Simulating the hot dip galvanizing process of high mast illumination poles. Part I: Finite element model development

Journal of Constructional Steel Research 162 (2019) 105705

Contents lists available at ScienceDirect

Journal of Constructional Steel Research

Thermally-induced demands due to hot dip galvanization of high mast illumination poles. Part I: Finite element model development 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 28 June 2019 Accepted 19 July 2019 Available online xxxx Keywords: Thermal stress and strain Cracking Hot-dip galvanizing Steel structures Finite element analysis Highway structures

a b s t r a c t Hot-dip galvanizing is a protective coating process widely-used to prevent corrosion damage in steel structures. Although the protective coating greatly reduces corrosion rates, there have been many documented cases in which cracks have formed in steel members during the galvanizing process, and the root causes of those cracks remain poorly understood. This paper presents a three-dimensional finite element (FE) model capable of simulating temperature-induced deformations during galvanization of high-mast illumination poles (HMIPs), which can be used to calculate the stress and strain demands at different stages of the galvanizing process. Thermomechanical analyses of the FE model were performed using the commercial finite element analysis software Abaqus. A user film-subroutine was developed to simulate the transition of a pole between two different temperature environments throughout four stages of the galvanizing process, dipping, dwelling, extraction, and cooling. Numerical simulation results showed regions of the pole with the highest potential for crack initiation at critical stages of the galvanizing process. Mechanical response variables of the simulations were highest at the bends of multi-sided poles, at the welded connection between the base plate and the pole. Inspection reports show that many cracks have been detected at this location, which corroborates the validity of the FE model. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Steel structures exposed to the environment are subjected to corrosion damage. Hot-dip galvanization, also known as dip and drain, is an economical and effective method to protect steel structures from corrosion. This process takes place at galvanizing plants, where steel specimens are submerged into a hot zinc bath (with a temperature of 445 to 455°C) by manually-operated cranes. The iron in the steel reacts with the molten zinc to form intermetallic coating layers that act as physical barriers between the steel substrate and the corrosive environment [1–6]. Although hot-dip galvanizing has been performed successfully on an industrial scale since the 1800s, there have been many documented cases in which cracks in steel members have formed during the process. One the most commonly-reported crack locations is at the base of HighMast Illumination Poles (HMIPs), at the toe of the welded connection between the pole and the base plate [7–20], on the pole. To date, however, there is no consensus about how to prevent these cracks from forming. Goyal et al. [21] and Dawood et al. [22] identified complex interactions between cold working, welding, and galvanizing as a potential source of the problem. According to Kinstler [23], the formation of ⁎ Corresponding author. E-mail address: [email protected] (A. Montoya).

https://doi.org/10.1016/j.jcsr.2019.105705 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

cracks may be associated with recent changes in steelmaking and galvanizing practices, in particular with respect to zinc bath composition. Kinstler [23] also suggested that the cracking phenomenon may have existed all along since the process was created, and that increases in the number of observations may potentially be due to improvement of inspection techniques and dissemination of inspection data. Initial studies investigating the catastrophic failure of galvanized HMIPs [24–29] did not account for the existence of cracks that formed during galvanizing. These studies focused on estimating fatigue life of undamaged poles due to wind load excitations. Because fatigue failures originate from localized cracks, the use of local approaches that include the effects of geometry, loading and material characteristics in the vicinity of the crack has become more common to evaluate the structural durability of welded joints and the likelihood of joint failure [30]. The most widely adopted techniques include hot spot structural stress methods for estimating fatigue strength [31], notch stress/strain analyses for determining crack initiation [32–34], and fracture mechanics-based methods for predicting crack propagation [35–37]. Goyal et al. [21] and Dawood et al. [22] were among the first to account for the impact of preexisting cracks on the fatigue life of poles used in Texas highways. These studies showed that HMIPs with collars exhibited considerably longer service lives than those without them [9,10,38–43]. Consistent with the recommendations from these studies, the Texas DOT Statewide Standard drawings for HMIPs [40] only include configurations with

2

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

multisided tabular steel poles and an external collar surrounding the pole, near the pole-to-base plate connection. In general, HMIP pole geometry and pole-to-base plate standard connection details vary by state, and the fatigue performance of different connection details is a topic that has not been studied in detail. Due to economic loss and potential safety hazard to the public, there is a pressing need to identify the factors contributing to the occurrence of weldment cracking during galvanization. A better understanding of this problem will help improve design and manufacturing practices to mitigate cracking and increase the fatigue life of HMIPs. A crucial step towards addressing this problem is to study the response of HMIPs to thermal shock during galvanizing. In past experiments, thermocouples and strain gauges have been attached at discrete locations on HMIPs to measure variations in temperature and strain during galvanizing [38]. Although these types of measurements are helpful for model calibration, they do not provide reliable means to capture highly localized strain demands at critical locations at the pole-to-base plate connection because measurements are few and discretized. Measurements like those obtained by Kleineck [38] must be complemented with finite element (FE) models to evaluate the temperature, strain, and stress fields throughout the entire HMIP. With that goal, Kleineck [38] developed a 3D thermomechanical FE model to simulate the galvanization of HMIPs. One of the most important unknowns in the simulation of the galvanizing process is the heat convection coefficient of the zinc bath. Kleineck [30] calibrated his FE model by comparing calculated temperatures and strains with experimental measurements from an HMIP pole during galvanizing. Although the study performed by Kleineck [30] provided an important foundation for future work, much

research remains necessary to develop a fuller understanding of the cracking phenomenon at the pole-to-base plate connection of HMIPs. The effect of many important geometric parameters on cracking propensity has not been studied, including the number of pole sides, pole thickness, base plate thickness, and poles with circular shape. There is also a need to study important characteristics of the pole-to-base plate connection on the susceptibility of the connection to develop cracks during galvanizing, including the effect of pole corner radii, the type of welded connection between the base plate and the pole, and the presence of the external collar used in Texas practice. Studies should include steel material models that account for the variation of mechanical and thermal properties with temperature. One of the key aspects of developing accurate models of the pole-to-base plate connection is the sensitivity of calculated stresses and strains to mesh density. Recognizing the importance of mesh sensitivity, AASHTO [29] provides mesh configuration recommendations with the goal of obtaining comparable results while evaluating the fatigue life of different HMIPs. The AASHTO [29] recommendations were developed for linear-elastic mechanical FE analyses of three-dimensional (3D) models of the pole-to-base plate welded connection, neglecting residual deformations induced during welding or galvanizing. In this study, a high-resolutionFE model was created to identify geometric configuration and connection detail parameters most likely to cause cracks during galvanizing. The FE model was significantly more refined and sophisticated than those employed in previous research studies, representing with greater accuracy the geometric configuration of the HMIP pole-to-base plate connection, the material behavior of steel, and the galvanizing process under

Fig. 1. Framework for the development of the finite element model.

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

plant conditions. The three-dimensional thermomechanical FE model is capable of simulating thermally-induced deformations in HMIPs during all stages of galvanization, including heat convection properties and temperatures in two different environments (ambient and hot zinc bath). The model also accounts for temperaturedependent material properties, inelastic mechanical properties, and contact interactions between metallic components. In addition, the weld toe geometry was finely meshed to accurately simulate behavior in the crack-susceptible region. 1.1. Goal and objectives The goal of this study was to develop a reliable high-resolutionFE model capable of simulating the thermo-mechanical response of HMIPs detailed according to Texas DOT practices throughout the entire galvanizing process. This capability is essential to determine if mechanical response variables (strains, stresses, and strain/stressdependent scalars) are large enough to induce cracking, particularly at the base plate-to-pole connection. There were four specific research objectives: 1. Develop an efficient numerical approach to simulate the galvanization of HMIPs, including a technique to model the transition of the HMIP from ambient conditions to a molten zinc bath and vice-versa. 2. Develop recommendations and best practices to simulate galvanizing HMIPs, outlining the analysis procedure, element types, meshing techniques and interaction options that should be used to improve the accuracy and efficiency of the simulation. 3. Corroborate the validity of the model by comparing the results with experimental data. 4. Identify critical stages of the galvanizing process, locations in the pole with the highest potential for crack initiation, and mechanical response variables that can be used as indicators of cracking during galvanization.

3

2. Model description The FE model was developed using the commercial finite element software Abaqus [44], although it can be replicated with any other FE software having similar capabilities. Fig. 1 illustrates the algorithm used in the pre-processing phase of the FE analysis. This phase consisted of defining the HMIP geometry, material models, type of analysis, loading type, mechanical and thermal interactions, connection type, mesh, and solver approach. Several options were considered with the goal of improving the accuracy and efficiency of the model. The model options that were identified to best replicate the actual galvanizing conditions and behavior of the HMIPs are marked in Fig. 1. The following subsections provide a detailed description of the specific criteria associated with each choice.

2.1. Model geometry HMIP structures typically consist of a long pole with plates welded at both ends. Standards adopted by each state in the US for the geometric configuration and pole-to-base plate connection of HMIPs vary [9,39,41,45–47], with the main parameters being the shape of the cross-section of the pole and the characteristics of the welded connections. Pole shafts have either round or multi-sided (typically 8, 10, 12, or 16 sides) cross-sections. Specifications for the type of welded connections are provided by each state Department of Transportation. For example, for the state of Texas, standard details are provided at the TxDOT [40] internet site. For the past few decades, pole-to-base plate connections of HMIP poles in Texas have included an additional collar based on research that shows its addition improves the fatigue life of the connection. Consistent with studies by Stam [9,10] and Kleineck [30], FE models developed in this study replicate standard details representative of that current practice. A 12-sided pole shaft with an external collar in conformance with the TxDOT [40] standard used in this study

Fig. 2. (a) HMIP geometry used in the state of Texas and (b) pole-to-base plate connection.

4

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705 Table 1 HMIP Part Dimensions. Component

Dimension (mm)

Base plate diameter Base plate thickness Access hole diameter Pole shaft diameter Collar height Collar diameter Collar thickness Top plate thickness

1200 76 560 830 305 813 6 25

2.2. Material properties

Table 2 Material Properties at room temperature (21 °C). Young Modulus (GPa) 200

Poisson Ratio

Density (g =mm3 )

Thermal expansion Coefficient(1

3.35

7.77 × 10−3

1.2 × 10

−5


°C

)

thick and 305 mm long, with twelve sides similar to the pole. Fig. 2 (b) shows that the external collar was connected to the pole and the base plate through fillet welds, while the base plate and pole were attached through a full penetration weld. The dimensions of the HMIP are presented in Table 1.

Specific Heat(
J ) g °C

Thermal Conductivity (
J ) mm °C

3.85 × 10−1

5.49 × 10−3

All parts were modeled with elastic-plastic material properties representative of Grade 50 steel (equivalent to ASTM 572-50). The mechanical and thermal properties at room temperature for Grade 50 steel are provided in Table 2. Temperature dependent variations of mechanical properties reported by Pilipenko [48] and Perić et al. [49] (see Appendix) were adopted. The nonlinear portion of the stress-strain response was simulated using isotropic hardening with von Mises yield criterion. Thermal and mechanical properties of the base plate steel and weld metal were assumed to be equivalent; several researchers [28,50–53] have adopted a similar strategy for modeling welded connections. 2.3. Analysis procedure

and the corresponding pole-to-base plate connection detail are shown in Fig. 2. The FE model is an assembly of the following parts: (a) a base plate with 12 anchor bolt holes, (b) a pole shaft, (c) an external collar, (d) welds, and (e) an upper plate. The base plate had a thickness of 76 mm, an outer diameter of 1200 mm, and an inner diameter of 560 mm. The plate at the opposite end of the pole had the same crosssection, but a thickness of 25 mm. Because the study centered on the connection to the base plate, the presence of bolt holes on the top plate was ignored. Fig. 2(a) shows a 4.3 m long twelve-sided pole with an 830 mm outer diameter and 8 mm thickness. A bend radius of 32 mm was specified at each corner. The external collar was 6 mm

Hot-dip galvanizing simulations were performed using coupled temperature-displacement analysis, a nonlinear procedure in which the displacement and the temperature fields are solved simultaneously. This analysis is typically used when the mechanical solution is affected by the thermal solution [54,55]. During galvanizing, the high temperatures of the zinc bath induce significant deformations in the HMIP pole. As the surface area of the fluid/solid interface expands, the convective heat transfer between the HMIP and the zinc increases [56]. In addition, the pole and external collar interact with each other as they deform. Thus, the coupled temperature-displacement was considered preferable for this problem. In addition, the geometric nonlinearity option was selected to account for large deformations that may arise during galvanizing. 2.4. Boundary conditions, interactions and connections

Fig. 3. Displacement and velocity boundary conditions.

2.4.1. Boundary conditions During galvanizing, dipping angle and speed are controlled by the crane operator. An angle of 8° was adopted in this study as representative of industry practice based on consultations with experts in commercial galvanizing of poles. The dipping process was simulated by vertical translation of the HMIP through two regions with temperatures representative of the zinc bath and room temperature. Translation of the HMIP was simulated by specifying velocity boundary conditions at grip points shown in Fig. 3. The simulation replicated dipping, dwelling, extraction and cooling stages by adjusting the amplitude of the velocity as a function of time (see Fig. 4). The HMIP vertical velocity was 13 mm/s during the dipping and extraction stages, and zero while

Fig. 4. Stages of the galvanizing process: dipping, dwelling, extraction and cooling. Note that the exterior collar is suppressed.

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

5

Fig. 5. Pseudocode for film subroutine.

Table 3 Environmental parameters. Ambient condition

Temperature °C

Heat convection coefficient W/(m2 K)

Molten zinc bath Air (ambient)

445 18

1500 1000

dwelling. To avoid any undesirable rotations of the HMIP, degrees of freedom in the out-of-plane direction were restrained at nodes located at the bottom edge of the two plates, as shown in Fig. 3.

2.4.2. Thermal interactions The process of submerging the HMIP in the molten zinc bath was simulated by specifying the surrounding temperature field as a function of the elevation of each node. The algorithm to define the temperature field was coded in a user-defined film-subroutine (Fig. 5) which was compiled and linked to Abaqus [36]. The film subroutine

assigned a temperature and heat convection coefficient to nodes located at the fluid/solid interface according to their coordinates. Sections of the HMIP above the molten zinc level (y = 0) were exposed to air at ambient temperature conditions. Nodes in these sections were assigned the heat convection coefficient of air, hair, and an ambient temperature of 18°C. Sections below the zinc level were exposed to the zinc bath. The thermal parameters of the ambient and zinc environments are listed in Table 3. The heat convection coefficient of molten zinc provided by Kleineck [38] was adopted as a reference value. Several calibration runs were performed to ensure that this parameter was appropriate for the external collar connection detail and mesh used in this model. The results of the calibration analysis are provided in the results section. 2.4.2.1. Connections. The HMIP base plate and pole shaft were attached using surface-to-surface tie constraints, replicating the full penetration weld shown in Fig. 2. Filet welds were modeled as individual parts, with surfaces attached to the external collar, plate, and pole

Fig. 6. Designation of bends and sides. Note that the collar part is suppressed in this figure for illustration purposes.

6

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

Fig. 7. Temperature field profile throughout the different stages of the galvanizing process. Note that the external collar is suppressed from view in this figure to display the temperature field in the pole.

using tie-constraints. The general contact algorithm in Abaqus [36] was used to simulate contact interactions between adjacent surfaces of parts not welded together that could come in contact due to

thermal expansion. This surface-to-surface penalty method prevented nodes located in each of the different parts of the HMIP from occupying the same space.

Fig. 8. Measured and calculated: (a) temperature; and (b) strain at a pole location 152 mm and 24 mm from the base plate, respectively. Note that the collar is suppressed from view in the figure.

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

2.5. Mesh As described, the 3D finite element model implemented in Abaqus consisted of five different parts: (1) pole shaft, (2) base plate, (3) external collar, (4) fillet welds, and (5) upper plate. All parts were discretized using 8-node reduced integration coupled temperature-displacement continuum elements, designated C3D8RT in Abaqus, to reduce the computational demand of the simulation. The HMIP model had a total of 594,400 nodes and 431,635 elements. Hourglass control was specified because large rotations were expected at critical stages of the galvanizing process. AASHTO [45] recommendations regarding maximum element size near the welded connection were followed in this study. Mesh size was controlled by the shaft thickness, t, which was 8 mm. AASHTO [37] recommendations indicate a maximum mesh size of t × t for at least three rows from the top of the weld, and at least two elements in the thickness direction. In addition, the mesh size at the interface region should not exceed a 1:4 aspect ratio. The size of the elements at the interface region was 5 × 5 mm. This element size was maintained constant along the length of the pole, up to 102 mm from the interface. The pole thickness was discretized into two elements according to AASHTO recommendations. The aspect ratio of elements at the interface region was approximately 1:1. Portions of the base plate, collar, and weld near the interface zones were also discretized with an element size of 5 mm. Because the area of greatest

7

interest was the region near the pole-to-base plate connection, the size of the elements away from the base plate gradually increased from 5 mm to 76 mm at the middle of the pole. The same mesh pattern was used for the top section of the pole. 2.6. Computational platform Analyses were performed using a 336-node Unix cluster at the University of Texas at San Antonio, named Shamu. Completion times varied by model, but in general ranged between 8 and 14 days. 3. Results and discussion This section describes the response of the HMIPs throughout the galvanizing process and the accuracy of the FE model. Critical stages of the galvanizing process and locations with the highest potential for crack initiation are identified, and parameters that can be used as indicators of crack initiation or severe damage are discussed. Because the temperature, displacement, strain, and stress fields varied with time, results are presented using fringe plots that illustrate the state of a particular field at discrete times, and history output plots that show the variation of a response parameter at a single nodal point or path throughout the entire simulation. To facilitate the description of the results, the bends and sides of the base plate were designated as

Fig. 9. Stress demands throughout the four stages of the galvanizing process. Note that the collar part is suppressed in this figure to display stress demands at the pole.

8

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

Fig. 10. Temperature distibution and deformed shape of HMIP during the dipping stage (amplified by factor of 50). Note that the collar part is suppressed in this figure to display pole temperatures.

shown in Fig. 6 (following a clockwise notation), where S-6 and S-12 are the first and last sides to be submerged into the bath, respectively. 3.1. Simulation of the galvanizing process 3.1.1. Temperature field history Fig. 7 shows the temperature field throughout the 4 stages of the galvanizing process: heating (steps 1–3), dwelling (steps 4–6), extraction (steps 7–9), and cooling (steps 10–12). At step 1, the entire HMIP is in air and subjected to a constant initial temperature of 18 °C. In steps 2 and 3, the portion of the HMIP below the molten zinc level experienced a rapid rise in temperature. Due to thermal conductivity, the temperature in the region immediately above the bath level increased rapidly as well, while the temperature of the upper portion of the specimen remained approximately equal to ambient temperature. In steps 4 and 5, sections of the HMIP that had been in the bath the longest had the highest temperatures. An important feature of the thermal response is that when the pole is first introduced into the zinc bath it approaches the temperature of the bath at a much higher rate than the base plate, giving rise to a significant temperature differential between the two. The difference in the temperature rates of change is attributed to the

fact that the pole is thin relative to the base plate. If the dwell time is sufficiently long, thermal conductivity and heat convection cause all parts to reach the bath temperature (step 6). At the extraction stage, cooling of the HMIP caused the temperature field to change in reverse order with respect to the heating stage (steps 7–9). The upper portion of the pole cooled faster than the upper plate, which exited the bath earlier (steps 8 and 9), because the pole was thinner than the plate. Similarly, the lower plate took the longest to cool down to ambient temperature owing to the higher thermal mass of that particular component. After extraction was completed, all parts of the HMIP reached ambient temperature (step 12), corresponding to steady state of the system, provided that a sufficiently long cooling time was specified in the simulation.

3.1.2. Calibration and validation of the model Experimental results reported by Kleineck [38] were used to calibrate and validate the temperature magnitudes calculated with the FE model. It was known a priori that the temperature output of the model would be sensitive to the heat convection coefficient of the zinc bath, hc, so this parameter was calibrated to match the experimental temperature and strain readings. After several analyses with different values of hc, it was

Fig. 11. Paths used for extraction of critical strains and stresses: (a) origin and direction of the paths and (b) distance between the paths and the top surface of the base plate.

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

9

Fig. 12. Maximum principal stress history for paths at: a) 5 mm; b) 10 mm; c) 20 mm; d) 51 mm away from the base plate.

concluded that hc = 1500 W/(m2 K) provided the best agreement between the model and the experimental data. Fig. 8 shows a comparison between measured and calculated pole temperature and strain near the pole-to-base plate connection. The points of comparison are located at 153 mm from the base plate for the thermocouple readings and 24 mm from the base plate for the strain gage readings. Results show that the model captured the abrupt temperature changes during dipping and dwelling of the thin pole very accurately (Fig. 8(a)). Despite failure of the strain gage early in the experiment (after 60 s), Fig. 8(b) shows that trend captured through the analysis was in good correlation with the measured strain presented by Kleineck [30]. 3.1.3. Stress history Maximum principal stress fields at the pole-to-base plate connection throughout the four stages of the galvanizing process are shown in Fig. 9. These mechanical responses are strongly dependent on the temperature differential between the parts of the HMIP at the different stages of the galvanizing process. Fig. 9 shows the bottom portion of the HMIP, at the connection between the base and the pole, where areas with the highest strain and stress demands were observed. During the dipping (immersion) stage, a band of high stress demands was observed at the immediate vicinity of the zinc-bath surface. During this stage the pole deformed in bending about a tangential axis perpendicular to the surface of the bath, as shown in Fig. 10. This deformation was caused by the temperature differential between the immersed and nonimmersed portions of the pole. While the zinc bath caused the immersed portion of the pole to expand, the non-immersed portion was exposed to the air environment and remained at a significantly lower temperature. This deformation pattern was also observed in galvanizing plants by Kuklik [57]. Strain demands at the weld toe of the pole-to-base plate connection associated with this behavior were very high. At the end of the dwelling stage, when the temperature differential between the parts of the HMIP was lowest, the band of high stress demands dissipated, although areas of localized high stress demand remained at bends of the pole (Fig. 9). Temperature differentials between immersed and non-immersed regions of the HMIP again gave rise to significant stresses during the extraction stage. Stresses at the bends of the pole during extraction were slightly higher than those at the end of the dipping and dwelling stages. Temperature differentials between HMIP components were lower during the extraction stage than during the dipping stage. As the HMIP cooled down to ambient

temperature during the cooling stage, stresses progressively decayed throughout most of the pole, leaving residual stresses only at the bends of the pole. 3.2. Critical stages of the galvanizing process Locations and times with the greatest stress and strain demands were identified based on an examination of strain and stress along circumferential paths in the pole, near the pole-to-base plate connection. Mechanical response parameters were extracted at four circumferential paths of interest, specifically at 5, 10, 20 and 51 mm away from the top surface of the base plate, as shown in Fig. 11. All paths were defined so they would originate at the midpoint of side S-12, between bend points B-1 and B-12, and advance in a clockwise direction. Fig. 12 shows the change in the maximum principal strain and stress during the galvanizing process, at the four paths of interest. These plots show that the maximum demands occurred during the dipping stage. Stress shocks were observed when the paths were partially submerged in the molten zinc bath and the temperature differential (ΔT = Tmax Tmin) within the path was maximum, as shown in Fig. 13. The 12 spikes of the plot correspond to the 12 bend locations, B1-B12. Nominal magnitudes of yield strain and yield stress for A572–50 structural steel at room temperature, 1700 με and 350 MPa, respectively, are shown for reference. Due to the temperature-dependence of these two properties, values corresponding to yield are different at higher temperatures. The yield strain and yield stress of steel at the galvanizing bath temperature

Fig. 13. Temperature differential and stress demand histories during galvanizing at path 5 mm above the base plate.

10

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

of 455°C specified in the steel model were approximately 1900 με and 190 MPa, respectively. The reference yield stress at room temperature was exceeded in the dipping stage for the paths at 5 mm and 10 mm away from the base plate. The strain and stress fields had lower magnitudes for paths further away from the base plate. During dwelling, all sections of the HMIP converged uniformly to the bath temperature and the mechanical response of the HMIP approached uniform

expansion (Fig. 7). During extraction, the magnitude of the principal stresses and strains increased due to the temperature differential between immersed and non-immersed regions of the HMIP. Like behavior observed in the dipping stage, stress demands were higher for paths closer to the interface between the pole and the base plate. The stress reached its peak during the dipping stage, and started to dissipate as the HMIP cooled to ambient temperature.

Fig. 14. (a) Peak maximum principal tensile stresses and (b) Peak maximum principal compressive stresses along circumferential paths.

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

11

sequence. The charts show the largest-computed principal stress during the entire galvanizing process, for each point around a circumferential path around the pole. Fig. 14 shows that the largest maximum principal stresses consistently occurred at the bends of the pole. For the path closest to the base plate, designated as 5 mm, localized spikes in principal tensile and compressive stresses were calculated at every bend location. The peak maximum principal tensile stress exceeded the room temperature yield stress (350 MPa) at 6 different locations, B-1, B-3, B-4, B-9, B10, and B-12. For all other paths, peak values of maximum principal tensile stress were largest at sides S-3 and S-9 (Fig. 7). For the path located 10 mm from the base, the room temperature yield stress was exceeded at these four bend locations. The maximum principal compressive stresses exhibited a similar pattern for the 5 mm path. For the remaining paths, peak values of maximum principal compressive stress were found at different locations along the paths, although the largest principal compressive stresses within a path always occurred in the lower portion of the pole. All HMIP pole models in this study were created with a bend radius of 4 t (Fig. 6) to achieve a realistic representation of the corner angle and obtain an accurate estimate of the stress and strain fields at the bends of the pole. Feedback from pole producers indicated that most HMIPs are fabricated with radii between 3 t and 5 t, so the 4 t value was chosen to be representative of this range. The FE analyses showed that the bends were the most critically stressed regions, and likely to have the highest potential for crack initiation during the galvanizing process. These locations coincide with cracks observations at galvanizing plants by Kleineck [38]. Fig. 15. (a) Temperature field at 4 discrete times during the dipping stage; (b) von Mises stress contour plots associated with the temperature changes; (c) stress field and deformations at the pole-to-base plate connection. Note that the external collar part is suppressed in this figure to display pole stresses.

3.3. Potential crack initiation sites Radar charts shown in Fig. 14 were created to visualize and identify locations within the four circumferential paths of interest where principal tensile and compressive stresses were largest during the galvanizing

3.4. Crack initiation/damage indicators Although peak principal compressive and tensile stresses were helpful for identifying regions where cracks are most likely to occur, these cannot be used as indicators of yielding or inelastic deformation in a solid under time-dependent multiaxial loading. Both yielding and plastic deformation are known to be conducive to crack initiation, so the Von Mises stress and the equivalent plastic strain were explored as potential mechanical response variables indicative of crack initiation potential.

Fig. 16. Equivalent plastic strain (PEEQ) history for selected paths.

12

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

3.4.1. Von Mises stresses The von Mises or equivalent stress, σe, is a single scalar value of stress computed on the basis of the Cauchy stress tensor components. The von Mises Criterion states that ductile materials yield when σe N σy, where σy is the yield stress measured with a uniaxial tensile test [58–64]. Thus, this parameter reveals the locations experiencing plastic deformation at any particular time during galvanizing. Fig. 15 shows von Mises contour plots at four discrete times of the simulation. It can be observed that the regions undergoing plastic deformation varied throughout the galvanizing process. Thus, the von Mises stress was a good indicator of the regions that yielded, but was not able to highlight the effects of accumulated damage throughout the galvanizing process. The highest von Mises stresses were calculated at bends B-3 and B-10, which was in good agreement with locations in which cracks have been observed during inspections immediately following galvanization of HMIP poles. 3.4.2. Equivalent plastic strain Another parameter evaluated as an indicator of potential for crack initiation is the equivalent plastic strain (PEEQ), also referred to as accumulated plastic strain, which is expressed by Eq. (1): Z t  pl  εpl ¼ εpl  þ ε_ dt 0

0

ð1Þ

where εpl j0 is the initial equivalent plastic strain. The rate evolution rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pl pl 2 pl pl _ _ ε_ : ε_ . component of this equation, ε , is determined as ε ¼ 3 Both tensile and compressive plastic strains contribute to the total

accumulated plastic strain throughout the galvanizing process [44]. According to Eq. (2), this parameter is cumulative over time and can be used to show the sections of the HMIP that undergo the largest inelastic deformation and associated cumulative damage, which may lead to crack initiation. The strain energy density formulation in an elastic-plastic material, W, is dependent on the von Mises stress and PEEQ as follows: W¼

ð1 þ υÞ 2 1−2υ 2 σ kk þ σ VM þ σ VM εpl 6E 3E

ð2Þ

where σ2kk indicates the summation of the diagonal elements of the squared stress matrix, σ2kk = σ211 + σ222 + σ233, σVM is the von Mises effective stress, and εpl is the PEEQ. This strain energy density is used in the J-integral to calculate the energy release rate in a cracked body. Thus, von Mises and PEEQ are good damage indicators and can be used to identify possible crack locations. Fig. 16 shows equivalent plastic strain in the previously described paths of interest over time. When the HMIP was dipped into the molten zinc bath, the equivalent plastic strain accumulated near the bends. The PEEQ values were inversely proportional to the distance between the path and the base plate, with the greatest PEEQ values calculated for the path closest to the base plate (5 mm). PEEQ values for paths at 20 mm and 51 mm were negligible compared with the calculated values for the 5 mm and 10 mm paths. For the 5 mm and 10 mm paths, PEEQ values were greatest at bends B-3 and B10. The largest increments in PEEQ were observed during the dipping stage, and occurred in a very sudden manner at the time when each particular location was submerged into the bath. The PEEQ remained nearly constant through the dwelling stage, and increased again during the cooling stage. Although the magnitude of the increment during the cooling stage was small compared with the dipping stage, the additional cumulative damage may be sufficient to cause crack initiation. Based on these observations, PEEQ provided an accurate indication of cumulative damage during galvanizing. Calculated values of PEEQ indicated that bends B-3 and B-10 had the highest potential for crack initiation. 3.4.3. Mesh sensitivity Six mesh densities were considered to analyze the effect of mesh size on the mechanical parameters of interest. The pole mesh was refined at the region where the highest stress demands were observed, from the bottom of the pole up to 305 mm above the base plate. Fig. 17 shows the sensitivity of temperature and stress at a location 5 mm from the base plate with respect to the number of elements at the refined section of the pole. Results show that the temperature field output was independent of mesh density, while the stress output was sensitive to the mesh density. The stress converged to a steady stress output after employing more than 50,000 elements in the refined mesh region. Hence, coarse meshes were avoided to prevent inaccurate results. 4. Conclusions

Fig. 17. Mesh sensitivity analysis at a location 5 mm from the base plate for: (a) Temperature; (b) Stress.

In this study, an FE model of an HMIP with an external collar at the pole-to-base plate connection was developed to simulate its mechanical and thermal response throughout the galvanizing process. The model simulated the transition of HMIP poles from ambient temperature conditions to a molten zinc bath and vice-versa through a user film routine in Abaqus. To replicate the actual behavior of the HMIP, the model

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

accounts for the effects of temperature-dependent material properties, inelastic material behavior, large deformations, and contact between metallic components. Mesh density in the region of the weld toe met AASHTO recommendations for fatigue analyses. The outcome of this study is the development of a high resolution, three-dimensional, nonlinear FE model for accurately quantifying thermally-induced stress/strain demands during the galvanization of HMIPs. The FE model was validated: (a) quantitatively by comparing the simulation results with experimental measurements from an HMIP pole instrumented with thermocouples and strain gages during galvanizing and (b) qualitatively by comparing observations from galvanizing plants with results from thermomechanical simulations of the galvanizing process. The qualitative comparison parameters were the deformed shape during the dipping stage of the galvanizing process and observed crack locations with respect to locations of highest calculated demands for the von Mises stress field, maximum principal stress field, and PEEQ. Numerical simulation results revealed the critical stages of the hot-dip galvanizing process and locations within the structure most vulnerable to damage during galvanizing. Numerical simulation indicated that maximum strain and stress demands occurred during the dipping stage. The peak stress demands were calculated when the HMIP was partially submerged. All mechanical response variables of the simulation were highest at pole bend locations, where cracks have been detected through inspections after galvanizing. The greatest demands were calculated at bends B-3 and B-10. Von Mises stress and equivalent plastic strain were evaluated as potential parameters indicative of cracking. Von Mises stress fields showed that critical locations in the HMIP yielded, while the equivalent plastic strain provided an indication of damage accumulation throughout the stages of galvanizing. PEEQ results indicate that a critical damage level can be achieved as a result of thermal shock during the dipping stage, or later during cooling, the last stage of the galvanizing process. The accuracy of these results provides confidence in the use of the FE model to evaluate the behavior of HMIP poles with different loading and geometric conditions. FE practices outlined in this paper regarding analysis procedures, mesh quality, material properties, and interaction options can be used to model temperatureinduced demands due to galvanizing for a wide range of metallic structures, including HMIPs with different pole-to-base plate connection details, beam girders and traffic light structures. Although it is expected that stress and strain demands will be different for other connection details, the methodology presented in the paper provides a common framework to study the relative propensity of different connection types and HMIP configurations to develop cracks during galvanizing. For example, a parametric study featuring HMIP-tobase plate connection details used in the state of Texas is presented in a companion paper investigating the effect of shape and galvanization practice parameters on the potential for cracks due to thermal shock. Simulation results obtained using the FE guidelines presented in this paper such as the parametric study in the companion paper, as well as future studies performed with the same methodology, will provide an objective basis for improving connection design and galvanization practices for HMIPs to limit the occurrence of galvanization cracks.

13

Appendix

Fig. 18. Variation of grade 50 steel (equivalent to ASTM 572–50) properties with temperature: (a) thermal properties; and (b) mechanical properties.

Acknowledgement This work received computational support from UTSA's HPC cluster Shamu, operated by the Office of Information Technology. The authors also acknowledge the valuable input pertaining galvanizing industry practice provided by Thomas Kinstler. The writers are also grateful to Mr. Carl Macchietto and Valmont industries for their input regarding the detailing and fabrication of high-mast illumination poles. References [1] AGA, Hot-Dip Galvanized Steel Bridges: A Practical Design Guide, American Galvanizers Association, Centennial, CO, 2017. [2] ASTM-A143, Standard Practice for Safeguarding Against Embrittlement of Hot-Dip Galvanized Structural Steel Products and Procedure for Detecting Embrittlement, ASTM International, 2014. [3] ASTM-A123, Standard Specification for Zinc (Hot-Dip Galvanized) Coatings on Iron and Steel Products. Pressed and Forged Steel Shapes, Plates, Bars, and Strip, 2017. [4] ASTM-A385, Standard Practice for Providing High-Quality Zinc Coatings (Hot-Dip), 2017.

14

R. Nasouri et al. / Journal of Constructional Steel Research 162 (2019) 105705

[5] M. Pourmajidian, J.R. McDermid, On the reactive wetting of a medium-Mn advanced high-strength steel during continuous galvanizing, Surf. Coat. Technol. 357 (2019) 418–426. [6] M. Sun, Z. Ma, Effects of heat-treatment and hot-dip galvanizing on mechanical properties of RHS, J. Constr. Steel Res. 153 (2019) 603–617. [7] Poles Standard Plans, Texas Department of Transportation (TXDOT), 1995. [8] T.H. Anderson, Fatigue Life Investigation of Traffic Signal Mast-Arm Connection Details, PhD diss University of Texas at Austin, 2007. [9] A.P. Stam, Fatigue Performance of Base Plate Connections Used in High Mast Lighting Towers, PhD diss University of Texas at Austin, 2009. [10] A. Stam, N. Richman, C. Pool, C. Rios, T. Anderson, K. Frank, Fatigue Life of Steel Base Plate to Pole Connections for Traffic Structures, No. FHWA/TX-11/9-1526-1 2011. [11] T. Nilsson, G. Engberg, H. Tragen, Scand J. Metallurgy, Fatigue properties of hot dip galvanized steels, Scand. J. Metall. 18 (4) (1989) 166–175. [12] R. Aichinger, W. Higgins, Toe cracks in base plate welds—30 years later, Electrical Transmission Line and Substation Structures: Structural Reliability in a Changing World 2007, pp. 274–285. [13] N. Suksawang, B. Mintz, A. Mirmiran, Remedial Action for Failed Pole/Base Plate Weld on High Mast Lighting Pole (HMLP), 2009. [14] K. Nguyen, R. Nasouri, C. Bennett, A. Matamoros, J. Li, A. Montoya, Sensitivity of Predicted Temperature in a Fillet Weld T-Joint to Parameters Used in Welding Simulation With Prescribed Temperature Approach. Science in the Age of Experience, Chicago, IL, USA, 2017 1–16. [15] K. Nguyen, R. Nasouri, C. Bennett, A. Matamoros, J. Li, A. Montoya, Distortion of steel plate girders due to hot dip galvanizing, National Steel Bridge Alliance (NSBA) World Steel Bridge Symposium (WSBS) Baltimore, MD, 2018. [16] K. Nguyen, R. Nasouri, C. Bennett, A. Matamoros, J. Li, A. Montoya, Thermomechanical modeling of welding and galvanizing a steel beam connection detail to examine susceptibility to cracking, Mater. Perform. Character. 7 (2) (2018) 165–190. [17] R.J. Connor, G. Callahan, M. Koob, I.C. Hodgson, B.L. Brakke, Field and Laboratory Studies on High-Mast Lighting Towers in Iowa. Mid-Continent Transportation Research SymposiumIowa Department of TransportationIowa State University, AmesMidwest Transportation Consortium, Citeseer, 2007. [18] J.H. Hall III, R.J. Connor, Influence of base plate flexibility on the fatigue performance of welded socket connections, J. Struct. Eng. 134 (6) (2008) 911–918. [19] R.J. Connor, Fatigue Loading and Design Methodology for High-Mast Lighting Towers, Transportation Research Board, 2012. [20] R.J. Connor, J.B. Lloyd, Maintenance Actions to Address Fatigue Cracking in Steel Bridge Structures: Proposed Guidelines and Commentary, 2017. [21] R. Goyal, H.B. Dhonde, M. Dawood, Fatigue Failure and Cracking in High Mast Poles, University of Houston. Department of Civil and Environmental Engineering, 2012. [22] M. Dawood, et al., Fatigue life assessment of cracked high-mast illumination poles, J. Perform. Constr. Facil. 28 (2) (2013) 311–320. [23] T. Kinstler, Current Knowledge of the Cracking of Steels during Galvanizing—A Synthesis of the Available Technical Literature and Collective Experience for the American Institute of Steel Construction, GalvaScience LLC, Springville, AL, 2005. [24] R.J. Dexter, et al., Transp. Res. Board 469 (2002). [25] J.S. Goode, J.W. van de Lindt, Development of a semiprescriptive selection procedure for reliability-based fatigue design of high-mast lighting structural supports, J. Perform. Constr. Facil. 21 (3) (2007) 193–206. [26] R. Dexter, Investigation of Cracking of High-Mast Lighting Structures, Final report to Iowa Department of Transportation, 2004. [27] C. Foley, Structural Analysis of Sign Bridge Structures and Luminaire Supports, 2004. [28] B. Chang, B.M. Phares, P.P. Sarkar, T.J. Wipf, Development of a procedure for fatigue design of slender support structures subjected to wind-induced vibration, Transp. Res. Rec. 2131 (2009) 23–33. [29] AASHTO, Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals, 6th edition American Association of State Highway and Transportation Officials (AASHTO), 2015 with 2015 Interim Revisions. [30] D. Radaj, C.M. Sonsino, W. Fricke, Fatigue Assessment of Welded Joints by Local Approaches, Woodhead publishing, 2006. [31] O.D. Dijkstra, J. De Back, Fatigue strength of tubular T-and X-joints, Offshore Technology Conference, 1980. [32] H. Neuber, Theory of Notch Stresses: Principles for Exact Stress Calculation, vol. 74, JW Edwards, 1946. [33] E. Siebel, Ungleichformige Spannung-sverteilung bei Schwingender Beanspruchung, VDIZ 97 (5) (1955) 121–126. [34] F.V. Lawrence, J.D. Burk, R.J. Mattos, Y. Higashida, Estimating the fatigue crack initiation life of welds, Fatigue Testing of Weldments, ASTM International, 1978.

[35] M.H. El Haddad, K.N. Smith, T.H. Topper, Fatigue crack propagation of short cracks, J. Eng. Mater. Technol. 101 (1) (1979) 42–46. [36] T.H. Topper, M.H. El Haddad, Fracture mechanics analysis for short fatigue cracks, Can. Metall. Q. 18 (2) (1979) 207–213. [37] M. El Haddad, T. Topper, K. Smith, Prediction of non propagating cracks, Eng. Fract. Mech. 11 (3) (1979) 573–584. [38] J.R. Kleineck, Galvanizing Crack Formation at Base Plate to Shaft Welds of High Mast Illumination Poles, 2011. [39] S. Roy, Y.C. Park, R. Sause, J.W. Fisher, Fatigue resistance of pole-to-base plate connections in high level lighting structures, Structures Congress, 2010. [40] S. Roy, Y.C. Park, R. Sause, J.W. Fisher, E.J. Kaufmann, Cost-Effective Connection Details for Highway Sign, Luminaire, and Traffic Signal Structures, 2011. [41] S. Roy, Y.C. Park, R. Sause, J.W. Fisher, Fatigue performance of stiffened pole-to-base plate socket connections in high-mast structures, J. Struct. Eng. 138 (10) (2012) 1203–1213. [42] M.T. Eason, Experimental Performance of High Mast Illumination Poles With PreExisting Cracks, 2016. [43] K.V. Belivanis, Assessment of Remaining Fatigue Performance of High Mast Illumination Poles, 2014. [44] A.V. Simulia, 6.13 Documentation. Dassault Systemes, 2013. [45] AASHTO, Standard Specifications for Structural Supports for Highway Signs, Luminaries, and Traffic Signals, American Association of State Highway and Transportation Officials (AASHTO), 2013. [46] C.S. Pool, Effect of Galvanization on the Fatigue Strength of High Mast Illumination Poles, PhD diss. 2010. [47] M.A. Morovat, Y.C. Chen, M.T. Eason, M.D. Engelhardt, L. Manuel, T.A. Helwig, E.B. Williamson, P.M. Clayton, Fatigue Resistance and Reliability of High Mast Illumination Poles (HMIPs) With Pre-Existing Cracks, 2018. [48] TxDOT, High Mast Illumination Poles, Available from ftp://ftp.dot.state.tx.us/pub/ txdot-info/cmd/cserve/standard/traffic/hmip-98.pdf 2019. [49] A. Pilipenko, Computer Simulation of Residual Stress and Distortion of Thick Plates in Multielectrode Submerged Arc Welding: Their Mitigation Techniques, 2001. [50] M. Perić, Z. Tonković, A. Rodić, M. Surjak, I. Garašić, I. Boras, S. Švaić, Numerical analysis and experimental investigation of welding residual stresses and distortions in a T-joint fillet weld, Mater. Des. 53 (2014) 1052–1063. [51] K.H. Chang, C.H. Lee, Finite element analysis of the residual stresses in T-joint fillet welds made of similar and dissimilar steels, Int. J. Adv. Manuf. Technol. 41 (3-4) (2009) 250. [52] T.L. Teng, C.P. Fung, P.H. Chang, W.C. Yang, Analysis of residual stresses and distortions in T-joint fillet welds, Int. J. Press. Vessel. Pip. 78 (8) (2001) 523–538. [53] M. Siddique, M. Abid, H.F. Junejo, R.A. Mufti, 3-D finite element simulation of welding residual stresses in pipe-flange joints: effect of welding parameters, Materials Science Forum, Trans Tech Publ, 2005. [54] N.X. Ma, Y. Ueda, H. Murakawa, H. Maeda, FEM Analysis of 3-D Welding Residual Stresses and Angular Distortion in T-Type Fillet Welds (Mechanics, Strength & Structural Design), 1995. [55] A.M. Harte, D. Williams, F. Grealish, A coupled temperature–displacement model for predicting the long-term performance of offshore pipeline insulation systems, J. Mater. Process. Technol. 155 (2004) 1242–1246. [56] Q.Q. He, Q.H. Zhang, K.Q. Liu, J.H. Chen, Fully coupled temperature-displacement simulation of H-shape metal cogging, J. Syst. Simul. 1 (2007) 007. [57] A. Montoya, H. Millwater, Sensitivity analysis in thermoelastic problems using the complex finite element method, J. Therm. Stresses 40 (3) (2017) 302–321. [58] V. Kuklik, Post on the issue of safety of steel structures of hot dip galvanized structural components, Proc. Eng. 40 (2012) 241–246. [59] R. Mises, Mechanik der festen Körper im plastisch-deformablen Zustand. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math. Phys. Klasse 1913 (4) (1913) 582–592. [60] M. Huber, Specific work of strain as a measure of material effort, Arch. Mech. 56 (3) (2004) 173–190. [61] G.I. Taylor, H. Quinney, The plastic distortion of metals, Phil. Trans. R. Soc. Lond. Ser. A 230 (1932) 323–362. [62] H. Hencky, On the theory of plastic deformations and the resulting stresses in the material, ZAMM J. Appl. Math. Mech. 4 (4) (1924) 323–334. [63] B. Schafer, T. Peköz, Computational modeling of cold-formed steel: characterizing geometric imperfections and residual stresses, J. Constr. Steel Res. 47 (3) (1998) 193–210. [64] B.W. Schafer, Z. Li, C.D. Moen, Computational modeling of cold-formed steel, ThinWalled Struct. 48 (10-11) (2010) 752–762.