Experimental Study and Residual Performance Evaluation of Corroded High-Tensile Steel Wires

Zheng, Xianglong; Xie, Xu; Li, Xiaozhang

doi:10.1061/(ASCE)BE.1943-5592.0001114

Open access

Technical Papers

Sep 1, 2017

Experimental Study and Residual Performance Evaluation of Corroded High-Tensile Steel Wires

Authors: Xianglong Zheng, Xu Xie [email protected], and Xiaozhang LiAuthor Affiliations

Publication: Journal of Bridge Engineering

Volume 22, Issue 11

https://doi.org/10.1061/(ASCE)BE.1943-5592.0001114

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Abstract

To evaluate the residual service performance of corroded high-tensile steel wires, a batch of in situ wires that had served for 13 years in the hangers of an arch bridge was investigated. Four types of corroded wires were derived from the in situ wires by placing them in the indoor environment for 1.5 years (Type A) or treating them in an alternate dry–wet environment for 0.25–1.5 years (Types B, C, and D). The mechanical properties of the corroded wires were investigated with tensile and fatigue tests, and the fracture characteristics were observed. Fatigue tests on Type A wires with different stress ranges were conducted, and the stress intensity factor range ΔK_p at the bottom of crack-initiation pits was analyzed. According to the S-N curve for Type A wires, the crack-propagation characteristics of steel wires were investigated. The linear elastic fracture mechanics (LEFM) approach was used to predict the residual life of corroded wires in two systems of arch bridges. The tests show that the ultimate strain of corroded wires decreased with an increase in degree of corrosion. The fatigue properties of wires were found to degrade significantly at the early corrosion stage, and the degradation rate slowed down with further development of corrosion. The correlation between the fatigue life and the stress intensity factor range ΔK_p at the bottom of corrosion pits shows that larger pitting size tended to have shorter life under the same stress range, and fatigue cracks were difficult to initiate at the corrosion pits below the fatigue threshold. The crack-growth parameters of the Paris law identified from the S-N curve of Type A wires were m = 2.87, C = 8 × 10 ⁻¹² under the stress ratio R = 0.5. The residual life predicted by LEFM shows that in a dry environment, corroded wires with an initial pitting depth of 0.6 mm can serve for more than 30 years in arch–beam combination-system bridges, whereas they can only serve for 5 years in floating-system arch bridges.

Introduction

The application of high-tensile steel cables adds convenience in the structural design and construction of long-span bridges. However, the mechanical properties of cable steel wires are very sensitive to corrosion. Corrosion of wires significantly degrades the service performance of cables (Nakamura et al. 2004). Since the 1960s, there have been numerous accidents involving the rupture of bridge cables caused by wire corrosion, such as the Point Pleasant Bridge and Maracaibo Bridge (Hopwood and Havens 1984), Guangzhou Haiyin Bridge (Lan 2009), and Chongqing Rainbow Bridge and Yibin South Gate Bridge (Li 2015). To avoid cable rupture in service, the corroded cables of many bridges were replaced according to inspection of the outward appearance. For example, the cables of the Pasco-Kennewick Bridge and the Köhlbrand Bridge (Hamilton et al. 1995) and the Chongqing Shimen Bridge (Lan 2009) were all replaced during the design service period. However, the criteria for determining whether a cable should be replaced have not been established, and most of the decisions of cable replacement are usually made on subjective judgment.

Tensile tests on laboratory-corroded wires (Barton et al. 2000) showed that the brittleness of corroded wires is mainly caused by pitting-stress concentration and hydrogen embrittlement. However, those effects have been proven to be limited on fractures for steel wires in service conditions (Betti et al. 2005), and fatigue seems to be the predominant failure mode in the general case (Mayrbaurl and Camo 2001; Nakamura and Suzumura 2009). Some studies have been conducted to explore the fatigue properties of corroded wires. For example, Nakamura et al. (2004) performed fatigue tests on steel wires with different corrosion degrees and found that the fatigue strength of corroded wires decreased significantly when steel corrosion progressed. Furthermore, Nakamura and Suzumura (2013) investigated the pitting effect on steel wire fatigue properties. The steel wires were notched on the surface to simulate the corrosion pits, and the fatigue tests showed that deeper and sharper pits resulted in a lower fatigue life. Based on those testing data, Ye et al. (2015) introduced the theory of critical distances (TCD) to predict the fatigue life of corroded wires. Essentially, the fatigue notch factor predicted by TCD corresponds to the crack-initiation stage, so whether this method is suitable for life prediction of precorroded components is debatable. Conversely, Lan (2009) used the Miner theory to evaluate the residual life distribution of a batch of corroded cable wires under service stress according to their S-N curves. The limitation of such a method is obvious in terms of the flexibility because S-N curves are deterministic parameters for the same kind of wires and cannot be directly used for another corrosion case. Currently, an effective method is lacking for fatigue evaluation of steel wires with different corrosion statuses.

This study focused on the residual performance of steel wires with different corrosion statuses. The mechanical properties of steel wires with different corrosion statuses were investigated with tensile and fatigue tests. The S-N curve of corroded wires with one status was used to analyze the crack-growth characteristics. Furthermore, the residual life of corroded wires under general service conditions was predicted by the linear elastic fracture mechanics (LEFM) approach, and the effect of the bridge structural system was considered.

Corrosion Status and Tensile Properties of Steel Wires

The steel wires for this research were sampled from a hanger of a half-through reinforced concrete arch bridge that has served for 13 years, the design safety factor κ of which is approximately 2.59. The nominal diameter and the minimum permissible strength σ_m of the original wires were 5 mm and 1,570 MPa, respectively. The in situ steel wires were corroded and covered by red rust on the surface, with average mass loss rate

\bar{w} = 0.4 %

and coefficient of variation of mass loss rate COV (w) = 0.19. After rust removal, the steel wires appeared to be smooth and glossy, with a few small dark brown rust spots on the surface.

To study the effects of corrosion degree on the mechanical properties of the wires, the in situ wires were further rusted into four types: (1) Type A wires with natural corrosion in indoor and dry environment conditions for approximately 18 months, for which

\bar{w} = 0.57 %

, COV(w) = 0.12; (2) Type B wires with dry–wet cycle accelerated-corrosion environment conditions in salt-water tank under room temperature for 3 months, for which

\bar{w} = 3.6 %

, COV(w) = 0.15; (3) Type C wires with dry–wet cycle accelerated-corrosion environment conditions in salt-water tank under room temperature for 12 months, for which

\bar{w} = 11.15 %

, COV(w) = 0.03; (4) Type D wires with dry–wet cycle accelerated-corrosion environment conditions in salt-water tank under room temperature for 18 months, for which

\bar{w} = 15.12 %

, COV(w) = 0.04. After rust removal, Type A wires appeared glossy, and there were few differences between Type A and in situ wires on the surface. Type B wires were peeling on the surface, and many contiguous corrosion pits were exposed after rust removal. Type C and Type D wires were both corroded seriously and covered with unconsolidated rust products. Their cleaned surfaces appeared rough, with obvious pitting defects. Fig. 1. shows the appearance of the four types of wires before and after rust removal.

Fig. 1. Samples of corroded wires before and after rust removal: (a) Type A; (b) Type B; (c) Type C; (d) Type D

The tensile tests on the steel wires were carried out according to the requirements of GB/T 17101-2008 (SAC 2008). The length of the test specimens was 500 mm, and the loading stress rate was 25 MPa/s. The nominal stress–strain curves of the tensile tests are shown in Fig. 2. As indicated in Fig. 2, the ductility of the corroded wires decreased sharply with an increase in corrosion degree. It can be seen that the ultimate strain of Type D decreased more than 75% compared with the in situ wires. There was also some reduction in tensile strength, but it was not as obvious.

Fig. 2. Nominal stress–strain curves of corroded wires

The analysis shows that the in situ wires, Type A wires, and Type B wires presented a cup- or cone-shaped fracture surface. In these fractures, the distribution of the fiber region (crack initiation), radial region (crack propagation), and shear lips (rapid fracture) were almost symmetrical [Fig. 3(a)]. For the Type C and Type D wires, some big corrosion pits significantly affected the stress distribution of the cross section. In those cases, the locations of the crack initiation were no longer centered, and the radial regions tended to converge with the bottom of the corrosion pits [Fig. 3(b)]. It can be concluded that the pitting-induced brittle mechanism caused more loss of strength of in the corroded wires.

Fig. 3. Morphology of tensile fracture surfaces of corroded steel wires: (a) mildly corroded wires; (b) severely corroded wires

Fatigue Properties of Corroded Steel Wires

Fatigue Tests of Corroded Steel Wires

Because it is an important aspect of mechanical properties, the fatigue performance of wires was investigated. To test the fatigue behavior of corroded wires, a clamping device for the resonant PLG-10 C (Jinan Testing Equipment IE Corporation, Jinan, China) high-frequency fatigue testing machine (f = 80 Hz) was developed (Fig. 4). With the protection of plastic spraying at the end of the specimens, the occurrence of fracture in the clamp was reduced to a low frequency. As shown in Fig. 4, the total length of the test specimens was 40 cm, and the effective length was 26 cm. Because of the high stress level of actual cables in service, the stress ratio R in the test was set as 0.5.

Fig. 4. Fatigue testing system and test sample size

The fatigue test results for the Type A wires are shown in Fig. 5. The broken designation signifies that the fatigue fracture occurred in the effective section of the specimens, and the data were all distributed in the high-stress range (360–520 MPa). The cycle number for termination was set as 5 million cycles, and the specimens that were unbroken after 5 million cycles were designated unbroken. It is difficult to get valid data under a low-stress range (Δσ ≤ 330 MPa) because of frequent clamping fracture in a long fatigue life. The specimens that broke in the clamp but after more than 2 million cycles were designated fixture broken. As shown in Fig. 5, the life under the low-stress range was much longer than that under the high-stress range, and it tended to be infinite as the stress range decreased. Therefore, the test data and S-N curve of the Type A wires were divided into the finite-life region and infinite-life region, and the turning point between the two regions was approximately 5 × 10⁵ cycles. For comparison, median S-N curves (R ≥ 0.4) from two references (Li et al. 1995; Lan 2009) are also given in Fig. 5. The dash-dotted S-N curve is for a type of new steel wires (σ_0.2 = 1,579 MPa, σ_u = 1,736 MPa), and the dashed one is for a batch of corroded wires sampled from a stay-cable bridge [

\bar{w}

= 2.66%, COV(w) = 1.13, σ_0.2 = 1,510 MPa, σ_u = 1,700 MPa]. The latter S-N curve was only about the finite-life region because no further data were given for the lower stress range (Δσ < 290 MPa) in the reference (Lan 2009). It can be seen from the Fig. 5 that the fatigue properties (life and strength) of the corroded wires were significantly poorer than those of the new wires. Although there was little difference in their corrosion degree, the S-N curve of Type A wires was very close to that of stay-cable corroded wires in the finite-life region.

Fig. 5. Fatigue testing data of steel wires

Table 1 shows the fatigue life of different types of corroded wires under the same nominal stress range of Δσ = 360 MPa. For new wires, the fatigue life under Δσ = 360 MPa was more than 2 × 10⁶ cycles (SAC 2008). However, the longest life of the corroded wires under this stress range was less than 5 × 10⁵ cycles, which means that the life of wires may transform from infinite to finite as soon as wires are rusted. It can be seen from the table that as the corrosion degree increased, the mean life and the standard deviation (SD) degraded more and more slowly.

Table 1. Comparison of Fatigue Life for Different Types of Corroded Steel Wires (Δσ = 360 MPa)

Sample	Fatigue life (× 10⁴)
Sample	Type A	Type B	Type C	Type D	New
1	35.8	24.5	15.9	14.8	>200
2	21.2	27.1	15.6	13.6
3	46.4	27.9	14.0	13.4
4	28.1	38.6	13.7	13.0
5	30.8	28.2	13.4	12.1
Mean	32.5	29.3	14.5	13.4	—
Standard deviation	8.4	4.8	1.1	1.0	—

Analysis of Fatigue Fracture for Corroded Steel Wires

The typical fatigue-fracture morphology of four types of corroded wires is shown in Fig. 6. It can be seen from the global view that all of the fracture surfaces can be divided into crack-propagation region (smooth and flat) and rupture region (rough). The rupture region consists of two parts: (1) the ductile fracture region (dark color; centered area), which contains a lot of small ridges and is similar to the radial region in tensile fracture; and (2) the brittle fracture region (light color; outer circle), which formed at the weakest antishear section and is similar to the shear lip in tensile fracture. From Fig. 6, it can be seen that with an increase in the corrosion degree, the area of the crack-propagation region decreased, and the ductile fracture region gradually became a circle.

Fig. 6. Fatigue-fracture morphology of corroded steel wires: (a) Type A; (b) Type B; (c) Type C; (d) Type D

Fig. 7 shows the defects of the crack-initiation sites in an enlarged view. The rim of the fracture surface for Type A and Type B wires was slightly affected by the corrosion pits [Figs. 7(a and b)], and it is obvious that the pitting scale of Type B was bigger than that of Type A. But for Type C and Type D wires, the rim of the fracture surface was severely changed by corrosion pits [Figs. 7(c and d)], and the pitting boundary was hard to define. It can be seen from Fig. 7 that the crack-initiation pits were of open shape, with a larger width and complicated interior morphology, thus being able to induce a multimicrocrack initiation in one pitting region. The crack trace generated by crack coalescence is marked in Figs. 7(a–c).

Fig. 7. Enlarged view of sites of fatigue-crack initiation: (a) Type A; (b) Type B; (c) Type C; (d) Type D

The stress intensity factor range ΔK_p at the bottom of the pits (hereinafter, the pitting ΔK_p) is the driving force for microcrack growth, the value of which can be estimated by Murakami’s equation (Murakami 1985):

Δ K_{p} = 0.65 Δ σ \sqrt{π \sqrt{area}}

(1)

where area is the projection area of the corrosion pits.

The value of pitting ΔK_p calculated by the crack-initiation pits of Type A wires is shown in Fig. 8. It can be seen from Fig. 8 that there was a correlation between the fatigue life and pitting ΔK. That is, the shorter life was more likely to be with the larger pitting size under the same stress range. However, the discreteness of the data indicates that fatigue life was not dominated by pitting size, and the effect of pitting size was weakened by an increase in the stress range. Moreover, the minimum value of ΔK found in this research was approximately 3.7

MPa \cdot \sqrt{m}

, which is close to the value of threshold ΔK_th = 3.8

MPa \cdot \sqrt{m}

(R = 0.5) of the high-tensile steel wires (Llorca and Sánchez-Gálvez 1987), indicating that the pitting ΔK below the threshold conditions was unlikely to form a fatigue crack.

Fig. 8. Fatigue life versus stress intensity factor range of corrosion pits

Crack Propagation of Corroded Steel Wires

Calculation of Crack-Propagation Life of Corroded Wires

Many researchers (Dolley et al. 2000; Medved et al. 2004) have employed the LEFM method to predict the fatigue life of precorroded components. It assumes that the effect of short cracks plays a small part in the pitting-crack transition. Actually, for high-tensile steel wires, the critical size of long and short cracks is quite small (<10 μm, equivalent to the grain size of a pearlite) (Beretta and Matteazzi 1996). Additionally, the propagation of short cracks is very fast, and nonpropagating cracks are seldom observed in wires (Llorca and Sánchez-Gálvez 1989). Therefore, the microcracks that have the chance to initiate at the very beginning of the cycles will grow into long cracks in a short life. Based on this analysis, the current study neglected the effect of short-crack propagation in the finite-life region of the corroded wires and applied the LEFM method to analyze the fatigue life.

In accordance with the LEFM theory, Paris’s formula is commonly used to describe the properties of long-crack propagation. It is expressed as follows (Paris and Erdogan 1963):

\frac{d a}{d N} = C \cdot Δ K^{m} = C \cdot {(Y \cdot Δ σ \cdot \sqrt{π a})}^{m}

(2)

where a = crack depth; m and C = crack-growth parameters for Region II, the crack-propagation rate of which is at steady state; and Y = crack-shape factor. Based on statistics, the crack propagation of steel wires can be simplified into a one-dimensional problem, and the equation of Y is as follows (Mahmoud 2007):

Y (\frac{a}{D}) = 0.7282 - 2.1425 (\frac{a}{D}) + 18.082 {(\frac{a}{D})}^{2} - 49.385 {(\frac{a}{D})}^{3} + 66.114 {(\frac{a}{D})}^{4}

(3)

where D = diameter of the steel wires. The crack-propagation life N_p can be obtained through the transposition and integral of Eq. (2), as follows:

N_{p} = \frac{1}{C Δ σ^{m}} \int_{a_{0}}^{a_{c}} {(Y \cdot \sqrt{π a})}^{- m} d a

(4)

where in a₀ = initial cracking depth, or approximate pitting depth; and a_c = critical crack depth, which can be calculated by the fracture toughness criterion through an iterative method (Mahmoud 2007), as follows:

K_{c} = Y σ_{\max} \sqrt{π a_{c}}

(5)

where K_c = plane-stress fracture toughness, and the average K_c of the steel wires in this study was approximately 60

MPa \cdot \sqrt{m}

; and σ_max = maximum stress, σ_max = Δσ/(1 – R).

Given the crack-growth parameters m and C, the fatigue life of corroded wires can be predicted by Eq. (4). However, the current research on the crack-propagation properties of high-tensile steel wires is quite insufficient. In this article, an inversion method will be used to identify the material parameters m and C.

Crack-Growth Parameters of Steel Wires

Generally, materials’ crack-growth parameters m and C are determined by standard crack-propagation tests (ASTM 2015). Because of the small size in diameters, steel wires cannot be tested through that standard procedure. Currently, fractography analysis is the major approach to this issue, and some special methods have been proposed to obtain fractures with distinguishable crack fronts, such as heat tinting (Llorca and Sánchez-Gálvez 1987) and load decreasing (Toribio et al. 2009). But those methods are not widely accepted because of the difficult operation and low efficiency. Previous studies (Tanaka and Akiniwa 2002; Cui 2002) have shown that the crack-growth parameters m and C derived from S-N data can make a rational prediction on fatigue life and thus provide a convenient way to obtain those parameters. To this end, the median S-N curve was chosen to be the known condition. For the typical reflection on fatigue behavior, a₀ is suggested to be the median depth of the corrosion pits (Newman and Abbott 2009). The observation by scanning electron microscopy revealed that the median depth of the corrosion pits of Type A wires was approximately 100 μm.

The crack-growth parameters of the testing wires were identified according to those conditions described previously, which are shown in Table 2. The parameters from two experimental studies (Llorca and Sánchez-Gálvez 1987; Toribio et al. 2009) are also given. In particular, the materials listed in Table 2 all belong to cold-drawn eutectoid pearlite steel (∼0.80% C), and the tests were conducted under R = 0.5. It can be seen that there were some differences between the three groups of crack-propagation parameters. The identified parameters in this study were at an intermediate level, and they are in line with the negative correlation between m and C.

Table 2. Crack-Propagation Parameters for High-Tensile Steel Wires (R = 0.5)

Author	Chemical elements	Mechanical property (MPa)	m	C	Method
Llorca and Sánchez-Gálvez (1987)	0.82% C, 0.60% Mn, 0.18% Si	σ_y = 1,370	2.29	2.05 × 10⁻¹¹	Tests
		σ_u = 1,720
Toribio et al. (2009)	0.79% C, 0.68% Mn, 0.21% Si	σ_y = 1,480	3.0	4.1 × 10⁻¹²	Tests
		σ_u = 1,820
This article	0.81% C, 0.72% Mn, 0.20% Si	σ_y = 1,580	2.87	8.0 × 10⁻¹²	Identified from Type A
		σ_u = 1,730

Based on the crack-growth parameters in Table 2, the median fatigue life under each testing stress range was calculated (Fig. 9). These calculations indicated that the fatigue life predicted by existing crack-growth parameters (Llorca and Sánchez-Gálvez 1987; Toribio et al. 2009) is nonconservative.

Fig. 9. Calculation of crack-propagation life and fitted *S-N* curves

Residual Life of Steel Wires under Service Conditions

In service conditions, the fatigue stresses of cables vary greatly for different bridge structural systems. The extent to which these different fatigue stresses affect the residual life of corroded cables is not very clear. In this paper, two systems of cable-supported arch bridges, a floating system and an arch–beam combination system, were taken as examples to investigate the residual life of corroded wires under service conditions.

Calculation Conditions

Equivalent Stress Range

An investigation was carried out on the fatigue stress of hangers in arch bridges; the results are shown in Table 3 (Zhang et al. 2010; Xu et al. 2014; Li 2015). In Table 3, Δσ_eq is the equivalent stress range, which is counted by the rain-flow method; Arch F and Arch C, respectively, refer to the floating-system arch bridge and the arch–beam combination-system bridge. For the number of small- and medium-span bridges in common environments, the Δσ_eq simulated by vehicles is intended to be representative because wind loads that will significantly affect the fatigue stress of the hangers are not very frequent during the service period. As indicated in Table 3, the equivalent stress range of the floating-system arch bridge (55–60 MPa) was significantly higher than that of the arch–beam combination-system bridge (16–28Mpa). As a numerical example, two typical values of Δσ_eq, 60 and 30 MPa, will be used for calculation.

Table 3. Characteristics of Fatigue Stress of Hangers of Arch Bridges

Author	Zhang et al. (2010)	Xu et al. (2014)		Li (2015)
Approach	Monitoring	Simulation	Simulation	Simulation
Type of bridge	Arch C	Arch F	Arch C	Arch F
Span (m)	138	100	150	120

The cycle number of stress range per unit time is another important parameter for fatigue-life evaluation, which is closely determined by the omission criterion of small loads. The studies just described showed that a reasonable value of the daily average cycle number N₀ of equivalent stress range was approximately 2,000–10,000 cycles/day for hangers. These figures are intended to be of the same order of magnitude as daily loads from heavy vehicles, which may cause fatigue damage on steel wires.

Environmental Factors

It is acknowledged that outdoor service conditions are much more complex than laboratory ones, which will definitely affect the residual performance of steel cables. Fatigue damage can be divided into pure mechanical fatigue and corrosion fatigue according to whether there are corrosion media. Failure of the protection system (e.g., polyethylene [PE] cover) will cause rainwater and air to touch the wires, so corrosion fatigue is a more common case for fatigue damage. To describe the crack-propagation rate (da/dN)_env in a corrosive environment, this paper refers to an approach proposed by Oberparleiter and Schütz (1981), and the environmental acceleration factor C_corr is introduced to the inertia model. The corrosion fatigue model is

{(d a / d N)}_{env} = C_{corr} \cdot C \cdot Δ K^{m}

(6)

In a corrosive environment, C_corr is the comprehensive reflection of load frequency, temperature, humidity, and chemical medium. A previous study (Martín and Sánchez-Gálvez 1988) showed that the value of C_corr may reach more than 10 under a high stress ratio and low loading frequency for steel wires in seawater. Although the causticity in cables is not as severe as it is in seawater, the value of C_corr for cable wires should not be underestimated because of the possible competition between corrosion and fatigue. Because there is less research on this issue, this study assumed two values, 1 and 6, to reflect the effect of C_corr in a dry environment and corrosive environment, respectively.

Initial Crack Depth

Corroded wires with high mass loss are very dangerous for practical use because fatigue cracks may already exist on the surface (Mayrbaurl and Camo 2001). The wires discussed in this paper are limited to be of moderate corrosion, in which case the fatigue cracks cannot exist. For safety consideration, the maximum pitting depth a_max of a corroded wire was assigned to be the initial crack depth, and a_max can be estimated by extreme value theory (Li et al. 2014) as follows:

\begin{matrix} a_{\max} = \bar{a} \cdot x = (1 - \sqrt{1 - w}) D / 2 \cdot x \\ F (x) = exp [- exp (- \frac{x - β}{α})] \end{matrix}

(7)

where

\bar{a}

= average pitting depth; w = mass loss rate of a steel wire; and α and β = scale parameter and position parameter of the Gumbel distribution, respectively. In the study by Li et al. (2014), α ≈ 0.954, and β is related to the length L of the steel wires: β ≈ 0.905 · ln (L/0.21) + 4.078. It can be seen from the previous equations that the longer the corroded steel wire is, the bigger the a_max will be. This study assumed that the interval length of the steel wires with similar corrosion characteristics was 10 m, so the value of quantile x corresponding to the cumulative probability of 0.99 is approximately 12.

Critical Crack Depth

In an inert environment, the critical crack depth a_c can be estimated by fracture toughness K_c through Eq. (5). But in a corrosive environment, the critical crack depth a_scc should be estimated by the threshold stress intensity for stress corrosion cracking K_ISCC. For high-tensile steel wires, K_ISCC is approximately 0.56K_c (Toribio 1998). If the maximum stress is given as σ_max ≈ σ_m/κ = 607 MPa, the estimated values of a_c and a_scc for steel wires with a diameter of 5 mm are approximately 2 mm and 1.4 mm respectively.

Crack Growth of Steel Wires in Service

The increment iteration method (Yin 2012) was employed to predict the crack propagation of corroded wires (w = 1% and w = 4%) under different service conditions. The relation curves for crack depth (millimeters) and time (years) are shown in Fig. 10. In these predictions, the crack-growth parameters m and C were assigned the values given by this article, and N₀ was assumed to be 5,000 cycles per day.

Fig. 10. Crack-growth curves of steel wires under different calculation conditions (N₀ = 5,000): (a) Δσ_eq = 60 MPa; (b) Δσ_eq = 30 MPa

As shown in Fig. 10, the crack-growth rates of the steel wires increased slowly at first and then faster, and the sharply increasing stage seemed to start at 1 and 0.5 mm for C_corr = 1 and C_corr = 6, respectively. In the case of C_corr = 6, the two critical depths a_c and a_scc were both at the sharply increasing stage, and their predictions for residual life only show 3% of the difference. Figs. 10(a and b) show that the residual life of corroded wires under high fatigue stress (Δσ_eq = 60 MPa) was significantly shorter than that under low fatigue stress (Δσ_eq = 30 MPa). Distinguishing these two cases is helpful to make decisions on the timing of replacement for cables. For example, the residual life of corroded wires with 4% mass loss rate (a₀ = 0.6 mm) was less than 5 years under Δσ_eq = 60 MPa, so the cables should be replaced in time when this corrosion occurs. In the case of Δσ_eq = 30 MPa, the same corroded wires can serve for more than 30 years if a dry service environment is established by appropriate anticorrosion maintenance. Conversely, it should be noted that the steel wire with a shallow initial pitting had a very long life under Δσ_eq = 30 MPa in the dry environment, which is shown in Fig. 10(b). Actually, this prediction is reasonable when compared with the residual life under Δσ_eq = 30 MPa, which is directly derived from the S-N curve of Type A wires. However, it is hardly possible for the cable anticorrosion system to be always in good condition in practice, so the residual life of cables should be updated periodically during service time.

In terms of the application, the floating system with high fatigue stress in hangers is not recommended for arch bridge designs, and more attention should be paid to these existing bridges.

Conclusions

In this study, the failure mechanism of corroded steel wires was analyzed with tensile tests and fatigue tests. The crack-propagation parameters of the steel wires were identified indirectly according to the fatigue properties of the corroded steel wires and the LEFM method. Moreover, the residual life of the corroded steel wires was predicted with regard to the service conditions of the steel cables in arch bridges. The conclusions of this study can be summarized as follows:

1.

The ductility of corroded wires decreases sharply with an increase in the corrosion degree, and the brittle mechanism is mainly caused by a local pitting effect.

2.

Corrosion causes a significant decrease in the fatigue properties of the steel wires. Fatigue properties degrade sharply at the early corrosion stage and slowly afterward. The crack-propagation life takes a large proportion in the finite-life region of the corroded steel wires.

3.

Fatigue tests show that the negative correlation between pitting size and fatigue life will be weakened by an increase of the stress range, and in a corrosion pit with a stress intensity factor range below the fatigue threshold, it is hard to form a fatigue crack.

4.

Based on the LEFM and fatigue tests, the crack-propagation parameters of the high-tensile steel wires are identified as m = 2.87, C = 8 × 10⁻¹², which are valid in the Paris region under R = 0.5.

5.

The predicted life shows that the residual life of corroded wires in floating-system arch bridges is much limited when compared with that in arch–beam combination-system bridges.

In addition, the degradation of the cross section and the competition between corrosion and fatigue may also have an impact on the residual life of steel wires. However, such a time-dependent model is closely related to the actual environments, and more experimental and theoretical studies should be conducted in the near future.

Acknowledgments

This study was sponsored by National Natural Science Foundation of China (Grant 51378460). The authors also acknowledge X. Pan and T. Zhang for their previous work on tensile tests and theoretical research.

References

ASTM. (2015). “ Standard test method for measurement of fatigue crack growth rates.” E647-15e1, West Conshohocken, PA.

Abstract

Introduction

Corrosion Status and Tensile Properties of Steel Wires

Fatigue Properties of Corroded Steel Wires

Fatigue Tests of Corroded Steel Wires

Analysis of Fatigue Fracture for Corroded Steel Wires

Crack Propagation of Corroded Steel Wires

Calculation of Crack-Propagation Life of Corroded Wires

Crack-Growth Parameters of Steel Wires

Residual Life of Steel Wires under Service Conditions

Calculation Conditions

Equivalent Stress Range

Environmental Factors

Initial Crack Depth

Critical Crack Depth

Crack Growth of Steel Wires in Service

Conclusions

Acknowledgments

References

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