Experimental research and analysis on residual stress distribution of circular steel tubes with different processing techniques

Thin-Walled Structures 144 (2019) 106268

Contents lists available at ScienceDirect

Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws

Full length article

Experimental research and analysis on residual stress distribution of circular steel tubes with different processing techniques

T

Xi-Feng Yana,*, Chao Yangb a b

Department of Architecture and Building Engineering, Kanagawa University, Kanagawa, 2218686, Japan Department of School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an, 710055, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: HK21B blind-hole drilling method Sectioning method Processing techniques Welded circular tube Residual stress Distribution model

To investigate and model the residual stress in 345 and 420 MPa normal strength steel (NSS) as well as 690 MPa high-strength steel (HSS) circular tube sections, an experimental study with a total of 45 specimens was conducted using the hole-drilling and sectioning methods. The parameters altered during the experiment included the processing techniques, diameter-to-thickness ratios, steel strengths and welding locations. More than 3064 original test data samples were used to quantify the distribution characteristics of the residual stresses. The results suggest that the magnitudes and distributions of the residual stresses in the welded circular tubes were significantly affected by the processing techniques, steel strengths and welding locations, while no obvious correlation was identified with the diameter-to-thickness ratios. The maximum compressive residual stress ratio gradually decreased with an increase in the steel strength. However, the variation in the tensile residual stress near the weld seam in the middle section was not affected by the variation in the parameters, and its maximum value was in the range of 0.1 π on both sides of the weld seam. Unlike those of the welded approach, the residual stresses along the circumferential direction of the inner or outer surfaces of the hot-rolled seamless circular steel tube sections were almost identical, which is basically consistent with the ECCS’s theoretical model. On the basis of the test results, a distribution model and its simplified forms for NSS were established, and Yang’s distribution model was further validated. The two distribution models can effectively describe the experimental results.

1. Introduction With the development of modern architecture and steel tube manufacturing technology, circular steel tubular components have been employed to construct large-span, super-tall structures, which can adapt to strong earthquakes and hostile environmental conditions, such as storms, floods and atmospheric corrosion. Compared to angle steel, circular steel tube structural members exhibit excellent material utilization and structural properties in terms of compression resistance, tensile strength, bending resistance and torsion resistance. Owing to its small wind carrier coefficient and effective mechanical properties, the cross-section of the circular steel tube has been proven as the optimal cross-sectional form for resisting wind, hydraulic, and wave loads. Moreover, with the continuous upgrading of power grid grades, the traditional angle steel tower cannot meet the requirements of current industrial developments. As a result, circular steel tubular members have become the major members in substation steel structures and transmission towers, and have therefore achieved significant economic and social benefits in the power industry.

*

Circular steel tubes can be categorized as seamless and welded tubes, according to the processing techniques used [1]. Owing to the different processing techniques applied, the initial imperfections and mechanical properties of circular steel tubes vary. The longitudinal residual stress (hereinafter referred to as the residual stress) is one of the most important initial imperfections. It has significant effects on the loading capacity, fatigue fracture, brittle failure, and stress corrosion cracking, particularly regarding the buckling strength of circular steel tubes with intermediate slenderness [2–6]. Thus far, several presentations of the residual stress in specifications for the design of steel structures, such as GB 50017-2017 [7], ANSI/AISC 360-16 [8], and Eurocode 3 [9], have mainly focused on normal strength steel (NSS) submerged arc welded (SAW) steel tube sections. However, investigations into residual stress distribution models and detailed calculation formulae for NSS and high-strength steel (HSS) circular tube sections using the different processing techniques have not yet been carried out. Consequently, to achieve the safe and effective application of circular steel tubes, it is necessary to conduct a comprehensive and in-depth investigation into the distribution and formulation of the residual stress

Corresponding author. E-mail address: [email protected] (X.-F. Yan).

https://doi.org/10.1016/j.tws.2019.106268 Received 6 February 2019; Received in revised form 11 May 2019; Accepted 24 June 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

in circular steel tube sections. Since the 1970s, numerous researchers have devoted substantial attention to the distribution of residual stresses. For example, the residual stress distribution of box sections was described when studying the overall buckling of box columns [10–12]. Early in 1976, a residual stress distribution model for rolled circular steel tube sections was proposed by European Convention for Constructional Steelworks (ECCS) [13]. By studying the design curve of the section beam of circular steel tubes, Wagner et al. [4] developed a two-fold linear hypothetical residual stress distribution model. Subsequently, in 1977, Chen et al. [2] performed tests on the residual stress of welded steel tube sections by employing the sectioning method. The results demonstrated that the distribution of the circumferential residual stress along the wall thickness direction was insignificant, and a multi-linear residual stress model was proposed for welded circular steel tube sections. In recent years, for investigating the residual stress distribution patterns of HSS welded circular steel tube sections, Shi et al. [14] and Yang et al. [15] conducted a series of experiments using the sectioning method. Based on the test results, the residual stress distribution models of HSS welded circular steel tubes were proposed. Moreover, finiteelement technology was applied to perform numerical simulations of the welding residual stress and welding deformation for circular steel tube sections [14,16,17]. At present, residual stress measurement techniques consist of destructive, semi-destructive, and non-destructive methods. As a semidestructive measurement method, the hole-drilling method is very popular for measuring residual stresses in steel structural members, owing to its advantages of economy, accuracy and adequacy. Lee et al. [18] launched an investigation into the residual stress distributions near the weld toe of HSS thin-walled T and Y-joints by employing the ASTM hole-drilling method. The effects of preheating, joint geometry and brace plate cutting on the residual stress distribution near the weld toe were analyzed. Recently, Jiang et al. [19] conducted an experimental study to discuss the effects of the welding process on the residual stress distributions of HSS built-up box columns using the ASTM hole-drilling method. In addition to semi-destructive method, destructive and non-destructive methods have been adopted to test the residual stresses in steel structural members. For example, Ban et al. [20,21] employed the sectioning method to measure the residual stresses in 460 MPa HSS welded I and box sections. X-ray diffraction, which offers the advantage of the direct evaluation of through-thickness residual stresses, was adopted to investigate the residual stress in cold-rolled stainless steel hollow sections [22]. From a length scale perspective, Withers [23] assessed the performance and capability of current residual stress measurement techniques, such as ultrasonic, magnetic, diffractive, and mechanical approaches. However, thus far, few experimental data have been provided for the residual stress distributions of circular steel tube sections under different processing techniques by means of the HK21B hole-drilling method. In this study, to provide an improved understanding of the residual stress distributions of circular steel tube sections, experimental tests were conducted to investigate the residual stress distributions of 345 and 420 MPa NSS as well as 690 MPa HSS circular tube sections. The residual stress measurements were obtained by employing the HK21B blind-hole and sectioning methods. Based on the test results, the effects of the processing techniques, diameter-to-thickness ratios, steel yield strengths and welding locations are discussed in this paper. The remainder of this paper is organized as follows: In Section 2, several important details of the specimen preparation and fabrication, as well as the experimental setup, such as the strain gauge scheme employed, are presented. Moreover, the HK21B blind-hole method and sectioning method are briefly reviewed. In Section 3, the results of the experimental study, including the effects of the processing techniques and other key geometrical parameters on the residual stress distribution, are reported. In Section 4, a distribution model and its simplified forms for NSS are established, and Yang’s model is further validated. The two

Table 1 Geometric dimensions of specimens. Processingtechnique

Steel types

Quantity

Sectional specification (mm)

D/t

Test method

Length (mm)

SAW

Q345B

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8

27.4 34.1 40.6 27.4 34.1 40.6 27.4 34.1 40.6 27.4 34.1 40.6 27.4 34.1 40.6

Blind-hole

1500

Q420B

Q690C

HFW

Q345B

HR

Q345B

Blind-hole

Blind-hole

Blind-hole

Blindhole/ Sectioning

distribution models can effectively describe the experimental results. Finally, Section 5 presents the conclusions.

2. Experimental program 2.1. Preparation and fabrication of specimens A total of 45 circular steel tubes were measured in this study, as indicated in Table 1. The processing techniques of the circular steel tubes were divided into SAW, high-frequency welding (HFW) and hotrolling (HR). The steel types using SAW comprised Q345B, Q420B, and Q690C, with nominal yield strengths of 345, 420, and 690 MPa, respectively, while the HFW and HR types consisted only of Q345B. The dimensions of the specimens were Φ219 × 8 mm, Φ273 × 8 mm and Φ325 × 8 mm, respectively, all of which were selected in consideration of real-life engineering applications (Chinese tower processing enterprise). To achieve more accurate measurements, the residual stress of each section was tested multiple times and then averaged. All specific welding and HR configurations are displayed in Tables 2–4 and Fig. 1. According to manual metal arc welding, during the SAW process, the welding groove with an angle of 60°–70° was divided into four sections, namely the final pass, second pass, root pass, and contact region. To prevent flux and welding slag from falling into the tube during the welding process, the contact region is usually 2 mm along the wall thickness direction. The shielding gas of the root pass and second pass was 80% Ar + 20% CO2, while the welding wire brand was WH-70-G with a diameter of 1.2 mm. The final pass employed SJ105G to protect the molten metal, and the corresponding welding wire diameter was 2.5 mm. According to GB 50661-2011 [24], from the root pass to the final pass, the welding speed, welding current, and welding voltage gradually increased with the increase in the welding area.

2.2. Material properties With reference to GB/T 2975-1998 [25], the tension coupons, in which the cutting direction was parallel to the rolling axis, were cut from the same parent circular steel tubes. The tension coupons were created based on the international standard ISO 6892-1:2016 [26]: Metallic materials–Tensile testing–Part 1: Method of test at room temperature. This standard is equivalent to the Chinese standard GB/T 228.1-2010 [27]: Metallic materials–Tensile testing at ambient temperature. The material properties of the specimens are summarized in Table 5, all of which were the averages of test results from three tension coupons. 2

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Table 2 Welding parameters of SAW. Welding groove

Straight welding line

Welding equipment Welding wire brand

NBC-500 (gas)/SAW-3000B (flux) WH-70-G

Power type

Direct current reverse polarity (DCEP)

Pass number

Shielding gasses /flux

Welding wire diameter (mm)

Welding speed (cm/min)

Welding current (A)

Welding voltage (V)

Root pass Second pass Final pass

80% Ar + 20% CO2 80% Ar + 20% CO2 SJ105G

1.2 1.2 2.5

20 to 32 24 to 38 40 to 45

120 to 160 220 to 240 380 to 420

18 to 23 24 to 28 36 to 39

could be determined by the following equation:

2.3. Measurement methods and principles

⎧ A = (ε1 + ε3)/(2σ ) ⎨ ⎩ B = (ε1 − ε3)/(2σ )

2.3.1. HK21B blind-hole method The blind-hole method offers high measurement accuracy and is less destructive to the specimen. The measurement principle is as follows [15]: if a residual stress field exists in the steel component, after drilling a small blind hole (diameter D, depth h), the residual stress around the blind hole will be released. As a result, the original residual stress field at this point is out of balance. To achieve equilibrium again and form a new stress field, a certain amount of release strain is generated. This strain, released by drilling, can be measured using the resistance strain gauge, and is displayed by the HK21B residual stress detector. If isotropic materials are used in this test, the residual stress anywhere in the component should be in a uniform plane state, as illustrated in Fig. 2. In this study, the BX120-3CA three-phase 45° rosette resistance strain gauge was used and pasted onto the pre-measured point o of plane P. According to the theory of plane stress in elastic mechanics, the maximum and minimum principal stresses, namely σ1 and σ2, respectively, and the angle of orientation ϕ can be obtained using Eq. (1), as follows: Δε + Δε

in which the release strains ε1 and ε3 were obtained by strain gauges 1 and 3, respectively. The test results of the calibration coefficients A and B are listed in Table 7. By substituting Eq. (2) into Eq. (1), the values of σ1 and σ2 could be obtained. Furthermore, according to the principles of material mechanics, the residual stress σr on the measuring surface could be determined, which is expressed by:

σr =

σ1 + σ2 σ − σ2 cos(2ϕ) + 1 2 2

(3)

It should be noted that, when the blind-hole method is used to measure the residual stress of the components, an additional strain εm will be generated owing to the cutter cutting and squeezing around the hole edge. The difference between the measured total strain Δεi' and additional εm is the real strain released by the drilling hole; that is, Δεi = Δεi' - εm, in which i = 1, 2, 3. Referring to CB/T 3395-2013 [28], the additional strain εm consists of drilling plastic strain εd and stress concentration plastic strain εs (only ε1s and ε3s). Here, εd is taken as 35 με. εs takes the value of 0, when the measured residual stress is less than 60% of the yield strength of material used. Conversely, εs can be given as follows: The transition coefficients N1 and N2 could be obtained by:

1

⎧ σ1 = 14A 3 + 4B (Δε1 − Δε3)2 + (2Δε2 − Δε1 − Δε3)2 ⎪ Δε + Δε 1 σ2 = 14A 3 − 4B (Δε1 − Δε3)2 + (2Δε2 − Δε1 − Δε3)2 ⎨ ⎪ tan2ϕ = 2Δε2 − Δε1 − Δε3 Δε3 − Δε1 ⎩

(2)

(1)

where Δε1, Δε2, and Δε3 are the measured relieved strains from three directions after drilling, with unit με, while ϕ is the angle between the maximum principal stress and the reference axis of strain gauge 1, which specifies that the clockwise direction is positive. Moreover, A and B represent calibration coefficients, both of which were measured by the calibration tests [28], as follows. According to the minimum distance between the blind hole and the boundary of the measured component, the working part width of the component was 60 mm, as depicted in Fig. 3(a). The same strain type was pasted onto the front and back of the component to correct the errors caused by load eccentricity and torsion, as illustrated in Fig. 3(b). The test method was as follows: it was assumed that the unidirectional stress field (σ1 = σ and σ2 = 0; strain gauges 1 and 3 were parallel to the directions of σ1 and σ2, respectively, namely ϕ = 0) was applied artificially in the components, and the calibration coefficients A and B

N1 =

3γ − 1 (Δε1′ − εd ) + (Δε3′ − εd ) 3−γ

(4)

N3 =

3γ − 1 (Δε3′ − εd ) + (Δε1′ − εd ) 3−γ

(5)

Δε3′ − εd Δε1′ − εd

(6)

γ=−

when the drilling parameters are selected as certain values, the plastic strains ε1s and ε3s caused by the stress concentration could be determined as follows:

ε1s = 0.4N3 + 78.4

(7)

ε3s = −0.2N1 − 39.3

(8)

Table 3 Welding parameters of HFW. Welding temperature (°C)

Welding pressure (MPa)

Opening-angle

Soldering station line width (mm)

Heat-affected zone (mm)

1380 to 1550

19.6 to 29.4

3°–6°

0.02 to 0.12

0.4 to 4

3

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Table 4 Parameters of HR. Initial temperature (°C)

Core bar initial temperature (°C)

Friction coefficient of steel pipe and roll

Friction coefficient of steel pipe and core bar

Exit speed(mm/ s)

Entrance speed(mm/s)

950 to 1050

130 to 200

0.2

0.7

2969.9

1500

no less than five times the hole diameter [28]. A drill hole with a diameter of 2.0 mm was employed in this study, and therefore the lateral spacing between the holes was ensured as greater than 10 mm (the minimum distance depicted in Fig. 5(a) is 18 mm). Simultaneously, the spacing between two adjacent holes should be set after considering the variations in the residual stress along the circumference. As the variation in the residual stress near the weld seam is more significant, the arrangement of the measuring points at this position is dense. Conversely, the arrangement of the measuring points at the position further from the weld seam becomes sparse, at which the variation in the residual stress is insignificant. According to Refs. [13,29], the theoretical distribution model of residual stress of the HR seamless circular steel tube is illustrated in Fig. 6. From Fig. 6, it can be seen that the residual stress on the inner surface was in the tensile state with a value of 0.15 σy, while that on the outer surface was the opposite. The residual stress distribution along the wall thickness can be approximated as a straight line. For the purpose of testing the validity of the theoretical distribution model, in this study, eight representative points were selected as measuring points, as illustrated in Fig. 7.

After subtracting the plastic strains ε1s and ε3s from Δε1'-εd and Δε3'εd, the elastic strains ε1e and ε3e could be obtained. Then, Δε1'-εd and Δε3'-εd in Eqs. (4)–(6) were replaced by the elastic strains ε1e and ε3e, the real stress concentration plastic strains ε1s and ε3s could be achieved by repeating the process of Eqs. (4)–(8) twice. 2.3.2. Sectioning method Owing to the limitations of the test conditions, when measuring the residual stress of the HR seamless circular steel tubes, it was difficult to use the HK21B blind-hole method to test the inner surfaces of the specimens. Therefore, in addition to the HK21B blind-hole method, the inner surface of the HR seamless circular steel tubes was tested using the sectioning method [14,15]. The measurement method was as follows. Firstly, the residual stresses on the outer surfaces of the specimens were measured by the HK21B blind-hole method. Subsequently, the sectioning method was introduced to divide the middle part of the circular steel tube, which had to have a minimum distance of 1.5–2.0 times the sectional lateral dimension to both ends of the steel profile. The length of the adopted middle part had to be no less than 3.0 times the lateral dimension. Two holes were prepared on each strip component with a distance of 10 in = 254 mm (as per the Whittemore strain gauge length) in between for installation of the strain gauge, as indicated in Fig. 4(a) and (b). Each strip was cut with a width of 10 mm, and the strips with different section sizes are listed in Table 6. To slice the specimen as accurately as possible and generate minimal heat input, a computer numerical controlled (CNC) wire-cut electrical discharge machining (EDM) machine was introduced in this method, as illustrated in Fig. 4(c). During the sectioning process, the small holes originally drilled by the blind-hole method on the outer surface were located in the middle of the cutting strip to avoid the cutting line. Thereby, the effect on the measured results caused by the target hole deformation was reduced. It is worth noting that the residual stresses on the inner surface were slightly smaller than those on the outer surface obtained by the blindhole method. This is mainly because the former was achieved from the initial reading data when the specimen was separated into two parts using the sectioning method [14]. During this sectioning procedure, the constraints of the two separated parts were removed, and as a result, a small part of the residual stress was released.

3. Experimental results and analysis The distributions of the measurements obtained from the drilling and strip specimens are illustrated in Figs. 8–11, and the extreme values of the corresponding distribution curves are listed in Tables 8–10. Owing to the symmetry of the circular steel tube section, half of the section was used as the research object in this study. Based on the test results, the distribution of the residual stress, effects of the diameter-tothickness ratios, steel yield strengths, welding sections and processing techniques are discussed in the following five sections. 3.1. Distribution of residual stress In Figs. 8–10, the y-coordinate is the ratio of the residual stress σr to the actual yield stress σy, and the x-coordinate indicates the ratio of the arc between the weld seam center and measuring point to π; that is, x = θ/π. In Fig. 11, the definition of the y-coordinate is the same as that in Figs. 8–10, while the x-coordinate represents the positions of the measuring points selected in Section 2.3. The black solid lines with black hollow (solid) quadrangles represent the sequential connections of the measurement results at each measuring point of the specimens with sectional dimensions of Φ219 × 8 mm. The red solid lines with red hollow (solid) circles represent the sequential connections of the measurement results at each measuring point of the specimens with

2.3.3. Layout of measuring points In this study, the measured positions of the welded specimens were divided into three parts, namely the middle sections, and the sections at a distance of 20 mm from the welding start and end. To ensure measurement accuracy, the minimum distance between two holes should be

Fig. 1. Diagram of HFW. 4

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Table 5 Mechanical properties of specimens. Processing technique

Steel types

Quantity

Sectional specification (mm)

Elastic modulus ( × 105 MPa)

Yield strength (MPa)

Ultimate strength (MPa)

Minimum elongation (%)

SAW

Q345B

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8

1.99 2.00 1.97 2.01 1.99 2.00 1.98 2.00 1.99 2.01 1.96 1.99 1.99 1.97 2.01

410 398 390 450 445 442 720 700 710 360 355 360 365 380 380

505 505 495 550 556 550 875 950 870 510 510 510 540 555 560

1.232 1.269 1.269 1.222 1.249 1.244 1.215 1.357 1.225 1.417 1.437 1.417 1.479 1.461 1.474

Q420B

Q690C

HFW

Q345B

HR

Q345B

Table 6 Number of cutting strips for each HR specimen. Specimen label

Specification

Outside diameter D (mm)

Number of cutting strips

HR

Φ219 × 8 Φ273 × 8 Φ325 × 8

219 273 325

68 86 102

Table 7 Calibration coefficients A and B. Processing techniques Q345B Q345B Q345B Q420B Q690C

Fig. 2. Schematic of testing residual stress using hole-drilling method.

sectional dimensions of Φ273 × 8 mm. The blue solid lines with blue hollow (solid) triangles represent the sequential connections of the measurement results at each measuring point of the specimens with sectional dimension of Φ325 × 8 mm. It can be observed from Fig. 8 that the overall distribution trends of the residual stresses obtained by the blind-hole method were almost identical, and the maximum tensile residual stress was reached within 0.1π of both sides of the weld seam, with a value quite close to 1. Meanwhile, as the distance from the weld seam center increased, the value of the tensile residual stress decreased sharply and became negative, namely compressive residual stress. When the compressive residual stress reached its maximum value, with a further increase in the distance, its value gradually decreased and eventually became smaller tensile residual stress in the range of 0 to 0.2σy at x = 1. From Fig. 11, it can be clearly observed that, unlike in the welded approach, the residual stresses along the circumferential direction of the inner or outer

Calibration coefficients

(HR) (HFW) (SAW) (SAW) (SAW)

A ( × 10−6/MPa)

B ( × 10−6/MPa)

−0.3342 −0.3216 −0.3461 −0.1962 −0.2015

−0.8258 −0.9019 −0.8876 −0.7225 −0.7187

surfaces of the HR seamless circular steel tube sections were almost identical. In Tables 8–10, σr represents the residual stress obtained experimentally (σr,max and σr,min are the maximum and minimum residual stresses, respectively), while σy is the yield strength of the steel. In Table 8, AT denotes the area enclosed by the tensile residual stress near weld seam and coordinate axes. The volatility deviation (VODEV) is the ratio of the sum of the diversions from all measuring points divided by the number of measuring points at the corresponding section. The diversion at each measuring point is the sum of the differences between the values measured multiple times at this location and their average value divided by the measurement times. In Table 10, the standard deviation (STDEV) reflects the extent to which the measurements on the outer or inner surfaces of the HR seamless circular tubes deviate from

Fig. 3. Dimensions of calibrated specimen and layout of strain rosette. 5

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Fig. 4. Operation procedure of sectioning method.

Fig. 5. Layout of measuring points for Φ325 × 8 welded circular steel tube sections.

steel yield strengths, welding sections and processing techniques on the variation in the residual stress at the middle section.

their arithmetic mean. From Table 8, it can be observed that the VODEV values of the Q345B HFW circular steel tubes were less than those of the Q345B SAW circular steel tubes. As the diameter-to-thickness ratio increased, the values of |σr,min/σy| decreased gradually, while those of σr,max/σy exhibited no evident differences. With the increase in the steel strength, the values of |σr,min/σy| decreased gradually, but the change between those of the Q345B and Q420B SAW circular steel tubes was not significant. Comparing Tables 8–9 and Figs. 8–10, the results demonstrate that the distributions and extrema of the residual stresses at the welding start or end were obviously different from those at the middle section. Based on the above observations, in the following four sections, the focus will be discussing the effects of the diameter-to-thickness ratios,

3.2. Effects of diameter-to-thickness ratios From Fig. 8, it can be observed that, as the diameter-to-thickness ratio of the welded circular steel tube increased, the distributions of the residual stresses at the middle section were almost identical; however, several slight differences were observed, as indicated in Table 8. From Table 8, it can be noted that when the diameter-to-thickness ratio of the welded circular steel tube was larger, the area (AT) surrounded by the tensile residual stress and coordinate axes near the weld seam was increased. The primary reason is that the constraint of the heat-affected 6

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

thickness ratios made little contribution to the residual stress distribution at the middle section of the welded circular steel tube. 3.3. Effects of steel yield strengths From Table 8, it can be observed that the variations in σr,max/σy at the middle section of the SAW circular steel tubes were not very obvious with the increase in the steel yield strength. However, the values of |σr,min/σy| decreased with the increase in the steel yield strength, but the changes between those of the 345 and 420 MPa NSS SAW circular steel tubes were not notable. The result demonstrates that, compared to NSS, HSS had a significant effect on the compressive residual stress magnitudes for the welded circular steel tubes. Moreover, the VODEV values of the residual stress distributions at the middle section of the SAW circular steel tubes decreased as the steel yield strength increased. This indicates that the HSS was insensitive to residual stress distribution compared to the NSS.

Fig. 6. Residual stress models for HR seamless circular steel tube sections.

3.4. Effects of welding locations From Figs. 8–10, compared to the residual stress distributions at the middle section of the welded circular steel tubes, there were no obvious distribution regulations of residual stresses at the welding start or end. The σr,max/σy and |σr,min/σy| values of the sections at the welding start or end were significantly reduced relative to those at the middle section. The peak values near the weld seam were almost equal to or even smaller than those of the sections at x = 1. Moreover, from Table 9, it can be observed that the peak values of the residual stresses of the sections at the welding start were larger than those at the welding end. The above variations are mainly attributed to the effects of the different boundary constraints caused by the cooling rate during the cooling process. It can be concluded that the welding locations had a significant influence on the residual stress distributions of the welded circular steel tube sections.

Fig. 7. Layout of measuring points for HR seamless circular steel tube sections.

zone of the large diameter was stronger than that of the small diameter, and the small diameter shrunk more easily in the heat-affected zone during cooling. The variation in σr,max/σy was insignificant with an increasing diameter-to-thickness ratio. However, the values in |σr,min/ σy| decreased slightly with the increase of the diameter-to-thickness ratio, but the difference was very small. Consequently, the diameter-to-

3.5. Effects of processing techniques From Table 8, it can be observed that there were no obvious

Fig. 8. Residual stress distributions at middle section for welded circular tubes. 7

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Fig. 9. Residual stress distributions at section of welded circular steel tubes 20 mm from welding start.

variations between the σr,max/σy values of the SAW and HFW circular steel tubes. The |σr,min/σy| values of the HFW circular steel tubes were lower than those of the SAW circular steel tubes, while the variations were not obvious. Besides, the VODEV values of the 345 MPa HFW circular steel tubes were smaller than those of the 345 MPa SAW circular steel tubes. This is because the heat input of HFW is relatively low compared to that of SAW. Consequently, the welding types had an influence on the volatility of the residual stress distribution of the welded circular steel tubes. By comparing Figs. 8 and 11, it can be observed that, unlike in the welded circular steel tubes, the residual stresses on the inner and outer surfaces of the HR seamless circular steel tubes were almost constant. This is mainly attributed to the different boundary constraints at the

sections generated by varying techniques in the process of manufacturing circular steel tubes. From Table 10, it can be observed that the measurements of most measuring points on the inner and outer surfaces of the HR seamless circular steel tubes were between 0.13 and 0.15σy. The average absolute values of the compressive (or tensile) residual stresses for different sectional dimensions were close to 0.145σy, with no obvious changes as the diameter-to-thickness ratio increased. Overall, it can be found that the residual stress distributions on the inner and outer surfaces of the HR seamless circular steel tubes were basically consistent with the theoretical distribution model in Refs. [13,29]. Based on the above observations, it can be concluded that the processing techniques had a remarkable influence on the residual stress

Fig. 10. Residual stress distributions at section of welded circular steel tubes 20 mm from welding end. 8

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Fig. 11. Residual stress distributions at middle section of HR seamless circular steel tubes.

expression was established to represent the residual stress distribution. In 1977, Chen et al. [2] measured the residual stress distributions of 10 welded circular steel tube sections by employing the sectioning method, and proposed a multi-linear distribution model, as depicted in Fig. 12. Unlike the residual stress distribution model by Wagner et al. [4], the basic conditions of the full cross-sectional self-equilibrated stress in the residual stress distribution model by Chen et al. [2] were not satisfied. In recent years, Yang et al. [15] proposed a residual stress distribution model for HSS welded circular steel tubes, which was based on limited test data. Therefore, it is necessary to verify the validity of the existing distribution models further based on test results.

Table 8 Peak values, VODEV of residual stress distribution at middle cross-sections, and area of tensile zone near weld seam. Specimen category

Sectional specification (mm)

D/t

σr,max/σy

σr,min/σy

VODEV

AT

Q345B-HFW

Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Ø325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8

27.4 34.1 40.6 27.4 34.1 40.6 27.4 34.1 40.6 27.4 34.1 40.6

0.967 0.977 0.965 0.991 0.975 0.986 0.938 0.971 0.941 0.911 0.936 0.967

−0.335 −0.321 −0.309 −0.342 −0.341 −0.324 −0.339 −0.330 −0.302 −0.232 −0.226 −0.202

0.052 0.050 0.045 0.080 0.091 0.094 0.076 0.079 0.080 0.041 0.063 0.049

0.0632 0.0653 0.0674 0.0691 0.0706 0.0797 0.0690 0.0846 0.1040 0.0499 0.0530 0.0577

Q345B-SAW

Q420B-SAW

Q690C-SAW

4.2. Simplified model for NSS (345 and 420 MPa) welded circular tube sections Section 3 of this paper presented the test results of the residual stress for NSS welded circular tube sections. The measured results from the middle sections of the NSS welded circular steel tubes were arranged in a graph and linearly fitted, as illustrated in Fig. 13. The hollow quadrangles, circles, and triangles in Fig. 13 represent the measurements obtained from the 345 MPa HFW, 345 MPa SAW, and 420 MPa SAW circular steel tubes, respectively. It can be observed from Fig. 13 that the measurement results of each type were distributed on both sides of the fitting lines. Moreover, the plane coordinates of the maximum tensile residual stress point, maximum compressive residual stress point and zero-stress points in the fitting lines are marked in Fig. 13. A simplified calculation formula was developed to represent the residual stress distribution of the NSS welded circular steel tube sections, which can be expressed as follows:

Table 9 Peak values of residual stress distributions at cross-sections 20 mm away from welding start and end. Specimen category

Q345B-HFW

Q345B-SAW

Q420B-SAW

Q690C-SAW

Sectional specification

Welding start

Welding end

(mm)

σr,max/σy

σr,min/σy

σr,max/σy

σr,min/σy

Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8 Φ219 × 8 Φ273 × 8 Φ325 × 8

0.110 0.065 0.087 0.128 0.066 0.115 0.102 0.113 0.100 0.100 0.088 0.098

−0.115 −0.083 −0.131 −0.144 −0.134 −0.106 −0.124 −0.116 −0.127 −0.076 −0.099 −0.083

0.042 0.030 0.058 0.053 0.052 0.071 0.036 0.059 0.075 0.048 0.052 0.044

−0.051 −0.052 −0.065 −0.064 −0.073 −0.092 −0.066 −0.059 −0.076 −0.040 −0.045 −0.052

− 6.045x + 1(0 ≤ x ≤ 0.22) y = ⎧ ⎨ ⎩ 0.59x − 0.46(0.22 < x ≤ 1)

(9)

As in Section 3.1, in this case, the y-coordinate is the ratio of the residual stress σr to the actual yield stress σy, while the x-coordinate represents the ratio of the arc between the weld seam center and measuring point to π; that is, x = θ/π. According to the characteristics of the full cross-sectional residual self-equilibrated stress in a component, the above Eq. (9) is preliminarily inspected. The integration of Eq. (9) is as follows:

distributions of the circular steel tubes.

0.22

4. Modeling of residual stress for NSS and HSS welded circular sections

1

∫ (−6.045x + 1) dx+ ∫ (0.59x − 0.46) dx = −0.0044 0

0.22

(10)

It can be observed from the calculation result of Eq. (10) that the tensile and compressive residual stresses are basically in equilibrium, which verifies the accuracy of Eq. (9). In combination with Fig. 13, it can be found from Eq. (9) that, with the increase in x (the measuring point slowly moves away from the center-line of the weld seam), the stress ratio y decreases rapidly. When x is equal to 0.22 (θ = 0.22π), the stress ratio y reaches the minimum value of −0.33; that is, the maximum compressive residual stress is equal to 0.33σy. Thereafter, with a

4.1. Existing models for welded circular sections Research on the residual stress distributions of welded circular steel tube sections remains in the relatively early stages. In 1976, Wagner et al. [4] proposed an assumed bilinear residual stress distribution model for welded circular steel tube sections, which was validated against compression tests of small-diameter circular steel tubes, as illustrated in Fig. 12. However, no corresponding mathematical 9

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

Table 10 Residual stress measurements at middle cross-sections of HR seamless circular steel tubes. Measuring points

Outer wall/(σr/σy)

Inner wall/(σr/σy)

Blind-hole

1 2 3 4 5 6 7 8 Mean STDEV

Sectioning

Sectioning

Φ219 × 8

Φ273 × 8

Φ325 × 8

Φ219 × 8

Φ273 × 8

Φ325 × 8

Φ219 × 8

Φ273 × 8

Φ325 × 8

−0.151 −0.146 −0.152 −0.144 −0.134 −0.130 −0.149 −0.151 −0.145 0.008

−0.145 −0.143 −0.139 −0.148 −0.139 −0.151 −0.141 −0.136 −0.143 0.005

−0.149 −0.141 −0.150 −0.140 −0.142 −0.143 −0.149 −0.146 −0.145 0.004

−0.133 −0.128 −0.156 −0.155 −0.127 −0.129 −0.144 −0.137 −0.139 0.012

−0.139 −0.153 −0.149 −0.132 −0.129 −0.154 −0.158 −0.135 −0.144 0.011

−0.124 −0.148 −0.155 −0.127 −0.143 −0.144 −0.148 −0.141 −0.141 0.011

0.137 0.149 0.128 0.146 0.159 0.138 0.154 0.129 0.143 0.011

0.148 0.152 0.142 0.146 0.134 0.153 0.155 0.132 0.145 0.009

0.140 0.138 0.151 0.139 0.148 0.117 0.146 0.143 0.140 0.010

Fig. 14. Comparison between proposed model and that of Wagner et al. Fig. 12. Existing residual stress models for welded circular steel tube sections.

residual stress distribution for the NSS welded circular tube sections is basically consistent with that of the example distribution model by Wagner et al. [4]. However, the line slopes and coordinates of the peak points differ. Compared to the residual stress distribution model by Wagner et al. [4], the slope of the descending segment of the proposed distribution model becomes steeper, while the ascending segment is the opposite. The maximum tensile residual stress of the NSS welded circular tube sections reaches the actual steel yield strength. The value of |σr,min/σy| in the distribution model by Wagner et al. [4] is 0.35, while that in the proposed distribution model is 0.33 (reduced by approximated 5.7%). Furthermore, from Fig. 8(a)–(c), it can be observed that the proposed distribution model for NSS can effectively describe the test results. Fig. 13. Linear fitting of residual stress measurements for 345 and 420 MPa welded circular steel tubes.

4.3. Verification of distribution model for 690 MPa HSS welded circular tube sections

further increase in x, the stress ratio y increases gradually until x is equal to 1 (θ = π). At this location, the stress ratio y is equal to 0.13; that is, the residual stress is in the tension state and equal to 0.13σy. Furthermore, a comparison between the proposed residual stress distribution model for the NSS welded circular tube sections in this study and that developed by Wagner et al. [4] is presented in Fig. 14. However, Wagner’s model is only one sample distribution model, which was assumed against a circular steel tube with sectional dimension of Φ254 × 17.3 mm and a yield stress of 241.5 MPa. This model failed to provide the mathematical expression of the residual stress distribution model and a method for determining the peak points. For the convenience of comparison, in this study, the peak values of the sample distribution model were defined by dividing the assumed values of the model proposed in Ref. [4] by the steel yield strength. Moreover, based on the basic conditions of the full cross-sectional self-equilibrated stress, the location of the maximum compressive residual stress in Wagner’s model was determined. From Fig. 14, it can be found that the curve shape of the proposed

Based on the regression analysis of the measured results of the 690 MPa HSS welded circular steel tubes, a bilinear residual stress distribution model is presented in Fig. 15. The plane coordinates of the maximum tensile residual stress point, maximum compressive residual stress point and zero-stress points in the distribution model are also marked in Fig. 15. For the convenience of comparison, the fitting bilinear distribution model in this study and that proposed by Yang et al. [15] are illustrated in Fig. 16. From Fig. 16, it can be seen that the value of |σr,min/σy| in Yang’s model is 0.2, while this ratio in the fitting bilinear distribution model is 0.21 (increased by about 5%). Although the line slopes and coordinates of the peak points in the two distribution models are slightly different, the fitting bilinear distribution model almost duplicate that proposed by Yang et al. [15]. This comparison further verifies the accuracy of Yang’s model. In addition, from Fig. 8(d), it can be observed that Yang’s model achieves good agreement with the distributions of experimental results. Therefore, Yang’s model can be applied to represent the residual stress distribution of the 10

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

validated. The two distribution models can effectively describe the experimental results. The research work in this paper has very important reference values for the initial imperfections of NSS and HSS circular steel tubular members, which provides valuable information for the further study on the buckling behavior of circular steel tubular columns. It may be helpful in improving the buckling design method and theory of NSS and HSS circular steel tube members, as well as promoting the engineering application of circular steel tube structures. Acknowledgements Fig. 15. Linear fitting of residual stress measurements for 690 MPa welded circular steel tubes.

The research work described in this paper was mainly supported by a 2014 research project of the State Grid Corporation of China (SGCC) supporting innovative construction and infrastructure technologies. Furthermore, this work was also supported by the Natural Science Foundation (2014JM7244) of Shaanxi Province, from the Education Institution of Shaanxi Province. Appendix A. Supplementary data Supplementary data related to this article can be found at https:// doi.org/10.1016/j.tws.2019.106268. References

Fig. 16. Comparison between fitting bilinear distribution model and that proposed by Yang et al.

[1] Code for Design of Steel Structures Committee. Application Construal of Code for Design of Steel Structures in China, China Planning Press, Beijing, 2003 (in Chinese). [2] W.F. Chen, D.A. Ross, Test of fabricated tubular columns, J. Struct. Div. ASCE 103 (ST3) (Mar 1977) 619–634. [3] W.F. Chen, D.A. Ross, The axial strength and behavior of cylindrical columns, OTC Paper No.2683, Offshore Technology Conference, 1976, pp. 742–754 https://doi. org/10.2118/6266-PA. [4] A.L. Wagner, W.H. Mueller, H. Erzurumlu, Design interaction curves for tubular steel beam-columns, OTC Paper No.2684, Offshore Technology Conference, 1976, pp. 755–764 https://doi.org/10.4043/2684-MS. [5] G. Shi, X. Jiang, W.J. Zhou, T.M. Chan, Y. Zhang, Experimental study on column buckling of 420 MPa high strength steel welded circular tubes, J. Constr. Steel Res. 100 (2014) 71–81 https://doi.org/10.1016/j.jcsr.2014.04.028. [6] C.H. Lee, J.H. Baek, K.H. Chang, Bending capacity of girth-welded circular steel tubes, J. Constr. Steel Res. 75 (2012) 142–151 https://doi.org/10.1016/j.jcsr.2012. 03.019. [7] GB 50017-2017, Standard for Design of Steel Structures, China Architecture & Building Press, Beijing, 2017. [8] ANSI/AISC 360-16, Specification for Structural Steel Building, AISC, Chicago, 2016. [9] BS EN 1993-1-1 Eurocode3, Design of Steel Structures: Part 1-1: General Rules and Rules for Buildings, (2005) Londin: BSI. [10] F. Nishino, Y. Ueda, L. Tall, Experimental Investigation of the Buckling of Plates with Residual Stresses. Test Methods for Compression Members. American Society for Testing and Materials, ASTM special technical publication, Philadelphia, PA, 1967, pp. 12–30 419. [11] T. Usami, Y. Fukumoto, Local and overall buckling of welded box columns, J. Struct. Div. 108 (3) (1982) 525–542. [12] T. Usami, Y. Fukumoto, Welded box compression members, J. Struct. Eng. 110 (10) (1984) 2457–2470 (1984)110:10(2457), https://doi.org/10.1061/(ASCE)07339445. [13] European convention for Constructional Steelworks (ECCS). Manual on Stability of Steel Structures: Part 2.2. Mechanical Properties and Residual Stresses, second ed. ECCS Publications, Brussels, Belgium. [14] G. Shi, X. Jiang, W.J. Zhou, T.M. Chan, Y. Zhang, Experimental investigation and modeling on residual stress of welded steel circular tubes, Int. J. Steel Struct. 13 (3) (2013) 495–508 https://doi.org/10.1007/s13296-013-3009-y. [15] C. Yang, J.F. Yang, M.Z. Su, Y. Li, Residual stress in high-strength-steel welded circular tube, Proc. Inst. Civ. Eng. Struct. Build. 170 (9) (2017) 631–640 https:// doi.org/10.1680/jstbu.16.00001. [16] K. Nasim, A.F.M. Arif, Y.N. Al-Nassar, M. Anis, Investigation of residual stress development in spiral welded pipe, J. Mater. Process. Technol. 215 (2015) 225–238 https://doi.org/10.1016/j.jmatprotec.2014.08.009. [17] A.M. Malik, E.M. Qureshi, N.U. Dar, I. Khan, Analysis of circumferentially arc welded thin-walled cylinders to investigate the residual field, Thin-Walled Struct. 46 (2008) 1391–1401 https://doi.org/10.1016/j.tws.2008.03.011. [18] C.K. Lee, S.P. Chiew, J. Jiang, Residual stress study of welded high strength steel thin-walled plate-to-plate joints, Part 1: Experimental study, Thin-Walled Struct. 56 (2012) 103–112 https://doi.org/10.1016/j.tws.2012.03.015. [19] J. Jiang, S.P. Chiew, C.K. Lee, P.L.Y. Tiong, An experimental study on residual

690 MPa HSS welded circular steel tube sections. 5. Conclusions To provide an improved understanding of the residual stress distributions of circular steel tube sections, experimental tests were conducted to investigate the residual stress distributions of 345 and 420 MPa NSS as well as 690 MPa HSS circular steel tube sections. The residual stress measurements were obtained by employing the HK21B blind-hole and sectioning methods. Based on the test results, the effects of the diameter-to-thickness ratios, steel yield strengths, welding locations, and processing techniques were discussed. The conclusions listed below can be found: (1) The diameter-to-thickness ratio has no significant effect on the residual stress distribution at the middle section of circular steel tubes. (2) Compared to NSS, the residual stress distribution of HSS tends to be gentle, and the maximum compressive residual stress ratio becomes smaller. That is, the steel yield strength affects the residual stress distribution of welded circular steel tubes. (3) The welding locations have a significant influence on the residual stress distributions of welded circular steel tubes, owing to the effects of the different boundary constraints caused by the cooling rate during the cooling process. (4) The welding types have an influence on the residual stress distributions of welded circular steel tubes owing to the different heat inputs generated by SAW and HFW. (5) The residual stress distribution model for the 345 MPa NSS HR seamless circular steel tube sections is basically consistent with the theoretical distribution model by ECCS. (6) The processing techniques have a remarkable influence on the residual stress distributions of circular steel tubes. (7) A distribution model and its simplified expressions for NSS have been proposed, and Yang’s distribution model was further

11

Thin-Walled Structures 144 (2019) 106268

X.-F. Yan and C. Yang

[20]

[21]

[22]

[23]

[24] [25] [26] [27] [28] [29]

Nomenclature

stresses of high strength steel box columns, J. Constr. Steel Res. 130 (2017) 12–21 https://doi.org/10.1016/j.jcsr.2016.11.025. H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Residual stress of 460 MPa high strength steel welded box section: Experimental investigation and modeling, Thin-Walled Struct. 64 (2013) 73–82 https://doi.org/10.1016/j.tws.2012.12.007. H.Y. Ban, G. Shi, Y.J. Shi, Y.Q. Wang, Residual stress tests of high-strength steel equal angles, J. Struct. Eng. 138 (12) (2012) 1446–1454 https://doi.org/10.1061/ (ASCE)ST.1943-541X.0000585. M. Jandera, L. Gardner, J. Machacek, Residual stress in cold-rolled stainless steel hollow sections, J. Constr. Steel Res. 64 (2008) 1255–1263 https://doi.org/10. 1016/j.jcsr.2008.07.022. P.J. Withers, H.K.D.H. Bhadeshia, Residual stress: Part 1: Measurement techniques, Mater. Sci. Technol. 17 (2001) 355–365 https://doi.org/10.1179/ 026708301101509980. GB 50661, Code for Welding of Steel Structures, China Architecture & Building Press, Beijing, 2011 2011 (in Chinese). GB/T 2975, Steel and Steel Products-Location and Preparation of Test Pieces for Mechanical Testing, Standard Press of China, Beijing, 1998. ISO 6892-1, Metallic Materials-Tensile Testing-Part 1: Method of Test at Room Temperature, BSI Standards Publication, 2016 2016. GB/T 228.1, Metallic Materials-Tensile Testing at Ambient Temperature, Standard Press of Ching, Beijing, 2010. CB/T 3395, Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method, China State Shipbuilding Corporation, Beijing, China, 2013. J. Chen, The stability calculation for steel circular tube columns under eccentric loads, J. Xi'an Univ. Archit. Technol. 3 (1982) 1–12.

A, B: Calibration coefficients D: Specimen diameter d: Blind hole diameter E: Elastic modulus L: Specimen length r1, r2: Distances from blind hole center to far and near ends of strain gauge, respectively t: Specimen thickness Δεi': Measured total strain εm: Additional strain due to cutter cutting and squeezing around edge of hole Δεi: Measured relieved strain ε1, ε2: Measured relieved strain on calibration test ϕ: Orientation angle σr: Longitudinal residual stress on horizontal cross-section σy: Steel yield stress σ1, σ2: Maximum and minimum principle stresses εd: Drilling plastic strain εs: Stress concentration plastic strain θ: Angle between weld seam center and measuring point NSS: Normal-strength steel HSS: High-strength steel SAW: Submerged arc welding HFW: High-frequency welding HR: Hot-rolling

12