Simulating the hot dip galvanizing process of high mast illumination poles. Part II: Effects of geometrical properties and galvanizing practices

Journal of Constructional Steel Research 159 (2019) 584–597

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Journal of Constructional Steel Research

Simulating the hot dip galvanizing process of high mast illumination poles. Part II: Effects of geometrical properties and galvanizing practices Reza Nasouri a, Kien Nguyen b, Arturo Montoya a,⁎, Adolfo Matamoros a, Caroline Bennett b, Jian Li b a b

Department of Civil and Environmental Engineering, University of Texas at San Antonio, San Antonio, TX, United States of America Department of Civil, Environmental and Architectural Engineering, University of Kansas, Lawrence, Kansas, United States of America

a r t i c l e

i n f o

Article history: Received 31 January 2019 Received in revised form 19 April 2019 Accepted 6 May 2019 Available online 27 May 2019 Keywords: Thermal stress and strain Cracking Hot-dip galvanizing Steel structures Finite element analysis Highway structures

a b s t r a c t Cracks that develop during galvanization of High Mast Illumination Poles (HMIPs), often at the pole-to-base plate connection, are an important concern to US fabricators and highway officials. If they are not detected during fabrication and are allowed to propagate during service, these cracks can pose a significant risk to the public due to the ubiquitous presence of HMIPs in close proximity to roads and highways. Economic losses caused by these cracks include the cost of detailed inspections to ascertain their presence and direct losses associated with discarded poles or repair of cracks that manifest while in service. Modifications to the design of HMIPs and/or the galvanization process to reduce the likelihood of galvanization cracks reduce economic loses, decrease fabrication costs, and improve public safety. This paper presents a parametric study evaluating the effects of geometric configuration and galvanization practices on thermally-induced stress/strain demands during the galvanization of HMIPs. Simulations were performed for poles with standard pole-to-base plate connection details adopted by the Texas DOT. Geometric parameters evaluated in the study included base plate-to-pole thickness ratio, pole shaft geometric shape, and bend radius. Galvanizing practice variables included dwell time, speed and angle of dipping, and cross-section orientation. Simulations were conducted using the commercial software Abaqus, following the methodology validated in a companion paper. In models having the same pole thickness, thermally-induced stresses and strains at critical locations increased with base plate-to-pole thickness ratio. In models with the same base plate thickness, stress and strain demands varied inversely proportional to pole thickness. Stress and strain demands were found to be lower for poles having circular shape than for multi-sided poles, and increases in bend radius led to reductions in localized strain demands. Dwell time was found to have a negligible effect on stress and strain demands, while increased dipping speed and dipping angle resulted in decreased stress and strain demands during galvanizing. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Corrosion damage is the main cause for inspection, maintenance, and repair of steel structures exposed to the environment. The global cost of corrosion damage is estimated at US $2.5 trillion, which represents approximately 3.4% of the world gross domestic product (GDP) [1]. Corrosive environments also affect other sources of damage, for example increasing the rate of crack growth and reducing the fatigue life of steel structures [1]. Hot-dip galvanizing is a highly effective corrosion prevention method [2] which consists of providing a corrosion resistant zinc-iron and zinc metal coating to protect steel substrates from corrosion. The galvanizing process consists of sequential immersions for caustic cleaning, pickling, and flux application, followed by immersion of the steel part(s) into a hot molten zinc bath, typically at 445 to 455°C [2–5]. ⁎ Corresponding author. E-mail address: [email protected] (A. Montoya).

https://doi.org/10.1016/j.jcsr.2019.05.010 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

During the past two decades, galvanizing-induced cracks have been observed with greater frequency in High Mast Illumination Poles (HMIPs) and other hot-dip galvanized steel assemblies. During this time, numerous fatigue failures of HMIPs have been reported in several states in the US, including Iowa, Florida, Wisconsin, California, Massachusetts, Wyoming, New Jersey and South Dakota [6–12]. The two problems are interrelated because flaws introduced by galvanization can propagate when HMIPs are in service and subjected to cyclic wind loads. The interrelation between these two problems is complex because measures that mitigate cracking during galvanizing can increase propensity for fatigue cracks in field applications, and vice versa. Fatigue cracks in HMIP poles in service have been observed at pole walls, near the pole-to-base plate welded connection, particularly at the weld toe [13–15]. Because in-service failures of HMIPs can lead to loss of life, substantial resources are allocated to detailed inspections of pole-to-base plate connections to detect galvanization flaws [7,11,12,16–19]. Numerous field and laboratory studies have investigated the effects of pole shape and galvanization on fatigue performance of high-mast

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lighting towers subjected to wind loads. Based on finite element analyses several researchers have concluded that base plate flexibility has the greatest influence on the magnitude of the local bending stress at the pole shaft, near the weld toe of the pole-to-base plate connection, and consequently that plate flexibility has a significant effect on fatigue life [17,20–26]. Researchers have also observed through experimentation that galvanized HMIPs have lower fatigue life than black steel (nongalvanized) poles, which supports the hypothesis that galvanization flaws propagate and grow when HMIPs are in service [10,11,27–34]. Similar trends were observed in experimental studies investigating the effect of zinc coatings on the fatigue life of steel joints, in which coated and uncoated subassemblies were subjected to similar cyclic loading protocols. Viespoli et al. [35] compared the fatigue lives of fillet welded galvanized and non-galvanized cruciform steel joints and found that galvanization caused a small reduction in fatigue life. Berto et al. [25,33] reached the same conclusion comparing the fatigue life of hot dip galvanized and uncoated steel bolted connections. Given the great level of difficulty associated with measuring stress, strain, and deformation fields during galvanizing, experimental studies have been complemented with numerical simulations to understand the response of HMIPs during galvanization, as well as the stress demands when the poles are in service and subjected to wind-induced fatigue loads. Ocel [9] and Warpinski [22] performed finite element (FE) analyses on three-dimensional HMIP models to calculate hotspot stresses at the pole-to-base plate connection. The stress concentration factor (SCF) obtained from the simulations was used as an indicator of the potential fatigue performance of the HMIPs. In addition, Ocel [9] conducted parametric studies to determine the effect of pole wall thickness, bend radius of multi-sided shapes, and base plate thickness on the SCF. The findings of these studies indicated that the SCF increased slightly with wall thickness. It was also found that in multisided HMIPs the SCF increased with decreasing bend angle, and that increasing base plate thickness led to exponential decreases of SCF. Other experimental and numerical studies, such as those by Stam et al. [27,36] have concluded that increasing base plate thickness is more effective in reducing the SCF than increasing shaft thickness. The studies by Stam also concluded that decreasing pole thickness leads to increasing localized strains at pole bends near the base plate-to-shaft connection. In light of these studies the use of thick base plates has been emphasized by State DOTs as a beneficial measure to increase the fatigue life of HMIPs. Research on the effects of geometric properties and galvanizing practices on galvanized-induced cracking of steel structures is limited [32,37–40]. Feldmann et al. [41,42] conducted numerical and experimental analyses on steel girders and showed that slower dipping speeds resulted in higher strain demands and SCFs at critical locations. Nguyen et al. [43,44] performed numerical simulations to study the combined effects of welding and galvanizing on strain demands in welded steel plate girders. They found that cumulative plastic strains induced during galvanization were on the order of 10 to 15% of those induced during welding, which suggests that the effect of residual strains due to welding on susceptibility to cracking is very important. One of the first numerical studies focusing on the mechanical performance of HMIPs during galvanizing was conducted by Kleineck [45], who modeled an HMIP with a standard pole-to-base plate connection detail used by the Texas Department of Transportation (TxDOT) [46]. Kleineck [32] analyzed thermally-induced stress and strain demands during galvanizing using a sequentially-coupled thermal-stress analysis. It was concluded that increasing the thickness of the shaft was the most effective means to decrease the strain demand at the pole-to-base plate connection. The goal of this study was to perform a suite of computer simulations with a more accurate representation of connection configuration, heat transfer, heat flow, and material properties during all stages of the hot-dip galvanizing process, and to use those simulations to evaluate a broader range of parameters that affect the formation of galvanization cracks. Hence, the current work was aimed at developing a more accurate understanding of the factors that affect the formation of cracks

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during galvanizing of HMIPs, studying where and when those cracks are most likely to form, and identifying design modifications and/or changes to the galvanization process that will reduce the occurrence of galvanization cracks in HMIPs. Accurate numerical models are needed for identifying factors that contribute to weldment cracking during galvanization of HMIPs. In the companion paper (Part I)[47], the authors described the characteristics and calibration of a 3D FE model to simulate thermally-induced demands during the galvanization of HMIPs. The 3D FE model is unique as it accounts for the effect of temperature on material behavior, changes in the temperature field of the HMIP during the complete galvanization and cooling cycle, and provides a more accurate representation of the components of the pole-to-base plate connection and their interactions, all aspects that were neglected or simplified in numerical studies found in literature. The steel material in the model developed by the authors had temperature-dependent mechanical and thermal properties, and included inelastic stress-strain behavior with isotropic hardening. The model was composed of the pole, base plate, full-penetration and fillet welds, an external collar, and was capable of simulating contact interactions between the surfaces of metallic components at locations not welded together. Coupled temperaturedisplacement analyses were employed in the commercial software Abaqus [48] to simulate interactions between the temperature, stress, strain and displacement fields during galvanizing. The modeling effort described in the companion paper resulted in best practice guidelines for thermomechanical modeling of HMIPs during galvanization which were adopted for this study. Regions of the model with the largest calculated strain/stress demands coincided with the location of galvanization cracks observed by fabricators and field inspections [7,11,12,16–19]. 1.1. Objective The objective of this study was to identify shape and galvanizing practice parameters that contribute the most to the formation of galvanization cracks. A parametric study was performed using the modeling approach described in the companion paper to simulate the galvanizing process of HMIPs with pole-to-base plate connection detail adopted by the Texas DOT [46]. The following shape and galvanizing practice parameters were varied with respect to a control model: base plate-topole thickness ratio, geometric shape of the pole cross-section, bend radii for multi-sided pole cross-sections, dwell time in the zinc bath, speed and angle of dipping, and cross-section orientation during dipping. The effects of these parameters on the likelihood of cracks developing during galvanizing were quantified by comparing the magnitude of the equivalent plastic strain, a cumulative measure of inelastic deformation at critical locations of the HMIP, and the von Mises stress, which provides an indication of yielding of ductile materials. 2. Finite element models Three-dimensional HMIP models with different geometric configurations were evaluated using coupled temperature-displacement analysis with the commercial software Abaqus. The reference model represents a typical HMIP with dimensions and connection details specified in the Texas Department of Transportation (TxDOT) [46] construction standards. Fig. 1 shows the reference model, which consists of the following parts: (1) a twelve sided pole with a length of 4.3 m, an outer diameter of 838 mm, a wall thickness of 8 mm, and an inner bend radius of 32 mm at its vertices; (2) a base plate with a large opening at the center, located at the lower end of the HMIP, with a thickness of 64 mm, an exterior diameter of 1200 mm, an opening diameter of 560 mm, and 12 anchor bolt holes with a diameter of 48 mm; (3) a full penetration weld that attaches the pole to the lower base plate; (4) a fillet weld between the inner surface of the pole and the base plate; (5) a 6 mm thick and 305 mm long external collar at the lower

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Fig. 1. (a) Boundary conditions used in the reference model; (b) HMIPref configuration in accordance with Texas DOT construction standards.

end of the pole, welded to the base plate and the pole; (6) a seal weld between the top face of the collar and the pole; and (7) a 25 mm thick top plate with the same cross-section dimensions as the bottom plate (Fig. 1(b)). The “reference” model, designated HMIPref, was submerged in the molten zinc bath at a dipping angle of 8°, in alignment with common practices in galvanizing plants. HMIPref was submerged and extracted at rates of 23 mm/s and 11 mm/s, respectively. Fig. 1(a) shows locations where the velocity boundary conditions were applied. These points simulate locations where the crane grips the HMIP. The ambient temperature (air temperature) was set to 18 °C, and the zinc bath temperature was 445°C. The heat convection coefficient of steel in the zinc bath, 1500 W/m2K, was determined through calibration described in the companion paper. A user-created film subroutine was used to specify ambient and hot zinc bath environmental properties at each node of the model, as described in the companion paper. The HMIPref parts were discretized using 8-node reduced integration coupled temperaturedisplacement continuum elements, designated as C3D8RT in Abaqus. A total of 37 models were evaluated in this research study. All numerical analyses were performed using Abaqus parallel computing features on a 336-node Unix cluster at the University of Texas at San Antonio. Models were grouped in different sets, according to the parameters varied with respect to the reference model, which were: (1) base plate-to-pole thickness ratio; (2) pole shape, (3) pole bend radius, (4) dwell time, (5) speed and angle of dipping, and (6) cross-section alignment. The details of each simulation group are discussed in the following sub-sections and summarized in Tables 1 to 6. 2.1. Set 1: Base plate-to-pole thickness ratio (Bp) The base plate-to-pole thickness ratio (B/P) has been identified by several researchers as one of the most critical parameters for the fatigue

life of HMIPs [7,23,27,49]. In this study, the effect of the B/P ratio on galvanization cracks was analyzed by considering two pole thicknesses, P of 8 mm and 13 mm, and six different base plate thicknesses (B), as summarized in Table 1. The combination of pole and plate thicknesses generated base plate-to-pole thickness (B/P) ratios ranging from 3 to 11. Fig. 2 illustrates the 8 mm-thick pole (designated as thin pole) with all six base plate thickness variations. No adjustments on the welded connections were made to accommodate the varying plate thicknesses. The 13 mm-thick pole is designated as thick pole throughout this paper. 2.2. Set 2: pole shape It is standard practice in the United States to manufacture the pole shaft of HMIPs with either a multisided or round cross-section [50]. Welded connection details are specified by each state Department of Transportation, which results in a few different types of connections used throughout the country. Roy et al. [12,51] suggested that in multi-sided tubular poles, the number of sides affects the fatigue life of the pole-to-base plate connections. In this study, the effect of the pole shape on galvanization cracks was evaluated by considering three different types of pole cross-sections: 12-sided (used in the reference model), 16-sided, and circular. The dimensions of these models are summarized in Table 2. Weld and external collar dimensions were adjusted based on the pole configuration. 2.3. Set 3: Pole bend radius (rb) During the fabrication of HMIPs, a brake press is typically employed to obtain the specified bend radius in the pole shafts. While this cold work process increases steel yield stress, it also decreases ductility. As a safeguard against the embrittlement effect during galvanizing, ASTM A143 [3] recommends that the cold bend radii in tabular configurations

Table 1 Base plate-to-pole thickness variations. Model

Pole Thickness (P) (mm)

Base Plate Thickness (B) (mm)

B Base to Pole Ratio ( ) ~ p

Thin Pole

1 2 3 4 5 6

8a

25 38 51 64 76a 89

3 5 6 8 9.5a 11

Thick Pole

7 8 9 10 11 12

13

25 38 51 64 76 89

2 3 4 5 6 7

a

Control model of this study (designated reference model).

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Table 2 Pole shape parameters. Model

No. of Sides

B (mm)

P (mm)

Bend Radius (mm)

1

12

76

8

32

2

16

76

8

32

3

∞ (Round)

76

8

32

should not be less than three times (t × 3) section thickness. To meet this ASTM guideline, the reference models should have a minimum bend radius of 24 mm. Table 3 shows the different bend radii evaluated in this study to quantify the effect of bend radius on stress/strain demands generated during galvanizing, which were chosen to extend well beyond the minimum specified by ASTM and typical values used in fabrication. 2.4. Set 4: dwell time effect The length of time for which the HMIP remains fully submerged in the zinc bath is determined by fabricators based on experience [45]. The strategy adopted at galvanizing plants is to maintain the HMIP within the hot zinc bath until all components reach the bath temperature (~450 °C). This approach ensures that the zinc layer properly bonds to the steel substrate at a molecular level and creates a coating layer that protects the HMIP from corrosion. The dwell time in the parametric study was varied between 240 s and 600 s (Table 4).

2.5. Set 5: speed and angle of dipping Steel components are lowered into the molten zinc kettle at an angle that allows zinc to flow into, over, and through the entire specimen [2]. Inclined dipping allows air to flow out of hollow shapes or any pockets freely. Fabricators usually attempt to submerge HMIPs with dipping angles between 4° and 8°. In practice, the dipping speed and angle vary depending on the execution of crane operators at galvanizing plants. A total of fifteen (15) models, summarized in Table 5, were created to investigate the effect of dipping speed and inclination on HMIP

Table 5 Angle of dipping and dipping speeds of parametric study. Model

No. of Sides

B (mm)

P (mm)

n (bend radius multiplier)

rb (mm) = n × ta

1 2b 3 4 5 6

12 12 12 12 12 12

76 76 76 76 76 76

8 8 8 8 8 8

3 4 6 8 10 14

24 32 48 64 80 112

a b

Speed of dipping

Speed of extraction

Angle of Dipping α°

v (mm/s) Speed variation

1 2 3 4 5 6 7

13 25 38 51 63 76 89

11 11 11 11 11 11 11

8 8 8 8 8 8 8

Angle variation

8 9 10 11 12 13 14 15

23 23 23 23 23 23 23 23

11 11 11 11 11 11 11 11

0 2 4 6 8 10 12 14

Table 3 Bend radii for models evaluated in parametric study. Model

Configuration

t: Pole thickness. Reference Model.

Table 4 Dwell times for models evaluated in the parametric study. Model

Speed of dipping

1 2 3 4

23 23 23 23

Speed of extraction

Angle of Dipping

Dipping Stage

Dwelling Stage

180 180 180 180

240 300 560 600

α°

v (mm/s) 11 11 11 11

8 8 8 8

Extraction Stage

Cooling Stage

Time (s) 360 360 360 360

1220 1160 920 860

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Table 6 Immersion orientation angles evaluated. Model

B (mm)

P (mm)

Immersion Orientation

1

76

8

0°

2

76

8

15°

galvanization cracks. Models 1–7 in Table 5 were used to investigate the effect of dipping speed, while models 8–15 evaluated the effect of dipping angle. A dipping angle of zero was considered as a limiting case although horizontal submersions are not used in practice because the zinc would not properly flow out of the pole. Also, the speed of extraction remained constant in the models. Its effect was assumed to be negligible because cooling occurs at a much lower rate than heating does during dipping.

Configuration

Set 6 consisted of two similar models immersed in the zinc bath with different orientations. The first pole was immersed with one of its sides oriented parallel to the surface of the zinc bath, while the second was immersed with one its bends at the lowest point, being the first point of the pole to come into contact with the zinc bath. Von Mises stresses and equivalent plastic strain demands were compared between two HMIP models to evaluate how these parameters were affected by immersion orientation. 3. Results and discussion

2.6. Set 6: cross-section orientation HMIPs are immersed into zinc baths with different orientations about the pole axis, depending on the choice of gripping points for the crane. Studying the effect of this parameter is important because poles may be immersed with random orientations, or practices may vary between galvanizing plants. The same problem is true for research studies, where outcomes may differ depending on the dipping orientation chosen by the researchers.

The likelihood of cracking during the galvanizing process was evaluated based on maximum stress/strain demands at critical locations of the pole, near the pole-to-base plate connection, which was identified as the region most prone to develop cracks in the companion study. Calculated stresses and strains in the immediate proximity of the pole-tobase plate connection are highly sensitive to distance from the weld and mesh configuration. Recommendations available in the literature for evaluating the fatigue life of HMIP poles based on hot spot stresses were adopted to establish uniformity between models. AASHTO [52]

Fig. 2. Models with 8 mm thick pole and different base plate-to-pole (B/P) thickness ratio (1 through 6 in Table 1).

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and Der Norske Veritas [53] recommendations suggest using the pffiffiffiffiffiffiffiffiffiffi hot spot stresses at a distance 0:1 r
t from the toe of the weld, where r is the radius of the outer faces and t is the thickness of the pole shaft. Fig. 3 shows a path 18 mm from the weld toe, from which results were extracted for purposes of comparison. The radial direction of the pole and collar were meshed with two elements through the thickness.

3.1. Base-to-pole thickness ratio (BP) Cumulative equivalent plastic strains (PEEQs) at the aforementioned path for the 12 models described in Table 1 are shown in Fig. 4. All plots contain two lines corresponding to PEEQ at the end of the simulation for the thin and thick pole configurations. All pole configuration evaluated had twelve PEEQ spikes, corresponding to each of the bend corners of the 12-sided pole. Peak magnitudes varied according to base plate and pole thickness. In HMIPs with the same base plate thickness, strain demands were higher for thin poles than for thick poles. In all the models, the largest plastic deformations occurred at bends 6 and 7. Observing the sequence of plots, from left to right in each row and from top to bottom (i.e. tBP ranging between 25 and 89 mm), PEEQs increased with base plate thickness for both thin and thick poles. Zero plastic strains were calculated throughout the simulated galvanization for models with thick poles and base plates, tBP, of 25 mm and 38 mm. A comparison of PEEQs calculated at the inside and outside surfaces of the poles (rows 1 and 2 vs. rows 3 and 4) shows that the magnitudes of the PEEQ at the inner surface were significantly higher than those at the outer surface. Also, the difference between PEEQs for the thin and thick poles was smaller for PEEQs at the inner surface of the pole than for PEEQs at the outer surface of the poles. For example, at bend B6 of the model with an 89 mm thick base plate (row two, column three), there was a 24% difference between the inner surface PEEQs of the thick and thin poles. For the same two poles there was a 72% difference between the outer surface PEEQs (row four, column three). Calculated PEEQs in bends 7 and 10 of the poles described in Table 1 and the maximum temperature differential between pole and base

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plate, ΔT, are plotted as a function of the base plate thickness in Figs. 5 (a)-(d). Because pole thickness remained constant, the B/P ratio in each graph increased with increasing plate thickness. Maximum temperature differentials are presented for the two stages of galvanization in which PEEQ increased, dipping and extraction. The upper row (Figs. 5(a)-(b)) corresponds to the results for thin poles, while the lower row (Figs. 5(c)-(d)) corresponds to thick poles. Both the temperature differential and the PEEQ increased with increasing base plate thickness and B/P ratio. The change in temperature differential as a function of base plate thickness was larger during the dipping stage than during the extraction stage. A comparison between results for HMIPs with different pole thickness and the same base plate thickness (e.g. Fig. 5(a) versus Fig. 5(c)), shows that the magnitude of both PEEQ and ΔT were lower for thick poles than for thin poles. For instance, for the HMIP with a base plate thickness of 76 mm, ΔT and PEEQ in B10 were 29% and 35% lower, respectively, during the dipping stage of the thick pole than they were during the dipping stage of the thin pole. In this comparison, configurations with the same plate thickness in Figs. 5(a) and 5(c) had lower B/P ratios in Fig. 5(c). The same is true for a comparison between Figs. 5 (b) and 5(d). Configurations with lower B/P ratios had lower temperature differentials and lower PEEQs than models with higher B/P ratios. Fig. 6 shows the effect of the B/P ratio on PEEQ. Models with the largest B/P ratios were associated with the greatest cumulative plastic strains, and HMIPs with the lowest B/P ratios had the best performance. For example, there was approximately an 85% difference in PEEQ magnitude between models with B/P ratios of 3 and 9.5. Poles with the same B/P ratio but different pole thickness had approximately the same PEEQ at the inside surface of the pole (see B/P ratios of 3, 5, and 6 in Fig. 6(a)). This was not the case for PEEQs at the outside surface of the poles, where thin poles had larger cumulative plastic strains than thick poles with the same B/P ratio. This observation is relevant because larger PEEQs have been shown to correlate with galvanization cracks that may propagate and grow due to fatigue loading when the HMIPs are placed in service [41,42]. Hence, the outer surface of a thin pole may more susceptible to fatigue cracks than the outer surface of a thick pole with the same B/P ratio. Fig. 6 also shows that in all cases PEEQs at the inside surface of the pole were higher than PEEQs at the outside surface, and that the difference between the maximum PEEQ at the two surfaces was greater in thick poles than in thin poles. 3.2. Pole geometry (round, 12, 16 sides)

Fig. 3. Pole locations for evaluating stress and strain demands according to AASHTO recommendations. Von Mises and cumulative plastic strain (PEEQ) were extracted from the circumferential path shown.

Fig. 7(a)-(c) show the impact of cross section shape on the stress demands at the pole-to-base plate connection. Peak von Mises stresses along a circumferential path near the weld toe of the pole-to-base plate connection are shown during the stages of dipping, extraction, and cooling for the three modeled configurations, i.e., 12-sided, 16sided, and round. In general, the stress curves for the round pole were smoother and had a slightly lower magnitude than the curves corresponding to the 12-sided and 16-sided poles. Regardless of the pole configuration, the largest stress demands occurred at the bottom portion of the pole, which is the surface that makes initial contact with the zinc bath. Stress demands at critical locations are capped by the yield stress, and further increases are limited by strain hardening properties of the steel. A different perspective is obtained by evaluating strain demands. The benefit of using round poles becomes much more evident by comparing the PEEQ at the end of the simulation, shown in Fig. 7(d). The PEEQ curves for multi-sided poles exhibited spikes in behavior at each of the corner bends, while the PEEQ curve for the round pole was much smoother (did not show peaks and valleys) and had a significantly lower magnitude. Fig. 7(d) shows that increasing the number of sides improved the galvanizing performance of multi-sided sections, with 16-sided poles exhibiting lower strain demands than 12-sided poles. Thus, a potential approach to reduce galvanization cracks would be to implement the

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Fig. 4. Cumulative equivalent plastic strains (PEEQs) for poles with different B/P ratios.

use of round poles, or where that is not possible due to fabrication constraints, increase the number of sides in multi-sided poles. 3.3. Effect of bend radius Fig. 8 shows the peak von Mises (σe) stress distributions at bend B10 for poles with six different bend radii. As the radius increased (from left to right, 3t to 14t), the stress magnitude decreased, both at the exterior surface of the pole and through the wall thickness. For instance, the maximum von Mises stress captured for the model with 24 mm (3t) bend radius was 327 MPa; for the 112 mm (14t) model, the stress reached a maximum value of 268 MPa. The cumulative plastic strains along the circumferential path of interest are shown in Fig. 9(a). Due to symmetry in the PEEQ values along the path, only the right half portion of the path is shown. Fig. 9 shows that poles with smaller bend radii exhibited sharper spikes in PEEQ at the corner bends of the pipe, while poles with larger bend radii had lower PEEQs (see magnified area in Fig. 9(a)). Maximum PEEQ values along the path versus bend radius are plotted in Fig. 9(b). The PEEQ decreased rapidly up to a bend radius of 80 mm

(10t), where it began to level off. The numerical analyses indicated that changing the bend radius from 3t to 14t led to a decrease of approximately 45% in PEEQ (Fig. 9(b)), although achieving bend radii as large as 14t may not be practical due to fabrication constraints. The steel model used in this study included inelastic behavior and temperaturedependent material properties, so the yield point of the steel decreased with increasing temperature from 345 MPa at room temperature to approximately 190 MPa at 445°C, as described in the companion paper. Due to the nonlinear properties of the steel model, small changes in maximum von Mises stress observed in Fig. 8 corresponded to large changes in PEEQ at the pole bends shown in Fig. 9. 3.4. Influence of dwell time Fig. 10(a) shows the von Mises stress history through the galvanizing process of a single element at bend ten (B10) of the pole, for dwell times of 240 s, 300 s, 540 s and 600 s. The stress demand leveled off during the dwell phase, reaching a plateau at a stress of 215 MPa. The plateau region of the dwell phase initiated after 480 s of total simulation time and 180 s

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Fig. 5. Maximum temperature differential between the base plate and the pole at dipping and extraction stages of: (a) Bend 10 in thin pole; (b) Bend 7 in thin pole; (c) Bend 10 in thick pole; (d) Bend 7 in thick pole.

of dwell time (Fig. 10(a)). All dwell times considered in the parametric analysis were sufficiently long to cause the stresses to reach the plateau during the dwell phase, and the stress demand in all four analyses remained nearly constant between the start of the plateau and the initiation of the extraction phase. Fig. 10(a) shows that maximum stress demands during the extraction phase were approximately equal to 310 MPa for all analyses, regardless of dwell time. Cumulative plastic strains (PEEQ) at the end of the simulation for elements along the circumferential path shown in Fig. 3 are shown in Fig. 10(b). Cumulative plastic strains extracted from each of the six models were nearly the same at the end of the simulations, which suggests that extending the dwell time is unlikely to reduce the risk of initiating cracks during galvanizing. 3.5. Angle and speed of dipping Fig. 11 presents PEEQs along a circumferential path near the weld toe for dipping speeds and angles listed in Table 4. The maximum PEEQ along the path decreased with increasing dipping angle (Fig. 11 (a)). PEEQ magnitudes decreased by 27% as the dipping angle changed

from 0° to 14°. The PEEQ on the outside surface of the pole was higher than the PEEQ on the inside surface, which is in agreement with the results obtained from parametric variations of the B/P ratio. As the dipping angle increased, the discrepancy between maximum PEEQ on the inside and outside surfaces of the pole increased. PEEQs along a circumferential path near the weld toe of the pole-tobase plate connection are shown in Fig. 11(b). Only results for dipping angles of 0°, 4° and 14° are presented in this plot for clarity. Regardless of the angle of inclination, the bottom portion of the pole shaft, particularly bends B6 and B7, exhibited the largest plastic deformations. PEEQ values at bends B6 and B7 and the side corners, i.e., B3-B4 and B9-B10, decreased considerably with increasing dipping angle. The variation of maximum PEEQ in the critical path as a function of dipping speed is shown in Fig. 11(c). The maximum PEEQ exhibited asymptotic behavior, rapidly decreasing with increasing speed, and leveling off at approximately 60 mm/s. These results indicate that increasing dipping speed is an effective approach to reduce plastic strain demands and the potential for galvanizing-induced cracks. In fact, the maximum PEEQ in the HMIP submerged at a rate of 89 mm/s was 50% lower than

Fig. 6. The effect of B/P ratio on PEEQ at: (a) inner surface of the pole; (b) outer surface of the pole.

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Fig. 7. (a) Von Mises stress distributions when zinc level is at B10; (b) von Mises stress distribution at the end of extraction stage; (c) von Mises stress distribution at the end of cooling stage; (d) cumulative plastic strains (PEEQs) along the path of interest at the end of the cooling stage.

the maximum PEEQ of the model dipped at the slowest speed (13 mm/s). Interestingly, PEEQs were always higher at the inner surface of the pole with the exception of the HMIP submerged at a speed of 13 mm/s. Fig. 11(d)shows that the location of maximum PEEQ is highly sensitive to dipping speed. At low speeds (e.g. 13 mm/s), the bends with maximum PEEQs were B3, B4, B9 and B10, located at the center of the pole. For intermediate speeds (e.g. 25 mm/s), the maximum PEEQs occurred in the lower portion of the pole, particularly at bends B6 and B7. At high speeds (89 mm/s was the highest), peak PEEQ values were found to be similar at all bends of the shaft. Hence, increasing dipping speed both eliminates the likelihood of excessive deformations at particular bends during galvanizing and reduces PEEQ demands overall. This behavior suggests that the deformation pattern at the highest immersion speeds is closer to being axisymmetric, while the deformation pattern at lower speeds tends to be highly distorted. Deformed shapes of the HMIP model immersed with seven different dipping speeds are presented in Fig. 12. Each row in Fig. 12 corresponds

to a different depth of immersion in the zinc bath during dipping. The temperature field is plotted on the undeformed shape of the reference HMIP model in column 1 of Fig. 12, with an arrow indicating the elevation of the surface of the zinc bath. The von Mises stress field is plotted on the top of the deformed shapes in columns 2–8 of the figure to show deformation patterns and identify the most highly stressed regions. At low immersion depths (d1 and d2), small deformations occurred at the lower portion of the pole. The largest deformations occurred when the zinc level reached the mid-depth of the pole cross-section (at d3). At depth d3, the magnitude of the deformations increased and the deformed shape became more distorted with decreasing dipping speed. Conversely, the magnitude of pole deformations decreased and the deformed shape became less distorted with increasing dipping speeds. At the lowest dipping speed of 13 mm/s, the sides of the pole developed a localized highly-stressed region at mid-depth of the pole cross-section, and the pole cross-section deformed with a distorted oval shape. At an immersion depth d4, submerged more than mid-depth of the pole cross-section, and a dipping speed of 13 mm/s, the deformed

Fig. 8. Effect of bend radius on maximum von Mises stress distributions experienced at Bend 10.

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Fig. 9. (a) Circumferential cumulative plastic strain along half the tubular pole (B1 to B6); (b) maximum PEEQs obtained in each model as a function of bend radius t.

shape was highly distorted with the upper portion of the pole deforming downward instead of upwards. The deformation pattern was similar, although less distorted and less pronounced, for speeds lower than 38 mm/s. At speeds greater than 38 mm/s pole deformations were significantly more axisymmetric and smaller. Although all poles tended to return to their original shape after the HMIPs were fully submerged, at a depth d5, permanent deformations remained at some of the bends. 3.6. Cross-section orientation

Fig. 10. Effect of dwell time on: a) von Mises stress at bend 7 for dwell times of 240, 300, 540 and 600 s; b) PEEQ at bend 7 for dwell times of 240, 300, 540 and 600 s.

Models with two different immersion orientations, with a difference of 15o with respect to pole axis, were analyzed to study the effect of immersion orientation on stress and strain demands (Fig. 13(a)). In the first orientation the reference model was immersed through the flat surface of the pole (Fig. 13(a)), between bends B6 and B7, while in the second orientation the pole entered the zinc bath through bend B6. The results in Fig. 13(b) show that this minor change in pole orientation during bath immersion caused significant differences in the PEEQs along the critical path around the pole cross-section. The PEEQ magnitude was reduced by 30% and 45% in bends B6 and B7, respectively, while in bends B1, B11, and B12, PEEQ magnitudes were reduced by 85%. Fig. 14 shows the distribution of the von Mises stress at eight discrete times during the dipping stage for the two models shown in Fig. 13(a). Although the deformation pattern of the two models was similar at all discrete times t1 to t8, the von Mises stress in the base plate of the reference model was considerably higher than in the base plate of the rotated model. Fig. 13(b) shows that maximum PEEQ demands occurred in bends B6 and B7, which had the largest stress and strain demands between times t2 and t3. Comparing stress demands between the two models at time t3, it is clear that the reference model experienced higher stress demands at the base plate and at the pole, near the pole-to-base plate connection. The stress patterns suggest that

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Fig. 11. (a) Maximum PEEQ along a circumferential path near the weld toe as a function of dipping angle; (b) PEEQ along a circumferential path as a function of dipping angle; (c) Maximum PEEQ along a circumferential path as a function of dipping speed; (d) PEEQ along a circumferential path as a function of dipping speed.

Fig. 12. Von Mises stress distribution throughout the dipping cycle at five depths, d1 to d5 (Note: deformations are magnified by scale factor of 50 for clarity).

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connection were significantly lower than observed at bends B6 and B7 at times t2 and t3, which is consistent with the distribution of PEEQs presented in Fig. 13(b). 4. Conclusions This study evaluated the effects of shape and galvanizing practices on temperature-induced critical stress and strain demands in HMIP poles during galvanizing. The poles evaluated in the study had poleto-base plate connection details in accordance with Texas DOT standards. Coupled thermal-mechanical analyses of a high resolution, three-dimensional, nonlinear FE model were performed to study the effect of a large set of parameters on the potential for developing galvanization cracks in HMIPs. The steel material model used in the study had nonlinear stress-strain behavior with isotropic hardening and temperature-dependent mechanical and thermal properties. The analysis of the simulations suggested that minor changes could be introduced in the geometry of HMIPs and/or galvanizing practices to reduce the likelihood in the occurrence of weld toe cracks. The following conclusions were drawn based on the simulation results:

Fig. 13. (a) Dipping orientation of reference model entering the bath through a flat surface between B6 and B7; (b) dipping orientation of rotated model entering the bath through bend B6.

temperature differentials as well as bending stiffness of the pole about an axis parallel to the bath surface may be the causes for the difference in PEEQ. Fig. 14 shows that at times t3 and t7 bends B3 and B9, located near the middle of the pole, experienced the largest lateral deformations in both models. Even though the deformation away from the base plate was largest at bends B3 and B9, stress demands at the pole-to-base plate

• Base plate-to-pole thickness ratio had a very significant effect on the potential for galvanization cracks in HMIPs. In models of 12-sided poles, strain demands decreased with decreasing base plate-to-pole thickness ratio, which indicates that limiting the base plate-to-pole thickness ratio is likely to be effective in reducing the potential for galvanizing cracks. This is in direct contrast to recommended practice to improve fatigue performance of HMIPs, based on FE analyses by several authors, which showed that increasing plate thickness greatly decreases the SCF and that pole thickness has a negligible effect on SCF. • Results showed that maximum strain and stress demands were greatest for the 12-sided pole model with a base plate thickness of 89 mm, which had the largest base plate-to-pole thickness ratio (11). A similar 12-sided configuration with the same pole thickness and the smallest base plate thicknesses (base plate-to-pole thickness ratio of 2) had the lowest strain demands among the 12-sided poles. A 12-sided pole configuration with the same base plate thickness as

Fig. 14. Influence of immersion orientation on von Mises stress and pole deformations at eight discrete times throughout the dipping stage (Note: deformations are magnified by a scale factor of 50). The exterior collar was suppressed to display stress demands in the pole.

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the reference model but a thinner pole shaft (base plate-to-pole thickness ratio of 6) had lower strain demands than the reference model, although greater than the model with base plate-to-pole thickness ratio of 3. The circular pole exhibited the lowest strain demands overall, particularly during the dipping phase, with magnitudes considerably lower than those observed in the reference model. Results indicate that using round poles instead of multi-sided poles would be equally effective to reduce the likelihood for galvanization cracks as reducing the base plate to thickness ratio. Small bend radii create sharp vertices which produce stress concentrations at the bends, while large bend radii reduce the stress/strain concentration factor. Reducing dipping time and increasing dipping angle as much as practically possible reduces the likelihood of distorted deformation patterns and reduces cumulative plastic strains, lowering the likelihood of cracks developing during galvanizing. Although the bottom portion of the pole experienced the largest plastic deformations, changing the immersion orientation with respect to pole axis so that one of the bends is at the lowest point during immersion resulted in significant reductions in PEEQs at critical locations. It is recommended that this orientation be used for the galvanization of multi-sided poles with the type of detail evaluated in this study.

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