings of the transducer. Apostolopoulos and Rodopoulos [36] conducted strain-controlled tests at Δε = ±2%, ±5%, and ±8%, amplitudes chosen to match typical seismic reported by Franchi et al. [37]. Hawileh et al. [23] applied sinusoidal axial strains of ±4%, ±5%, and ±6% to corroded bars, selecting these levels to suppress inertia effects under large plastic excursions. The testing frequency was set to 0.1 Hz, and the strain amplitudes used in the LCF tests were ε = ±1.5%, ±3.0% (±3.5% for diameter 20 mm), and ±5.0%. The strain amplitudes were selected empirically to simulate bar strains under earthquakes of varying intensities.

For corroded bars, surface morphology, especially pitting corrosion, directly affects mechanical behavior. Any modification in the geometry would alter the nature of the material, thus giving misleading results. Therefore, no mechanical processing was applied to the specimens except for the cleaning procedure. It should be noted that the failure of the specimen is taken to be the point at which the bar is completely fractured. The evaluated LCF properties for the different levels of corrosion damage were the number of strain reversals to failure (2N_f), which was also known as LCF life.

3. Experimental Results and Discussion

3.1. Corrosion Morphology

After cleaning and drying, a detailed observation was made of the corrosion condition on the surface of the specimens. Corrosion took place throughout the unprotected gauge length. At a lower corrosion rate, the surface characteristics of the steel bar were almost retained, the corrosion was nearly uniform, and only small defects appeared on several ribs. With increasing corrosion rate, flaky rusty spots gradually appeared at various positions on the surface, and lamellar spalling occurred when corroded rebars were struck. In the meantime, obvious notches and pits can be observed on the bottom of some diagonal ribs and longitudinal ribs. When the rate was further increased, the overall height of the ribs was significantly reduced, and the ribs in some areas were severely damaged or even missing. Irregularly shaped grooves were formed in the nearby area, causing a serious local reduction in the cross-section of the rebar. In highly corroded bars, two types of grooves appeared. First, the adjacent continuous diagonal ribs were severely corroded and propagated to the gap between them, creating a local depression. Second, a long range of longitudinal ribs vanished, leaving a strip-shaped corrosion area. Figure 5 displays the typical corrosion characteristics of the specimen surface. The surface morphology was compared between the accelerated-corroded bars and naturally corroded bars [38]. Similar pit locations, shapes, and corrosion progression were noted. These parallels suggest the method can effectively reflect the natural corrosion of steel bars. The test results should therefore approximate the real performance degradation of corroded bars.

3.2. Impact of Corrosion on the Fracture Characteristics of Specimens

It is observed that the fracture position of the specimen under low-cycle fatigue loading is affected by corrosion. When the strain amplitude was small (ε = ±1.5%), for the corroded specimens, the occurrence of the fracture cross-section was similar to that of intact steel. It appeared at the midpoint, one-third of the test gauge length, or near the grips. Under low strain amplitudes, the cross-sectional strain field is nearly uniform. Cracks therefore consistently initiate at the weakest point along the gauge length. This happens whether the bars are corroded or intact. The difference is that the fractures are more likely to occur at locations with a relatively high degree of corrosion (shown in Figure 6a) in corroded ones. This is because stress concentration takes place, and the stress amplitude increases at these pit locations due to load eccentricity and the reduced section induced by the non-uniform corrosion imperfections. Greater corrosion severity and deeper pits intensify stress concentration and sectional loss. Cracks then initiate at pit edges and propagate inward or link with adjacent pits. Consequently, in Figure 6a, the fracture points align almost entirely with the most severely pitted regions. It can be considered that the different levels of surface corrosion determine the location where the corroded specimen fractures.

When the strain amplitude was relatively large (ε ≥ ±3.0%), the buckling of bars became obvious. Most fracture points were located in the middle part of the specimen, where the plastic hinge was (shown in Figure 6b). Even if there were severe corrosion-damaged cross-sections at other locations, the fracture did not occur there (tagged with arrows in Figure 6b). This observation was somewhat different from Kashani’s work [31], which reported that under cyclic loading, highly corroded bars started fracturing in tension at the location with severe localized pitting corrosion. This phenomenon occurred in specimens with a gauge length of 15d₀ and a mass loss ratio above 30%. However, in the present study, the gauge length of the bars was 6d₀, the maximum corrosion rate was under 20%, and no such phenomenon was observed. This indicates that under large strain amplitudes for the rebars with small effective length and moderate level of corrosion, the point of the fracture depends more on the buckling location where the severe plastic deformation occurs. The fracture location does not coincide with the region of greatest corrosion damage. When the gauge length of rebars is limited, the restraint effect of the grips on the ends of the specimens makes up the weakness caused by section reduction due to corrosion. This demonstrates that even for severely corroded reinforcing bars, confining the effective length through lateral restraint markedly preserves performance and delays failure. Consequently, seismic design of corrosion-threatened RC structures must prioritize robust anti-buckling detailing for longitudinal reinforcement.

When severe corrosion appears at mid-span, the effects of buckling and corrosion combine. Due to the combined effect of axial and bending strains, the inner side of the buckling bar carries a larger strain than the outer side. If pits are present there, the bar tends to bend toward the corroded side. On the inner surface, pitting-induced stress concentration, local section loss, and higher strain amplitude work together. They speed up crack growth and lead to earlier fracture.

It was also observed that corrosion had an effect on the morphological changes of the fracture surface of the steel bars. The fracture section of specimens under small strains had a regular shape, neat edges, and was generally a 45° oblique plane with a smooth and bright crystalline surface (shown in Figure 7a). However, with the increasing strain amplitude and the level of corrosion, the section morphology changed significantly. The development of the fracture surface was affected by the state of local corrosion. After the initiation of the crack, it essentially developed along the bottom of the adjacent ribs or pits with severe corrosion. Therefore, the perimeter shape of the fracture section exhibited obvious irregularity. The section surface was jagged and had a grey fibrous appearance (shown in Figure 7b). Fracture inspection confirmed that corrosion pits acted as crack initiators and facilitated subsequent crack propagation. They weaken the bar’s deformation resistance and reduce the fatigue life.

3.3. Impact of Corrosion on Hysteresis Behavior and LCF Life

A comparison between the typical hysteresis response of uncorroded and corroded 20 mm diameter rebars is shown in Figure 8. In the hysteresis curves, the characteristics of the tension part and the compression part show obvious differences. This is because the effects of fatigue cracks on the tensile and compression strength of steel bars are unalike. After the formation of cracks, the cross-sectional area of the steel bar under tension decreased, but it was not affected by the crack when it was compressed. This effect resulted in much higher degradation in the tensile strength than the compression strength. And this distinction in strength degradation was more prominent when the strain amplitude was small. The higher the strain amplitude was, the more significant the degradation of the peak stress in each cycle. In addition, with the increase in the corrosion rate, the reduction in the peak stress in each cycle increased gradually.

A slight pinching effect was seen in the stress–strain curves of rebars due to the geometrical nonlinearity caused by buckling. As the level of corrosion increased, the pinching effect in corroded rebars also increased. This observation aligns with Kashani’s findings [39]. Although the gauge length was set at 6d₀, progressive corrosion increases the effective slenderness ratio of the bar, resulting in an increase in the pinching effect. Compared with the intact rebar curves, the stress degradation gradient of the corroded rebar curves in each cycle is accelerated. The corrosion also led to a significant reduction in the number of loading cycles that the specimens can sustain before fracture. As a result, the total areas of the corroded rebars’ hysteresis curves decreased, and subsequently, the total energy dissipation capacity, which can be evaluated as the sum of the areas confined within the hysteretic loops using Green’s theorem, was reduced.

As expected, the level of corrosion damage has a significant impact on LCF life of rebars. The numbers of half cycles to fracture for tested rebars are plotted in Figure 9. The detailed results are tabulated in Appendix A of this paper. With increasing mass loss rate, an obvious reduction in half cycles to failure is observed.

The results indicate that at low strain level of ±1.5%, a steeper LCF life reduction occurs when the corrosion level is low, and even a small mass loss rate leads to a significant decrease in the number of half cycles to fracture. In contrast, at a large strain level of ±5%, the reduction observed seems to be gentler and more stable. For specimens from d₀ = 20 mm with similar corrosion damage, like (γ = 8.24%, ε = ±1.5%), (γ = 7.29%, ε = ±3.5%), and (γ = 8.19%, ε = ±5.0%), the reduction rate of the half cycles to failure is 60.7%, 58.7%, and 37.5%, respectively, compared to intact specimens. This shows that the lower the strain level is, the more significant the degradation of LCF life caused by corrosion. And it is shown from the change of tangent slope of each curve that as the level of corrosion damage increases, its impact on fatigue life degradation decreases. These findings also confirm the conclusions reported in previous studies [20,23]. To gain further insight into the influence parameters of LCF characteristics of corroded rebars, the number of strain reversals to failure for each corroded specimen (2N_f’) is normalized to their corresponding uncorroded specimen (2N_f) and plotted versus mass loss rate in Figure 10.

The best linear fit to the experimental data in Figure 10 shows that corrosion significantly reduces the number of half cycles to failure for specimens with both diameters. In a previous study on uncorroded rebars [10], Brown reported that bars with larger diameters (25.4 mm) exhibited a longer fatigue life at lower strain amplitudes. With increasing strains (ε beyond about 2.25%), this trend reversed, with smaller-diameter bars (19.1 mm) showing longer fatigue life than larger-diameter bars. In the present experiments involving corrosion, compared with large-diameter ones, it was found that the degradation of LCF life caused by corrosion in smaller-diameter reinforcing bars is more significant. By comparing the fitting relationship in Figure 10, it can be observed that the values of the reduction factor of 16 mm rebars are higher than that of 20 mm rebars at both strain amplitudes. It is indicated that corrosion has more significant adverse effect on the LCF life of smaller-diameter bars than that of larger-diameter ones. Meanwhile, such deterioration of fatigue life due to corrosion is also more prominent at smaller strain levels. As the strain amplitude increases, the degradation rate of LCF life caused by corrosion slows down, especially for larger-diameter rebars, the adverse effects of corrosion are alleviated. However, no larger-diameter rebars were tested in the present study. It would be interesting to see if these trends continue further with increasing bar size to better understand the influence of corrosion on rebars with different diameters.

It is noted from Figure 10 that, among 20 mm bars, some specimens show nearly identical fatigue lives despite markedly different corrosion levels. One possible explanation is that for ribbed bars, cracks initiate at rib roots because of stress concentrates, so smooth bars have a longer fatigue life than ribbed ones. Consequently, even when corrosion is more severe, if the attack is uniform along the bar, removing the ribs to reduce the diameter and smooth the surface can yield a higher fatigue life. This was also reported in Kashani’s study [25].

4. Modeling the Influence of Corrosion on Low-Cycle Fatigue Life

A comprehensive description of the performance of rebars consists of monotonic and cyclic response. Fatigue life models serve to predict the failure of rebars under cyclic loading. Earlier reviews show that corroded bars follow the same fatigue life versus strain amplitude trend as uncorroded bars. Yet corrosion does accelerate the reduction in fatigue life with increasing cyclic strain. Thus, material model for corroded rebars should incorporate factors reflecting the impact of corrosion on fatigue life.

4.1. Existing LCF Models for Uncorroded and Corroded Rebars

To predict the time to failure or fracture of rebars under low-cycle fatigue loading, the well-known Coffin–Manson (CM) equation and its variants were commonly used. This model relates plastic strain amplitude (ε_p) with the total number of strain reversals to failure (2N_f) as follows [9]:

$${\epsilon }_{\mathrm{p}}={\displaystyle \frac{∆{\epsilon }_{\mathrm{p}}}{2}}={\displaystyle \frac{1}{2}}\left({\epsilon }_{\mathrm{p},\mathrm{m}\mathrm{a}\mathrm{x}}-{\epsilon }_{\mathrm{p},\mathrm{m}\mathrm{i}\mathrm{n}}\right)=\theta {\left(2N_{\mathrm{f}}\right)}^{\alpha }$$

(2)

where ε_p,max and ε_p,min are the maximum and minimum plastic strain in an intermediate cycle, while θ and α are the material constants representing fatigue ductility.

Considering the nonlinearity of the plastic strain–fatigue life curve to Bauschinger effects, one variant of the CM model using the total strain amplitude (ε_a) was proposed by Koh and Stephens [14] as Equation (3), which will be called the Koh–Stephens (KS) model hereafter in this study.

$${\epsilon }_{\mathrm{a}}={\displaystyle \frac{∆\epsilon }{2}}=M{\left(2N_{\mathrm{f}}\right)}^m$$

(3)

where M and m are the material constants. In addition, the total strain amplitude is easier to obtain than the plastic strain amplitude in the experimental study. Many fatigue life models based on above structure have been obtained in previous studies [10,11,12,16] for uncorroded rebars. Each of such models is applicable to a particular rebar style or size with a high correlation coefficient (R²) value.

After a double logarithmic transformation, both the CM and KS models can become linear, and then the material constants θ and α can be solved simply by linear regression. The KS model was found to outperform the CM model on account of smaller modeling errors [16]; for this reason, the subsequent model in the present study will use the total strain. Besides the abovementioned classical models, some innovative modeling techniques have been introduced to LCF life model estimation [40,41]. The popular artificial neural network technology is also used to predict the LCF life of steel bars, using the strain ratio, the maximum tensile amplitude, and dissipated energy as input parameters [42,43].

When the problem was related to the effect of corrosion, Apostolopoulos and Michalopoulos [21] concluded from a series of experimental results that the fatigue life and total energy dissipation were fitted by an exponential decay curve, as shown in Equation (4).

$$f\left(t\right)=C_1+C_2{e}^{\left(C_{3}t\right)}$$

(4)

where C₁, C₂, and C₃ were material parameters for different corrosion levels and strain amplitudes. The variable t in Equation (4) is the number of days for the accelerated corrosion procedure from the salt spray chamber method conducted in the study. Therefore, the direct relationship between fatigue life and corrosion level has not been established.

Few LCF life models are available in the public domain. On the basis of the CM model, Kashani et al. [31] have conducted some worthwhile work. Using experimental data from Apostolopoulos [20], Kashani et al. [31] conducted statistical analyses and introduced γ to modify the material constant for corrosion effects. They claimed that the effect of corrosion on θ was negligible, while that on $\alpha$ was significant. An empirical relationship ${\alpha }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}/\alpha =1+0.4\gamma$, in which α_corr stands for the fatigue ductility exponent of corroded rebars, was proposed to modify $\alpha$ for nonuniform pitting impacts. The deficiency is that the sample size of the statistical study is relatively small, and the R² value of the equation is only 0.62, indicating further study is needed for in-depth exploration in the description of corrosion effects. Based on the aforementioned experimental data, Chen et al. [44] proposed a four-step meta-analysis method to strip the laboratory errors among the results from different teams and establish a unified rebar LCF model.

4.2. Modeling the LCF Life for Corroded Rebars

In this study, the KS model serves as the base model structure, and the corrosion rate (in terms of mass loss) is integrated to establish the LCF life model of corroded steel bars. The relationship between total strain amplitude (ε_a) and total number of strain reversals to failure (2N_f) is the backbone of the statistical modeling. To check the rationality of the experimental data after incorporating this parameter, and to determine if there is a good correlation among experimental variables, statistical data inspection is necessary. As mentioned earlier, after double logarithmic transformation, the KS model becomes linear. The key experimental parameters are converted to natural logarithm form. The correlation between them is tested, and multiple linear regression analysis is performed. The three parameters of interest in the present study are total strain amplitude (ε_a), the total number of strain reversals to failure (2N_f), and corrosion rate or mass loss ratio (γ).

In the KS model equation, from a statistical perspective, (ε_a) is the response variable, while (2N_f) is the predictor variable. When incorporating a new predictor variable (γ) into the equation, it is crucial to assess the significance of the variable to the response variable to clarify its impact on the model. In addition, it is necessary to investigate whether there is a strong linear correlation between the predictor variables, i.e., to test for multicollinearity in the model. If multicollinearity is present, the model will not be able to correctly reflect the independent influence of each predictor variable on the response variable, compromising its predictive capability and stability.

In the analysis, ln(2N_f) and ln(γ) serve as independent variables, with ln(ε_a) as the dependent variable. Through multiple linear regression analysis, significance and collinearity diagnostics of the independent variables are conducted for different rebar diameters. The significance test method used in this study is the t-test, and the diagnostic results are presented in

Table 3. Results of statistics analyses of experiment data.

Diameter (d0)	t Test		VIF for Collinearity Diagnosis
	ln(2Nf)	ln(γ)	ln(2Nf)	ln(γ)
ϕ16	0.000	0.000	1.049	1.049
ϕ20	0.000	0.007	1.077	1.077

.

Table 3 shows that for each diameter of rebar, the significance values of the t-test for ln(γ) are much less than 0.05, indicating a significant influence of the corrosion rate. Usually, the variance inflation factor (VIF) is checked for evaluating the multicollinearity among variables. A VIF between 0 and 10 indicates no multicollinearity, while values from 10 to 100 and above 100 show strong and serious multicollinearity, respectively. Clearly, the results in Table 3 show no obvious linear correlation between ln(2N_f) and ln(γ), so the model established with these two parameters as independent variables has no multicollinearity.

The linear relationship can be expressed as

$$y=\alpha +{\beta }_1{x}_1+{\beta }_2{x}_2$$

(5)

where y = ln(ε_a), x₁ = ln(2N_f), x₂ = ln(γ), and α, β₁, and β₂ are constants derived from experimental data. Least-squares regression was used in statistical analysis, and with the coefficients obtained, the fatigue life expressions for corroded steel bars of the following two diameters can be established:

$$16 \mathrm{mm}\to \ln ({\epsilon }_{\mathrm{a}}) = -1.303 + (-0.546)\ln (2N_{\mathrm{f}}) + (-0.026)\ln (\gamma )$$

(6)

$$20 \mathrm{mm}\to \ln ({\epsilon }_{\mathrm{a}})=-1.488 + (-0.483)\ln (2N_{\mathrm{f}}) + (-0.022)\ln (\gamma )$$

(7)

Table 4. Regression analysis results.

Model Structure	R2	RM	RMSE	SSR
ϕ16 in KS	0.892	0.000	0.159	0.508
ϕ16 with γ	0.952	0.000	0.105	0.225
ϕ20 in KS	0.877	0.000	0.178	0.505
ϕ20 with γ	0.928	0.000	0.136	0.295

compares the regression statistics for the KS model and its corrosion-inclusive extension, such as residual mean (RM), root-mean-square error (RMSE), and sum of squared residuals (SSR).

Higher R² values and improved residual diagnostics indicate that incorporating the mass loss ratio (γ) yields stronger consistency between the fatigue life equation and the observed experimental data. Therefore, the integration of mass loss into the KS model constitutes a significant and valuable advancement. By exponentiating both sides of the equations using the natural constant e, the following set of LCF life models for corroded rebars was derived:

$$16 \mathrm{mm}\to {\epsilon }_{\mathrm{a}} = {\mathit{e}}^{-1.303}{\left(2N_f\right)}^{-0.546}{\left(\gamma \right)}^{-0.026}$$

(8)

$$20 \mathrm{mm}\to {\epsilon }_{\mathrm{a}}={\mathit{e}}^{-1.488}{\left(2N_f\right)}^{-0.483}{\left(\gamma \right)}^{-0.022}$$

(9)

The proposed models can refine the material constitutive laws for specific reinforcing steels under corrosion. They can then be applied to assess the seismic performance of aging RC structures.

4.3. Generalized Fatigue Life Model

The above fatigue models of corroded steel bars are established for different strength grades and different diameters of rebars, which are limited in application. In order to seek better applicability, a series of experimental results from the existing literature [20,25,33,45] are combined with the data obtained in this paper to expand the basic experimental database of the model. In this case, a database containing 310 LCF testing results is established. The database includes the main factors of the LCF models, namely, the total strain amplitude (ε_a) and the number of strain reversals to failure (2N_f), the nominal diameter of rebar (d₀), the span-to-diameter ratio (L/d₀), the yielding strength of intact rebar (f_y), and the corrosion rate or mass loss ratio (γ). As in the previous analysis, multiple linear regression analysis was carried out on the natural logarithm form of such parameters. The significance diagnosis through the t-test of the independent variables was conducted at the same time.

Linear regression analysis on the whole test database yields Equation (10) with ln(2N_f), ln(d₀), ln(L/d₀), ln (f_y), and ln(γ) as independent variables and ln(ε_a) as the dependent variable. The generalized fatigue life model of corroded steel bars can be obtained. The VIF values show that parameters in this model do not show multicollinearity.

$$\ln ({\epsilon }_{\mathrm{a}})= -3.89+(-0.397)\ln (2N_f)+(-0.007)\ln (\gamma )+(-0.312)\ln (d_0)+(-0.751\left)\ln \right(f_{\mathrm{y}})+(-0.289)\ln (L/d_0)$$

(10)

Similarly, the above expression can be reformulated as

$${\epsilon }_{\mathrm{a}}={ e}^{-3.89} {\left({2N}_{\mathrm{f}}\right)}^{-0.397}{\left(\gamma \right)}^{-0.007}{\left(d_0\right)}^{-0.26}{\left(f_{\mathrm{y}}\right)}^{-0.751}{(L/d_0)}^{-0.289}$$

(11)

With R² = 0.795, the unified model displays reduced accuracy as sample size and the involved parameter count rise, yet it marks a substantial advance over previous LCF life model considering corrosion. Nevertheless, the model carries unavoidable limitations and latent biases.

Theoretically, the effect of pitting corrosion on smaller diameter bars is more pronounced. At equal pit depth, the relative loss of effective diameter is much higher. Separating diameter from corrosion impact is therefore difficult. Moreover, the mass loss ratio alone cannot describe the variability of corrosion morphology, particularly pitting severity. It is noted that all specimens in the database are ribbed bars. The ribs themselves have a direct adverse effect on fatigue life [22]. In some cases [25], fatigue life unexpectedly increased with mass loss. The authors attributed this to a more uniform pit distribution under higher mass loss. An alternative explanation is that severe corrosion erodes the ribs, converting the bar into a smoother, smaller-diameter plain bar and thereby extending fatigue life. The mass loss ratio is unable to capture this mechanism, which is also a limitation of the model.

Because the dataset aggregates results from multiple independent studies, it lacks a unified design. Consequently, the observations are unevenly and irregularly distributed across the control parameters. Although different teams have designed controlled trials to conduct research, due to the lack of a unified trial plan, systematic differences exist among these studies. Differences across studies may stem from disparities in accelerated corrosion methods, loading condition, strain history, material characteristics (e.g., dimension and chemical composition of rebar), etc. These factors lead to systematic bias and errors in test results, which partly explain the limited fitting accuracy of the generalized model presented in this paper. For instance, Hawileh et al. [12] reported that the LCF life differences in different types of reinforcing bars lies in the chemical composition of the steel rather than yield strength alone. This indicates that yield strength itself is not enough to explain material-related variations. However, in most relevant studies, the impact of chemical composition is hard to quantify via a specific parameter, making it even more challenging to incorporate into material models.

Furthermore, while each parameter item in Equation (11) is independent, there may be interaction terms among factors such as strain and diameter, span-to-diameter ratio and mass loss ratio, and other intrinsic connections that have not been discovered in current studies. For instance, published research has found that corrosion usually aggravates the local buckling due to mass loss and diameter reduction. Therefore, there seems to be an internal connection between the corrosion level and the buckling performance. In particular, the corrosion of the steel bars embedded inside the concrete does not occur in the form of general corrosion but rather in the form of pitting corrosion. This can be traced back to the long-standing debate over whether mass loss is an indicator criterion to characterize corrosion. All of these can affect the fitting accuracy of the model to the experimental data.

4.4. Design Provisions for Low-Cycle Fatigue

Worldwide, design codes provide no explicit “low-cycle fatigue life” values for reinforcing bars. Instead, they rely on tiered strategies: material qualification, ductility indices, and detailing rules.

In the United States, ASTM E606/E606M-19 [46] supplies the low-cycle fatigue data through strain-controlled testing. The provisions of yield strength, yield–flexural ratio, elongation minima, and weldability limits for seismic rebar were determined by ASTM A706/A706M [47]. ACI 318-19 [48] mandates ASTM A706 bars where plastic hinging is expected and put forward some seismic detailing rules that keep splices/welds out of plastic hinges and provide confinement.

In Europe, Eurocode 2 [49] prescribe uniform elongation and tensile/yield ratios to classify the ductility level of reinforcing bars. Eurocode 8 [50] requires Class B or C (medium ductility) or Class C (high ductility) bars in dissipative zones, and splices within hinges are strictly restricted.

In China, GB/T 15248-2008 [51] governs low-cycle fatigue testing for steel bars. The ductility and cyclic resistance are ensured via E-grade seismic rebar requirements in GB1499.2-2024 [52] (ratio of measured tensile strength to measured yield strength, ratio of measured yield strength to standard specified yield strength, and total elongation at maximum force). GB 50011 [53] and GB 50010 [54] detail confinement, anchorage, lap lengths, and hinge zone splice restrictions to limit low-cycle fatigue demand in structure design.

Overall, in coastal or chloride-rich environments, chloride accelerates steel corrosion, creating localized pits on the bar surface. Stress concentration around these pits intensifies markedly. During low-cycle fatigue, cracks initiate from the pits and propagate rapidly as corrosion advances, shortening fatigue life. Because fatigue failure typically occurs in plastic hinge zones, premature bar failure during earthquakes drains structural energy dissipation and ductility, risking early member collapse or total structural failure. Corrosion-driven fatigue degradation thus not only shortens the rebar’s own life but also contracts the residual service life of the entire RC system. This study delivers a robust LCF model for corroded bars, enabling prediction of remaining life and seismic reliability in chloride-contaminated RC structures.

5. Conclusions

In this study, an accelerated corrosion procedure of steel bars is carried out by using the method of wet salty sand combined with impressed current. The low-cycle fatigue performance of corroded HRB400 is then investigated. The corrosion morphology and fracture mode are systematically analyzed to clarify how mechanical properties evolve. A significant advancement is achieved in the LCF life model of corroded bars by integrating mass loss into the KS model. Based on a broad database of corroded bars from multiple studies, a unified fatigue life prediction model is developed. The main conclusions are summarized as follows:

(1)

The accelerated corrosion method employed produces corroded bars that closely replicate natural corrosion features.

(2)

Surface morphology affects the LCF behavior of corroded bars. Pitting dominates crack initiation and propagation. Buckling couples with corrosion to speed cracking and prompt early failure. Adequate lateral restraint mitigates these effects.

(3)

Corrosion reduces the low-cycle fatigue life of small bars more than that of large bars. The present tests, however, covered only 16 mm and 20 mm bars, so larger diameters need further verification. Comparative tests are also needed to verify whether these conclusions hold for naturally corroded bars.

(4)

A comprehensive LCF database of 310 corroded and uncorroded rebar tests was compiled. From it, a unified model was established to predict the LCF life of reinforcing steel bars contaminated by corrosion. The proposed model can be applied to time-dependent seismic reliability assessment of aging structures.

In general, this study provides an insight into the complex low-cycle fatigue behavior of corroded rebars and delivers a robust experimental dataset for future work. However, the study is limited by a corrosion rate below 15%, two bar diameters, and a single steel grade. The unified model also offers limited insight into the interaction among parameters. In future research, applying advanced techniques such as machine learning and nonlinear fitting may help improve the prediction accuracy of the model.