Experimental and numerical study on mechanical behavior of high-strength lockbolted friction grip connections

Abstract

Despite the wide application of high-strength bolts joint in steel bridges, there are still some issues with this jointing technology such as large variation in the bolt preload, looseness of the joint as well as the fatigue problem. In this study, the high-strength lockbolted friction grip (HSLFG) connections were proposed as an alternative and the experimental results indicated that HSLFG connections have comparable mechanical behavior and strength to that of high-strength bolted friction grip (HSBFG) connections. First, the experiments were carried out on four HSLFG connections and four conventional HSBFG connections, in which the mechanical properties of both connections such as the failure modes, load-bearing behavior, and load-strain relationships were obtained and compared. The experimentally results indicate that the preload of the high-strength lockbolts satisfy the requirements of Eurocode3 and JTG D64-2015. Refined finite element (FE) models were established and were verified against the experimental results which proved the FE models could effectively predict the elastic-plastic behavior and positions of rupture of the HSLFG connections. Furthermore, the parametric analysis of FE model was conducted to investigate the effect of element types, friction coefficients on the mechanical property of the HSLFG connections. This research provided a promising strategy for the development requirements of HSLFG connections in steel bridges.

Keywords

high-strength lockbolted friction grip connection high-strength bolted friction grip connection test finite element model load-bearing behavior failure modes steel bridges

Introduction

The high-strength bolts and hot-driven rivets are conventionally used for the construction of steel bridges (Kuduzovic et al., 2014; Sanclemente and Hess, 2007; Shahani and Shakeri, 2015; Zhou et al., 2018). Despite the wide application of high-strength bolts joint and hot-driven rivets joint in steel bridges, there are still some issues with these jointing technologies, such as the riveting process of hot-driven rivets is complex, inconvenient to disassemble, easy of polluting environments, large variation in preload of high-strength bolts using the torque-tightening method, the risk of self-loosening by vibration loads as well as the low fatigue resistance for vehicular loads (Ebert et al., 2017; Hobbs et al., 2000; Majzoobi et al., 2005; Noda et al., 2016). In addition, torque is an indirect measurement of the tension applied to the high-strength bolts. Different from the high-strength bolts, the tightening of the high-strength lockbolt is directly controlled by tension rather than torque (Meng, 2008). The lockbolt fastener was already invented in the 1930s and mainly used for the aviation and space industry. Later on, the lockbolt fastener has been further developed and applied in many other fields such as railway transportation, agriculture, mining, military, and steel construction (Mariam et al., 2018; Mohammad et al., 2017; Smith and Potticary, 2000). As an illustration, Figure 1 shows the application of high-strength lockbolts in a typical high-strength lockbolted friction grip (HSLFG) joint of a continuous steel-concrete composite beam bridge of Chengdu Tianfu International Airport Expressway in China. It is noted that the high-strength lockbolt is installed via a direct tension technique, in which the pin tail is pulled and the collar is fully swaged into the locking grooves (Glienke et al., 2017).

Figure 1.

HSLFG joints of continuous steel-concrete composite beam bridge.

To date, no consensus has been reached regarding the design criterion of HSLFG joints, which hinders the application of HSLFG joints in steel bridges (Glienke et al., 2020a, 2020b). In general, the lockbolted joint can be designed as either slip-resistant or bearing-type, depending on different load-bearing patterns. Deng et al. (2016) investigated the shearing behavior of lockbolted connection through static tests and identified three failure modes for this connection. Their test results indicated that lockbolted joints have the advantages of convenient installation, good anti-looseness effect, and found this type of joint worked in a pressure-bearing manner. However, the cover plates and inner plates in their test were all aluminum alloy material. Chen et al. (2018) studied the shearing performance of lockbolt connection through numerical modeling method. In their study, a numerical model considering the lockbolt preload, mesh densities, friction coefficients, and element types was established to simulate the shearing behavior of this lap connection. Meanwhile, experimental tests of the lockbolted connection were also conducted to verify the numerical model. The results indicated that the pretension of lockbolt provided very limited friction force between aluminum alloy plates. Although the lockbolted connections, normally used for aluminum alloy plates, can be designed as bearing-type, some applications call for lockbolt use in slip-resistant connections, such as lattice towers for wind turbines in Germany (Glienke et al., 2020a, 2020b). Ebert et al. (2017) experimentally compared the slip-resistant connections of both the high-strength bolts and bobtail lockbolts, which indicated that the tightening procedure for lockbolts is different from the high-strength bolts which adopt torque method. The major advantage of the tensioning method for lockbolts over high-strength bolts was that the preload shows less variation and less loss during the operation.

As a new type of connection, very limited research related to HSLFG connections have been reported publicly in the literature, while lots of research related to high-strength bolted friction grip (HSBFG) connections and riveted connections have been reported in previous investigation, and some of which are summarized as follows. Marmo (2011) conducted the experimental and numerical investigation on shear behavior of hot-driven riveting connections. They proposed a method to predict the performance of different types of riveted connections. By comparing the numerical results with the proposed theoretical equations, it was proved that their method had good accuracy and reliability. Davide et al. (2020) studied the preload of as-built hot-driven rivets extracted from an old steel bridge. Their test results showed that the larger the grip length over diameter ratio, the larger was the preload. In addition, the numerical model proposed by them could be used to predict the development of preload after rivet installation. Wang et al. (2019) presented experimental and numerical investigations on the shear behaviors of the lap connections connected by the threaded-fixed one-side bolts, and the study results showed that failure modes of the lap connection vary with the thickness of screwed shear plate. What’s more, the preload only affected the connection behavior in the initial friction and plate slipping stage, and it had insignificant effect on the failure mode and ultimate shear resistance of the lap connection. The predicted ultimate shear resistance was conservative unless on the condition that the bolt shank appeared tilting. Guo et al. (2016) conducted a testing program to assess the performance of a new occlusive high-strength bolt connection. The results revealed that the load-bearing capacity of this kind of connection was improved significantly. Kim et al. (2016) and Ahn et al. (2016) carried out a series of test to investigate the mechanical behavior of the friction connection using a high-strength bolt. The study showed that the friction resistance was reduced and the reduction ratio depended on the sectional damage level of the bolt head. Huang et al. (2010) studied the mechanical behavior of HSBFG joint numerically and experimentally, in which the slip-load relationship, force transmission, and stress distribution of this type of joint was investigated.

The discussions indicate that previous studies mainly focused on shearing behavior and preload level of HSBFG connection and little attention has been paid to the mechanical performance of the HSLFG connection under shear loads. In this study, a comprehensive study of a new type HSLFG connection is conducted through experimental tests and numerical simulations, in which the load-bearing behavior, failure modes as well as the mechanical performance has been revealed. The new type fastener is composed of a high-strength lockbolt and a collar, and the high-strength lockbolt is made of high-strength alloy steel 40CrMo and the collar is made of ML35Al.

The remainder of this article is outlined as follows. Firstly, the test program was introduced and the preload of high-strength lockbolts as well as high-strength bolts in the assembly process was obtained. Next, experiments were carried out on four HSLFG connections and four conventional HSBFG connections to investigate the mechanical performance of HSLFG connections under shear loads. The basic mechanical properties of HSLFG connections and HSBFG connections, such as the failure modes, load-bearing behavior, and load-strain relationships were compared. After that, the refined finite element (FE) models were established and were verified against the experimental results. Finally, parametric analysis of FE model was conducted to further investigate the effect of element types and friction coefficients on the mechanical property of the HSLFG connections.

Experimental program

In this section, the experimental program is introduced which include the specimen design, installing process of high-strength lockbolts as well as high-strength bolts, preload measurement, strain and displacement measurement, test setup and loading scheme, and tensile test results.

Specimen design

The load-bearing behavior of four HSLFG connections and four HSBFG connections was examined and compared through the tensile-loading tests. Figure 2 shows the operation drawing of HSLFG connection specimens. For single lapped HSLFG connection, the inner plates were 20 mm thick and 60 mm wide, and with one 26 mm diameter hole. The cover plates were 20 mm thick and 60 mm wide, and with two 26 mm diameter holes. They were cut from the same plate to give approximately equal thickness. For double lapped HSLFG connection, the inner plates were 24 mm thick and 60 mm wide, with one 26 mm diameter hole. The cover plates were 12 mm thick and 60 mm wide, and with two 26 mm diameter holes. The size of steel plates and drilled holes of HSBFG connection were the same as the HSLFG connection, and the diameter of high-strength lockbolt and the high-strength bolt is 24 mm. All steel surface of the plate was grit blasted.

Figure 2.

Operation drawing of HSLFG connection specimens (unit: mm). (a) Single lapped HSLFG connections, (b) Double lapped HSLFG connections.

Preload of high-strength lockbolts

The high-strength lockbolt used in the joint, from which the high-strength lockbolt is mainly composed of a pin and collar, see Figure 3(a). The tensile strains of the high-strength lockbolt shanks were used to control the pretension during installation. Two holes were generated at the flanged head of each high-strength lockbolt to allow the strain gauge wires pass through. The strain gauges glued to the shank are two-quarter bridges. The data acquisition system of DH3816 N was used to collect the test data. The sensitive grid size of strain gauge is 2.8 × 2 mm, and the substrate size is 6.6 × 3.2 mm. In order to minimize the influence of the cut on the preload, the strain gauges have been plastered in size 25 × 10 mm cutting plane, as shown in Figure 3(b). The mechanical principle of the high-strength lockbolt is different from the high-strength bolt in that the tightening of the high-strength lockbolt is controlled by tension rather than torque. The preload was applied with the use of a pneumatic tool (Figure 3(c)) that pulled the pin tail until the collar was swaged onto the end of the high-strength lockbolt to retain the pretension (Figure 3(d)). The assembly spacing and feasibility were considered when designing the test specimen. Before riveting the first high-strength lockbolt, both high-strength lockbolts have been preassembled, and then riveting the first and second high-strength lockbolt of a HSLFG connection with pneumatic tool in turn. The installing process of high-strength lockbolts for HSLFG connection mainly consists of four steps: firstly, the pin was inserted into the hole, and the collar was spun onto the pin; next, a puller drew the pin tail into the pneumatic tool; then, the collar was fully swaged into the locking grooves; finally, the pneumatic tool ejected the fastener and released the puller, which developed the predetermined force.

Figure 3.

Installation of high-strength lockbolts. (a) Locations of strain gauges on high-strength lockbolt, (b) Operation drawing of high-strength lockbolt (unit: mm), (c) Pneumatic tool, (d) Installing process of high-strength lockbolts.

The preload-time curves for the assembly of HSLFG connection are shown in Figure 4(a). The P_max marks the end of the cold-forming process of the collar material into the pin’s lock grooves. The residual load in the high-strength lockbolt after removing the pneumatic tool is denoted as the initial preload P_in. According to measurement results shown in Figure 4(a), the mean value of P_in was 265.1 kN, and the minimum value of P_in was 251.9 kN, which meets the requirements of CEN (2005) Eurocode3 (2005) and JTG D64-2015 (2012). The high-strength bolt was 10.9 grade M24 with hole diameter of 26 mm, and the tightening torque was applied by a torque wrench in two tightening steps. According to Technical Specification for High Strength Bolt Connections of Steel Structures (JGJ 82-2011, 2011), M_A = 386.1 Nm (= 0.55 × k_m × P_in × d) was applied during the first tightening step, and the high-strength bolts were preloaded in a second tightening step to the torque M_A = 772.2 Nm (=1.1 × k_m × P_in × d). The initialized preload P_in was determined one second after the torque wrench was removed, see Figure 4(b). From this point on, the reduction in the tightening force can be assumed to be a result of setting effects. For all specimens with the grit-blasted surface, the mean value of P_in was 278.1 kN, the target value of the preload P_in = 247.5 kN was reliably achieved. The standard deviation of the preload of HSLFG connections was 8.3 kN while the standard deviation of the preload of HSBFG connections was 15.3 kN, and therefore the results in Figure 4 demonstrated that the tensioning method used for high-strength lockbolts could result in preload with much less variation compared with that used for high-strength bolts.

Figure 4.

Preload-time curves for the assembly of test specimen. (a) HSLFG connection (a) HSBFG connection.

Strain and displacement measurement

Figure 5(a) shows the arrangement of the strain and displacement gauges used to monitor the strain and displacement of the single lapped connection (specimen SH1-1, SH1-2, SB1-1 and SB1-2) during the test. As shown in Figure 5(a), four displacement meters are implemented to measure the relative slip distance of the specimen in vertical direction, in which the displacement meters D1 and D2 were placed besides the upper part of the specimen and the displacement meters D3 and D4 were placed besides the lower part of the specimen. The D1 and D2 were used to measure the total displacement of the test specimen, and the D3 and D4 were used to measure the displacement from the center line of the test specimen to the lower clamping end. The displacement from the center line of the test specimen to the upper clamping end was deduced by subtracting the average value of the displacement meters D3 and D4 from the average value of the displacement meters D1 and D2. In addition, the accuracy of this meter is 0.001 mm. In total, 20 strain gauges, denoted as S1 to S20, were mounted at the specimen to measure the strain. Sixteen strain gauges (S1-S4, S5-S8, S9-S12, and S13-S16) were placed on cover plate of the test connection specimens, and the vertical and horizontal distance between the sensitive grid center of the strain gauge and the hole center is 20 mm. According to the strains of the strain gauges (S1-S4, S5-S8, S9-S12 and S13-S16), the stress distributions around the hole of the connection cover plates could be deduced. In addition, four strain gauges (S17-S20) were placed on inner plates. According to the strains of the strain gauges (S17-S20), the tensile load of could be deduced. The data acquisition system of DH3816 N was used to collect the test data. For the double lapped connection (specimen SH2-1, SH2-2, SB2-1 and SB2-2), the arrangement of the strain and displacement gauges is very similar to that of the single lapped connection, as shown in Figure 5(b).

Figure 5.

The arrangement of strain and displacement measurement of the test specimens (unit: mm). (a) Single lapped connection, (b) Double lapped connection.

Test setup and loading scheme

Tensile-loading tests were performed using a universal test machine with a loading capacity of 1000 kN, as shown in Figure 6. After the installation of each specimen, a trial load, which was approximately 10% of the design slip resistance, was first applied on the specimen to check the measuring equipment. All the eight specimens were tested under tension-loading until final failure, with which the changes in strength and behavior of both high-strength bolt and high-strength lockbolt could be evaluated.

Figure 6.

Test setup.

Tensile tests

All the steel plates were made of Q345qD (construction steel of bridge, the nominal yield stress of which is 345 MPa), and the material of the high-strength bolts was 10.9 grade (the nominal yield stress of which is 900 MPa, and the nominal ultimate stress of which is 1000 MPa) (GB 50017-2017, 2017). The mechanical properties of steel plates were obtained from the tensile tests (GB/T 228.1-2010, 2011). Four tensile specimens (C1-C4) were cut from steel plates, the mechanical properties of the tensile specimens are listed in Table 1, where E is the elastic modulus, f_y is the yield strength, f_u is the ultimate tensile strength, δ is the percentage elongation after fracture, and Ψ is the percentage of contraction after fracture.

Table 1.

Mechanical property of the tensile specimens.

Specimen number	E/GPa	f_y/MPa	f_u/MPa	δ/%	Ψ/%
C1	204.6	383.5	565.1	28.9	39.7
C2	210.2	367.9	569.3	26.4	35.8
C3	199.4	355.3	573.4	29.6	40.2
C4	202.5	385.7	597.9	29.7	41.3
Mean value	204.2	373.1	576.4	28.7	39.3
Standard deviation	3.9	12.4	14.7	1.3	2.1

Notes: E-Elastic modulus; f_y-Yield strength; f_u-Ultimate strength; δ-Percentage elongation; Ψ-Percentage of contraction.

Results and discussion

Failure modes of specimens

Figure 7 illustrates the typical failure modes of HSLFG connections under tensile loads, in which Figure 7(a) and (b) correspond to the specimen SH1-1 (single lapped connection) and Figure 7(c) and (d) correspond to the specimen SH2-1 (double lapped connection). When the tensile load increased to 111.3 kN, there was relative slip between the inner plate and the cover plate of SH1-1. As shown in Figure 7(a), the collar was squeezed continuously accompanied by out-of-plane deformation of the cover plate when the tensile load increased to 212.2 kN. Meanwhile, it is clearly observed from Figure 7(a) and (b) that the inner plate and the cover plate were separated, and the shank of high-strength lockbolt was sheared off parallel to the direction of tensile loading. The failure mode of specimen SH1-2 was essentially consistent with specimen SH1-1. For the specimen SH2-1, there were horizontal rupture on one side and obvious necking deformation on the other side at the net section of the downward inner plate (Figure 7(c)). What’s more, the net section of the upward inner plate has obvious necking under tensile test load. The main failure mode of specimen SH2-2 was horizontal rupture at the net section of the upward cover plate and serious necking deformation at the net section of the downward cover plate.

Figure 7.

Failure modes of HSLFG connections. (a) Deformation of SH1-1, (b) Fracture of high-strength lockbolt for SH1-1, (c) Necking deformation of net section for SH2-1, (d) Transverse fracture of inner plate for SH2-1.

Figure 8 shows the typical failure modes of HSBFG connections under tensile loads, which is essentially consistent with the HSLFG connections as shown in Figure 7. It is noted that when the tensile load increased to 278.1 kN, the plate was seriously warped and deformed (Figure 8(a)), after which a loud sound suddenly occurred during the tensile-loading test owing to the first thread of the downward high-strength bolt fracture failure. As shown in Figure 8(b), the smooth surface emerged around the drilled hole due to friction and slip. In addition, for the specimen SB2-1, there was squeezed sharply in front of the hole accompanied by shear fracture of high-strength bolt, and downward cover plate failed by tensile net-section fracture in the horizontal direction of loading, as shown in Figure 8(c) and (d).

Figure 8.

Failure modes of HSBFG connections. (a) Warping deformation of steel plates for SB1-1, (b) Fracture of high-strength bolt for SB1-1, (c) Horizontal rupture of cover plate for SB2-1, (d) Fracture of high-strength bolt for SB2-1.

According to the experimentally results, the typical failure modes of HSLFG connection under shear force involve with: rupture of high-strength lockbolt as depicted in Figure 9(a) and horizontal rupture of net cross-section as depicted Figure 9(b). It should also be noted that various degrees of bearing deformation at the lockbolt hole can be observed during the failure process. In addition, it was found that the failure position of high-strength bolt is at the thread, the failure position of high-strength lockbolt is at the shank, and the locking groove did not fracture. On the whole, there is no substantial difference between the failure modes of HSLFG connection and HSBFG connection.

Figure 9.

Typical failure modes of HSLFG connection. (a) Shear failure of high-strength lockbolt, (b) Horizontal rupture of net cross-section.

Load-displacement curves

According to the experimental results, the load-displacement curves of HSLFG and HSBFG connection specimens share some similarities, and the load-displacement curves of both HSLFG connection and HSBFG connection undergo three different stages, that is, the friction stage (Figure 10(c), OA), the slip stage (Figure 10(c), AB), the bearing and failure stage (Figure 10(c), BC), during the loading process, as shown in Figure 10. In the friction stage, the tensile loading is transmitted through static friction, and the steel plates deform elastically. At this stage of loading, the load-displacement curves are almost linear. Moreover, when the tensile loading exceeds the slip resistant of HSLFG/HSBFG connection specimens, relative slip appears between inner plate and cover plate. In the third stage, the tension load is begin transmitting by the bearing pressure between the lockbolt/bolt hole and the lockbolt/bolt shank, and the local plastic deformation appears in steel plate and lockbolt/bolt with load increment. Before the HSLFG/HSBFG connection failure, the slope of the load-displacement curve is close to zero. Finally, the lockbolt/bolt is ruptured. However, somewhat difference of slip position and ultimate bearing position between the HSLFG connection and HSBFG connection can also be observed from the load-displacement curves, which may be due to the specimen differences in fastener types, fastener preload and the fracture position.

Figure 10.

Load-displacement curves of specimens. (a) SH1-1, (b) SH1-2, (c) SH2-1, (d) SH2-2, (e) SB1-1, (f) SB1-2, (g) SB2-1, (h) SB2-2.

According to the tensile test results, HSLFG connections have comparable mechanical behavior and strength to that of HSBFG connections, and it is obvious that this type of HSLFG connection actually works in a friction manner. The slip resistance F_s, ultimate load F_u and its deformation Δ_u, failure modes of each specimen are summarized in Table 2. The schematic of failure modes is plotted in Figure 9. Because the bearing-type connections are not suitable for the dynamic load directly, the slip-resistance connections are mostly used in the steel bridges. It indicates that the terminal value of friction stage can be adopted as the design bearing capacity of the HSLFG connection. In this case, the ratio of ultimate bearing capacity and slip resistance of single lapped and double lapped HSLFG connections are 2.70 and 2.74. As shown in Table 2, the standard deviation of the slip resistance of the HSLFG connections is lower than that of corresponding HSBFG connections, and which the results in Figure 4 can also reveal this conclusion.

Table 2.

Load-bearing behavior, deformation and failure modes of test specimens.

Specimen number	F_s/kN	Mean F_s/kN	Standard deviation of F_s/kN	F_u/kN	Mean F_u/kN	Standard deviation of F_u/kN	F_u/F_s	Δ_u/mm	Failure modes
SH1-1	111.3	108.1	3.2	289.4	291.3	1.90	2.60	22.1	a
SH1-2	104.9	108.1	3.2	293.2	291.3	1.90	2.80	24.1	a
SB1-1	130.9	124.4	6.5	279.8	280.5	0.65	2.14	24.2	a
SB1-2	117.9	124.4	6.5	281.1	280.5	0.65	2.38	21.9	a
SH2-1	154.3	173.7	19.4	464.4	471.2	6.75	3.01	28.3	b
SH2-2	193.1	173.7	19.4	477.9	471.2	6.75	2.47	24.2	b
SB2-1	233.4	202.9	30.6	464.1	464.3	0.15	1.99	28.4	a and b
SB2-2	172.3	202.9	30.6	464.4	464.3	0.15	2.70	27.4	b

Notes: F_s-Slip resistance; F_u-Ultimate bearing capacity; Δ_u-Deformation.

Load-strain curves

The load-strain curves of the test specimens are plotted in Figure 11. At the friction stage of specimen SH1-2, the cover plate strain was small, and the load-strain curves of the symmetrical strain gauges, that is, S1 and S2, S3, and S4, were almost completely overlap (Figure 11(a)). In addition, at slip stage, there were multiple relative slips between the inner plate and the cover plate. The net cross-section was converted from a uniform force to a larger load at the hole and the stress at the measuring point of the cover plate was redistributed. Before the failure of HSLFG connection SH1-2, the load-strain curves became flat, implying the plastic was developed on the cover plates. For the test specimen SB1-1 as shown in Figure 11(b), the load-strain curve of strain measurement points S3 and S4 did not completely overlap in the elastic stage, but the trend was the same. This might due to the defects during the manufacturing processing of the specimen or a slight eccentricity of the applied tensile load. At the loading level of 256.2 kN, the measurement points S3 and S4 of SB1-1 cover plate were −1677.3 με and −1901.0 με while the SH1-2 cover plate were −3104.8 με and −4869.0 με, respectively, indicating that SH1-2 was warped more severely than SB1-1. This also demonstrated that the secondary effect has more significant influence on the single lapped HSLFG connections than single lapped HSBFG connection.

Figure 11.

Load-strain curves obtained from the test specimens. (a) SH1-2, (b) SB1-1, (c) SH2-2, (d) SB2-1.

As shown in Figure 11(c), when the applied load continued to increase and at the range of 193.1–203.2 kN, multiple relative slips between the inner plate and the cover plate occurred, resulting in multiple stress redistributions. Moreover, due to the minor assembly errors of the symmetrical position of the test specimen, the strain of the measuring points S1 and S2 of SB2-1 cover plate had a certain degree of difference, and the strain after slipped differ greatly, as shown in Figure 11(d). When the tensile load at 385.6 kN, the measurement points S3 and S4 of SB2-1 cover plate were 1407.4 με and 810.3 με while the SH2-2 cover plate were 2511.2 με and 3486.5 με respectively. It was obvious that the strains of the HSLFG connection SH2-2 were much larger than that of the HSBFG connection SB2-2, and this might be caused by the difference of horizontal rupture position between SH2-2 and SB2-1. In addition, the difference in preload between the high-strength lockbolts and the high-strength bolts also caused different strain at the cover plate.

Numerical study and discussions

Finite element model simplification and mesh

For a better understanding on the mechanical behavior of the HSLFG connection, the refined FE analysis has been carried out using the commercial software ABAQUS 6.14/standard (2014). Due to the geometric symmetry of the specimen as well as its load and boundary condition, only half model of the specimen were established, in order to balance the accuracy and computational cost, as shown in Figure 13(a). As such the specimen is the modeled using the 3D 8-nodes solid elements C3D8R (Wang et al., 2019) in combination with the hexahedral meshing. In addition, the option of reduced integral has been activated to further improve the computational efficiency (Cho and Kim, 2016). During the modeling, the neutral axis algorithm was used to obtain a higher quality grid of the FE model. Considering the stress distribution in the vicinity of the hole is of particular interest in the study, refined meshing has been applied around the hole with a minimum element size of 1.8 mm. Away from the hole, the element size of the steel plate is gradually increased to 10 mm. Additionally, the high-strength lockbolt and collar were also established with a refined model with maximum element size of 3.9 mm and 2.3 mm, respectively.

Material properties

The nominal stress-strain relationship can be obtained from tensile tests by dividing the applied force by the cross-sectional area. However, it does not give a true reflection of the material behavior of steels at large deformations since the change in the area is ignored (Kim and Kuwamura, 2007). To this end, the true stress and strain are considered in this study, as shown in equations (1)–(2).

σ_{t} = σ_{n} (1 + ε_{t})

(1)

ε_{t} = ln (1 + ε_{n})

(2)

where σ_t and σ_n are, respectively, the true stress and nominal stress; ε_t and ε_n are the true strain and the nominal strain, respectively.

Since elastic-to-plastic behavior is involved in the FE analysis, the plastic true strain is applied instead of total true strain, as shown in equation (3).

ε_{p l} = ε_{t} - ε_{e t} = ε_{t} - σ_{t} / E

(3)

where ε_pl and ε_t represent the true plastic strain and total true strain; ε_et is the true elastic strain; E stands for the elastic modulus.

The behavior of Q345qD steel was simulated through the tri-linear elastic-plastic model (Ma et al., 2020) shown in Figure 12(a), which was determined by equations (1)–(3). In addition, the high-strength lockbolt was made of 40CrMo (GB/T 36993-2018, 2019) while the collar was made of ML35Al (GB/T 36993-2018, 2019), and their material behavior has been simulated by the bilinear elastic-plastic model shown in Figure 12(b). Meanwhile, the kinematic hardening criterion has been adopted in combination with the von Mises yield criterion.

Figure 12.

Constitutive model of HSLFG connections. (a) Constitutive model of steel, (b) Constitutive model of high-strength lockbolt.

Contact behavior & Boundary condition

The contact behavior has been considered for the interfaces between the cover plate, inner plate, and high-strength lockbolt. The face-to-face hard contact algorithm (Wulan et al., 2018) has been employed in accordance with the friction coefficient of 0.5 (JTG D64-2015, 2012). To this end, only the compressive contact force can be transferred between the two objects while separation is allowed. The slip formula was finite slip and the discretization method was surface to surface (Lacey et al., 2019). In case of the connection between the shank and collar, the binding algorithm has been adopted, through which the displacement of nodes on the contact surface is compatible. Figure 13(b) illustrates the contact interfaces of the HSLFG connection in the FE model.

Figure 13.

FE model. (a) The element size of FE model, (b) Contact interfaces of HSLFG connection, (c) Boundary conditions of HSLFG connection, (d) Preload of high-strength lockbolt.

The boundary conditions of the FE model are shown in the Figure 13(c). On the clamping part, the model is fully constraint at the end of the cover plate. Since the 1/2 model has been employed to utilize the symmetry, the y-z section of the cover plate has been constrained with the symmetry condition. Meanwhile, the load is applied in the displacement-controlled way (Lyu et al., 2020) to simulate the actual loading process in the test. The clamping part of the cover plate has been coupled at a virtual reference point located at the center. The reference point is then constraint with all the degree of freedom except the displacement in the x-direction, that is, the loading direction.

Preload of high-strength lockbolt

The preload in the high-strength lockbolt has been applied using the bolt load tool in the Abaqus/Standard solver, as shown in Figure 13(d). During the simulation, a total of two solution steps have been used, including: (1) the preloading of high-strength lockbolts in the first analysis step, of which the result is set as the initial stress condition for the next step; (2) the application of displacement-controlled load in the second step.

Validation of the FE Model

The established FE model has been verified against the experimental results, in terms of the failure modes and load-displacement relationship. The single lapped and double lapped HSLFG connections were selected to demonstrate the validation process. Figure 14 shows the comparison of the load-displacement curves obtained from the test and the FE analysis. It is observed from Figure 14 that, by introducing the elastic-plastic constitutive model and contact interaction, the numerical derived load-displacement relationship matches quite well with the experimental results. This indicates that the proposed FE model is able to predict the elastic-plastic behavior of the specimen.

Figure 14.

Load-displacement curves comparison between experimental and FE analysis. (a) Single lapped HSLFG connections, (b) Double lapped HSLFG connections.

For better comparison, Table 3 summarizes a list of load-bearing behavior from the test and FE analysis. The result shows that except for slip resistance of double lapped HSLFG connection whose difference between the test and numerical result reaches up to −17.3%, the differences of all the other key indices between the test and numerical results are less than 6.3%. The relative difference between the numerical and test results may be due to minor fabrication errors and unintended introduction of friction in the experiment.

Table 3.

The feature point of load-displacement curve obtained from numerical and test results.

Specimen number	Slip resistance		Ultimate bearing capacity		F_{S, FEM} -F_{S, Test}	F_{U, FEM} -F_{U, Test}
Specimen number	F_{S, Test}/kN	F_{S, FEM}/kN	F_{U, Test}/kN	F_{U, FEM}/kN	/F_{S, Test} (%)	/F_{U, Test} (%)
SH1-1	111.3	114.9	289.4	307.0	6.3	5.4
SH1-2	104.9	114.9	293.2	307.0	6.3	5.4
SH2-1	154.3	143.6	464.4	491.8	−17.3	4.4
SH2-2	193.1	143.6	477.9	491.8	−17.3	4.4

Note: F_S-Slip resistance; F_U-Ultimate bearing capacity; Test-Test value; FEM-Finite element model value.

Further comparison has been made on the failure modes between FE prediction and experiment result, as shown in Figure 15. The result also suggests a high similarity between the prediction and test. Especially, in the single lapped HSLFG connection, the out-of-plane deformation of the cover plate is well simulated by the numerical model. Meanwhile, the comparison in terms of the double lapped HSLFG connection also suggests a high similarity between the test and numerical analysis. For instance, the FE analysis indicates the failure of horizontal rupture, the plastic extrusion in front of the hole, and necking deformation at the net section, which are observed in the test. Based on the above comparisons, the established FE model is effective to reflect the mechanical behavior of the HSLFG connection.

Figure 15.

Failure modes comparison between test and FE analysis. (a) SH1-1, (b) SH2-1.

Axial stress analysis of shank

Figure 16 shows the axial stress distribution along shank direction under three load-levels. For better illustration, two parallel paths have been predefined at the two opposite edges of the high-strength lockbolt shank, that is, the Path A on the upper edge and Path B on the lower edge. At the load of 50 kN in the single lapped HSLFG connection, tensile stress can be found on both the Path A and Path B, indicating that the high-strength lockbolt shank is full in tension. Meanwhile, the stress concentration can be observed in the high-strength lockbolt at the root of first lock groove near the collar, and which is 810.3 MPa at the upper edge and 847.3 MPa at the lower edge. When the load increases to 100 kN in the single lapped HSLFG connection, the upper edge near the shank root is in tension while the lower edge is in compression. However, with the increase in the distance from the shank root, the upper edge gradually becomes in compression while the lower edge transfers in tension.

Figure 16.

High-strength lockbolt axial stress-distance curves for FE analysis. (a) Single lapped connections, (b) Double lapped connections.

In the case of the double lapped HSLFG connection, when the load step increases to 60 kN, the upper edge and the lower edge of high-strength lockbolt shank are all in tension. When the load step increases to 120 kN, the high-strength lockbolt shank is in bending form, and the stress is 427.4 MPa and 37.6 MPa for upper and lower edge in the middle of shank respectively. When the loading step increases to 240 kN, the stress increased by 85.0% for lower edge in the middle of high-strength lockbolt shank while the upper edge in tension was transformed into the upper edge in compression.

Parametric analysis of FE model

Element types

The influence of element selection on the prediction result has been investigated through the comparison between the previously applied element C3D8R (with reduced linear integral) and the 3D 8-nodes hexahedral model C3D8I which enables the linear incompatible model (Hu et al., 2016). Since the additional degree of freedom is introduced in the C3D8I, a much higher accuracy can be expected in the result when the meshing distortion is not serious compared with the C3D8R (Egan et al., 2012). The FE prediction results from the model using C3D8R and the one using C3D8I are shown in the Figure 18(a) and (b). Overall, the results demonstrate the consistent trend in load-displacement curves simulated by the two elements. On this end, the element type has no significant effect on the load-displacement curves, which reflects the global behavior. However, different types of elements have a certain effect on the convergence of the FE calculation.

Moreover, further comparison has been made between the FE analysis and test, including the slip resistance and ultimate bearing capacity, as shown in Figure 17. For the slip resistance of single lapped HSLFG connections, the difference between the prediction result of C3D8R, C3D8I FE models and mean test value is 6.3%, 5.9% while the difference for ultimate bearing capacity is 5.4% and 2.7%. For the slip resistance of double lapped HSLFG connections, respectively, the difference between the prediction result of C3D8R, C3D8I FE models and mean test value is 17.3%, 15.7% while the difference value for ultimate bearing capacity is 4.4% and 3.2%. As a result, a slightly higher accuracy can be reached using the C3D8I than the C3D8R.

Figure 17.

Typical load comparison between test and FE analysis with different element types. (a) Single lapped connections, (b) Double lapped connections.

Friction coefficients

In the engineering practice of steel bridge constructions, various surface treatment methods can be applied for different purpose (Fernandez et al., 2010), which in turn results in different surface roughness condition and friction coefficients. Thus, further investigation has been made on the influence of various surface roughness condition on the load-displacement of the single lapped HSLFG connection. During the FE analysis, various combinations of friction coefficients μ₁ and μ₂ ranging from 0.2 to 0.6 are adopted, in which μ₁ denotes the friction coefficient between steel plate and μ₂ denotes the friction coefficient between high-strength lockbolt and steel plate.

As shown in the Figure 18(c), the slip resistance increases from 84.5 kN to 117.6 kN as the coefficient μ₁ increases from 0.2 to 0.6, indicating its notable effect on the slip resistance. It is interesting that the load-displacement curves predicted with different μ₁ in the FE model almost coincided at the second half of bearing and failure stage. The major reason can be attributed to the separation of steel plates at the bearing and failure stage. As a result, the effect of μ₁ on the friction force decreased gradually. Load-displacement curves of various μ₂ in the FE model are shown in the Figure 18(d). The slip resistance increases from 87.2 kN to 112.8 kN when the friction coefficient μ₂ increases from 0.2 to 0.6, thus μ₁ has more significant effect on the slip resistance of HSLFG connection than μ₂.

Figure 18.

Load-displacement curves corresponding to different parametric analysis of FE model. (a) Single lapped connection with different element types, (b) Double lapped connection with different element types, (c) Single lapped connection with different μ_1,, (d) Single lapped connection with different μ₂.

Conclusions

This research presented a comparative study on the mechanical behavior of HSLFG connections and HSBFG connections. Additionally, the results demonstrated the feasibility of using the high-strength lockbolts in steel bridges, which provided a promising strategy for the development requirements of HSLFG connections in steel bridges. The following conclusions were drawn from the study.

1. The preload of the high-strength lockbolt was found to meet the requirements of Eurocode3 and JTG D64-2015 based on the experimental results. According to the test results, the failure modes of HSLFG connections were essentially in consistent with the HSBFG connections under tensile loads, and this type of HSLFG connection actually worked in a friction manner. In addition, HSLFG connections have comparable mechanical behavior and strength to that of HSBFG connections.

2. The load-displacement curves of HSLFG connection underwent three different stages, that is, the friction stage, the slip stage, the bearing and failure stage, during the loading process. It indicated that the terminal value of friction stage could be adopted as the design bearing capacity of the HSLFG connection. In this case, the ratio of ultimate bearing capacity and slip resistance of single lapped and double lapped HSLFG connections were 2.70 and 2.74.

3. Refined FE models could effectively predict the elastic-plastic behavior and positions of rupture of the HSLFG connections, and a slightly higher accuracy could be expected using the C3D8I element compared with the C3D8R element. For the slip resistance of single lapped HSLFG connections, the difference between the prediction result of C3D8R, C3D8I FE models and mean test value was 6.3%, 5.9% while the difference for ultimate bearing capacity was 5.4% and 2.7%. For the slip resistance of double lapped HSLFG connections, the difference between the prediction result of C3D8R, C3D8I FE models and mean test value was 17.3%, 15.7% while the difference value for ultimate bearing capacity was 4.4% and 3.2%. Furthermore, the FE analysis results also showed that μ₁ has more significant effect on slip resistance of single lapped HSLFG connections than μ₂.

Footnotes

Acknowledgements

The experimental investigation referred in this paper has been conducted at Southwest Jiaotong University, China. The writers wish to express their gratitude to the group members who have conducted the experimental works.

Declaration of conflicting interests

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

Funding

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

ORCID iDs

Kaifeng Zheng

Jin Zhu

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