Application of strain-life fatigue-corrosion model for fillet-welded connections of sign support structures

Abstract

Fatigue-related corrosion is a complex phenomenon that induces damage accumulation and electrochemical deterioration throughout the service life of the structure. This article presents a previously proposed and modified strain-life Smith–Watson–Topper corrosion model for details on fillet-welded connection of highway sign support structures. To evaluate the degree of corrosion activity, hot-dip galvanized, weathering, and low-carbon steel are investigated with respect to chemical compositions, material properties, and the corresponding corrosion resistance indices. The existing fatigue testing data were analyzed and used to evaluate fatigue resistance under various corrosion environments. A modified Smith–Watson–Topper corrosion model is further utilized to determine acceptable constant amplitude fatigue thresholds for the American Association of State Highway and Transportation Officials fatigue limits under each corrosion category. It was found that low constant amplitude fatigue threshold values were observed for ASTM A588, A595, and A572 steels in locations with corrosion categories exposed to severe corrosive environments. Under these conditions, hot-dip galvanization or other surface treatments of the steel components of the sign supports are recommended to achieve higher constant amplitude fatigue threshold values.

Keywords

fillet-welded tube-to-transverse plate connection fatigue-corrosion sign structure strain life Smith-Watson-Topper (SWT) model

Introduction

Fillet-welded socket connections, also known as tube-to-transverse plate connections, are widely used for mast-arm and base plate connection for highway signs, luminaires, and traffic signals across the United States. However, there has been a fatigue concern on these connections, and it was determined that wind-induced cyclic fatigue stresses are the primary source of failure in welded connections according to previous investigations and published reports (Fisher et al., 1991; Foley et al., 2008; Gilani and Whittaker, 2000; John and Dexter, 1998; Kaczinski et al., 1998). Although the socket connections are cost-effective and easy to fabricate for support structures, a recent experimental research (Roy et al., 2011) reported that fillet-welded tube-to-transverse plate connection showed a poor fatigue resistance compared to other connection types (i.e. groove-welded connection). For details on socket connection, the fatigue critical location is defined as the toe of fillet welds, and localized fatigue cracks and failures are expected due to the increased high-stress concentration (Ni et al., 2010).

In 1996, along Route 147 in New Jersey, a sign failure resulted in fatigue loading at the aluminum shoe base socket connection. A failure report (John and Dexter, 1998) indicated that the poles experienced repeated stress cycles exceeding 12 ksi during the night of the failure. However, the socket connection shoe base was designed as category E′, which has a constant amplitude fatigue threshold (CAFT) equal to 1.0 ksi for aluminum structures. In 2003, a 140-ft high-mast lighting tower along I-29 near Sioux City, IA, collapsed due to fatigue loads. A forensic study by Connor and Hodgson (2006) revealed that fatigue is the main cause of the failures at the base plate-to-column weld, at the handhole detail, or of anchor rods. At the time of collapse, the pole experienced a large cyclic stress range, which was induced by a vortex shedding phenomenon. The reports of this investigation also stated that corrosion of the tube wall was also determined as a potential cause of failure in addition to fatigue.

Fatigue corrosion is a complex phenomenon that is induced by the damage accumulation and electrochemical deterioration process throughout the service life of any structure. This coupled action takes place in the long-term performance of engineering structures. To take into account time-dependent corrosion effects under cyclic loadings, both numerical and experimental studies (Kayser and Nowak, 1989; Nowak and Szerszen, 2001) were performed under different environmental conditions. Section loss using an exponential function (Komp, 1987), the average corrosion penetration rate, and deterioration rate including corresponding coefficients were measured for time-dependent structural capacity. In addition to the field-measured stress spectra for fatigue life assessment of welding details (Ye et al., 2012), recent studies (Deng et al., 2019; Hosseini et al., 2013; Ye et al., 2017; Zhang and Yuan, 2014) investigated composite steel girder bridges to evaluate the long-term structural deterioration of composite bridge under combined fatigue–corrosion behavior. Variation of stress level considering section loss of steel girder was evaluated in finite element (FE) model. Statistical and reliability-based approaches were used for remaining life prediction of structure.

However, the results of these proposed methods can cause possible discrepancies and inaccuracy of determining the reduction of overall stiffness of a structural member. Furthermore, there are difficulties in evaluating the corrosion effects for the long-term structural deterioration due to imprecise corrosion factors such as annual deterioration rate, losses, as well as the corrosion pattern with very limited experimental research work. It is noted that deterioration curves evaluated by the proposed methods are focused on the section loss of steel girder in composite bridge structures. Therefore, the fatigue–corrosion behavior of welded connection details is an unfamiliar research topic with limited information.

The main objective of this research is to utilize a proposed and calibrated strain-life Smith–Watson–Topper (SWT) model (El Aghoury and Galal, 2014) to take into account the effects of corrosion on the performance of fillet-welded tube-to-transverse plate connection details, which are typically used in highway sign support structures. In this study, a previously proposed SWT strain-life corrosion model is further advanced by implementing average corrosion rates as well as different treatment types. Chemical components and material properties of corrosion-resistant weathering steel (WS) and low-carbon steel (LS) are investigated by following ASTM standards. A corrosion index is obtained according to ASTM G101 (2004) to estimate the corrosion resistance. Hot-dip galvanized steel (HGS), which protects from corrosion by forming the zinc patina, is also evaluated to determine the corrosion resistance under fatigue loading. In addition, fatigue testing data are used to determine coupled fatigue–corrosion resistance under various corrosion categories. The SWT corrosion model is further investigated to propose new CAFTs to provide the guideline for fatigue design.

Background

Socket connection detail: tube-to-transverse plate connection

For details on unstiffened socket connection, fillet welds are applied at the top of the base plate and inside the cut-out in the base plate, between the bottom surface of the pole and the sides of the base plate. The fillet welding at the top is the more structurally significant weld because it resists shear and tensile stresses (Azzam, 2006). Figure 1 shows a typical socket connection (tube-to-transverse plate connection). With regard to the stress-life infinite fatigue life design requirement where no crack is anticipated, the wind-induced stress range must be lower than CAFT (constant amplitude fatigue resistance) for infinite fatigue life.

Figure 1.

Socket connection detail: tube-to-transverse plate connection.

Chemical compositions and material properties of ASTM steels

ASTM A595 and A572 are specified as steel materials for structural supports for highway signs, luminaires, and traffic signals according to the American Association of State Highway and Transportation Officials (AASHTO, 2015). To use the strain-life corrosion fatigue life prediction model for ASTM A588 Grade B WS (El Aghoury and Galal, 2014) for structural supports, the chemical requirements and material properties are investigated herein.

ASTM A595 Grades A and B are defined as low-carbon and high-strength low-alloy steel, respectively, and A595 Grade C steel is the weathering-resistant steel. Another type of structural steel used for support structures is the high-strength low-alloy columbium–vanadium A572 steel structural steel (ASTM A572/A572M, 2015). ASTM A558 and A595 Grade C are WS composed of nickel (Ni), copper (Cu), and chromium (Cr) that provide a higher corrosion resistance (ASTM A588/A588M, 2004). Chemical requirements of ASTM A588, A595, and A572 steel are summarized in Table 1. Certain chemical elements such as silicon (Si) and phosphorus (P) affect hot-dip galvanizing and zinc coating by prolonging the reaction between iron and molten zinc in the surface (ISO 14713-2:2009, 2009).

Table 1.

Chemical requirements of ASTM A588, A595, and A572.

Designation	Grade	C	Mn	Si	P	S	Cr	Ni	Cu
ASTM A588	Grade A	0.19	0.18–1.25	0.30–0.65	0.03	0.03	0.40–0.65	0.4	0.25–0.40
	Grade B	0.20	0.75–1.35	0.15–0.50	0.03	0.03	0.40–0.70	0.5	0.20–0.40
ASTM A595	Grade A	0.15–0.25	0.30–0.90	0.060	0.035	0.035	–	–	–
	Grade B	0.15–0.25	0.40–1.35	0.060	0.035	0.035	–	–	–
	Grade C	0.19–0.22	0.50–1.35	0.15–0.65	0.04	0.05	0.40–0.70	0.5	0.20–0.50
ASTM A572	Grade 42 – 65	0.21–0.26	1.35	0.15–0.40	0.03	0.03	–	–	–

With respect to the material properties of ASTM steels, the yield strength, ultimate tensile strength, and elongation are obtained from ASTM standard specifications (ASTM A572/A572M, 2015; ASTM A588/A588M, 2015; ASTM A595/A595M, 2014). This information is summarized in Table 2. These properties are used to determine fatigue coefficients for strain-life analysis using the uniform material law (Baumel and Seeger, 1990).

Table 2.

Material properties and corrosion resistance index of weathering and low-carbon steel.

Designation	Grade	Yield strength (MPa)	Ultimate tensile strength (MPa)	Elongation (%)	Corrosion resistance index 6.3.1	Corrosion resistance index 6.3.2
ASTM A588	Grade A	345	485	21	5.07–6.86	5.53–7.74
	Grade B	345	485	21	5.07–6.86	5.53–7.74
ASTM A595	Grade A	380	450	23	0.13–0.69	0.68–1.57
	Grade B	410	480	21	0.13–0.69	0.89–2.35
	Grade C	410	480	21	5.07–6.86	5.53–7.74
ASTM A572	Grade 42	290	415	24	0.74–1.11	2.80–3.78
	Grade 50	345	450	21	0.74–1.11	2.83–3.81
	Grade 55	380	485	20	0.74–1.11	2.85–3.83
	Grade 60	415	520	18	0.74–1.11	3.84
	Grade 65	450	550	17	0.74–1.11	4.15

Characterization of the corrosion resistance index (ASTM G101)

ASTM G101 (2004) provides the guide to estimate the atmospheric corrosion resistance of low-alloy WSs. The corrosion resistance index, I, is obtained using the chemical composition of the steel under consideration. In section 6.3.1 of ASTM G101, the modified Legault–Leckie equation is introduced from industrial atmospheric exposure test data (Legault and Leckie, 1974). Based on the statistical analysis of the effects of chemical composition, the averaged corrosion resistance index can be calculated using the corrosion loss data from three different locations (Townsend, 1999).

Using both methods, the corrosion resistance indices are obtained in the form of a range of values to evaluate the corrosion resistance of various ASTM steels used for highway signs, luminaires, and traffic signals. WSs such as A558 and A595 Grade C have higher corrosion indices compared to LSs. Since higher index values represent greater corrosion resistance, it is expected to observe lower reductions in fatigue resistance of WSs compared to LSs. Obtaining corrosion indices for HGS was not possible because ASTM G101 does not provide guidelines for calculating the corrosion index for HGS similar to those given for WS and LS.

HGS and WS

Hot-dip galvanization protects against corrosion by forming the zinc patina as well as providing cathodic protection. WS is known as corrosion-resistant steel, and the presence of the rust layers produces a protective barrier that prevents further oxidation of the metal. However, WS exhibits accelerated corrosion when frequent high humidity or fog conditions exist (American Galvanizers Association, 2012).

Although hot-dip galvanizing helps to minimize corrosion risks, fatigue testing and synthetic data analysis (Choi, 2018; Ocel, 2014) showed that fatigue resistance is reduced due to the galvanization. In this study, the strain-life fatigue analysis is performed for connections made of HGS, WS, or LS for different corrosion categories.

Development of the strain-life corrosion model

Strain-life fatigue coefficients

In strain-life fatigue analysis, the total strain is composed of two parts: an elastic region and a plastic region. The cyclic stress–strain behavior is represented by the Ramberg–Osgood relationship expressed in equation (1)

ε_{t o t a l} = ε_{e} + ε_{p} = \frac{σ}{E} + {(\frac{σ}{K^{'}})}^{1 / n'}

(1)

where E is Young’s modulus, $n'$ is a measurement of the working hardening behavior of the material, and $K'$ represents the cyclic strength coefficient (Ramberg and Osgood, 1943). While the cyclic properties are determined from the stress–strain response, the fatigue properties can be obtained from the steady-state hysteresis loops. The total strain amplitude can be resolved into elastic and plastic strain components, and curves for both elastic and plastic strains are fitted separately as straight lines, as shown in Figure 2. At large strains, the plastic strain component is predominant, but the elastic strain is predominant at small strains. The intercepts of the two straight lines at $2 N_{f} = 1$ are the elastic component and plastic component of the strain. This is represented by equation (2) (Morrow, 1968)

ε_{a} = \frac{Δ ε}{2} = \frac{Δ ε_{e}}{2} + \frac{Δ ε_{p}}{2} = \frac{{σ'}_{f}}{E} (2 N_{f})^{b} + {ε'}_{f} (2 N_{f})^{c}

(2)

where ${ε'}_{f}$ is the fatigue ductility coefficient and ${σ'}_{f}$ is the fatigue strength coefficient. The factors b and c represent the slopes of the elastic and plastic lines, respectively.

Figure 2.

Strain amplitude versus reversals to failure for A595 Grade C.

Using the uniform material law (Baumel and Seeger, 1990), coefficients for strain-life analysis were obtained. For example, when using ASTM A595 Grade C WS for tube-to-transverse connection details, Young’s modulus, yield strength, ultimate tensile strength, and elongation were 200 GPA, 410 MPa, 480 MPa, and 21%, respectively. The coefficients needed for strain-life analysis: K,’ n,’ $σ_{f}'$ , b, $ε_{f}'$ , and c were obtained using the uniform material law from uniaxial tensile test results for smooth specimens. In this study, the strain-life coefficients were obtained by fitting the curve for the notch at the tip toe of the fillet weld that raises localized stress concentration. These values were the following: $K' =$ 0 1400 MPa, $n' =$ 0 0.15, $σ_{f}' =$ 720 MPa, $b = - 0.087$ , $ε_{f}' =$ 0.59, and $c = - 0.58$ . Figure 2 shows the strain amplitude versus reversals to failure for A595 Grade C steel.

SWT corrosion model

To account for the long-term corrosion effect, a recent study (El Aghoury and Galal, 2014) proposed a strain-life corrosion model using the SWT equation (Smith et al., 1970). Researchers validated the strain-life model using the experimental work on A588 Grade B steel by Albrecht and Shabshab (1994). In their experimental work, 24 rolled beams were weathered for 5–6 years and were boldly exposed to air, moist freshwater, and sprayed with a salt solution to simulate the use of deicing salts. The results obtained for the expected life for each specimen are presented as a range of values, and a good agreement was observed using their strain-life corrosion model (El Aghoury and Galal, 2014). The modified SWT strain-life corrosion model (El Aghoury and Galal, 2014) was written as shown in equation (3)

ε_{a} σ_{\max} = ε_{a} (σ_{a} + σ_{m}) = \frac{{({σ'}_{f})}^{2}}{E} (2 N_{f})^{2 b'} + {σ'}_{f} {ε'}_{f} (2 N_{f})^{b' + c'}

(3)

where $σ_{\max}$ is the maximum applied tensile stress, which is obtained by adding stress amplitude, $σ_{a}$ , and mean stress, $σ_{m}$ . In the SWT model, it is assumed that the SWT parameter, defined as the strain energy density, remains constant with different combinations of strain amplitude and maximum stresses for a given life (Stephens et al., 2000). To take into account the corrosion effects, new factors $b'$ and $c'$ are introduced and are defined in equations (4) and (5)

b' = b (1 + γ_{corr} γ_{α} α_{b})

(4)

c' = c (1 + γ_{corr} γ_{α} α_{c})

(5)

According to International Organization for Standardization (ISO 9223:1992, 1992; ISO 9223:2012, 2012; ISO 9224:1992, 1992), the corrosion factor, $γ_{α}$ , represents the average corrosion rate and the high corrosion penetration rates yield a higher value of $γ_{corr}$ compared to unity environmental condition corresponding to an upper limit exposure to a 3.5% NaCl solution for typical fatigue tests (El Aghoury and Galal, 2014). To evaluate the modified SWT strain-life corrosion model, the highest values corresponding to the worst environmental case are used for each corrosion category. Based on examining several values for the $γ_{α}$ factor (El Aghoury and Galal, 2014), the range of the values of ±0.05 proved to result in more accurate fatigue life predictions. Table 3 summarizes the $γ_{α}$ values for hot-dipped zinc galvanized steel, WS, and LS from ISO 1992. In this study, the maximum values of $γ_{α}$ and $γ_{corr}$ were selected for each corrosion category.

Table 3.

$γ_{α}$ values for hot-dip galvanized, weathering, and carbon steel (ISO 9224:1992, 1992).

Corrosion category	$γ_{α}$ , Average corrosion rate (µm/year)
Corrosion category	Hot-dip galvanized steel	Weathering steel	Low-carbon steel
C1	$γ_{α} \leq 0.1$	$γ_{α} \leq 0.1$	$γ_{α} \leq 0.5$
C2	$0.1 < γ_{α} \leq 0.5$	$0.1 < γ_{α} \leq 2$	$0.5 < γ_{α} \leq 5$
C3	$0.5 < γ_{α} \leq 2$	$2 < γ_{α} \leq 8$	$5 < γ_{α} \leq 12$
C4	$2 < γ_{α} \leq 4$	$8 < γ_{α} \leq 15$	$12 < γ_{α} \leq 30$
C5	$4 < γ_{α} \leq 10$	$15 < γ_{α} \leq 80$	$30 < γ_{α} \leq 100$

The two corrosion material constants $α_{b} = 0.182$ and $α_{c} = 0.034$ proposed by El Aghoury and Galal, (2014) are used for this study. It should be noted that these factors were derived from 2-year JIS-JMS WS fatigue test data (Kunihiro et al., 1972). Therefore, future experimental fatigue data are needed to update and adjust the corrosion material constants for the LS. The descriptions of the proposed $γ_{corr}$ for each corrosion category are summarized in Table 4 (ISO 14713-1:2009, 2009; El Aghoury and Galal, 2014). The SO₂ compound represents the concentration of sulfur dioxide in a particular steel.

Table 4.

Corrosion categories and proposed $γ_{corr}$ (El Aghoury and Galal, 2014; ISO 14713-1:2009, 2009).

Corrosion category	Corrosivity	Descriptions	Proposed $γ_{corr}$
C1	Very low	Dry or cold zone, atmospheric environment with very low pollution and time of wetness	$0 < γ_{corr} \leq 0.09$
C2	Low	Temperature zone, atmospheric environment with low pollution (SO₂ < 5 µg/m³)	$0.09 < γ_{corr} \leq 0.29$
C3	Medium	Temperature zone, atmospheric environment with medium pollution (SO₂: 5–30 µg/m³)	$0.29 < γ_{corr} \leq 0.47$
C4	High	Temperature zone, atmospheric environment with high pollution (SO₂: 30–90 µg/m³)	$0.47 < γ_{corr} \leq 0.57$
C5	Very high	Temperature and subtropical zones, atmospheric environment with very high pollution (SO₂: 90–250 µg/m³)	$0.57 < γ_{corr} \leq 1.00$

Results from SWT corrosion model analysis

The analysis procedure for the SWT corrosion model was applied to the different AASHTO fatigue categories. The results from the SWT analysis as well as the results from the synthetic data analysis are presented and discussed in this section. The strain-life SWT corrosion model flowchart is illustrated in Figure 3.

Figure 3.

Strain-life SWT corrosion model flowchart.

Evaluation of fatigue resistance for AASHTO categories

To evaluate the modified SWT strain corrosion model, different AASHTO fatigue categories, which indicate fatigue design limits or thresholds, were indicated in the strain-life plot. The y-axis represents the strain amplitude, and the x-axis represents the reversals to failure. The Ramberg–Osgood relationship, which was described in equation (1), was used for developing the strain-life plots. The fatigue coefficients K’ and n’ were obtained using the universal material method (Baumel and Seeger, 1990). The obtained cyclic strength coefficient K’ was 1400 MPa (203 ksi), and the cyclic strain hardening component n’ was 0.15. These coefficients are used to obtain the plots in Figure 4.

Figure 4.

Strain amplitude versus reversals to failure for AASHTO categories.

Strain-life coefficients b and c that determine the slope of the strain-life curve for the elastic and plastic curves were obtained by fitting the two curves. The values for b and c obtained were −0.33 and −2.25, respectively. It is worth noting here that the obtained values of b and c are applicable to all AASHTO categories having different intercept values. The proposed modification corrosion factors $γ_{corr}$ for HGS, WS, and LS were calculated using equations (4) and (5) and are summarized in Table 5.

Table 5.

Corrosion factors for hot-dip galvanized, weathering, and low-carbon steel.

Hot-dip galvanized steel/category	b	$b'$ (min)	$b'$ (max)	c	$c'$ (min)	$c'$ (max)	$γ_{corr} γ_{α} (\min)$	$γ_{corr} γ_{α} (\max)$
C1	−0.330	−0.33	−0.33	−2.25	−2.25	−2.25	0.00	0.01
C2	−0.330	−0.34	−0.34	−2.25	−2.26	−2.26	0.12	0.17
C3	−0.330	−0.38	−0.39	−2.25	−2.31	−2.33	0.84	1.04
C4	−0.330	−0.45	−0.48	−2.25	−2.41	−2.44	2.08	2.48
C5	−0.330	−0.90	−0.96	−2.25	−2.98	−3.05	9.50	10.50
Weathering steel/category	b	$b'$ (min)	$b'$ (max)	c	$c'$ (min)	$c'$ (max)	$γ_{corr} γ_{α} (\min)$	$γ_{corr} γ_{α} (\max)$
C1	−0.330	−0.33	−0.33	−2.25	−2.25	−2.25	0.00	0.01
C2	−0.330	−0.36	−0.37	−2.25	−2.29	−2.30	0.48	0.68
C3	−0.330	−0.53	−0.58	−2.25	−2.51	−2.57	3.36	4.16
C4	−0.330	−0.79	−0.89	−2.25	−2.85	−2.96	7.80	9.30
C5	−0.330	−4.89	−5.38	−2.25	−8.06	−8.68	76.00	84.00
Low-carbon steel/category	b	$b'$ (min)	$b'$ (max)	c	$c'$ (min)	$c'$ (max)	$γ_{corr} γ_{α} (\min)$	$γ_{corr} γ_{α} (\max)$
C1	−0.330	−0.33	−0.33	−2.25	−2.25	−2.26	0.02	0.07
C2	−0.330	−0.40	−0.43	−2.25	−2.34	−2.38	1.20	1.70
C3	−0.330	−0.63	−0.70	−2.25	−2.64	−2.73	5.04	6.24
C4	−0.330	−1.27	−1.45	−2.25	−3.44	−3.67	15.60	18.60
C5	−0.330	−6.04	−6.64	−2.25	−9.52	−10.28	95.00	105.00

For AASHTO category E, the modified SWT strain-life equation presented by El Aghoury and Galal (2014) was used to account for the corrosion effects of HGS under the corrosion category of C2, WS, and LS as shown in Figure 5. In the SWT plot in Figure 5, the y-axis represents the strain energy density defined as the strain amplitude multiplied by the maximum applied stress. As anticipated, significant reductions with respect to fatigue life were observed for LS, while for HGS, the reduction in fatigue life was not significant.

Figure 5.

Corrosion effects of AASHTO category E under the corrosion category of C2.

To convert a modified SWT stain-life plot to a stress-life plot, the total strain which is obtained by using the Ramberg–Osgood relation (Ramberg and Osgood, 1943) is transferred to a stress range with a cyclic strength coefficient K′ of 1400 MPa (203 ksi) and a cyclic strain hardening exponent n′ of 0.15. Using fatigue coefficient A and slope m of 3, the number of cycles that can achieve infinite fatigue life and also can be used for fatigue design was determined. The proposed CAFT range for each corrosion category is summarized in Table 6.

Table 6.

Proposed CAFT range for AASHTO categories.

Fatigue category		E′	E	D	C	B	A
CAFT (AASHTO)	HGS, WS, and LS	2.6 ksi	4.5 ksi	7 ksi	10 ksi	16 ksi	24 ksi
Proposed	HGS	2.58–2.58	4.45–4.47	6.95–6.98	9.89–9.95	15.8–15.9	23.6–23.8
CAFT (C1)	WS	2.58–2.58	4.45–4.47	6.95–6.98	9.89–9.95	15.8–15.9	23.6–23.8
	LS	2.54–2.58	4.33–4.44	6.73–6.92	9.56–9.86	15.2–15.7	22.7–23.5
Proposed	HGS	2.48–2.51	4.17–4.24	6.38–6.55	8.98–9.26	14.2–14.7	21.1–21.9
CAFT (C2)	WS	2.19–2.30	3.37–3.64	4.95–5.44	6.72–7.50	10.2–11.6	14.9–17.0
	LS	1.76–1.96	2.41–2.81	3.31–3.97	4.21–5.20	5.84–7.53	8.12–10.7
Proposed	HGS	2.03–2.12	2.95–3.17	4.24–4.61	5.61–6.19	8.23–9.24	11.8–13.4
CAFT (C3)	WS	1.05–1.24	1.35–1.60	1.75–2.09	2.07–2.50	2.52–3.13	3.18–4.04
	LS	0.69–0.88	0.89–1.13	1.16–1.46	1.35–1.72	1.62–2.06	1.99–2.56
Proposed	HGS	1.49–1.69	1.97–2.17	2.62–2.94	3.21–3.66	4.20–4.92	5.61–6.72
CAFT (C4)	WS	0.37–0.50	0.49–0.65	0.65–0.86	0.77–1.01	0.92–1.21	1.14–1.49
	LS	0.05–0.10	0.08–0.14	0.11–0.20	0.14–0.24	0.17–0.30	0.23–0.38
Proposed	HGS	0.29–0.36	0.39–0.47	0.52–0.61	0.61–0.73	0.73–0.89	0.92–1.10
CAFT (C5)	WS	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00
	LS	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00	0.00–0.00

CAFT: constant amplitude fatigue threshold; HGS: hot-dip galvanized steel; LS: low-carbon steel; WS: weathering steel.

HGS that has a zinc coating layer showed the best corrosion protection by achieving the highest proposed CAFT values for all AASHTO categories. Under corrosion category 1, no significant reductions in fatigue life were observed in both HGS and WS. However, under severe corrosion environments such as categories 3 and 4, significant reductions in fatigue life were observed in both WS and LS. For corrosion category C5, which has a 3.5% of NaCl solution similar to an environment in subtropical area with an atmospheric environment of very high pollution, the CAFT values from the proposed analysis were very small, indicating that no alternative designs should be considered and additional protective measures from the severe corrosion should be implemented.

Evaluation of fatigue resistance for the synthetic data analysis

To estimate the effects of surface treatments such as hot-dip galvanized or zinc coating, the synthetic data analysis results were used. Based on the regression analysis results of existing test data for unstiffened fillet-welded socket connection (Koenigs et al., 2003; Ocel, 2014; Stam et al., 2011), the mean minus two standard deviation regression lines were shifted down slightly to establish a lower bound. With a 2.3% probability of failure and assuming the fatigue life logarithms to be normally distributed (Johns and Dexter, 1998; Schneider and Maddox, 2003), this approach is commonly used for design purposes.

According to the synthetic data analysis results (Choi, 2018), the unstiffened fillet-welded socket connection details were grouped to take into account the parameters that significantly influence the fatigue resistance. Group 1 represents nongalvanized round tube-shaped specimens that have plate thicknesses greater than 50.8 mm (2 inch). Group 2 has the same condition as Group I except that the surface treatment involves zinc bath coating. The fatigue coefficients A were obtained as 1.04E + 08 for Group 1 and 6.58E + 07 for Group 2. These results show that there is a reduction in fatigue resistance for galvanized steel as it was found from fatigue testing results (Ocel, 2014).

The corrosion coefficient factors from ISO coefficients (ISO 9224:1992, 1992) and the proposed corrosion factors by El Aghoury and Galal (2014) were used in the implementation of the SWT corrosion model. The number of cycles was set at 10 million cycles to achieve infinite fatigue life (Puckett et al., 2014). Figure 6 shows the the stress range versus number of cycles curve for Groups 1 and 2 with the corresponding CAFT values.

Figure 6.

S–N curve for Groups 1 and 2 with proposed CAFTs.

The results for Group 1 test data with a nongalvanized socket connection show a CAFT value of 2.18 ksi. Under corrosion category C2, the CAFT values of the WS and LS decreased to 1.88 and 1.52 ksi, respectively. The results for Group 2 with galvanized, zinc-coated specimens are also plotted to compare with the nongalvanized specimens exposed to the corrosion environment. The CAFT value for Group 2 is 1.88 ksi. As observed in Figure 6, a CAFT value of 1.87 ksi was obtained for the nongalvanized WS under C2 corrosion conditions. Based on these results, it can be concluded that WS is not a good candidate for locations with corrosion categories C3, C4, and C5. For these situations, it is recommended to provide galvanization treatments for the steel components for the tube-to-transverse connection detail. Table 7 summarizes the obtained CAFT values for group 1.

Table 7.

Proposed CAFT for AASHTO categories.

Fatigue category		Group 1
CAFT (no corrosion)	WSLS	2.18
Proposed CAFT (C1)	WS	2.16–2.17
	LS	2.14–2.16
Proposed CAFT (C2)	WS	1.88–1.96
	LS	1.52–1.68
Proposed CAFT (C3)	WS	0.94–1.10
	LS	0.63–0.79
Proposed CAFT (C4)	WS	0.35–0.46
	LS	0.06–0.10
Proposed CAFT (C5)	WS	0.00–0.00
	LS	0.00–0.00

CAFT: constant amplitude fatigue threshold; LS: low-carbon steel; WS: weathering steel.

Discussion

SWT model validation

The SWT corrosion model proposed by El Aghoury and Galal (2014) used the results of the experimental study by Albrecht and Shabshab (1994) to validate the corrosion model. They performed fatigue tests to evaluate the fatigue behavior of 24 corroded rolled beams made of A588 WS. The beams were weathered for approximately 5–6 years under three different corrosion conditions. Therefore, the corrosion duration period needs to be considered for the proposed SWT model.

Material constant coefficients

The proposed corrosion material constants as α_b = 0.182 and α_b = 0.034 in the SWT model were adopted from the previous study by El Aghoury and Galal (2014). It should be noted that these factors were derived from 2-year JIS-JMS WS fatigue testing data (Kunihiro et al., 1972), which indicate that these factors are dependent on the 2-year study data. Hence, experimental research work can be performed for factor modifications. In addition to WS, the accuracy of the SWT corrosion model can be improved by testing results for both LS and HGS.

Effects of hot-dip galvanization versus corrosion effects

Without any corrosion effect, a recent experimental result (Ocel, 2014) found that the hot-dip galvanization reduced the fatigue resistance for fillet-welded tube connection while formed zinc patina provides cathodic protection to protect the specimens. This determines that galvanization has an advantage in corrosion protection but a disadvantage in fatigue resistance. This study utilized the synthetic data analysis results (Choi, 2018) into the modified SWT model for the unstiffened socket connection details. With respect to WS, which protects corrosion by having the protective rust layers, it was treated as nongalvanized steel and corrosion coefficient factors were used for the proposed SWT corrosion model. It was revealed that WS can be a good option in environments with corrosion categories of C1 and C2 but better to have galvanization treatments under C3, C4, and C5.

Conclusion

In this article, a previously proposed and modified strain-life SWT corrosion model was investigated for fillet-welded tube-to-transverse connection details of highway sign support structures. The following conclusions can be presented from this study:

A modified strain-life SWT corrosion model was studied to evaluate corrosion effects on fatigue resistance of connection of sign supports. This previously proposed model was used to establish a range of CAFTs for various corrosion categories for infinite fatigue life design.

Although galvanization steel has a disadvantage in fatigue resistance, HGS showed the best corrosion protection by achieving the highest CAFT values for all AASHTO fatigue categories.

Very low values of CAFT were observed for WS for locations with corrosion categories C3, C4, and C5. Hot-galvanization treatments or other surface treatments of the steel components are recommended to achieve higher values of CAFT under these exposed conditions.

There is a need for further testing of stiffened and unstiffened connections to validate corrosion factors of a proposed SWT corrosion model with respect to different types of steel such as LS, WS, and HGS under moderate and severe corrosion conditions.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Hyungjoo Choi

Husam Najm

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