Experimental and numerical study on tensile properties of bolted GFRP joints at high and low temperatures

： This paper presents both experimental and numerical studies on bolted glass fiber reinforced polymer (GFRP) joints subjected to uniaxial tension and different thermal conditions (-20 ℃ , 20 ℃ and 60 ℃ ). Laboratory tests are conducted to obtain strength, elastic modulus and deformation of the joints. The numerical model is developed using the discrete element method (DEM) that can predict not only the above properties of the joints, but also the failure modes with detailed meso/micro damages that are in consistent with the observations from the tests. The DEM model is also used in the parametric studies to study the influence of the end distance to bolt/hole diameter ratio and the lap width to bolt/hole diameter ratio on the properties and failure models of the joints.


Introduction
Fiber reinforced polymer (FRP) is a new high-performance material made of matrix material (such as epoxy resin, polyester resin, etc.) and fiber material (such as glass fiber, carbon fiber, etc.) mixed in a certain proportion and compounded by extrusion, drawing and other processes [1,2] . Since the 1970s, FRP has been gradually used as the critical components of building and bridge structures [3][4][5][6] . In recent years, GFRP has been increasingly used in building structures as load-bearing materials. These structures usually use bolted joints to transfer internal load between components, with the advantages of easy assembly, dis-assembly, and maintenance. Pultruded GFRP is an orthotropic elastic-brittle material. The load transfer and failure of a bolted GRFP joint are more complex than those of a steel connection, more than half of the failures of which occur in the connection part [7,8] . In addition, with the frequent occurrence of extreme weather around the world, the components used in civil engineering generally exposed to severe environment, resulting in great changes in the ambient temperature. For example, in some African countries, the temperature of structures exposed to the outdoor may experience to temperature exceeding 50 ℃, while in some Asia countries, the temperature in winter is also below 0 ℃. The ambient temperature inevitably affects the performance of the composites [9][10][11] . Previous studies have also showed that the material properties of GFRP, such as microstructure and failure mode [12] , strength, stiffness [9,13] and shear behaviour [14] , etc., changed greatly at high and low temperatures. Therefore, it is practically important to study the failure characteristics and mechanical responses of bolted GFRP joints under a full range of service temperature range.
Construction and building materials need to meet the requirements of bearing capacity and deformation under normal service conditions. A number of studies have been carried out on the mechanical properties of composite laminates and bolted joints of different geometry and under different temperature conditions [15][16][17][18] .
Abd-El-Naby and Hollaway [19,20] conducted a series of tensile tests on single and double bolts, considering mainly the influence of the area of plates, the clamping area of bolts, as well as the influence of end distance to bolt on the strength. Turvey [21,22] tested pultruded GFRP materials, bolted joints and sub-structures/full-scale structures subjected to tensile, compressive, bending, buckling and collapse loads. Liu et al [23] conducted tensile tests on pultrusion GFRP single-lap single-bolt connections for various bolt-diameter to plate-thickness ratio, splice plate configurations and loading directions. P.V. Inbanaathan et al. [24] carried out tensile and flexural tests on GFRP laminates and bonded joints to obtain the ultimate tensile strength, stress strain curves and the flexural modulus. Yang et al. [25] presented the mechanical performances of the single-bolted double-lap joints with steel bolts by torque-preload and tensile experiments. The results of these investigations show that the size and shape of components have a significant effect on the test results. In addition, temperature conditions were also considered in some of the reported research. Bai et al. [26] conducted axial compression experiments on GFRP laminates under elevated temperatures, and compared the failure mode at different temperatures. Cooper and Turvey et al. [27][28][29] studied the bearing capacity and deformation of pultruded GFRP single-bolt joints of different lap width to bolt / hole diameter ratios (W/D), end distance to bolt / hole diameter ratios (E/D) when they were under four different test temperatures. Toubia et al. [30] evaluated the residual strengths and failure mechanisms 2 of bolted double lap pultruded joints in regions of low-to-moderate heat induced exposure.
The above research studied mainly the failure modes of the joints and the influence of some design factors from experimental observations. In order to have a better understanding of the failure of GFRP joints and take full advantages of GFRP in practical design, further numerical research into the failure mechanism, including the consideration of temperature, is required [31,32] . Traditional finite element methods are usually used to predict crack initiation and stress distribution, but due to the inherited limitations of classical continuum mechanics, it is difficult to simulate the process of dynamic damage formation and propagation. The non-homogeneous multiphase structure of GFRP leads to the complexity of component failure. It has been shown that discrete element method has advantages in tracking the failure path and predicting the final failure strength at both mesoand micro-scale [33,34] .
In this respect, with the help of discrete element method, Maheo et al. [35] simulated the failure of composites under uniaxial tensile load, Le et al. [36] simulated the delamination, matrix cracking and fiber fracture of FRP laminates. Thus, using the micro modeling method, DEM can effectively determine initial crack and matrix crack distribution [37,38] . To the authors' best knowledge, only a few studies have used DEM to simulate materials of larger scale [35,37,39,40] . Zha et al. [41] simulated the failure of metal sandwich plate under uniform pressure with DEM. Yu et al. [42] first tried to simulate bolted joints by DEM and present a procedure to calibrate the micromechanical parameters of the model subjected to axial tension at room temperature. The research has shown great potential of the DEM model in predicting strength of composite materials and structures and presenting detailed local damage and damage propagation at micro-scale. This paper develops the model further to study the uniaxial tensile mechanical properties of bolted GFRP joints at high and low temperatures.
Experimental tests are carried out to calibrate the microscopic mechanical parameters for using the discrete element model at high and low temperatures. Geometric parameters of the bolts considered in the study include end distance to bolt/hole diameter ratio (E/D) and lap width to bolt/hole diameter ratio (W/D). Finally, the failure mechanism of the bolted GFRP joints at different temperatures is studied.

Tensile tests at high and low temperatures
In order to study the effect of the normal service temperature on the mechanical properties of bolted GFRP joints, tensile properties of bolted joints with end distance of 25 mm are tested at -20 ℃, 20 ℃ and 60 ℃. The bolts of the joints are toque to 3 N-m, which is sufficient to secure the integrity of the joints and enables to qualify the lower bound load capacity of the joints. The mechanical properties and failure modes of the bolted joints at high and low temperatures are obtained by video measurement system, and the influence of temperatures on the GFRP laminates and the bolted GFRP joints is analyzed.

Specimen details
The test specimens are EXTREN®500 series pultruded GFRP laminates manufactured by Stronwell, UK.
The weight percentages of glass fibers and resin are about 30% and 70%, respectively. The glass fibers in the samples are in the form of unidirectional parallel fiber roving (UPFR) and continuous filament mat (CFM) [42] , which determine the rigidity and ultimate stress along the fiber direction, and the properties of the specimens in 3 the transverse (perpendicular to the fiber) direction. The type of the matrix resin is polyester. The maximum recommended operating temperature for GFRP pultrusion is 65 ℃, as it is about the point the matrix changes phase from solid to flow. Laminates with fiber orientation of 0° and 90° and single bolted joints consisting of two laminates with fiber orientation of 0° are tested in this study. The illustrative diagram and dimension of the GFRP samples are shown in Fig. 1 and Table 1, respectively, and the sample dimensions are based on BS 2782 and the specifications defined in [43].   25 10 In Table 1, the sample ID in the first column shows the type of the samples and the test temperature. L and J denote, respectively, laminates and bolted joints. X and Y refer to the fiber direction of 0° and 90°. N and P indicate whether the test temperature is Negative or Positive. For example, LX-N20 represents a laminate with fiber orientation of 0° that is tested under an environmental temperature of -20 o C.

Experimental set-up and procedure
As shown in Fig. 2, the electric furnace is used to heat and control the temperature of the specimen. The 30 tons universal testing machine is used to apply loading, and the non-contact video measuring system is used to measure the deformation. The IMETRUM non-contact video gauge (video gauge5.0) has an accuracy of up to 1 μm, which can track more than 100 target points at the same time and perform dynamic real-time analysis with measurement frequency of over 400Hz. The non-contact video measuring system is also used in the previous work [42] , where detailed settings for the tests can be found. In this paper a specifically designed arrangement for the lamp belts and mirrors is used to simultaneously measure the deformation on the front and side of the joints to capture their complex 3D deformation. Considering that the video measuring instrument is sensitive to light intensity, two high and low temperature resistant lamp belts are configured to reduce reflection, thus providing The surface of the specimen is pretreated and marked with speckles and lines for strain measurement and identification of measuring points. Two high speed cameras are used, one of which is aimed at the front of the specimen, and the other records the side of the specimen through the reflection of the mirror installed in the furnace as shown in Fig. 2(b). The video measuring system is turned on before the furnace is heated, so that the deformation of the specimen during the stage of rising temperatures can be observed in real time. After the displacement-time curve is stabilized, a tensile load at a rate of 1 mm / min is applied until the specimen fails.
During the loading process, the temperature fluctuation is controlled within ±1 ℃. The real time data, including deformation, strain and temperature, are collected by the system ready for further analysis. The images of the damaged specimens are taken after the specimens are cooled down.  In order to study the failure mechanism of the bolted joints at different temperatures, the non-contact video measuring instrument introduced in the last section was again used to record the damage evolution of the front and the side surface of the joints at different temperatures, as shown in Fig. 6 and Fig. 7 respectively.  respectively. The peak stress at -20 o C is 11% higher than that at 20 o C, with a lower ductility. At 60 o C, the peak stress of the bolted joint is 20% lower than that at 20 o C, but with a much higher ductility. The peak strains before failure are 0.016, 0.022 and 0.038 respectively. Compared with 20 o C, the peak strain at -20 o C and 60 o C are increased by -24% and +76%, respectively. The elastic modulus at -20 o C and 60 o C increased by +52% and -47% respectively compared with normal temperature.

Strength and deformation
Under the three temperatures, the cracks of the bolted joints start from different positions around the hole and develop along different paths, producing three different failure modes, namely delamination failure, splitting failure and shear failure, which shows that temperature has a great influence on the failure mode of the bolted joints. This also means that the tensile failure mechanism of the bolted joints subjected to different temperatures is also different. Comparing the tensile properties of the bolted joints at -20 o C and 60 o C to those at 20 ℃, it appears that the properties of the bolted joints are more sensitive to a temperature increase.
As the temperature increases, the reinforcing effect of the fibers in the material decreases gradually, and the elastic modulus and peak stress also decrease. The strain of the laminates at failure is minimal at a lower temperature, and increases with the increase of temperature. This is because with the increase of temperature, the matrix material of the laminate becomes softer and the fracture strain increases, resulting in an increase in the overall strain of the bolted joints. While at a lower temperature, the matrix material becomes more brittle and the overall fracture strain decreases, resulting in a reduction in the strain of the bolted joints.
The above test results will be used in the following section to calibrate the micro parameter for the discrete element numerical model.  [38] concluded that the extended two-dimensional hexagons and squares have better simulation results for composite laminates. Therefore, the laminate model in this paper selects a regular square arrangement, with particles arranged orthogonally and of the same size. The fiber and matrix are homogenized with anisotropy properties, as shown in Fig. 9(a). The contacts between particles are the linear parallel-bond, which can transmit both force and moment across the interfaces. The damping coefficient of the model is set to be 0.5 to approimate the quasi-static conditions. The bolted joint to be modelled is composed of two laminated plates that are jointed together with a metal bolt of diameter 10mm, as shown in Fig. 9(b). In order to reduce the complexity of the model, the small tightness generated by the bolt is ignored. The bonds between the two laminates and between the plates and the bolt are simulated by the ball-to-ball and the ball-clump model [44] , respectively, as shown in Fig. 9. The particle size of the laminates can be defined by either x y z the ratio of the width of the model to the number of particles across the width, or the ratio of the thickness of the model to the number of particles across the thickness, such that one of the ratios is an integer and the other is as close to an integer as possible. If one of the ratios is not an integer, the size of the model may be slightly smaller than the actual size of the sample, representing an approximate and conservative model of the sample. Table 2 shows that the size of the model when the width direction and the thickness direction are, respectively, exactly divided by the number of particles and the associated errors in the size of other directions. It can be seen that when the diameter is 1.25mm, the width direction is exactly divided by the number of particles while thickness of the model is 2.34% thinner than that of the sample. This causes a small error in the bearing capacity of the model, which was rectified by multiplying the stress at failure with the actual cross section area of sample.
1.25mm is selected as the diameter of the particles in the following simulation. when ̅ is 70MPa, the predicted tensile force is almost equal to the failure forced from the test (Fig. 8).

Calibration of the model at high and low temperatures
Similarly, by fixing ̅ , it is found that from Fig. 10 Table 3 shows the calibrated bond strength at different temperatures.  The failure mode of the bolted joints at 20 ℃ in Fig. 11 shows that ̅ has an important impact on the failure mode of the bolted joints. When s nxy = 20MPa, the failure mode of the bolted joints is splitting failure ( Fig. 11 (a)). With the increase of s nxy , the ratio of s nxx and s nxy decreases, and the failure mode changes from splitting failure to tensile failure ( Fig. 11 (b)). As s nxy continues to increase, the load capacity of the bolted joints increases but at a significantly reduced rate. When s nxy increases to a value that fails the bond only in the Z direction of the laminates, the failure mode changes from tensile failure to delamination failure in the Z direction ( Fig. 11 (c)). To sum up, the failure mode and ultimate peak stress of the bolted joints are different with different s nxy , which suggests that if the failure mode and peak stress of the bolted joints are known, s nxy can be determined by comparing the peak stress (Fig. 8) and failure mode from the bolted joint tensile tests and the simulation results.

Comparison between simulation and test results
After the above parametric calibration, the bolt joint is modelled by the DEM at different temperatures. The simulation results are compared with the experimental results. The simulated failure modes at different temperatures are shown in Fig. 12, which is consistent with the failure modes observed from the experiment. The top is the particle diagram, which presents the particle  At -20 ℃, 20 ℃ and 60 ℃, the difference between the peak stress from the numerical simulation and the tests is 3.2%, 4.5% and 1.5%, respectively, with good agreement of the ascending branches of the curves. In general, the model predicts smaller peak stress, especially when the temperature is higher, which is attributed mainly to the linear contact law for the bonds between particles, thus the softening of the matrix material is not considered.    Fig. 15(a). In Fig. 15, tensile and shear failure of the bonds are denoted by green and red, respectively.

Failure mechanism
It can be seen from Fig. 15 (b) that the closer to the hole, the more likely the bonds are to fracture to form cracks at -20 ℃. And through cracks (red bonds) in the XY plane (x = 0.108m, 0.110m) have clearly occurred within the laminate. At 20 ℃ (Fig. 15(c)), the internal damage in the XY plane is few, mainly concentrated around the hole, and the damage of each section also changes little in the Y direction, indicating that the bolted joint at 20 ℃ mainly occurs splitting failure. At 60 ℃, the relative displacement of each layer within the plate is not significant (Fig. 12(c)). However, the closer to the contact surface of the two plates, the wider the fracture range of the bond is ( Fig. 15 (d)). The diffuse nature of the bond damage at z = 0.004m suggests that the cracks start from the hole of the plate and gradually transfer to the outer side of the plate. And the cracks are through in the thickness direction. Although the visible cracks in the test are shear and tensile cracks, in fact, the damage is also very serious inside the plate.
In practical tests, the failure laws and processes of bolted joints cannot be visualized intuitively. Instead, 15 with the help of discrete element model, the failure processes and mechanism can be accurately simulated and revealed.

The impact of geometric design on the failure of bolted joints
Several experimental studies have shown that E/D and W/D of a bolted joint have a great impact on the failure of the joint [22,29,38,45] . Therefore, in this section, the calibrated discrete element model is used to simulate and analyze a set of bolted joints with different E/D (2,2.5,3,4,5) and W/D (3,4,5,6) at different temperatures. At -20 ℃, the simulations show delamination failure ( Fig. 16 (a)) for all the E/D considered here. However, when E/D≥ 3, transverse cracks begin to appear around the hole and become more and more obvious with the increase of E/D. The results also show that no cracks through the cross section are formed before delamination failure occurs. Compared with the side view of bolted joints, it can be seen that E/D has little effect on the rotation of bolts. 16 At 20 ℃ (Fig. 16 (b)), when E/D is less than 3, the bolted joints fail due to splitting. When E/D =2, radial cracks are formed around the hole, but the main crack is the one leading to the free edge; When E/D = 2.5, the transverse crack develops rapidly. Due to the early formation of the longitudinal crack leading to the free edge, the overall failure mode of the bolted joints is still splitting failure. When E/D ≥ 3, there fewer radial cracks around the hole, and the fracture energy is mainly dissipated through the transverse crack across the width of the laminate, thus the failure mode changes to tensile failure. Therefore, as E/D increases, the crack causing failure changes from the longitudinal to transverse crack, and the failure mode changes from splitting to tensile.

The influence of E/D
At 60 ℃, when E/D = 2 and 2.5, the bolted joints fail due to shear (Fig. 16 (c)). The particle diagram shows From the stress-strain curves of the bolted joints at different temperatures (Fig. 17) and the relationship between the peak stress and E/D (Fig. 18), it can be seen that with the increase of E/D, the peak stress and the peak strain increase. However, when E/D exceeds 3, the increase rate of the peak stress decreases. The peak stress decreases with the increase of temperature, and the ductility at 60 ℃ is much greater than that at -20 ℃ and 20 ℃. For a given temperature, the stiffness of the joints with different E/D are virtually the same in the loading stage before the maximum is reached, and are also not much different after the peak stress at 20 ℃ and 60 ℃ expect E/D=2. Therefore, it can be concluded that E/D has little effect on the elasticity and ductility of the bolted joints.   Fig.19 that any increase of the edge distance of the plate, E, does not increase the load capacity significantly after E/D reaches 2.5, especially when the temperature is higher. This is confirmed by the failure modes shown in Fig. 16 where the failure of the joints is likely to be transverse cracking when E/D is greater than 2.5, while end splitting is more likely when E/D is smaller than 2.5. From the test and simulation results of the bolted joints with different E/D (Fig. 19), E/D has little impact on the peak stress of the joints when it is greater than 2.5. Therefore, the parameter analysis of the impact of  When W/D increases to 5 or 6, there are still some interior cracks, and damage caused by bolt extrusion appears near the pressed surface of the hole. This indicates that when W/D increases, the failure of bolted joints changes from delamination failure to pressure failure at a low temperature. At 20 ℃ and 60 ℃, when W/D < 5, the bolted joints are failed by tension; When W/D = 5, pressure failure occurs at 20 ℃. At 60 ℃, tensile and shear failure coexist. When W/D > 5, the bolted joints fail due to end splitting and shear failure, respectively, at 20 ℃ and 20 60 ℃. Fig. 21 and Fig. 22 show the stress-strain relations and the peak stress of the bolted joints at different temperatures. With the increase of W/D, the peak stress increases gradually. The peak stress increases more quickly When W/D is smaller than 4. Fig. 21 shows that stiffness of the joints is almost the same for the W/D before their respective peak stress is reached, while the slop of the descending branches of the curves only shows good consistency at 60 ℃. The main reason for this observation is attributed to the fact that the influence of W/D  on the failure mode at 60 ℃ is not as great as that at the lower temperatures.

Conclusions
In this paper, tensile properties of bolted GFRP joints at high and low temperatures are tested and modeled by the discrete element method that can simulate damage of the material at meso/micro scale. The main work and conclusions are as follows: (1) The tensile tests of the bolted GFRP joints at -20 ℃, 20 ℃ and 60 ℃ have shown that temperature has a significant effect on the failure mode of the bolted joints. The three main failure modes are delamination, splitting and shear failure at -20 ℃, 20 ℃ and 60 ℃, respectively. The increase of temperature reduces the peak stress of the bolted GFRP joints, but increases their ductility. (3) The calibrated discrete element model is capable of simulating bolted GFRP joints, offering not only global predictions to, e.g., strength, stiffness, deformation, etc., but also simulations of delamination and transverse cracking that may occur simultaneously.