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Experimental and FEM analysis of AFRP strengthened short and long steel tube under axial compression
Thin-Walled Structures 139 (2019) 9–23
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Full length article
Experimental and FEM analysis of AFRP strengthened short and long steel tube under axial compression
T
⁎
Abderrahim Djerrada,b, , Feng Fana,b, Xudong Zhia,b, Qijian Wua,b a
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China
b
A R T I C LE I N FO
A B S T R A C T
Keywords: Circular hollow section Fiber-reinforced polymer FEM Axial load Load capacity Steel tube Aramid AFRP CZM Debonding
This paper presents the results of an experimental and numerical study of the behavior of circular hollow section (CHS) steel tubes strengthened by Aramid fiber-reinforced polymer (AFRP). The aramid fiber used for this experiment is available under the trade name of Kevlar 49. In this study, thin-walled circular steel tubes externally bonded with fiber in the hoop direction were tested under axial compression to examine the effects of the AFRP thickness, on their axial load carrying and shortening capacity. The three-dimensional finite element models (FEM) of AFRP strengthened circular hollow section (CHS) was developed using ANSYS Workbench Ver. 19.0 and ACP (ANSYS Composite Prep/Post) tool considering both geometric and material nonlinearities. The effects combined of AFRP damage and interlaminar failures for the bonded interface are modeled within FEM using “Hashin” failure criteria and Cohesive Zone Model (CZM), respectively, to provide an accurate simulation. The results involving the failure modes, load vs. axial shortening curve and ultimate load capacity, were obtained from the experimental and numerical simulation and compared for validation. Both the experimental and numerical results are consistent, demonstrating that AFRP external strengthening can considerably enhance the strength of steel tube columns by 96% for short tubes and 23% for long tubes using 3 mm thickness of AFRP.
1. Introduction The application of fiber reinforced polymer (FRP) such as carbon fiber-reinforced polymer (CFRP) composites and glass fiber-reinforced polymer (GFRP) composites in civil engineering for repairing, rehabilitation [1] and retrofitting metallic structures is increasingly attractive to researchers due to their in-service and high mechanical properties, including high strength and stiffness-to-weight ratio. External strengthening using FRP material significantly improves structural properties such as buckling behavior, stiffness, and load-carrying capacity. Over the past decade, many studies have been conducted to understand the behavior of FRP strengthened steel structures subjected to static axial compression loading and the results are well documented in many research articles. For example, Shatt and Fam [2–4] investigated the behavior of short SHS columns under axial compression retrofitting with CFRP in the transverse direction and found it was possible to increase the axial strength and the stiffness by delaying local and global buckling through
the confinement effects of CFRP. In another study, Teng and Hu [5] conducted axial load tests on cylindrical steel columns retrofitted with GFRP. The result shows that the ductility of the columns can be significantly improved through retrofitting in the hoop direction by delaying local buckling in the outward direction. Lam and Clark [6] showed experimentally and numerically that CFRP-retrofitting improves the load-carrying capacity with a relatively small gain in elastic stiffness. Bambach M.R et al. [7] experimentally studied steel SHS externally bonded CFRP with different slenderness ratios. The retrofitted section steel with CFRP increased the axial capacity to that of twice the capacity of the steel section without any retrofitting. Silvestre et al. [8] investigated the non-linear behavior, and load-carrying capacity of the CFRP strengthened lipped channel steel columns, and they observed a significant increase in the buckling load and improvement of the postbuckling behavior. Haedir et al. [9,10] performed experimental tests on CHS beams strengthened with CFRP to measure the influence of the slenderness ratio in bending capacity. Zhao and Zhang [11], and Teng et al. [12] have both provided a detailed review of the previous research on the use of FRP strengthening steel structures.
⁎ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China. E-mail address: [email protected] (A. Djerrad).
https://doi.org/10.1016/j.tws.2019.02.032 Received 25 September 2018; Received in revised form 25 February 2019; Accepted 25 February 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 139 (2019) 9–23
0.51 4.16 1.70 4.00 0.60 ~ ~ ~ ~ ~
CFRP GFRP GFRP CFRP + GFRP CFRP + GFRP CFRP CFRP FRP sheet strengthened circular hollow long steel tubes under axial compression FRP filament reinforced circular hollow short steel tubes under axial compression FRP jacketed circular hollow steel tubes under axial compression FRP laminates strengthened short & long square hollow steel tubes Wrap circular hollow steel tubes with FRP sheets Wrap square and circular hollow aluminum tubes with FRP laminates Wrap square hollow steel tubes with FRP laminates
0.24 2.00 0.17 2.00 0.70 1.50 0.18
~ 0.48
30 ~ 40 5 8 5 ~ 68 80 57 ~ 153 6 ~ 10
15–39% 38–60% 5–10% 18–23% 26–84% 33–170% 16–33%
The previous researchers cited above have proved that external FRP strengthening offers a significant solution to enhance the strength and rigidity of steel tubes. Some of the previous results are summarized in Table 1. While the common FRP used for strengthening in their studies were carbon (CFRP) and glass (GFRP), aramid (AFRP) was rarely taken into account. Furthermore, the recent research using AFRP for jacketing is limited to Concrete-Filled Steel (CFT), and FRP confined concrete columns. Such studies involving AFRP include Malvar et al. [13] developed a finite element model of circular and square concrete strengthened with AFRP. Experimental and numerical research by Wu et al. [14] on circular concrete columns confined by AFRP. Both of these studies demonstrated that the strength of the columns with discontinuous AFRP wrapping increased, whereas the ductility did not significantly increase. Additional research by Vincent et Ozbakkaloglu [15] on the influence of slenderness on stress-strain behavior of concrete-filled AFRP tubes, indicates that the strength and strain enhancements increased significantly with a decrease of slenderness to a certain ratio. Although research involving CFRP, GFRP, and AFRP have been promising, knowledge on the behavior of AFRP strengthened steel tubes is very limited. AFRP, compared to other commercially available fibers, are characterized by very high strength to weight ratio, a smaller density compared to CFRP and GFRP, and better properties for fireproofing, anti-impact, and anti-fatigue. The elongation-to-failure is larger compared to carbon fibers, and about half of glass fibers. This paper presents much-needed research that further studies the behavior of Aramid fiber composite materials (AFRP) in strengthening thin-walled steel tubes under static axial compression loading. The proposed model used is a circular steel hollow section strengthened using Kevlar 49. A total of 15 specimens were tested to study the structural efficiency of AFRP strengthening systems on circular hollow sections using various parameters including the effect of the thickness of AFRP layers, the thickness of the steel tube and slenderness ratio. The load-shortening, load-strain relationships were measured. Furthermore, the increase in load carrying capacities, stiffness, ductility and the failure modes of the FRP tubes were also discussed. A comparison between the control tubes and AFRP strengthened steel tubes to evaluate the performance enhancement of strengthened specimens. In addition, this study focuses on developing a three-dimensional finite element (FE) model and simulation process of AFRP strengthened circular hollow sections considering both the geometric and material nonlinearities using ANSYS Workbench 19.0 and ACP (ANSYS Composite Prep/Post) tool, to investigate its structural behavior and failure modes. FEM also take into account the combination of intralaminar damage mechanisms such as matrix cracking, fiber fracture, and interlaminar failure corresponding to debonding along the surface between steel and AFRP. The failure modes of the AFRP composite laminates are based on “Hashin Failure Criteria” and material damage evolution law. Cohesive Zone Method (CZM) have been adopted to precisely simulate the interface debonding behavior. This method has the ability to predict both crack initiation and propagation without the need to define a pre-crack. However, this method is numerically expensive and requires fine meshes size to analyze the damaged interface. The developed finite element model is validated by comparing the numerical results with experimental tests. These experimental studies using finite element software provides valuable results concerning strengthening with composite materials [22–25]. 2. Experimental program
Kumar and Senthil [16] Wu, Wang [17] Teng and Hu [5] Shaat and Fam [2,3] Gao, Balendra [18] Feng, Hu [19] Park, Yeom [20]
Composite Strengthening method Reference
Table 1 Summary of FRP strengthening columns under axial compression.
FRP thickness (mm)
Slenderness ratio kl/r (λ)
% Gain in strength (Pmax)
A. Djerrad, et al.
2.1. Test specimens To investigate the effect of AFRP strengthening steel tubes, a total of 15 specimens with and without an FRP were tested at Harbin Institute of Technology Structural and Seismic Test Center. The specimens include 12 AFRP (Kevlar 49 fiber reinforced E-51 epoxy composites) 10
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Table 2 Details of the specimens. Specimen Short Tubes S1-200-A0 S1-200-A1 S1-200-A2 S1-200-A3 S1.5-200-A0 S1.5-200-A3 S2-200-A0 S2-200-A1 S2-200-A2 Long Tubes S1-900-A1 S1-900-A2 S1-900-A3 S1.5-900-A3 S2-900-A1 S2-900-A2
Steel cross-section (OD × thickness) (mm)
FRP thickness (mm)
Specimen Length (mm)
Slenderness ratio (kl/r)
Fiber orientation
58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.5 58 × 1.5 58 × 2.0 58 × 2.0 58 × 2.0
– 1 2 3 – 3 – 1 2
200 200 200 200 200 200 200 200 200
10
– Transverse Transverse Transverse – Transverse – Transverse Transverse
58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.5 58 × 2.0 58 × 2.0
1 2 3 3 1 2
900 900 900 900 900 900
47
Transverse Transverse Transverse Transverse Transverse Transverse
The nomenclature consists of three items: The First item denotes the steel tube with the thickness, the second item indicates the length of steel tubes; Last item the letter A for AFRP followed by the FRP thickness.
2.3. Specimen preparation
strengthening circular hollow section (CHS) tested under axial compression loading, while the last 3 specimens were tested without any FRP reinforcement system. The steel tubes had an outer diameter of 58 mm. The parameters used for the tests were the thickness of FRP layer (1, 2 and 3 mm) corresponding to (4, 8 and 12 plies) respectively, the thickness of the steel tube (1.0, 1.5 and 2.0 mm) and the length of the tube (200 and 900 mm). Haedir, Zhao [21] showed that for short tubes FRP layers oriented in the transversal direction had their strength much more improved compared to the column with longitudinal layers. Therefore, based on this research, all the specimens were strengthened with AFRP in the transversal direction. The specimen details are given in Table 2.
Three circular steel tubes straight-seam welded pipes of a length of 3 m were confined with AFRP yarns using the winding filament technique by wrapping epoxy resin-impregnated with fibers in the hoop direction to form a wrap with the required thickness. Prior to warping, the top surfaces of the steel tubes were polished with sandpaper for smoothing rough surfaces and remove the dirt from the surface producing a high-energy surface. Immediate follow-up with an excess acetone cleaning to ensure that corrosion does not form and contaminate the newly exposed Steel tube and ensure a bond between steel and AFRP after that we should consider a short time as possible between the grit blasting and the initial the primer to avoid adhesive failure between Steel and FRP. The steel tubes were precisely cut to ensure flat cross-section to the required length as shown in Table 2.
2.2. Material properties Steel tube with thicknesses of 1, 1.5 and 2 mm was used as the inner layer steel formwork in this study. The mechanical properties of the steel tube were determined by of tensile coupon tests. The coupons were cut from the same original steel tube in the longitudinal direction — their dimensions conformed to the ASTM D3039. The 1 mm steel thickness tube has significantly different properties compared to 1.5 and 2 mm thickness steel. The nonlinear behavior of the steel was modeled by specifying the stress-strain curve. The measured values of the steel tubes are given in Table 3. AFRP composite used in this experiment to provide the outer layer confinement is a unidirectional aramid fiber (Kevlar 49) supplied by DuPont. The composite was made with Vf = 60% fibers and Vm= 40% epoxy matrix. The mechanical properties of the AFRP material are provided by the manufacturer. Epoxy resin E-51 based on two-component solvent-free epoxy resin was used in this study; epoxy resin mix was used to soak the fibers together and to bond them to the steel surface. Material properties of the composite are listed in Table 4 and Table 5.
2.4. Test setup and instrumentation For the short specimens eight strain gauges with four in the axial direction and four in the hoop direction, were bonded on the surface of the specimen in the mid-height of the tubes at 45° apart from each other to measure the vertical and transversal strains, for the long specimens, in addition to the mid-height gauges, two strain gauges were bonded about 50 mm from the two ends of the specimen in the vertical direction to measure any deformation that would occur in those sections. Axial shortening of the specimens was measured by using four linear variable displacement transducers (LVDTs) installed vertically on each corner of the bottom supporting steel plates as shown in Figs. 1 and 2, the average of the 4 values was determined to be the axial shortening. Also, for the long specimens, four additional LVDTs were installed horizontally at mid height to measure displacement in the transverse direction of the specimens. The strain gauges had a length of 5 mm. Measuring instrument arrangement and test setups are shown in Fig. 1 and 2. All specimens were tested using a hydraulic jack and monitored using a 500 kN capacity load cell to evaluate the load capacity under
Table 3 Material properties of steel tubes. Steel thickness (mm)
Young Modulus Es (GPa)
Yield strength Fy (MPa)
Yield strain εy (µε)
Ultimate strength Fs (MPa)
Poisson ratio υ
1.0 1.5/2.0
196 208
370 272
1992 1991
549 410
0.3 0.3
11
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140 280
The results are presented in terms of load–axial displacement curves and load-strain curves (Longitudinal and Transverse direction) for the short tubes also, load–axial and lateral displacement curves for the long tube. The behavior of AFRP strengthening steel tubes and the gains in strength and stiffness using different parameters are also discussed. 3.1. Failure modes
30
The deformation modes of the short specimens after failure for unstrengthened and strengthened tubes are shown in Figs. 3 and 4, the damage occurs mostly at approximately the mid-height while some failed at the near the ends of the specimen. This variation in failure shape may be caused by the initial geometric imperfection. After reaching the peak load, failure of the strengthened specimens was by the inward local buckling of the steel tube followed by a significant drop in the axial load. At this moment, rupture of the AFRP starts forming accompanied by a cracking sound. The direction of the rupture is related to the orientation of fibers. For specimen with 1 mm AFRP thickness, there was no major failure of the fibers except some cracking of the resin in the area where local buckling occurs Fig. 4. Also, no interlaminar debonding was directly observed, AFRP retrofitting just followed the deformation of the steel tube. For specimens with AFRP thickness of 2 and 3 mm, the fiber was damaged, and the resin breaks precisely where the local buckling of the steel tube occurs Fig. 4. For long specimens, failure was due to the global deformation of the specimen. Lateral buckling was observed at mid-height of all specimens. During the experiment, there was no sign of debonding or rupture of AFRP was observed until the specimens reached peak load. Beyond the peak load, rupture of AFRP and large deformation was observed in mid-height of the specimen and sudden drop in the axial load due to overall buckling Fig. 5(a). In specimens with AFRP thickness of 2 and 3 mm, the resin tearing and fiber rupture in the transversal direction was noticed in the stretched and compressed side, see Fig. 5(b).
1: Longitudinal Direction, 2–3: Transverse Direction. a Composition: 60% Kevlar 49 Unidirectional fibers in an epoxy matrix.
1400 2.0 2.3 79 AFRP Kevlar 49a
5.5
Out-of-plane Shear modulus G23 (GPa) In-plane Shear modulus G12, G13 (GPa) Tensile Modulus E1 (GPa)
Tensile Modulus E2, E3 (GPa)
axial compression. To have a uniform stress distribution within the cross-section, the two ends of the specimens were fixed with steel box support filled with high-strength a-gypsum. The specimens were mounted between the top fixed reaction frame and the loading actuator, centered using a laser level to avoid any eccentricity of and to ensure that load is applied vertically. The axial compressive load was applied slowly in small increments at a rate of 0.5 mm/min the specimens were then tested until failure. The strains, axial load, and axial deformation values were recorded simultaneously using a data acquisition system at regular time intervals during the tests. 3. Experimental results and discussions
Property
Table 4 Material Properties of Kevlar 49 Embedded E51-Epoxy and Hashin's damage criteria parameters.
Tensile strength T1 (MPa)
Tensile strength T2 (MPa)
Compressive strength C1 (MPa)
Compressive strength C2 (MPa)
A. Djerrad, et al.
3.2. Axial load capacities 3.2.1. Short column The axial load-shortening curves are shown in Fig. 6; the axial shortening values are the average of four vertical LVDTs. Table 6 summarizes the ultimate axial load capacity and the displacement at peak load obtained from the experimental test. Also, the percentage increases in axial load compared to the control tube. The AFRP strengthening effectiveness can be determined by examining the degrees of improvement in the ultimate load carrying capacity. As shown in Table 6 the experiment ultimate load capacity (PEXP) of the steel tube with 1 mm thickness was enhanced from 28% to 68% by AFRP retrofitting compared to control tube. For specimen S1200-A1 and S1-200-A3 increasing the thickness of AFRP by 3 times (from 1 mm to 3 mm) increases the ultimate load capacity by 31% (from 110 kN to 144 kN). For 2 mm thickness steel tube, ultimate load capacity was enhanced from 64% to 72% compared to control tube. Specimen S1.5-200-A3, with 3 mm AFRP thickness in the hoop 12
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Table 5 Epoxy resin E-51 for Cohesive interface parameters. E – Young's Modulus (GPa)
G – Shear modulus (GPa)
σult – Tensile strength (MPa)
τult – Shear strength (MPa)
GI – Mode I fracture energy (N/mm)
GII – Mode II fracture energy (N/mm)
4.21
3.16
37.38
44.76
0.36
1.33
continually increases until the specimens reached the maximum peak load, then the lateral displacement begins to increase rapidly and the load decreases until the specimen fails completely. It was observed from the results that FRP retrofitting steel tube in transverse direction (90°) is an efficient method for the enhancement of the load-carrying capacity and delaying overall buckling. Also, the lateral deformation improved with increasing of AFRP Thickness.
direction, reached the highest gain of 90% (from 68.63 kN to 134 kN) in strength compared to control steel tube. Both Table 6 and Fig. 6 shows that the ductility of the steel tube was also significantly improved by AFRP retrofitting. The axial deformation at peak load is enhanced by about 3 times. For all short specimens, it is observed that the ultimate load capacity and axial deformation capacity increased as the number of AFRP ply increases. Therefore, it was verified that AFRP retrofitting in the hoop direction (90°) contributed to increase the maximum load capacity and delay the outward local buckling of short tubes.
3.3. Strain - axial load relationship 3.3.1. Short column The axial load vs. axial/lateral strain curves of all short specimens are shown in Fig. 9. For these curves the positive strain represents elongation, and negative strain represents shortening. The strains were captured using the strain gauges; it should be noted that strain values represent only the local result where the gauges are fixed and reliant on the direction and type of failure of the specimen. So, the result may be varied if the local buckling or AFRP rupture occurs at the strain gauge location. As expected, axial strain starts increasing at an earlier stage of loading, since the load is applied in this direction. While the lateral strain starts developing at later stages of loading when the steel tube begins to dilate in the hope direction. The strain development is similar between strengthened and un-strengthened specimens. Nevertheless, strain in the un-strengthened specimens starts to increase at a lower axial load. This is reasonable since the compressive strength of un-strengthened specimens is lower than that of AFRP strengthened. For the strengthened specimens, it is observed that the longitudinal and lateral strains curves (gauge G1 and G2) behave linearly until the specimen reached about 80% of its maximum load capacity and also, for this stage, the elastic deformation seems to be reduced for the strengthened specimens compared to the control specimen. The lateral strain (gauge G2) at the ultimate load decreased with the increase of AFRP thickness, as for example, the transverse strain of specimens S1-200-A1, S1-200-A2, and S1-200-A3 at ultimate load were
3.2.2. Long column Axial load - axial displacement curves of all long specimens are shown in Fig. 7. The axial displacement values correspond to the average of four longitudinal LVDTs. Table 7 summarizes the resulting ultimate load and displacement values reached from the axial compression in the experimental test, where (PEXP) is the maximum load capacity, Ux and Uz are respectively the axial and lateral displacement at peak load. For the specimens S1-900-A1, S1-900-A2, and S1-900-A3, it can be seen that strength and stiffness of specimens increase by increasing the FRP retrofitting thickness. S1-900-A3 and S1-900-A2 specimens attained respectively 7% and 13% higher load capacity compared to S1900-A1. For the specimens with 2 mm thickness steel tube, the load capacity was enhanced by 5% and 13% compared to control tube; the results were compared to the FEM due to the leak if the experimental test for control tube. Same for the 1.5 mm thickness steel tube the load capacity improved only 10% even with 3 mm AFRP retrofitting. It was noticed that for every specimen a sudden drop in load occurs and it is caused by the AFRP failure. Fig. 8 shows the load-axial shortening and lateral displacement curves of all long specimens. The lateral displacement curves were plotted using the absolute average values of two opposite lateral LDVT in the direction where the buckling occurred at mid-height of the columns. From this curve, it can be noted that the lateral displacement
Fig. 1. Experimental setup and instrumentation for short tubes. 13
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Fig. 2. Experimental setup and instrumentation for long tubes.
3412με, 2893με and 2692με, respectively. which suggests that the AFRP retrofitting improves the stability of the specimens and can confine the outward buckling.
3.3.2. Long column Fig. 10 shows the axial load against axial and lateral strains curves of AFRP strengthened and un-strengthened specimens. The strain was measured from the gauges at the mid-height of the specimen from two opposite side in the direction where the overall buckling occurs. We can notice from the curves that at the beginning of the loading both sides (gauges G1 and G2), are compressed, while the tensile strain occurred at the hoop direction. until the specimens reach the peak load, were the specimen starts a global buckling, beyond this point, the deformations on one side (gauge G2) increase further in compression while the other side is switched to tension (gauge G1) as the loading continued. The same deformation behavior is observed for all long specimens. The axial strains decreased for the AFRP strengthened specimens compared to the control tube and also decrease with the increase of the AFRP thickness.
Steel tube
Steel tubee
1mm AFRP Ply
2 mm AFRP Ply
3 mm AFRP Ply
Fig. 4. Typical failure of short specimens.
4. Finite element modeling 4.1. Boundary conditions, load application, and mesh details To investigate the contributions of AFRP strengthening steel tube a non-linear finite element model was developed using the commercially available finite element package ANSYS Workbench V19 and ACP (ANSYS Composite Prep/Post) tool. The model considers material, geometric and contact nonlinearity. The numerical analysis results were compared with the experimental results, in terms of the axial load-
1 mm AFRP Ply
3 mm AFR RP Ply
Fig. 3. Typical failure of short specimens (Top view). 14
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a) Overall bucklingg
b) Failure of th he AFRP
Fig. 5. Typical failure of long specimens.
displacement relationship. The behavior of thin-walled steel and retrofitting material involving AFRP was modeled using a layered structural solid element SOLID185 Fig. 13(a). SOLID185 is used for 3D modeling of solid structures. The solid element is defined by 8 nodes having three degrees-of-freedom at each node: three translations in the directions x, y, and z. Also, the element can supports plasticity, large deflection and large strain capabilities as it is described in the ANSYS element library [25]. The mesh element size is chosen adequately for a better convergence without necessarily a high computational time cost. A mesh size sensitivity analysis has been performed. After the analysis, the adopted mesh size is a 2 mm × 2 mm (length-width) mesh size for short tube and 3 mm × 3 mm for the long tube Fig. 13(c). Boundaries conditions are provided in the model according to the experimental test setup, In the experiment, the support condition used for the test suggested being close to a simply supported for both ends, but, during the test of short specimens a slight rotation was observed in the bottom plate in x, y axes, the FEA simulation also indicates that a clamped - hinged support condition leads to much closer results compared to the experiment. Thus, the clamped - hinged support is assumed for short specimens Fig. 1(a) and simply supported for the long specimens Fig. 2(a). The axial compression load is applied as a displacement on the top edge of the model with a rigid behavior, and then the load was captured using a force reaction prob at the bottom edge.
Table 6 Short specimens comparison between experimental results and present FE analysis. Specimen
S1-200-A0 (Control) S1-200-A1 S1-200-A2 S1-200-A3 S1.5-200-A0 (Control) S1.5-200-A3 S2-200-A0 (Control) S2-200-A1 S2-200-A2
Load capacity % Gain or reduction
Load Ratio PEXP/ PFEA
PEXP
PFEA
85.85
86.13
Control
0.997
110.11 132.04 144.78 68.63
108.12 121.24 137.34 73.42
28.26 53.80 68.64 Control
1.018 1.089 1.054 0.935
134.94 93.41
124.83 98.58
96.62 Control
1.080 0.948
153.54 161.45
145.50 157.10
64.37 72.84 Mean COV
1.055 1.021 1.022 0.054
4.2. Material modeling The steel material was considered to be homogeneous and isotropic. The isotropic properties such as Young's modulus, Yield stress and Poisson's ratio of the steel tubes were obtained from the experimental coupon test. The nonlinear behavior of the steel was modeled by specifying the stress-strain curve defined by the multilinear isotropic
180
180
EXP S1-200-A0 EXP S1-200-A1 EXP S1-200-A2 EXP S1-200-A3
160 140
EXP S1.5-200-A0 EXP S1.5-200-A3 EXP S2-200-A0 EXP S2-200-A1 EXP S2-200-A2
160 140 120 Load (kN)
120 Load (kN)
Ultimate Load (kN)
100 80
100 80
60
60
40
40
20
20 0
0 0
5
10 15 20 25 Axial displacement (mm)
30
35
0
5
10 15 20 25 Axial displacement (mm)
Fig. 6. Load–axial displacement curves for short specimens. 15
30
35
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90
90
EXP S1-900-A1 EXP S1-900-A2 EXP S1-900-A3
80 70
70
60
60 Load (kN)
Load (kN)
EXP S2-900-A1 EXP S2-900-A2 EXP S1.5-900-A3
80
50 40
50 40
30
30
20
20
10
10
0
0
0
5
10 15 20 Axial displacement (mm)
25
30
0
a) 1 mm thickness steel tubes
5
10 15 20 Axial displacement (mm)
25
30
b) 1.5 and 2 mm thickness steel tubes
Fig. 7. Load-axial displacement curves for long specimens.
deformed geometry and mesh that are based on a deformation result from eigenvalue buckling analysis [25]. This approach is ideal to introduce initial imperfections to an otherwise perfect geometry for a nonlinear simulation. In this FE model, the first mode shape with a scaling factor of 0.1 (10% of the tube thickness) is imposed to the final geometry. The initial geometric imperfection had an important influence on the ultimate load capacity and the descending part of the loadaxial shortening relationship curves for long specimens. The load-carrying capacity decreased with the increase of the initial geometric imperfection factor; contrariwise, it didn’t have a high influence on the short tube.
hardening option in ANSYS. The AFRP composites are considered as an orthotropic material. Which means their properties are different in all directions, the material properties of AFRP are collected from the material testing data of the manufacturer. The AFRP laminates are modeled using ANSYS Composite Prep-Post (ACP) and assumed to behave linearly plastic until failure. To simulate the progressive degradation and failure behavior of AFRP, “Hashin failure criterion” have been used for damage initiation criteria (DMGI), and material property degradation method (MPDG) is used for damage evolution law, which is based on instant stiffness reduction [25]. Thus, once the stress reaches the damage limit, the stiffness is immediately reduced. The amount of stiffness reduction can be defined in between 0% and 100% of the undamaged stiffness. Here, the stiffness is assumed to be reduced by 50% for all modes [26]. In ANSYS, using engineering data module, all these parameters have been defined by the following proprieties: orthotropic elasticity, orthotropic stress and stress limits, damage initiation criteria and damage evolution law. All the material properties and model parameters for Hashin failure criteria used for the FE analysis are presented in Tables 3, 4.
4.4. Interlaminar damage interface The interlaminar damage in this model occurs in the form of debonding at the adhesive layer (referred to as “cohesive layer” hereafter) that connects the steel tube and the AFRP. The two materials are bonded to each other using E-51 epoxy resin. Thus, the cohesive layer takes the same properties of the resin. The adhesive performance of the E-51 epoxy resin used in this experiment has been tested in previous research. In this study, the Cohesive Zone Method (CZM) is used to simulate the damage and progressive failure of the cohesive layer (adhesive layer) during the debonding process. This method introduces a failure mechanism by a progressive stiffness reduction along the cohesive layer. Initially, the element is at the zero-stress. As the load is applied, cohesive zone debonding allows three distinct failure modes: Mode I (normal separation) and Mode II (shear slip) or mixed mode. The advantage of using CZM rather than other method is that there is no need
4.3. Initial imperfection The initial geometrical imperfections of the model are based on creating a small imperfection or perturbation in the mesh. This can be incorporated automatically through a linear eigenvalue buckling analysis performed into the finite element model. In practice, the first buckling mode shape is taken as the critical imperfection shape. ANSYS Workbench enables you to directly link and transfer the Table 7 Long specimens comparison between experimental results and present FE analysis. Specimen
S1-900-A0 (Control) S1-900-A1 S1-900-A2 S1-900-A3 S1.5-900-A0 (Control) S1.5-900-A3 S2-900-A0 (Control) S2-900-A1 S2-900-A2
Ultimate Load (kN) PEXP
PFEA
– 54.83 58.79 62.34 – 71.04 – 77.27 86.77
50.43 53.02 56.48 59.40 64.37 71.34 76.78 84.42 88.66
Load capacity % Gain or reduction
Axial displacement at peak load UX (mm)
Lateral displacement at peak load UZ (mm)
Load Ratio PEXP/ PFEA
Control 8.72 16.57 23.60 Control 10.36 Control 5.66 13.02
– 2.66 3.10 2.98 – 2.89 – 2.51 3.87
16
– 7.58 9.15 10.03 – 2.47 – 4.53 4.66 Mean COV
– 0.967 0.961 0.953 – 0.996 – 0.961 0.979 0.969 0.016
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90
90 EXP S1-900-A1 EXP S1-900-A2 EXP S1-900-A3
80 70
70
60
60 Load (kN)
Load (kN)
EXP S2-900-A1 EXP S2-900-A2 EXP S1.5-900-A3
80
50 40
50 40
30
30
20
20
10
10
0 0
5
10
15 20 25 30 Lateral displacement (mm)
35
40
0
45
0
a) 1 mm thickness steel tubes
5
10
15 20 25 30 Lateral displacement (mm)
35
40
45
b) 1.5 and 2 mm thickness steel tubes
Fig. 8. Load-lateral displacement curves for long specimens.
160
G1 G2
140
140
120
120 Load (kN)
Load (kN)
160
100 80 60 40 20
100 80 60
S1-200-A0 S1-200-A1 S1-200-A2 S1-200-A3
G1
40 G2
20
0
G1 G2
S2-200-A0 S2-200-A1 S2-200-A2 S1.5-200-A0 S1.5-200-A3
G1 G2
0 -8000 -6000 -4000 -2000 0 2000 4000 Longitudinal strain G1 (µe) Transveral strain G2 (µe)
-8000 -6000 -4000 -2000 Longitudinal strain G1 (µe)
a) 1 mm thickness steel tubes
0
2000 4000 6000 8000 Transveral strain G2 (µe)
b) 1.5 and 2 mm thickness steel tubes
Fig. 9. Load-strain curves for short specimens.
and AFRP using ACP module Fig. 11(3). Second, the interface is imported in structural module Fig. 11(4) and defined as bonded contact regions. Finally, a contact debonding object is specified along with the bonded contact region that intends to separate using CZM material model. The CZM material behavior is governed by bilinear tractionseparation law as described by Alfano and Crisfield [27], available in
to place an initial crack manually in the FE model. Also, the method allows several crack initiations and propagations in the cohesive layer. A detailed description of the CZM technique can be found in ANSYS Theory Manual [25]. In ANSYS Workbench, debonding behavior simulations start initially, by modeling an interface layer with zero thickness between steel
Fig. 10. Load-strain curves for long specimens at mid-length. 17
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Fig. 11. ANSYS Workbench schematic; 1. Static Structural module to run the linear elastic analysis, 2. Run a linear buckling analysis and exporting the geometry with imperfection for nonlinear analysis, 3. ACP module used to design the composite material with the required parameters, 4. Start the Nonlinear Analysis of the final model.
Fig. 12. Bilinear traction-separation laws for the adhesives. (a) normal stress vs. gap (Mode I). (b) shear stress vs. slip (Mode II).
Fig. 13. a) SOLID185 Layered Structural Solid Geometry, b) FE model with interface debonding layer (CZM), c) Detail of finite element mesh of column with initial geometric imperfection (exaggerated).
18
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Fig. 14. Comparison between experimental and FEA load vs. axial load curves (Short tubes).
19
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90
90 EXP S1-900-A1 FEA S1-900-A1 FEA S1-900-A1 (CZM)
80 70
70 60 Load (kN)
Load (kN)
60 50 40
40 30
20
20
10
10 0 0
5
10 15 20 Axial displacement (mm)
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30
0
90
5
10 15 20 Axial displacement (mm)
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30
90 EXP S1-900-A3 FEA S1-900-A3 FEA S1-900-A3 (CZM)
80 70
EXP S2-900-A1 FEA S2-900-A1 FEA S2-900-A1 (CZM)
80 70 Load (kN)
60 Load (kN)
50
30
0
50 40
60 50 40
30
30
20
20
10
10
0
0 0
5
10 15 20 Axial displacement (mm)
25
30
0
5
10 15 20 Axial displacement (mm)
25
30
90
90 EXP S2-900-A2 FEA S2-900-A2 FEA S2-900-A2 (CZM)
80 70
EXP S1.5-900-A3 FEA S1.5-900-A3 FEA S1.5-900-A3 (CZM)
80 70
60
Load (kN)
Load (kN)
EXP S1-900-A2 FEA S1-900-A2 FEA S1-900-A2 (CZM)
80
50 40
60 50 40
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30
20
20
10
10 0
0 0
5
10 15 20 Axial displacement (mm)
25
30
0
5
10 15 20 Axial displacement (mm)
25
30
Fig. 15. Comparison between experimental and FEA load vs axial load curves (Long tubes).
tolerances are specified to 0.5%. The numerical analysis of a debonding process (initiation and progression) using CZM approach is complex and computational consuming, and can result in convergence problems. To overcome the convergence difficulty the analysis required quite a large number of iterations and small mesh sizing. As a result, the analysis will run quite slowly. Also, it has been shown by Gao and Bower [28] that the convergence difficulty can be avoided by introducing a small artificial damping coefficient in the cohesive zone law that characterizes the interface. In this study, the damping coefficient was set to 0.001 which gives a stable and accurate solution.
ANSYS material data as CZM separation-distance based debonding. This material data requires the values of the maximum allowable normal stresses (σ) for mode I, and shear stresses (τ) for mode II, and the corresponding separation (δ) causing failure of the bond as shown in Fig. 12. 4.5. Nonlinear solution Nonlinear FEM is solved iteratively using the Newton-Raphson (NR) method in ANSYS. The load is applied by increments and assumed to vary linearly within each load steps. The solution performs a number of equilibrium iterations at each load increment to achieve convergence, within an adequate tolerance. Both force and displacement convergence 20
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1 mm AFRP P Ply
Stteel tube with hout Strengtthening
2 mm m AFRP Ply
3 mm AFRP P Ply
Fig. 16. Experimental and FEM typical failure mode of short specimens (failure of AFRP indicated by Hashin's damage status, 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged).
(a)
For long tubes, there was a good correlation between the experimental results and the FEM results, and the load-axis displacement curves followed the same path for all the specimens as shown in Fig. 15. The ultimate load in FEM with CZM dropped by 8% on average compared to specimens with fully bonded contact; however, there was no significant difference in the behavior of the post-peak load curve. The reason is that during the FE analysis with CZM the stress in the cohesive zone did not reach the failure limit Fig. 18(a) to initiate debonding phenomena between the steel and AFRP. From Tables 6 and 7 a good agreement is observed in load capacity, the experiment ultimate load values (PEXP) were quite similar to the ultimate load values (PFEA) obtained from FE analysis. The mean and coefficient of variance of the ratio PEXP/ PFEA were 1.022 and 0.054 respectively for short specimens, and 0.969 and 0.016 respectively for long specimens.
(b)
Fig. 17. Typical failure of the CZM interface for short tubes S2-200-A1: a) Sliding distance between AFRP and Steel, b) Contact status.
5.2. Failure mode 5. Numerical results
In addition to load-displacement curves, the final failure mode shape for un-strengthened and strengthened specimens obtained from the experimental test were similar to those obtained from the FEM analysis as shown in Figs. 16–18. The FE model is able to predict the different failure mechanisms such as FRP failure modes, which is represented by Hashin's damage status (an enum type with values of 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged) shown in Figs. 16 and 18(c, b), and also can capture the debonding damage Figs. 17 and 18(a). The failure modes included in Hashin's criteria are tensile fiber failure, compressive fiber failure, tensile matrix failure, compressive matrix failure. As can be seen in Fig. 16, for all tubes the AFRP failure location in the experimental matches with FE models. Debonding in the cohesive zone was observed for all short model this is due to the excessive deformation of the steel tube Fig. 17. The drop-in load capacity for CZM model compared to the fully bonded model can be explained by energy absorbed due to the sliding between AFRP and steel tube as shown in Fig. 18(a). From the results, it can be concluded that the FEA results matched quite well with the experimental test. Therefore, the developed FE model used for this analysis can predict the behavior of AFRP
5.1. Load-displacement curves All the findings obtained from the FE analysis are compared with the current experiments tests to verify the developed FE model. Comparison between axial load (kN) – axial displacement (mm) curves obtained from FE results and the corresponding experiment are shown in Figs. 14 and 15 for both short and long specimens. The figures also include the load-displacement curves for the FE model with a perfectly bonded contact (no-debonding allowed) and FE model with interface debonding contact. For short tubes, load-displacement curves agree perfectly between experiment and FEM that include CZM as shown Fig. 14. As it can be seen, by including the debonding behavior in the FEM a significate correlation to the experiment results is observed in post-peak load. The ultimate load decreased on average by 6% compared to the model without CZM. Specimen S1.5-200-A3 had different behavior compared to the experiment; it may be caused by the initial imperfection of the steel tube, test setup or load speed. 21
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Fig. 18. Typical failure mode of long specimens: a) Overall buckling, b) Compression side, c) Traction side, Hashin's damage status of AFRP, 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged.
strengthening thin-walled steel tubes. Including the interface debonding (CZM) in the numerical solution improved the accuracy of the results significantly however the cost in computational time was considerable. On a medium-performance PC, the average computational time for each model was 2 h for models without debonding interface and 12 h for models with CZM.
• •
6. Conclusion In this paper, 15 specimens of a thin-walled circular hollow section (CHS) steel tube strengthened with AFRP in the transverse direction subjected to a static axial compressive load. All specimens were tested to study the effect of AFRP retrofitting on maximum load carrying capacity, stiffness and failure modes. The test parameters were the thickness of AFRP ply (1, 2 and 3 mm), the thickness (1, 1.5 and 2 mm) and the length (200 mm and 900 mm) of steel tubes. Furthermore, the finite element software ANSYS Workbench ver. 19 and ACP (ANSYS Composite Prep/Post) tool were used for this nonlinear simulation to predict the behavior of AFRP strengthening steel tubes. The FE model accounts for material and geometric nonlinearities and also combines the effect of AFRP damage using “Hashin failure criteria” and interlaminar failures of the bonded interface using “Cohesive Zone Model,” to provide an accurate simulation. Based on the experimental and FEA results, the verdict was as follows:
• • • •
• The AFRP efficiency increases with the increase of the AFRP thick-
ness, and it is more distinct for specimens with small slenderness ratio than the specimens with large slenderness ratio. For short specimens, a maximum increase of 96% was reached in axial load
capacity with 3 mm of AFRP in the hoop direction. For the long specimens, the effectiveness of the AFRP is less significant, where the highest ultimate load increase is about 23% with 3 mm of AFRP. The stiffness and ductility of the FRP strengthened specimens improved considerably compared to un-strengthened specimens and also increased with the increase of AFRP thickness within the range of the parameters explored in this study. External strengthening using FRP does not change the buckling shape of the steel tube, but can effectively delay the local buckling and confine the outward one, and also delay the overall buckling of long specimens. The developed nonlinear FE model used for the analysis is successfully validated by comparing the load-displacement responses and failure modes with the experimental tests, which verifies the reliability to use the model in future analysis. The FE Model is capable of predicting load carrying capacity and AFRP failure using “Hashin damage criteria” with tolerable accuracy. The cohesive zone model (CZM) defined by bilinear traction-displacement softening law was successfully employed to capture debonding initiation and propagation between steel and AFRP accurately. The FE model can effectively simulate the specimens post-peak load behavior by taking into account the FRP debonding phenomena. However, it can be ignored for specimens with a high slenderness ratio, as the effect on the results is minimal, which can avoid a complex and time-consuming simulation.
It is evident that much more experimental tests and numerical simulations on a large number of specimens have to be performed to 22
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cover wider ranges of parameters. Future research focuses on finding an optimal strengthening combination to minimize the cost-benefit ratio, including other types of fibers (GFRP, CFRP), effects of fiber orientation, and strengthening scheme. More research is also needed to explore the behavior of AFRP strengthened thin walled tubes under impact load conditions where aramid fibers excel the most; this will be shown in a subsequent article.
Eng. Struct. 29 (8) (2007) 1808–1823. [12] J.G. Teng, T. Yu, D. Fernando, Strengthening of steel structures with fiber-reinforced polymer composites, J. Constr. Steel Res. 78 (2012) 131–143. [13] L.J. Malvar, K.B. Morrill, J.E. Crawford, Numerical modeling of concrete confined by fiber-reinforced composites, J. Compos. Constr. 8 (4) (2004) 315–322. [14] H.L. Wu, et al., Experimental and computational studies on high-strength concrete circular columns confined by aramid fiber-reinforced polymer sheets, J. Compos. Constr. 13 (2) (2009) 125–134. [15] T. Vincent, T. Ozbakkaloglu, Influence of slenderness on stress-strain behavior of concrete-filled FRP tubes: experimental study, J. Compos. Constr. 19 (1) (2015). [16] A.P. Kumar, R. Senthil, Behavior of CFRP strengthened CHS under axial static and axial cyclic loading, KSCE J. Civil. Eng. 20 (4) (2016) 1493–1500. [17] Q.J. Wu, C. Wang, X.D. Zhi, Exp. Simul. Stud. Fail. Modes GFRP-Reinf. Short. Steel Tubes axially Compress. loads. 35 (2018) 184–191. [18] X. Gao, T. Balendra, C. Koh, Buckling strength of slender circular tubular steel braces strengthened by CFRP, Eng. Struct. 46 (2013) 547–556. [19] P. Feng, et al., Buckling behavior of CFRP-aluminum alloy hybrid tubes in axial compression, Eng. Struct. 132 (2017) 624–636. [20] J.W. Park, H.J. Yeom, J.H. Yoo, Axial loading tests and FEM analysis of slender square hollow section (SHS) stub columns strengthened with carbon fiber reinforced polymers, Int. J. Steel Struct. 13 (4) (2013) 731–743. [21] J. Haedir, et al., Analysis of CFRP externally-reinforced steel CHS tubular beams, Compos. Struct. 92 (12) (2010) 2992–3001. [22] M.H. Abdallah, et al., Nonlinear finite element analysis of short and long reinforced concrete columns confined with GFRP tubes, J. Reinf. Plast. Compos. 36 (13) (2017) 972–987. [23] K.K. Bhetwal, S. Yamada, Effects of Cfrp reinforcements on the buckling behavior of thin-walled steel cylinders under compression, Int. J. Struct. Stab. Dyn. 12 (1) (2012) 131–151. [24] U. Devi, K.M. Amanat, Non-linear finite element investigation on the behavior of CFRP strengthened steel square HSS columns under compression, Int. J. Steel Struct. 15 (3) (2015) 671–680. [25] ANSYS Mechanical User’s Guide: PDF Documentation for Release 17.2. ANSYS, Inc., 2016. [26] E.J. Barbero, M. Shahbazi, Determination of material properties for ANSYS progressive damage analysis of laminated composites, Compos. Struct. 176 (2017) 768–779. [27] G. Alfano, M.A. Crisfield, Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, Int. J. Numer. Methods Eng. 50 (7) (2001) 1701–1736. [28] Y.F. Gao, A.F. Bower, A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces, Model. Simul. Mater. Sci. Eng. 12 (3) (2004) 453–463.
Acknowledgments The financial support of Chinese National Natural Science Foundation (Grant No. 51478144) is gratefully acknowledged. References [1] M. Lesani, M.R. Bahaari, M.M. Shokrieh, FRP wrapping for the rehabilitation of Circular Hollow Section (CHS) tubular steel connections, Thin-Walled Struct. 90 (2015) 216–234. [2] A. Shaat, A. Fam, Axial loading tests on short and long hollow structural steel columns retrofitted using carbon fibre reinforced polymers, Can. J. Civil. Eng. 33 (4) (2006) 458–470. [3] A. Shaat, A. Fam, Fiber-element model for slender HSS columns retrofitted with bonded high-modulus composites, J. Struct. Eng. - ASCE 133 (1) (2007) 85–95. [4] A. Shaat, A. Fam, Finite element analysis of slender HSS columns strengthened with high modulus composites, Steel Compos. Struct. 7 (1) (2007) 19–34. [5] J.G. Teng, Y.M. Hu, Behaviour of FRP-jacketed circular steel tubes and cylindrical shells under axial compression, Constr. Build. Mater. 21 (4) (2007) 827–838. [6] D. Lam, K.A. Clark, Strengthening steel sections using carbon fibre reinforced polymers laminates, Adv. Struct. Vols 1 and 2 (2003) 1369–1374. [7] M.R. Bambach, H.H. Jama, M. Elchalakani, Axial capacity and design of thin-walled steel SHS strengthened with CFRP, Thin-Walled Struct. 47 (10) (2009) 1112–1121. [8] N. Silvestre, B. Young, D. Camotim, Non-linear behaviour and load-carrying capacity of CFRP-strengthened lipped channel steel columns, Eng. Struct. 30 (10) (2008) 2613–2630. [9] J. Haedir, et al., Strength of circular hollow sections (CHS) tubular beams externally reinforced by carbon FRP sheets in pure bending, Thin-Walled Struct. 47 (10) (2009) 1136–1147. [10] J. Haedir, X.L. Zhao, Design of CFRP-strengthened steel CHS tubular beams, J. Constr. Steel Res. 72 (2012) 203–218. [11] X.L. Zhao, L. Zhang, State-of-the-art review on FRP strengthened steel structures,
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Full length article
Experimental and FEM analysis of AFRP strengthened short and long steel tube under axial compression
T
⁎
Abderrahim Djerrada,b, , Feng Fana,b, Xudong Zhia,b, Qijian Wua,b a
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China
b
A R T I C LE I N FO
A B S T R A C T
Keywords: Circular hollow section Fiber-reinforced polymer FEM Axial load Load capacity Steel tube Aramid AFRP CZM Debonding
This paper presents the results of an experimental and numerical study of the behavior of circular hollow section (CHS) steel tubes strengthened by Aramid fiber-reinforced polymer (AFRP). The aramid fiber used for this experiment is available under the trade name of Kevlar 49. In this study, thin-walled circular steel tubes externally bonded with fiber in the hoop direction were tested under axial compression to examine the effects of the AFRP thickness, on their axial load carrying and shortening capacity. The three-dimensional finite element models (FEM) of AFRP strengthened circular hollow section (CHS) was developed using ANSYS Workbench Ver. 19.0 and ACP (ANSYS Composite Prep/Post) tool considering both geometric and material nonlinearities. The effects combined of AFRP damage and interlaminar failures for the bonded interface are modeled within FEM using “Hashin” failure criteria and Cohesive Zone Model (CZM), respectively, to provide an accurate simulation. The results involving the failure modes, load vs. axial shortening curve and ultimate load capacity, were obtained from the experimental and numerical simulation and compared for validation. Both the experimental and numerical results are consistent, demonstrating that AFRP external strengthening can considerably enhance the strength of steel tube columns by 96% for short tubes and 23% for long tubes using 3 mm thickness of AFRP.
1. Introduction The application of fiber reinforced polymer (FRP) such as carbon fiber-reinforced polymer (CFRP) composites and glass fiber-reinforced polymer (GFRP) composites in civil engineering for repairing, rehabilitation [1] and retrofitting metallic structures is increasingly attractive to researchers due to their in-service and high mechanical properties, including high strength and stiffness-to-weight ratio. External strengthening using FRP material significantly improves structural properties such as buckling behavior, stiffness, and load-carrying capacity. Over the past decade, many studies have been conducted to understand the behavior of FRP strengthened steel structures subjected to static axial compression loading and the results are well documented in many research articles. For example, Shatt and Fam [2–4] investigated the behavior of short SHS columns under axial compression retrofitting with CFRP in the transverse direction and found it was possible to increase the axial strength and the stiffness by delaying local and global buckling through
the confinement effects of CFRP. In another study, Teng and Hu [5] conducted axial load tests on cylindrical steel columns retrofitted with GFRP. The result shows that the ductility of the columns can be significantly improved through retrofitting in the hoop direction by delaying local buckling in the outward direction. Lam and Clark [6] showed experimentally and numerically that CFRP-retrofitting improves the load-carrying capacity with a relatively small gain in elastic stiffness. Bambach M.R et al. [7] experimentally studied steel SHS externally bonded CFRP with different slenderness ratios. The retrofitted section steel with CFRP increased the axial capacity to that of twice the capacity of the steel section without any retrofitting. Silvestre et al. [8] investigated the non-linear behavior, and load-carrying capacity of the CFRP strengthened lipped channel steel columns, and they observed a significant increase in the buckling load and improvement of the postbuckling behavior. Haedir et al. [9,10] performed experimental tests on CHS beams strengthened with CFRP to measure the influence of the slenderness ratio in bending capacity. Zhao and Zhang [11], and Teng et al. [12] have both provided a detailed review of the previous research on the use of FRP strengthening steel structures.
⁎ Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China. E-mail address: [email protected] (A. Djerrad).
https://doi.org/10.1016/j.tws.2019.02.032 Received 25 September 2018; Received in revised form 25 February 2019; Accepted 25 February 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
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0.51 4.16 1.70 4.00 0.60 ~ ~ ~ ~ ~
CFRP GFRP GFRP CFRP + GFRP CFRP + GFRP CFRP CFRP FRP sheet strengthened circular hollow long steel tubes under axial compression FRP filament reinforced circular hollow short steel tubes under axial compression FRP jacketed circular hollow steel tubes under axial compression FRP laminates strengthened short & long square hollow steel tubes Wrap circular hollow steel tubes with FRP sheets Wrap square and circular hollow aluminum tubes with FRP laminates Wrap square hollow steel tubes with FRP laminates
0.24 2.00 0.17 2.00 0.70 1.50 0.18
~ 0.48
30 ~ 40 5 8 5 ~ 68 80 57 ~ 153 6 ~ 10
15–39% 38–60% 5–10% 18–23% 26–84% 33–170% 16–33%
The previous researchers cited above have proved that external FRP strengthening offers a significant solution to enhance the strength and rigidity of steel tubes. Some of the previous results are summarized in Table 1. While the common FRP used for strengthening in their studies were carbon (CFRP) and glass (GFRP), aramid (AFRP) was rarely taken into account. Furthermore, the recent research using AFRP for jacketing is limited to Concrete-Filled Steel (CFT), and FRP confined concrete columns. Such studies involving AFRP include Malvar et al. [13] developed a finite element model of circular and square concrete strengthened with AFRP. Experimental and numerical research by Wu et al. [14] on circular concrete columns confined by AFRP. Both of these studies demonstrated that the strength of the columns with discontinuous AFRP wrapping increased, whereas the ductility did not significantly increase. Additional research by Vincent et Ozbakkaloglu [15] on the influence of slenderness on stress-strain behavior of concrete-filled AFRP tubes, indicates that the strength and strain enhancements increased significantly with a decrease of slenderness to a certain ratio. Although research involving CFRP, GFRP, and AFRP have been promising, knowledge on the behavior of AFRP strengthened steel tubes is very limited. AFRP, compared to other commercially available fibers, are characterized by very high strength to weight ratio, a smaller density compared to CFRP and GFRP, and better properties for fireproofing, anti-impact, and anti-fatigue. The elongation-to-failure is larger compared to carbon fibers, and about half of glass fibers. This paper presents much-needed research that further studies the behavior of Aramid fiber composite materials (AFRP) in strengthening thin-walled steel tubes under static axial compression loading. The proposed model used is a circular steel hollow section strengthened using Kevlar 49. A total of 15 specimens were tested to study the structural efficiency of AFRP strengthening systems on circular hollow sections using various parameters including the effect of the thickness of AFRP layers, the thickness of the steel tube and slenderness ratio. The load-shortening, load-strain relationships were measured. Furthermore, the increase in load carrying capacities, stiffness, ductility and the failure modes of the FRP tubes were also discussed. A comparison between the control tubes and AFRP strengthened steel tubes to evaluate the performance enhancement of strengthened specimens. In addition, this study focuses on developing a three-dimensional finite element (FE) model and simulation process of AFRP strengthened circular hollow sections considering both the geometric and material nonlinearities using ANSYS Workbench 19.0 and ACP (ANSYS Composite Prep/Post) tool, to investigate its structural behavior and failure modes. FEM also take into account the combination of intralaminar damage mechanisms such as matrix cracking, fiber fracture, and interlaminar failure corresponding to debonding along the surface between steel and AFRP. The failure modes of the AFRP composite laminates are based on “Hashin Failure Criteria” and material damage evolution law. Cohesive Zone Method (CZM) have been adopted to precisely simulate the interface debonding behavior. This method has the ability to predict both crack initiation and propagation without the need to define a pre-crack. However, this method is numerically expensive and requires fine meshes size to analyze the damaged interface. The developed finite element model is validated by comparing the numerical results with experimental tests. These experimental studies using finite element software provides valuable results concerning strengthening with composite materials [22–25]. 2. Experimental program
Kumar and Senthil [16] Wu, Wang [17] Teng and Hu [5] Shaat and Fam [2,3] Gao, Balendra [18] Feng, Hu [19] Park, Yeom [20]
Composite Strengthening method Reference
Table 1 Summary of FRP strengthening columns under axial compression.
FRP thickness (mm)
Slenderness ratio kl/r (λ)
% Gain in strength (Pmax)
A. Djerrad, et al.
2.1. Test specimens To investigate the effect of AFRP strengthening steel tubes, a total of 15 specimens with and without an FRP were tested at Harbin Institute of Technology Structural and Seismic Test Center. The specimens include 12 AFRP (Kevlar 49 fiber reinforced E-51 epoxy composites) 10
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Table 2 Details of the specimens. Specimen Short Tubes S1-200-A0 S1-200-A1 S1-200-A2 S1-200-A3 S1.5-200-A0 S1.5-200-A3 S2-200-A0 S2-200-A1 S2-200-A2 Long Tubes S1-900-A1 S1-900-A2 S1-900-A3 S1.5-900-A3 S2-900-A1 S2-900-A2
Steel cross-section (OD × thickness) (mm)
FRP thickness (mm)
Specimen Length (mm)
Slenderness ratio (kl/r)
Fiber orientation
58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.5 58 × 1.5 58 × 2.0 58 × 2.0 58 × 2.0
– 1 2 3 – 3 – 1 2
200 200 200 200 200 200 200 200 200
10
– Transverse Transverse Transverse – Transverse – Transverse Transverse
58 × 1.0 58 × 1.0 58 × 1.0 58 × 1.5 58 × 2.0 58 × 2.0
1 2 3 3 1 2
900 900 900 900 900 900
47
Transverse Transverse Transverse Transverse Transverse Transverse
The nomenclature consists of three items: The First item denotes the steel tube with the thickness, the second item indicates the length of steel tubes; Last item the letter A for AFRP followed by the FRP thickness.
2.3. Specimen preparation
strengthening circular hollow section (CHS) tested under axial compression loading, while the last 3 specimens were tested without any FRP reinforcement system. The steel tubes had an outer diameter of 58 mm. The parameters used for the tests were the thickness of FRP layer (1, 2 and 3 mm) corresponding to (4, 8 and 12 plies) respectively, the thickness of the steel tube (1.0, 1.5 and 2.0 mm) and the length of the tube (200 and 900 mm). Haedir, Zhao [21] showed that for short tubes FRP layers oriented in the transversal direction had their strength much more improved compared to the column with longitudinal layers. Therefore, based on this research, all the specimens were strengthened with AFRP in the transversal direction. The specimen details are given in Table 2.
Three circular steel tubes straight-seam welded pipes of a length of 3 m were confined with AFRP yarns using the winding filament technique by wrapping epoxy resin-impregnated with fibers in the hoop direction to form a wrap with the required thickness. Prior to warping, the top surfaces of the steel tubes were polished with sandpaper for smoothing rough surfaces and remove the dirt from the surface producing a high-energy surface. Immediate follow-up with an excess acetone cleaning to ensure that corrosion does not form and contaminate the newly exposed Steel tube and ensure a bond between steel and AFRP after that we should consider a short time as possible between the grit blasting and the initial the primer to avoid adhesive failure between Steel and FRP. The steel tubes were precisely cut to ensure flat cross-section to the required length as shown in Table 2.
2.2. Material properties Steel tube with thicknesses of 1, 1.5 and 2 mm was used as the inner layer steel formwork in this study. The mechanical properties of the steel tube were determined by of tensile coupon tests. The coupons were cut from the same original steel tube in the longitudinal direction — their dimensions conformed to the ASTM D3039. The 1 mm steel thickness tube has significantly different properties compared to 1.5 and 2 mm thickness steel. The nonlinear behavior of the steel was modeled by specifying the stress-strain curve. The measured values of the steel tubes are given in Table 3. AFRP composite used in this experiment to provide the outer layer confinement is a unidirectional aramid fiber (Kevlar 49) supplied by DuPont. The composite was made with Vf = 60% fibers and Vm= 40% epoxy matrix. The mechanical properties of the AFRP material are provided by the manufacturer. Epoxy resin E-51 based on two-component solvent-free epoxy resin was used in this study; epoxy resin mix was used to soak the fibers together and to bond them to the steel surface. Material properties of the composite are listed in Table 4 and Table 5.
2.4. Test setup and instrumentation For the short specimens eight strain gauges with four in the axial direction and four in the hoop direction, were bonded on the surface of the specimen in the mid-height of the tubes at 45° apart from each other to measure the vertical and transversal strains, for the long specimens, in addition to the mid-height gauges, two strain gauges were bonded about 50 mm from the two ends of the specimen in the vertical direction to measure any deformation that would occur in those sections. Axial shortening of the specimens was measured by using four linear variable displacement transducers (LVDTs) installed vertically on each corner of the bottom supporting steel plates as shown in Figs. 1 and 2, the average of the 4 values was determined to be the axial shortening. Also, for the long specimens, four additional LVDTs were installed horizontally at mid height to measure displacement in the transverse direction of the specimens. The strain gauges had a length of 5 mm. Measuring instrument arrangement and test setups are shown in Fig. 1 and 2. All specimens were tested using a hydraulic jack and monitored using a 500 kN capacity load cell to evaluate the load capacity under
Table 3 Material properties of steel tubes. Steel thickness (mm)
Young Modulus Es (GPa)
Yield strength Fy (MPa)
Yield strain εy (µε)
Ultimate strength Fs (MPa)
Poisson ratio υ
1.0 1.5/2.0
196 208
370 272
1992 1991
549 410
0.3 0.3
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140 280
The results are presented in terms of load–axial displacement curves and load-strain curves (Longitudinal and Transverse direction) for the short tubes also, load–axial and lateral displacement curves for the long tube. The behavior of AFRP strengthening steel tubes and the gains in strength and stiffness using different parameters are also discussed. 3.1. Failure modes
30
The deformation modes of the short specimens after failure for unstrengthened and strengthened tubes are shown in Figs. 3 and 4, the damage occurs mostly at approximately the mid-height while some failed at the near the ends of the specimen. This variation in failure shape may be caused by the initial geometric imperfection. After reaching the peak load, failure of the strengthened specimens was by the inward local buckling of the steel tube followed by a significant drop in the axial load. At this moment, rupture of the AFRP starts forming accompanied by a cracking sound. The direction of the rupture is related to the orientation of fibers. For specimen with 1 mm AFRP thickness, there was no major failure of the fibers except some cracking of the resin in the area where local buckling occurs Fig. 4. Also, no interlaminar debonding was directly observed, AFRP retrofitting just followed the deformation of the steel tube. For specimens with AFRP thickness of 2 and 3 mm, the fiber was damaged, and the resin breaks precisely where the local buckling of the steel tube occurs Fig. 4. For long specimens, failure was due to the global deformation of the specimen. Lateral buckling was observed at mid-height of all specimens. During the experiment, there was no sign of debonding or rupture of AFRP was observed until the specimens reached peak load. Beyond the peak load, rupture of AFRP and large deformation was observed in mid-height of the specimen and sudden drop in the axial load due to overall buckling Fig. 5(a). In specimens with AFRP thickness of 2 and 3 mm, the resin tearing and fiber rupture in the transversal direction was noticed in the stretched and compressed side, see Fig. 5(b).
1: Longitudinal Direction, 2–3: Transverse Direction. a Composition: 60% Kevlar 49 Unidirectional fibers in an epoxy matrix.
1400 2.0 2.3 79 AFRP Kevlar 49a
5.5
Out-of-plane Shear modulus G23 (GPa) In-plane Shear modulus G12, G13 (GPa) Tensile Modulus E1 (GPa)
Tensile Modulus E2, E3 (GPa)
axial compression. To have a uniform stress distribution within the cross-section, the two ends of the specimens were fixed with steel box support filled with high-strength a-gypsum. The specimens were mounted between the top fixed reaction frame and the loading actuator, centered using a laser level to avoid any eccentricity of and to ensure that load is applied vertically. The axial compressive load was applied slowly in small increments at a rate of 0.5 mm/min the specimens were then tested until failure. The strains, axial load, and axial deformation values were recorded simultaneously using a data acquisition system at regular time intervals during the tests. 3. Experimental results and discussions
Property
Table 4 Material Properties of Kevlar 49 Embedded E51-Epoxy and Hashin's damage criteria parameters.
Tensile strength T1 (MPa)
Tensile strength T2 (MPa)
Compressive strength C1 (MPa)
Compressive strength C2 (MPa)
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3.2. Axial load capacities 3.2.1. Short column The axial load-shortening curves are shown in Fig. 6; the axial shortening values are the average of four vertical LVDTs. Table 6 summarizes the ultimate axial load capacity and the displacement at peak load obtained from the experimental test. Also, the percentage increases in axial load compared to the control tube. The AFRP strengthening effectiveness can be determined by examining the degrees of improvement in the ultimate load carrying capacity. As shown in Table 6 the experiment ultimate load capacity (PEXP) of the steel tube with 1 mm thickness was enhanced from 28% to 68% by AFRP retrofitting compared to control tube. For specimen S1200-A1 and S1-200-A3 increasing the thickness of AFRP by 3 times (from 1 mm to 3 mm) increases the ultimate load capacity by 31% (from 110 kN to 144 kN). For 2 mm thickness steel tube, ultimate load capacity was enhanced from 64% to 72% compared to control tube. Specimen S1.5-200-A3, with 3 mm AFRP thickness in the hoop 12
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Table 5 Epoxy resin E-51 for Cohesive interface parameters. E – Young's Modulus (GPa)
G – Shear modulus (GPa)
σult – Tensile strength (MPa)
τult – Shear strength (MPa)
GI – Mode I fracture energy (N/mm)
GII – Mode II fracture energy (N/mm)
4.21
3.16
37.38
44.76
0.36
1.33
continually increases until the specimens reached the maximum peak load, then the lateral displacement begins to increase rapidly and the load decreases until the specimen fails completely. It was observed from the results that FRP retrofitting steel tube in transverse direction (90°) is an efficient method for the enhancement of the load-carrying capacity and delaying overall buckling. Also, the lateral deformation improved with increasing of AFRP Thickness.
direction, reached the highest gain of 90% (from 68.63 kN to 134 kN) in strength compared to control steel tube. Both Table 6 and Fig. 6 shows that the ductility of the steel tube was also significantly improved by AFRP retrofitting. The axial deformation at peak load is enhanced by about 3 times. For all short specimens, it is observed that the ultimate load capacity and axial deformation capacity increased as the number of AFRP ply increases. Therefore, it was verified that AFRP retrofitting in the hoop direction (90°) contributed to increase the maximum load capacity and delay the outward local buckling of short tubes.
3.3. Strain - axial load relationship 3.3.1. Short column The axial load vs. axial/lateral strain curves of all short specimens are shown in Fig. 9. For these curves the positive strain represents elongation, and negative strain represents shortening. The strains were captured using the strain gauges; it should be noted that strain values represent only the local result where the gauges are fixed and reliant on the direction and type of failure of the specimen. So, the result may be varied if the local buckling or AFRP rupture occurs at the strain gauge location. As expected, axial strain starts increasing at an earlier stage of loading, since the load is applied in this direction. While the lateral strain starts developing at later stages of loading when the steel tube begins to dilate in the hope direction. The strain development is similar between strengthened and un-strengthened specimens. Nevertheless, strain in the un-strengthened specimens starts to increase at a lower axial load. This is reasonable since the compressive strength of un-strengthened specimens is lower than that of AFRP strengthened. For the strengthened specimens, it is observed that the longitudinal and lateral strains curves (gauge G1 and G2) behave linearly until the specimen reached about 80% of its maximum load capacity and also, for this stage, the elastic deformation seems to be reduced for the strengthened specimens compared to the control specimen. The lateral strain (gauge G2) at the ultimate load decreased with the increase of AFRP thickness, as for example, the transverse strain of specimens S1-200-A1, S1-200-A2, and S1-200-A3 at ultimate load were
3.2.2. Long column Axial load - axial displacement curves of all long specimens are shown in Fig. 7. The axial displacement values correspond to the average of four longitudinal LVDTs. Table 7 summarizes the resulting ultimate load and displacement values reached from the axial compression in the experimental test, where (PEXP) is the maximum load capacity, Ux and Uz are respectively the axial and lateral displacement at peak load. For the specimens S1-900-A1, S1-900-A2, and S1-900-A3, it can be seen that strength and stiffness of specimens increase by increasing the FRP retrofitting thickness. S1-900-A3 and S1-900-A2 specimens attained respectively 7% and 13% higher load capacity compared to S1900-A1. For the specimens with 2 mm thickness steel tube, the load capacity was enhanced by 5% and 13% compared to control tube; the results were compared to the FEM due to the leak if the experimental test for control tube. Same for the 1.5 mm thickness steel tube the load capacity improved only 10% even with 3 mm AFRP retrofitting. It was noticed that for every specimen a sudden drop in load occurs and it is caused by the AFRP failure. Fig. 8 shows the load-axial shortening and lateral displacement curves of all long specimens. The lateral displacement curves were plotted using the absolute average values of two opposite lateral LDVT in the direction where the buckling occurred at mid-height of the columns. From this curve, it can be noted that the lateral displacement
Fig. 1. Experimental setup and instrumentation for short tubes. 13
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Fig. 2. Experimental setup and instrumentation for long tubes.
3412με, 2893με and 2692με, respectively. which suggests that the AFRP retrofitting improves the stability of the specimens and can confine the outward buckling.
3.3.2. Long column Fig. 10 shows the axial load against axial and lateral strains curves of AFRP strengthened and un-strengthened specimens. The strain was measured from the gauges at the mid-height of the specimen from two opposite side in the direction where the overall buckling occurs. We can notice from the curves that at the beginning of the loading both sides (gauges G1 and G2), are compressed, while the tensile strain occurred at the hoop direction. until the specimens reach the peak load, were the specimen starts a global buckling, beyond this point, the deformations on one side (gauge G2) increase further in compression while the other side is switched to tension (gauge G1) as the loading continued. The same deformation behavior is observed for all long specimens. The axial strains decreased for the AFRP strengthened specimens compared to the control tube and also decrease with the increase of the AFRP thickness.
Steel tube
Steel tubee
1mm AFRP Ply
2 mm AFRP Ply
3 mm AFRP Ply
Fig. 4. Typical failure of short specimens.
4. Finite element modeling 4.1. Boundary conditions, load application, and mesh details To investigate the contributions of AFRP strengthening steel tube a non-linear finite element model was developed using the commercially available finite element package ANSYS Workbench V19 and ACP (ANSYS Composite Prep/Post) tool. The model considers material, geometric and contact nonlinearity. The numerical analysis results were compared with the experimental results, in terms of the axial load-
1 mm AFRP Ply
3 mm AFR RP Ply
Fig. 3. Typical failure of short specimens (Top view). 14
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a) Overall bucklingg
b) Failure of th he AFRP
Fig. 5. Typical failure of long specimens.
displacement relationship. The behavior of thin-walled steel and retrofitting material involving AFRP was modeled using a layered structural solid element SOLID185 Fig. 13(a). SOLID185 is used for 3D modeling of solid structures. The solid element is defined by 8 nodes having three degrees-of-freedom at each node: three translations in the directions x, y, and z. Also, the element can supports plasticity, large deflection and large strain capabilities as it is described in the ANSYS element library [25]. The mesh element size is chosen adequately for a better convergence without necessarily a high computational time cost. A mesh size sensitivity analysis has been performed. After the analysis, the adopted mesh size is a 2 mm × 2 mm (length-width) mesh size for short tube and 3 mm × 3 mm for the long tube Fig. 13(c). Boundaries conditions are provided in the model according to the experimental test setup, In the experiment, the support condition used for the test suggested being close to a simply supported for both ends, but, during the test of short specimens a slight rotation was observed in the bottom plate in x, y axes, the FEA simulation also indicates that a clamped - hinged support condition leads to much closer results compared to the experiment. Thus, the clamped - hinged support is assumed for short specimens Fig. 1(a) and simply supported for the long specimens Fig. 2(a). The axial compression load is applied as a displacement on the top edge of the model with a rigid behavior, and then the load was captured using a force reaction prob at the bottom edge.
Table 6 Short specimens comparison between experimental results and present FE analysis. Specimen
S1-200-A0 (Control) S1-200-A1 S1-200-A2 S1-200-A3 S1.5-200-A0 (Control) S1.5-200-A3 S2-200-A0 (Control) S2-200-A1 S2-200-A2
Load capacity % Gain or reduction
Load Ratio PEXP/ PFEA
PEXP
PFEA
85.85
86.13
Control
0.997
110.11 132.04 144.78 68.63
108.12 121.24 137.34 73.42
28.26 53.80 68.64 Control
1.018 1.089 1.054 0.935
134.94 93.41
124.83 98.58
96.62 Control
1.080 0.948
153.54 161.45
145.50 157.10
64.37 72.84 Mean COV
1.055 1.021 1.022 0.054
4.2. Material modeling The steel material was considered to be homogeneous and isotropic. The isotropic properties such as Young's modulus, Yield stress and Poisson's ratio of the steel tubes were obtained from the experimental coupon test. The nonlinear behavior of the steel was modeled by specifying the stress-strain curve defined by the multilinear isotropic
180
180
EXP S1-200-A0 EXP S1-200-A1 EXP S1-200-A2 EXP S1-200-A3
160 140
EXP S1.5-200-A0 EXP S1.5-200-A3 EXP S2-200-A0 EXP S2-200-A1 EXP S2-200-A2
160 140 120 Load (kN)
120 Load (kN)
Ultimate Load (kN)
100 80
100 80
60
60
40
40
20
20 0
0 0
5
10 15 20 25 Axial displacement (mm)
30
35
0
5
10 15 20 25 Axial displacement (mm)
Fig. 6. Load–axial displacement curves for short specimens. 15
30
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90
90
EXP S1-900-A1 EXP S1-900-A2 EXP S1-900-A3
80 70
70
60
60 Load (kN)
Load (kN)
EXP S2-900-A1 EXP S2-900-A2 EXP S1.5-900-A3
80
50 40
50 40
30
30
20
20
10
10
0
0
0
5
10 15 20 Axial displacement (mm)
25
30
0
a) 1 mm thickness steel tubes
5
10 15 20 Axial displacement (mm)
25
30
b) 1.5 and 2 mm thickness steel tubes
Fig. 7. Load-axial displacement curves for long specimens.
deformed geometry and mesh that are based on a deformation result from eigenvalue buckling analysis [25]. This approach is ideal to introduce initial imperfections to an otherwise perfect geometry for a nonlinear simulation. In this FE model, the first mode shape with a scaling factor of 0.1 (10% of the tube thickness) is imposed to the final geometry. The initial geometric imperfection had an important influence on the ultimate load capacity and the descending part of the loadaxial shortening relationship curves for long specimens. The load-carrying capacity decreased with the increase of the initial geometric imperfection factor; contrariwise, it didn’t have a high influence on the short tube.
hardening option in ANSYS. The AFRP composites are considered as an orthotropic material. Which means their properties are different in all directions, the material properties of AFRP are collected from the material testing data of the manufacturer. The AFRP laminates are modeled using ANSYS Composite Prep-Post (ACP) and assumed to behave linearly plastic until failure. To simulate the progressive degradation and failure behavior of AFRP, “Hashin failure criterion” have been used for damage initiation criteria (DMGI), and material property degradation method (MPDG) is used for damage evolution law, which is based on instant stiffness reduction [25]. Thus, once the stress reaches the damage limit, the stiffness is immediately reduced. The amount of stiffness reduction can be defined in between 0% and 100% of the undamaged stiffness. Here, the stiffness is assumed to be reduced by 50% for all modes [26]. In ANSYS, using engineering data module, all these parameters have been defined by the following proprieties: orthotropic elasticity, orthotropic stress and stress limits, damage initiation criteria and damage evolution law. All the material properties and model parameters for Hashin failure criteria used for the FE analysis are presented in Tables 3, 4.
4.4. Interlaminar damage interface The interlaminar damage in this model occurs in the form of debonding at the adhesive layer (referred to as “cohesive layer” hereafter) that connects the steel tube and the AFRP. The two materials are bonded to each other using E-51 epoxy resin. Thus, the cohesive layer takes the same properties of the resin. The adhesive performance of the E-51 epoxy resin used in this experiment has been tested in previous research. In this study, the Cohesive Zone Method (CZM) is used to simulate the damage and progressive failure of the cohesive layer (adhesive layer) during the debonding process. This method introduces a failure mechanism by a progressive stiffness reduction along the cohesive layer. Initially, the element is at the zero-stress. As the load is applied, cohesive zone debonding allows three distinct failure modes: Mode I (normal separation) and Mode II (shear slip) or mixed mode. The advantage of using CZM rather than other method is that there is no need
4.3. Initial imperfection The initial geometrical imperfections of the model are based on creating a small imperfection or perturbation in the mesh. This can be incorporated automatically through a linear eigenvalue buckling analysis performed into the finite element model. In practice, the first buckling mode shape is taken as the critical imperfection shape. ANSYS Workbench enables you to directly link and transfer the Table 7 Long specimens comparison between experimental results and present FE analysis. Specimen
S1-900-A0 (Control) S1-900-A1 S1-900-A2 S1-900-A3 S1.5-900-A0 (Control) S1.5-900-A3 S2-900-A0 (Control) S2-900-A1 S2-900-A2
Ultimate Load (kN) PEXP
PFEA
– 54.83 58.79 62.34 – 71.04 – 77.27 86.77
50.43 53.02 56.48 59.40 64.37 71.34 76.78 84.42 88.66
Load capacity % Gain or reduction
Axial displacement at peak load UX (mm)
Lateral displacement at peak load UZ (mm)
Load Ratio PEXP/ PFEA
Control 8.72 16.57 23.60 Control 10.36 Control 5.66 13.02
– 2.66 3.10 2.98 – 2.89 – 2.51 3.87
16
– 7.58 9.15 10.03 – 2.47 – 4.53 4.66 Mean COV
– 0.967 0.961 0.953 – 0.996 – 0.961 0.979 0.969 0.016
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90
90 EXP S1-900-A1 EXP S1-900-A2 EXP S1-900-A3
80 70
70
60
60 Load (kN)
Load (kN)
EXP S2-900-A1 EXP S2-900-A2 EXP S1.5-900-A3
80
50 40
50 40
30
30
20
20
10
10
0 0
5
10
15 20 25 30 Lateral displacement (mm)
35
40
0
45
0
a) 1 mm thickness steel tubes
5
10
15 20 25 30 Lateral displacement (mm)
35
40
45
b) 1.5 and 2 mm thickness steel tubes
Fig. 8. Load-lateral displacement curves for long specimens.
160
G1 G2
140
140
120
120 Load (kN)
Load (kN)
160
100 80 60 40 20
100 80 60
S1-200-A0 S1-200-A1 S1-200-A2 S1-200-A3
G1
40 G2
20
0
G1 G2
S2-200-A0 S2-200-A1 S2-200-A2 S1.5-200-A0 S1.5-200-A3
G1 G2
0 -8000 -6000 -4000 -2000 0 2000 4000 Longitudinal strain G1 (µe) Transveral strain G2 (µe)
-8000 -6000 -4000 -2000 Longitudinal strain G1 (µe)
a) 1 mm thickness steel tubes
0
2000 4000 6000 8000 Transveral strain G2 (µe)
b) 1.5 and 2 mm thickness steel tubes
Fig. 9. Load-strain curves for short specimens.
and AFRP using ACP module Fig. 11(3). Second, the interface is imported in structural module Fig. 11(4) and defined as bonded contact regions. Finally, a contact debonding object is specified along with the bonded contact region that intends to separate using CZM material model. The CZM material behavior is governed by bilinear tractionseparation law as described by Alfano and Crisfield [27], available in
to place an initial crack manually in the FE model. Also, the method allows several crack initiations and propagations in the cohesive layer. A detailed description of the CZM technique can be found in ANSYS Theory Manual [25]. In ANSYS Workbench, debonding behavior simulations start initially, by modeling an interface layer with zero thickness between steel
Fig. 10. Load-strain curves for long specimens at mid-length. 17
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Fig. 11. ANSYS Workbench schematic; 1. Static Structural module to run the linear elastic analysis, 2. Run a linear buckling analysis and exporting the geometry with imperfection for nonlinear analysis, 3. ACP module used to design the composite material with the required parameters, 4. Start the Nonlinear Analysis of the final model.
Fig. 12. Bilinear traction-separation laws for the adhesives. (a) normal stress vs. gap (Mode I). (b) shear stress vs. slip (Mode II).
Fig. 13. a) SOLID185 Layered Structural Solid Geometry, b) FE model with interface debonding layer (CZM), c) Detail of finite element mesh of column with initial geometric imperfection (exaggerated).
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Fig. 14. Comparison between experimental and FEA load vs. axial load curves (Short tubes).
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90
90 EXP S1-900-A1 FEA S1-900-A1 FEA S1-900-A1 (CZM)
80 70
70 60 Load (kN)
Load (kN)
60 50 40
40 30
20
20
10
10 0 0
5
10 15 20 Axial displacement (mm)
25
30
0
90
5
10 15 20 Axial displacement (mm)
25
30
90 EXP S1-900-A3 FEA S1-900-A3 FEA S1-900-A3 (CZM)
80 70
EXP S2-900-A1 FEA S2-900-A1 FEA S2-900-A1 (CZM)
80 70 Load (kN)
60 Load (kN)
50
30
0
50 40
60 50 40
30
30
20
20
10
10
0
0 0
5
10 15 20 Axial displacement (mm)
25
30
0
5
10 15 20 Axial displacement (mm)
25
30
90
90 EXP S2-900-A2 FEA S2-900-A2 FEA S2-900-A2 (CZM)
80 70
EXP S1.5-900-A3 FEA S1.5-900-A3 FEA S1.5-900-A3 (CZM)
80 70
60
Load (kN)
Load (kN)
EXP S1-900-A2 FEA S1-900-A2 FEA S1-900-A2 (CZM)
80
50 40
60 50 40
30
30
20
20
10
10 0
0 0
5
10 15 20 Axial displacement (mm)
25
30
0
5
10 15 20 Axial displacement (mm)
25
30
Fig. 15. Comparison between experimental and FEA load vs axial load curves (Long tubes).
tolerances are specified to 0.5%. The numerical analysis of a debonding process (initiation and progression) using CZM approach is complex and computational consuming, and can result in convergence problems. To overcome the convergence difficulty the analysis required quite a large number of iterations and small mesh sizing. As a result, the analysis will run quite slowly. Also, it has been shown by Gao and Bower [28] that the convergence difficulty can be avoided by introducing a small artificial damping coefficient in the cohesive zone law that characterizes the interface. In this study, the damping coefficient was set to 0.001 which gives a stable and accurate solution.
ANSYS material data as CZM separation-distance based debonding. This material data requires the values of the maximum allowable normal stresses (σ) for mode I, and shear stresses (τ) for mode II, and the corresponding separation (δ) causing failure of the bond as shown in Fig. 12. 4.5. Nonlinear solution Nonlinear FEM is solved iteratively using the Newton-Raphson (NR) method in ANSYS. The load is applied by increments and assumed to vary linearly within each load steps. The solution performs a number of equilibrium iterations at each load increment to achieve convergence, within an adequate tolerance. Both force and displacement convergence 20
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1 mm AFRP P Ply
Stteel tube with hout Strengtthening
2 mm m AFRP Ply
3 mm AFRP P Ply
Fig. 16. Experimental and FEM typical failure mode of short specimens (failure of AFRP indicated by Hashin's damage status, 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged).
(a)
For long tubes, there was a good correlation between the experimental results and the FEM results, and the load-axis displacement curves followed the same path for all the specimens as shown in Fig. 15. The ultimate load in FEM with CZM dropped by 8% on average compared to specimens with fully bonded contact; however, there was no significant difference in the behavior of the post-peak load curve. The reason is that during the FE analysis with CZM the stress in the cohesive zone did not reach the failure limit Fig. 18(a) to initiate debonding phenomena between the steel and AFRP. From Tables 6 and 7 a good agreement is observed in load capacity, the experiment ultimate load values (PEXP) were quite similar to the ultimate load values (PFEA) obtained from FE analysis. The mean and coefficient of variance of the ratio PEXP/ PFEA were 1.022 and 0.054 respectively for short specimens, and 0.969 and 0.016 respectively for long specimens.
(b)
Fig. 17. Typical failure of the CZM interface for short tubes S2-200-A1: a) Sliding distance between AFRP and Steel, b) Contact status.
5.2. Failure mode 5. Numerical results
In addition to load-displacement curves, the final failure mode shape for un-strengthened and strengthened specimens obtained from the experimental test were similar to those obtained from the FEM analysis as shown in Figs. 16–18. The FE model is able to predict the different failure mechanisms such as FRP failure modes, which is represented by Hashin's damage status (an enum type with values of 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged) shown in Figs. 16 and 18(c, b), and also can capture the debonding damage Figs. 17 and 18(a). The failure modes included in Hashin's criteria are tensile fiber failure, compressive fiber failure, tensile matrix failure, compressive matrix failure. As can be seen in Fig. 16, for all tubes the AFRP failure location in the experimental matches with FE models. Debonding in the cohesive zone was observed for all short model this is due to the excessive deformation of the steel tube Fig. 17. The drop-in load capacity for CZM model compared to the fully bonded model can be explained by energy absorbed due to the sliding between AFRP and steel tube as shown in Fig. 18(a). From the results, it can be concluded that the FEA results matched quite well with the experimental test. Therefore, the developed FE model used for this analysis can predict the behavior of AFRP
5.1. Load-displacement curves All the findings obtained from the FE analysis are compared with the current experiments tests to verify the developed FE model. Comparison between axial load (kN) – axial displacement (mm) curves obtained from FE results and the corresponding experiment are shown in Figs. 14 and 15 for both short and long specimens. The figures also include the load-displacement curves for the FE model with a perfectly bonded contact (no-debonding allowed) and FE model with interface debonding contact. For short tubes, load-displacement curves agree perfectly between experiment and FEM that include CZM as shown Fig. 14. As it can be seen, by including the debonding behavior in the FEM a significate correlation to the experiment results is observed in post-peak load. The ultimate load decreased on average by 6% compared to the model without CZM. Specimen S1.5-200-A3 had different behavior compared to the experiment; it may be caused by the initial imperfection of the steel tube, test setup or load speed. 21
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Fig. 18. Typical failure mode of long specimens: a) Overall buckling, b) Compression side, c) Traction side, Hashin's damage status of AFRP, 0 = undamaged, 0.5 = partially damaged, 1 = completely damaged.
strengthening thin-walled steel tubes. Including the interface debonding (CZM) in the numerical solution improved the accuracy of the results significantly however the cost in computational time was considerable. On a medium-performance PC, the average computational time for each model was 2 h for models without debonding interface and 12 h for models with CZM.
• •
6. Conclusion In this paper, 15 specimens of a thin-walled circular hollow section (CHS) steel tube strengthened with AFRP in the transverse direction subjected to a static axial compressive load. All specimens were tested to study the effect of AFRP retrofitting on maximum load carrying capacity, stiffness and failure modes. The test parameters were the thickness of AFRP ply (1, 2 and 3 mm), the thickness (1, 1.5 and 2 mm) and the length (200 mm and 900 mm) of steel tubes. Furthermore, the finite element software ANSYS Workbench ver. 19 and ACP (ANSYS Composite Prep/Post) tool were used for this nonlinear simulation to predict the behavior of AFRP strengthening steel tubes. The FE model accounts for material and geometric nonlinearities and also combines the effect of AFRP damage using “Hashin failure criteria” and interlaminar failures of the bonded interface using “Cohesive Zone Model,” to provide an accurate simulation. Based on the experimental and FEA results, the verdict was as follows:
• • • •
• The AFRP efficiency increases with the increase of the AFRP thick-
ness, and it is more distinct for specimens with small slenderness ratio than the specimens with large slenderness ratio. For short specimens, a maximum increase of 96% was reached in axial load
capacity with 3 mm of AFRP in the hoop direction. For the long specimens, the effectiveness of the AFRP is less significant, where the highest ultimate load increase is about 23% with 3 mm of AFRP. The stiffness and ductility of the FRP strengthened specimens improved considerably compared to un-strengthened specimens and also increased with the increase of AFRP thickness within the range of the parameters explored in this study. External strengthening using FRP does not change the buckling shape of the steel tube, but can effectively delay the local buckling and confine the outward one, and also delay the overall buckling of long specimens. The developed nonlinear FE model used for the analysis is successfully validated by comparing the load-displacement responses and failure modes with the experimental tests, which verifies the reliability to use the model in future analysis. The FE Model is capable of predicting load carrying capacity and AFRP failure using “Hashin damage criteria” with tolerable accuracy. The cohesive zone model (CZM) defined by bilinear traction-displacement softening law was successfully employed to capture debonding initiation and propagation between steel and AFRP accurately. The FE model can effectively simulate the specimens post-peak load behavior by taking into account the FRP debonding phenomena. However, it can be ignored for specimens with a high slenderness ratio, as the effect on the results is minimal, which can avoid a complex and time-consuming simulation.
It is evident that much more experimental tests and numerical simulations on a large number of specimens have to be performed to 22
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cover wider ranges of parameters. Future research focuses on finding an optimal strengthening combination to minimize the cost-benefit ratio, including other types of fibers (GFRP, CFRP), effects of fiber orientation, and strengthening scheme. More research is also needed to explore the behavior of AFRP strengthened thin walled tubes under impact load conditions where aramid fibers excel the most; this will be shown in a subsequent article.
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