Prestressed Carbon Fiber Reinforced Polymer Plates Research Articles

Experimental and numerical study on high-temperature performance of prestressed CFRP-reinforced steel columns

The behavior of prestressed carbon fiber reinforced polymer (CFRP)-reinforced steel columns is intricately linked to CFRP stiffness and stress; when the system is exposed to fire, the performance is more complex because of the degradation of CFRP mechanical properties. Therefore, transient fire tests are first conducted on four prestressed CFRP-reinforced steel columns under axial preloading using the ISO 834 standard curve to investigate their high-temperature performance. The entire failure process is revealed, three significant time points (i.e., CFRP failure time, buckling time, and critical time) influencing system behavior are identified, and the effect of preload and prestress level on the time points is elucidated. It is observed that CFRP plates fail with a final hair-like rupture; steel columns undergo symmetric and asymmetric failure modes, related to the initial imperfection. Subsequently, the finite element models (FEMs) are established and validated by test results, followed by a parametric analysis. It indicates that the high-temperature behavior of the prestressed CFRP-reinforced steel columns is dependent on the preload, CFRP prestress level, and initial imperfection; the buckling and critical time of such columns decrease with increasing preload and initial imperfection, while an increase in prestress leads to an increase in the buckling and critical time. Moreover, even CFRP plates without protection, and prestressed CFRP plates can improve the high-temperature performance of steel columns when the preload is not very large or the initial imperfection is not very small. These findings serve as a valuable reference for applying such columns when considering fire issues.

A full-range fatigue life prediction model for RC beams strengthened with prestressed CFRP plates accounting for the impact of FRP debonding

To predict the fatigue life of a reinforced concrete (RC) flexural member strengthened with externally bonded prestressed Fiber Reinforced Polymer (FRP) laminate accurately, the interaction between components with different degrees of degradation must be carefully taken into account. Furthermore, as the debonding of FRP plates is a recurrent problem, this has to be incorporated into the prediction model. In this study, a nonlinear analysis method for the entire process of fatigue damage in RC beams strengthened with prestressed Carbon Fiber Reinforced Polymer (CFRP) plates was proposed. In this model, all the components of the strengthened beam had independent fatigue degradation properties and failure criteria, and debonding growth was also explicitly considered. The comparison between the analytical and experimental results were used for model validation and good agreement was found.

Numerical and experimental investigation on the flexural stiffness of RC beams strengthened with prestressed CFRP plate exposed to wetting/drying cycles

The load-deflection relationship is critical for the serviceability and structural durability of reinforced concrete (RC) structures strengthened with prestressed carbon fiber-reinforced polymer (CFRP) plates. This study aims to investigate the impact of prestressing levels and wetting/drying cycles (WDCs) on the flexural stiffness of prestressed CFRP-strengthened RC beams. A modified flexural stiffness prediction model was proposed by incorporating prestressing levels, interfacial bond slip, and softening after WDCs. Subsequently, four-point bending tests were conducted on 11 strengthened beams with different prestressing levels and WDCs to estimate flexural behavior. The results suggest that WDCs can adversely affect the flexural stiffness of the strengthened beams, particularly for the post-cracking stiffness of the non-prestressed specimens. However, prestressed strengthening can mitigate the stiffness degradation caused by WDCs. Moreover, a finite element (FE) model utilizing a traction separation model can accurately predict flexural stiffness. Finally, the flexural stiffness was computed using both the existing and proposed models and the proposed model provides the closest prediction of the flexural stiffness for CFRP-strengthened beams under WDC and prestressing.

Experimental and theoretical study on flexural behavior of steel–concrete composite beams strengthened by CFRP plates with unbonded retrofit systems

In this paper, the flexural behaviors of steel-concrete composite beams strengthened by prestressed carbon fiber-reinforced polymer (CFRP) plate with unbonded retrofit systems were investigated via four-point bending experiments. Three composite beams were strengthened by two groups of CFRP plate with thickness of 2mm or 3mm and prestress level of 10% or 15%, while one un-strengthened composite beam played a role as reference specimen. CFRP plate was transversely stretched by two scissors-type jacks and fixed on the tension flange of steel girder by an independently designed mechanical anchorage system. The experimental results reveal that the application of prestressed CFRP plate efficiently increased the yielding load and ultimate load of steel-concrete composite beams, but the ultimate deflection of mid-span was little affected. The increase of cross-sectional area of CFRP plates contributes more to stiffness of beams than that of prestress level. The CFRP strength utilization ratios of strengthened beams BS-1 and BS-3 at failure are 80%, under the condition of proper anchorage. Moreover, the prestress loss of CFRP plate was monitored for about 100h before test, which was less than 3%. Furthermore, a theoretical model was proposed to calculate the ultimate flexural resistance of strengthened steel-concrete composite beams with unbonded retrofit systems, which was validated with the experimental results.

Flexural strengthening of damaged steel beams with prestressed CFRP plates using a novel prestressing system

This study developed a novel prestressing system of the carbon fiber reinforced polymer (CFRP) plate to strengthen damaged steel beams, which reduced the operation space at the tensioning end, thereby extending the application range of prestressing system. Flexural tests were conducted to verify this system and investigate the effects of the adhesive layer, prestressing level, and CFRP plate area on the strengthening efficiency, and subsequently, a parametric analysis was carried out using finite element modeling to obtain more influencing rules of the unbonded CFRP plate-strengthened steel beams. The results indicated that satisfactory strengthening efficiency could be achieved by the novel prestressing system. The adhesive layer significantly affected the strain distributions of the steel–CFRP composite section, whereas it had a very slight effect on the flexural behavior of the steel beams, and the bonded and unbonded CFRP plates had a similar strengthening efficiency. Nonprestressed CFRP plate exhibited limited improvement in the flexural capacity and stiffness of the damaged steel beams under the normal service state; in contrast, the prestressed CFRP significantly increased the flexural behavior of the beams in the elastic and elastic–plastic stages owing to the high strength utilization of the CFRP plate. In addition, as the prestressing level increased, strengthening efficiency increased. Solely increasing the area or elastic modulus of the CFRP plate improved the strengthening efficiency slightly, whereas applying a prestress simultaneously clearly increases the strengthening efficiency. The strengthening efficiency increases with artificial notch depth.

Case Study on Prestressed CFRP Plates Applied for Strengthening Hollow-Section Beam Removed from an Old Bridge.

With the wide application of carbon fiber reinforced polymer (CFRP) plate, used for strengthening existed concrete structures, the prestressing technology of CFRP plate is becoming a hot topic, in order to sufficiently develop its high-strength peculiarity. In this paper, a full-scale hollow-section beam with length of 16 m taken from an old bridge which was in service for about 20 years was first examined for existed cracks and repaired by filling epoxy adhesive, and then the beam was strengthened with prestressed CFRP plates. The CFRP plates were tensioned and fixed with flat-plate anchorages at ends and bonded with adhesive on the bottom surface of the beam. The strengthened beam was experimentally studied using a four-point test to measure the concrete strain along the height of the mid-span section and the mid-span deflection. The finite element model of the strengthened beam was verified by the comparison of test results and used for an extending study of parametric analysis considering the effect of the length and amount of CFRP plates. Results indicated that with an increase in the length and amount of CFRP plates, the mid-span deflection of the beam decreases with the increased cracking resistance and bearing capacity, while the ultimate failure mode transfers from the under-reinforcement to the over-reinforcement.

Flexural Strengthening of Large-Scale RC Beams with Nonprestressed and Prestressed CFRP Using Different Anchorages.

Externally bonded carbon-fiber-reinforced polymer (CFRP) technology can be used by different methods based on the anchorage device, CFRP type, and prestressing/nonprestressing. However, a direct comparison between the strengthening efficacies of different methods is still lacking. Seven large-scale RC beams were tested in this study to investigate the influences of the anchorage method, CFRP type, prestress, and prestressing system on the flexural strengthening efficacy of RC beams. The test results showed that the ultimate load increased by 38.3%, whereas the cracking and yielding loads were slightly affected when the anchorage method was enhanced from CFRP U-wraps to wedge-clamp anchors. The CFRP plate and CFRP sheet could provide a rather close flexural strengthening efficacy under the same CFRP strengthening amount. Compared to the nonprestressed CFRP plate, the prestressed CFRP plate was highly superior in improving the flexural behavior of RC beams. The cracking, yielding, and ultimate loads of the prestressed CFRP-strengthened specimens were 57.1%, 22.9%, and 5.9%, respectively, higher than those of the nonprestressed CFRP-strengthened specimen with an effective anchorage. The two types of prestressing systems based on the adhesive-friction anchor and wedge-clamp anchor were proven to be effective for flexural strengthening of RC beams with prestressed CFRP plates, and they could provide almost the same strengthening effect.

Experimental Study on the Flexural Behavior of Large-Scale Reinforced Concrete Beams Strengthened with Prestressed CFRP Plates

Carbon fiber–reinforced polymer (CFRP) systems have been widely used to strengthen concrete structures. To further study the flexural strengthening of concrete beams with prestressed CFRP plates, flexural tests of large-scale reinforced concrete beams were performed, and a tensioning and anchorage system suitable for engineering applications was used in this study. The effects of the prestressing level, strengthening amount, type, and bonding position of the prestressed CFRP plate on the flexural behavior were investigated. The test results showed that the cracking load, yielding load, and ultimate load of all prestressed strengthened beams could reach 2.25–3.38 times, 1.27–1.53 times, and 1.24–1.61 times those of the unstrengthened beam, respectively. The postcracking stiffness, cracking load, and yielding load could be increased by increasing the prestressing level and strengthening the amount of the prestressed CFRP plate. However, a high prestressing level of 50% could lead to a premature intermediate debonding of the CFRP plate before yielding of the steel reinforcements and a reduction in the ultimate load. The use of a low-strength prestressed CFRP plate could achieve a strengthening efficacy similar to that of a high-strength CFRP plate before yielding of the steel reinforcements, whereas the low-strength CFRP plate reduced the ultimate load by 25 kN compared with the high-strength one. The prestressed CFRP plate bonded on the two sides provided a lower flexural strengthening efficacy than that bonded on the bottom of the beam owing to the shorter force arm and the nonuniform stress of the side-bonded CFRP plate.

An experimental study on fatigue debonding growth of RC beams strengthened with prestressed CFRP plates

Externally bonded Fiber Reinforced Polymer (FRP) laminates are increasingly used to strengthen Reinforced Concrete (RC) members. However, FRP debonding remains a major drawback of this strengthening method. To better understand the mechanisms of FRP debonding, six RC beams strengthened with prestressed or non-prestressed Carbon Fiber Reinforced Polymer (CFRP) plates were subjected to static and fatigue loading. CFRP plate debonding was observed in both cases. However, the mechanism of debonding differed: under cyclical fatigue loading, debonding was initiated under both loading points simultaneously and propagated synchronously towards the nearest support whereas in static tests debonding began under a single loading point and progressed suddenly towards its adjacent support. The results also showed that stress redistribution induced coupling between accumulated fatigue damage in the steel reinforcement and fatigue debonding of the CFRP plate, accelerating the fatigue failure of the specimens.

Fatigue behavior of notched steel beams strengthened by a prestressed CFRP plate subjected to wetting/drying cycles

Prestressed carbon fiber reinforced polymer (CFRP) strengthening is effective in suppressing crack propagation of steel beams. However, the fatigue behavior of notched steel beams with prestressed CFRP under a hygrothermal environment is not fully understood. Generally, notch machining on the steel beam is an ordinary method to simulate a fatigue defect for laboratory tests. In this study, the interfacial energy release rate at the notch location was first derived for strengthened steel beams. The theoretical results show that the interfacial energy release rate can be significantly reduced by prestressed CFRP strengthening, contributing to improving the interfacial fatigue performance. In addition, notched steel beams strengthened by prestressed CFRP (with a prestress level of 25% of tensile strength of CFRP plate) were exposed to wetting/drying cycles (WDCs) and then tested under fatigue loading. The experimental results show that prestressed CFRP strengthening increases the fatigue resistance of interfacial debonding initiation and failure 3.47 times and 7.83 times, respectively, which agrees with the tendency revealed by the theoretical results. In contrast, WDC exposure reduced the fatigue lives of interfacial debonding initiation and failure by 34.6% and 27.2%, respectively. An S – N curve based on the maximum principal interfacial stress at the notch location was proposed to predict the tendency of fatigue life of debonding initiation for strengthened steel beams. Moreover, the tendency prediction for fatigue life of interfacial debonding development for the strengthened steel beams with/without WDC exposure was developed based on Paris’ law. • Theoretically reveals that the prestressed CFRP reduces the interfacial energy release rate. • Prestressed CFRP strengthening significantly improves interfacial fatigue life. • Hygrothermal exposure leads to a significant reduction of interfacial fatigue life.

The anti-arch inhibition effect of multispan continuous girder bridge strengthened with prestressed CFRP plates

To study the interactions of longitudinal deformations on multispan continuous girder bridges strengthened with the prestressed Carbon fiber reinforced polymer (CFRP) plates, the reinforcement mechanism, and the stress distribution of bridges are analyzed. Then, a refined three-dimensional numerical model of continuous girder bridge strengthened with prestressed CFRP plates is established to study the influence of the number of adjacent spans on the reinforcement effect. The study shows that there is an “anti-arch inhibition effect” when multispan continuous girder bridges are strengthened with prestressed CFRP plates. Finally, to assess the “anti-arch inhibition effect”, the tension prestress of a continuous girder bridge strengthened with prestressed CFRP plates is optimized so that each span of a multispan continuous girder bridge can achieve a balanced reinforcement effect. The results show that the interaction between adjacent spans should be considered, and the ultimate reinforcement effect of the full-bridge is not optimal when the tensile prestress of the CFRP plate is the same for each span. By optimizing the prestressed ratio of the CFRP plates, the reinforcement effect can be optimized, the adverse effects of adjacent spans can be reduced, and the utilization rate of CFRP reinforcement can be improved.

Fatigue behavior of corroded steel plates strengthened with CFRP plates

This paper presents an experimental study performed to investigate the effectiveness of carbon fiber reinforced polymer (CFRP) plates in extending fatigue life of corroded steel plates. Specimens with five kinds of corrosion damage level, four kinds of strengthening configuration and four kinds of applied fatigue stress amplitude were tested and the primary fatigue behavior indications consist of failure mode, fatigue fractography, fatigue life and crack propagation were analyzed. Results showed that externally patching CFRP plates significantly strengthened the fatigue behavior of corroded steel plates, and even made the fatigue life of corroded steel plates recovered or exceeded that of the un-corroded ones, the fatigue life of the patched specimen which presented the most significant strengthening effectiveness even showed a fatigue life extension of more than 85.3 times with respect to the un-patched corroded steel plate and approximately 2 times over the un-corroded steel plate. Results also indicated that different strengthening configurations appeared to have diversity effect on the fatigue life extension and crack growth retardation of corroded steel plates, end anchorage measures effectively delayed the failure process of CFRP bonding interface and improved the fatigue strengthening effect, increasing CFRP strengthening stiffness or adopting prestressed CFRP plates significantly reduced the crack growth rate and extended the fatigue life of corroded steel plates. The outcome of the tests provided meaningful references and essential data for the reliable application of CFRP strengthening system in the fatigue performance improvement of corroded steel structures.

Stress Intensity Factor Assessment for the Reinforcement of Cracked Steel Plates Using Prestressed or Non-Prestressed Adhesively Bonded CFRP.

The use of adhesively bonded carbon fiber reinforced polymer (CFRP) materials to reinforce cracked steel elements has gained widespread acceptance in order to extend the lifespan of metallic structures. This allows an important reduction of the stress intensity factor (SIF) at the crack tip and thus a significant increase of the fatigue life. This paper deals with the assessment of the SIF for repaired cracked steel plates, using semi-empirical analysis and finite element analysis. Metallic plates with only one crack originating from a center hole were investigated. Virtual crack closure technique (VCCT) was used to define and evaluate the stress intensity factor at crack tip. The obtained modeling results are compared with experimental investigations led by the authors for different reinforcement configurations including symmetrical and non-symmetrical reinforcement, normal modulus and ultra-high-modulus CFRP plates, and pre-stressed CFRP plates. Results show that finite element model (FEM) analysis can obviously simulate the fatigue performance of the CFRP bonded steel plates with different reinforcement configurations. Moreover, a parametric analysis of the influence of the pre-stressing level was also conducted. The results show that an increase of the pre-stressing level results in an increase of the fatigue life of the element.

Experimental study on the mechanical and self-sensing behaviors of prestressed carbon fiber–reinforced polymer reinforced concrete composite structures

A type of self-sensing prestressed carbon fiber–reinforced polymer reinforced concrete composite structure was proposed and studied, composed of reinforced concrete beam, prestressed carbon fiber–reinforced polymer plate, and long-gauge fiber Bragg grating sensors. The carbon fiber–reinforced polymer plate was prestressed and bonded to the bottom of the reinforced concrete beam. Two types of anchorage systems were compared and studied. The long-gauge fiber Bragg grating sensors were used as active elements for the self-sensing of mechanical responses, which were installed on the tensile rebars, carbon fiber–reinforced polymer plates, and concrete. A series of static and fatigue 4-point flexural experiments were carried out to study the bending and fatigue performances of the composite structures. After a prescribed number of fatigue loading cycles, monotonic flexural bending was performed to investigate the deterioration of properties. The results showed that the long-gauge fiber Bragg grating sensor is valid for the mechanical response sensing of the proposed structures. The compatibility of the prestressed carbon fiber–reinforced polymer plate and concrete in the pure bending zone is excellent even under fatigue loading. The load-carrying capacities were improved by more than 30% due to the application of prestressed carbon fiber–reinforced polymer plates. The stiffness was also improved remarkably and generally decreased with the accumulation of fatigue cycles linearly.

Experimental and analytical study on flexural strengthening of RC beams via prestressed EBROG CFRP plates

The present manuscript reports results obtained from both experimental and analytical studies on the behavior of reinforced concrete (RC) beams strengthened in flexure using prestressed carbon-fiber-reinforced polymer (CFRP) plates via the externally bonded reinforcement on grooves (EBROG) method. A major concern in strengthening beams with prestressed FRP plates is the proper transfer of prestressing force to the beam. The present study pioneers the use of EBROG technique in prestressed CFRP plates considering the proven superiority of the bond efficiency created by the EBROG technique over that by the EBR. For the purposes of this study, seven RC beams with cross-sections of 200 × 300 mm and lengths of 2600 mm were subjected to the four-point loading test in order to investigate the effects of different parameters including prestressing level, using anchorage system, and the strengthening technique employed. Experimental results indicated that the EBROG technique, in the absence of any end anchorage, was well capable of transferring the prestressing stresses to the beam, which obviously led to significant reductions in strengthening costs. Compared to the specimens strengthened through the EBR technique, those strengthened via the EBROG technique exhibited an enhanced flexural behavior as evidenced by their increased load carrying capacity, ductility, and CFRP debonding strain that were higher by 18, 53, and 36%, respectively. It was also observed that prestressing CFRP plates attached via EBROG method was able to postpone the debonding and increase the strength efficiency of the FRP plates. A maximum enhancement of 20% in ultimate load-carrying capacity was measured in prestressed beams strengthened via the EBROG technique relative to the non-prestressed ones.

Failure mechanisms governing anchoring force of friction-based wedge anchorage for prestressed CFRP plate

An efficient anchorage system is demanded for the Carbon Fiber Reinforced Polymer (CFRP) plates with various sizes in structure reinforcements. The short-term governing failure modes were studied experimentally and numerically in determining the anchoring force of friction-based wedge anchorages to fulfill for all failure criteria for different variables, including the barrel and wedge thickness, length of wedge corner cut, roughness of contact surface, and the pretension load. A series of anchorages were investigated using pull-off tests to obtain the maximum anchoring force and the sequence of failure modes. The anchorage behavior was then simulated by three-dimensional numerical models to attain the maximum anchoring force for each performance criterion under varying conditions. Both the sliding and interlaminar debonding, rather than the tensile rupture, were found to determine the maximum anchoring force of a compact anchorage in the specific range of the parameter values involved. The wide and thin CFRP plate in the anchorage zone was prone to interlaminar debonding and the narrow and thick one tended to sliding or rupture. The parametric studies demonstrated that the CFRP size, the friction coefficient, and the bolt pretension load have significant influences on the maximum anchoring force of the friction-based anchorages.

Design optimization and experimental validation of a novel wedge-shaped bond anchorage system for prestressed CFRP plates

An efficient anchorage system plays a significant role in the strengthening and repair of existing structures in prestressed carbon fiber reinforced polymer (CFRP) plates. In the present study, a novel wedge-bond anchor was proposed to provide a reliable anchorage load-bearing capacity for the prestressed CFRP plate. Accordingly, interface bond tests were conducted to optimize the anchor parameters. The results revealed that the minimum bond length of the wedge-bond anchor was 100 mm and 120 mm for the adhesives Tc and T1, respectively. After optimization, the weight of the anchor was reduced by 58.3%. A mechanical model was built to analyze the load transfer path and evaluate the anchorage bearing capacity. Based on these, the ultimate anchorage bearing capacity was predicted to be higher than 4.70 GPa and 4.10 GPa for the adhesives Tc and T1, respectively. Tensile tests of the optimized anchor showed that a) the stress in the anchorage zone of the CFRP plate was distributed uniformly, and b) the stress concentration of CFRP in the anchor was avoided, which provided a higher anchorage bearing capacity. The extension applications of wedge-bond anchor were carried out for a larger size of CFRP plates (100 mm × 1.4 mm). Accordingly, it successfully led to CFRP bursting, yet no debonding occurred in the anchor.

Experimental study on prestressed concrete hollow slabs in service strengthened with prestressed CFRP plates

PurposeMost existing studies are confined to model beam tests, which cannot reflect the actual strengthening effects provided by prestressed carbon-fiber-reinforced polymer (CFRP) plates to existing bridges. Hence, the actual capacity for strengthening existing bridges with prestressed CFRP plates is becoming an important concern for researchers. The paper aims to discuss these issues.Design/methodology/approachStatic load tests of in-service prestressed concrete hollow slabs before and after strengthening are conducted. Based on the results of the tests, the failure characteristics, failure mechanism and bending performance of the slabs are compared and analyzed. Nonlinear finite element method is also used to calculate the flexural strength of the strengthened beams prestressed with CFRP plates.FindingsTest results show that prestressed CFRP plate strengthening technology changes the failure mode of hollow slabs, delays the development of deflection and cracks, raises cracking and ultimate load-carrying capacity and remarkably improves mechanical behavior of the slab. In addition, the nonlinear finite element analyses are in good agreement with the test results.Originality/valueStrengthening with prestressed CFRP plates has greater advantages compared to traditional CFRP plate strengthening technology and improves active material utilization. The presented finite element method can be applied in the flexural response calculations of strengthened beams prestressed with CFRP plates. The research results provide technical basis for maintenance and reinforcement design of existing bridges.

Prestressed CFRP-strengthening and long-term wireless monitoring of an old roadway metallic bridge

This paper presents an application of prestressed carbon fiber-reinforced polymer (CFRP) plates for the strengthening of metallic girders of a roadway bridge in Melbourne, Australia. The study also describes the application of a wireless sensor network (WSN) system for long-term structural monitoring of the retrofitted bridge girders. A flat prestressed unbonded retrofit (FPUR) system was developed to apply prestressed CFRP plates to the steel girders of the Diamond Creek Bridge (122 years old), which is subjected to daily passenger and heavy vehicles. The first section explains the results of sets of static and fatigue tests performed in the laboratory to examine the efficiency of the proposed FPUR system prior to its installation on the bridge. The second section presents details of different aspects of the CFRP strengthening of the bridge girders, fatigue design criteria, and layouts for short- and long-term monitoring. For the short-term measurements, the bridge was loaded with a 42.5-ton semi-trailer before and after strengthening. The CFRP plates were prestressed up to approximately 980 MPa (≈38% of the CFRP ultimate tensile strength), which resulted in about 50% reduction in the maximum tensile stress in the bridge girders. The third section discusses the development, installation, and preliminary results of the WSN system used to monitor the pre-stress level in the CFRP plates. The results of the short- and long-term measurements in this study show that the FPUR system is very effective for flexural and fatigue strengthening of bridge girders. Finally, a set of recommendations for long-term structural monitoring is provided.

Determination of S-N fatigue curves for damaged steel plates strengthened with prestressed CFRP plates under tension loading

To promote a straightforward design guideline, a determination model of S-N fatigue curves was established to consider effects of the initial crack and stress ratio (R-ratio) on the fatigue performance of damaged steel plates strengthened with non- and prestressed CFRP (Carbon Fiber-reinforced Polymer) plates. The modified Paris’ law employing the effective stress intensity factor range was first used to model the fatigue crack growth data obtained from an extensive literature review for various R-ratios, including edge- and center-notched reinforced steel plates under fatigue loadings. Based on these analysis, the fatigue S-N curve function including the fatigue strength Δσc and fatigue threshold ΔσL, was derived to consider the effects of the initial crack and R-ratio. The model was validated using fatigue results of approximately two hundred specimens with various notch sizes and stress ratios. Specific handbooks provided distinctly different values of C and m for mild steel, and among them the recommended values are 6.86 × 10−12 (with the unit of MPa and meter) and 3.0 through the validation using existing test data reported in the literatures. The comparison of the experimental and predicted fatigue lives confirms the feasibility of the proposed S-N curve determination. Furthermore, the practical value U of the crack closure effect is recommended as 1.0 in the negative R region (R < −0.5) considering the crack closure effect would be overestimated. The sensitivity analysis of critical factors also shows that the initial damage level dramatically influences the S-N curve, and the prestress level also has a dominant impact not only on the reduction of stress range but also the upgrade of fatigue threshold.