Impact behaviour of carbon fibre reinforced polymer (CFRP) strengthened square hollow steel tubes: A numerical simulation

Thin-Walled Structures 131 (2018) 245–257

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Full length article

Impact behaviour of carbon fibre reinforced polymer (CFRP) strengthened square hollow steel tubes: A numerical simulation

T

⁎

Chamila Batuwitagea, , Sabrina Fawziaa, David Thambiratnama, Xuemei Liua, Riadh Al-Mahaidib, Mohammed Elchalakanic a

School of Civil Engineering and Built Environment, Faculty of Science and Engineering, Queensland University of Technology, 2 George Street, Brisbane QLD 4000, Australia b School Engineering, Department of Civil and Construction Engineering, Swinburne University of Technology, Melbourne, Australia c School of Civil, Environmental and Mining Engineering, Faculty of Engineering Computing and Mathematics, University of Western Australia, Australia

A R T I C LE I N FO

A B S T R A C T

Keywords: CFRP Axial impact Square hollow section (SHS) FE modelling Strengthening

Carbon fibre reinforced polymer (CFRP) has become popular and used in various engineering applications. Strengthening of hollow steel sections using CFRP has proven improved structural characteristics under static loading conditions. However, there are very few studies available related to the axial dynamic impact behaviour of CFRP strengthened steel hollow sections. This paper evaluates the behaviour of CFRP wrapped hollow square steel tube sections under axial impact loading through validated numerical models. A comprehensive parametric study has been conducted to evaluate the effects of impact mass, impact velocity, adhesive strength and fibre modulus on the impact performance of these tubes. Crash behaviour is studied by comparing the peak impact force, axial deflection, absorbed internal energy and failure modes between CFRP wrapped and bare steel models. The results show that the variations in impact velocity and fibre modulus can have significant effect on the impact response of CFRP wrapped tubes.

1. Introduction Structural hollow steel sections are widely used in construction industry as well as in automobile industry. CFRP technology has been used as an external reinforcement system for steel structural systems to serve the same purpose as steel jacketing but with some added advantages [1]. The improved strength and behaviour of steel tubular sections wrapped with CFRP under static loading have proven that this CFRP wrapping technique is an efficient strengthening method [2–9]. The use of CFRP appears to be an excellent solution for retrofitting and strengthening of steel structures because of its superior physical and mechanical properties. CFRP wrapped steel tubes are considered as an innovative retrofitting solution because of its advantages, such as high strength compare to the traditional method, lighter construction, aesthetically pleasant, minor interruption of the structures during strengthening or rehabilitation, no heavy scaffolding or cranes and limited workforce requirement during the instalment. Most of the earlier research focused on the flexural and tensile behaviour of CFRP wrapped steel. However, there is limited research on the CFRP wrapped steel tubes to resist axial loading. There are even fewer studies to investigate the behaviour of CFRP wrapped steel tubes when subjected to

⁎

axial impact loading. Teng and Hu [8] studied the behaviour of CFRP wrapped circular steel tubes and cylindrical shells under axial compression and concluded that CFRP wrapping is a very promising strengthening technique for retrofitting circular hollow steel sections in terms of improving the ductility of steel. In contrast, load carrying capacity was not greatly increased. Bambach [10] investigated the axial capacity and crushing behaviour of metal-fibre stainless steel and aluminium square tubes with CFRP under axial impact loading. Tubes with different metal square hollow section (SHS) geometries and two different matrix layouts of CFRP were studied, and a general theory was developed to predict the axial capacity, axial collapse and mean crush loads of these tubes and validated using experimental data. This study concluded that CFRP could be used as an externally bonded reinforcement to steel square hollow section (SHS) successfully. Such applications may improve the performance of existing structures and play a major role in the design of new structures with enhanced strength-weight and energy absorption-weight ratios. Furthermore, different strengthening schemes of CFRP wrapped steel tubes have been studied by various researchers [11–15] including double-strap joints [16,17], lap joints, CFRP wrapped concrete filled tubes and open steel sections.

Corresponding author. E-mail address: [email protected] (C. Batuwitage).

https://doi.org/10.1016/j.tws.2018.06.033 Received 13 April 2018; Received in revised form 14 June 2018; Accepted 26 June 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature COV Dmax Emax NFLS Pave SEA SFLS tad tCFRP XC

XT YC YT β

Coefficient of variance Maximum axial deflection Maximum absorbed energy Tensile failure strength of adhesive Average crushing force Specific energy absorption Shear failure strength of adhesive Thickness of the adhesive Thickness of CFRP Compressive strength in a direction

έ σaa σad σbb σCFRP σ(eq) CFRP τab

Tensile strength in a direction Compressive strength in b direction Tensile strength in b direction Weighting factor for the ratio of shear stress to shear strength Strain rate of steel Stress in direction a Tensile strength of adhesive Stress in direction b Tensile strength of CFRP Tensile strength of the composite Shear stress

independent interacting components of the model. In this simulation, penalty based contact types were used. single surface contact was used to avoid the interpenetration of nodes during the folding of the tube. Tie-break contact was used to define the contacts between Steel tube and CFRP and between two CFRP layers. Tiebreak allows the separation of the surfaces, and ultimately the failure of the tied surfaces will occur under the failure criterion expressed in Eq. (1).

The material properties are significantly affected by the strain rate. Research studies related to steel showed that steel properties such as yield strength and failure strain were dependent on the strain rate [18–21]. However, the behaviour of CFRP under high strain rates is not clearly understood, and it is a complicated procedure because of the involvement of a large number of material properties due to its nonisotropic behaviour. A recent research work carried out by Orton et al [22]. showed that there is no increase in the tensile strength of the CFRP material in the range of 0.0015–7.81 s−1 strain rates. In contrast, another study conducted [23] on CFRP materials showed that CFRP and adhesive properties were strain rate dependent within the tested loading rates. Studying the behaviour of CFRP wrapped steel sections under axial impact load is vital to evaluate their potential as crash energy absorbers. The majority of the research works related to CFRP-steel composites have been conducted under static loading conditions. This paper aims to evaluate the crashworthiness properties of the CFRP wrapped steel tubes under axial impact conditions. Finite element (FE) models were developed and validated using existing experimental data [24]. The experimental study consisted of CFRP wrapped hollow steel tubes with two different fibre layouts. The SHS members were tested under axial impact load in a drop-mass rig using a mass of 574 kg from a height of 1.835 m, resulting in a nominal impact velocity of 6 ms−1 and impact energy of 10.3 kJ. FE modelling and analysis were performed using LS-DYNA finite element code. The validated FE models were used to conduct a detailed parametric study to evaluate the influence of several structural parameters including peak impact force, axial displacement and internal energy of CFRP wrapped tubes. The structural response was evaluated by varying the impact mass, impact velocity, adhesive strength and fibre modulus.

2 2 ⎛ σn ⎞ + ⎛ σs ⎞ ≥1 ⎝ NFLS ⎠ ⎝ SFLS ⎠

(1)

where NFLS is tensile failure strength, and SFLS is shear failure strength of the adhesive. σn and σs are respectively the tensile stress and the shear stress. Strength of the epoxy (36 MPa) was nominated as the NFLS and SFLS values in the tie-break model since this is the maximum possible value to be reached during the tie-break process. All models were meshed with quadrilateral elements with a dimension at 2.5 mm × 2.5 mm. The mesh size was selected based on mesh convergence study and also with consideration of the relative dimensions of the steel tube and CFRP layers. Full geometry was modelled. The geometry and the FE mesh of the model are presented in Fig. 1. 2.2. Material properties Table 1 summarises the Material properties used for FE models created based on the experimental results available in the literature [24]. The summary of the details of the FE models created is shown in Table 2 with current FE model identification. The steel used in the experiment had 350 MPa nominal strength, and commercially available CFRP type CF-130 was used with Araldite 420 epoxy. Impact force was applied by dropping a mass of 574 kg from a height of 1.835 m resulting in an impact velocity of 6 ms−1 and with impact energy of 10.3 kJ.

2. Finite element modelling 2.1. Model description

2.3. Material models and failure criteria

The steel tubes were modelled with four node shell elements [25] containing five integration points through element thickness with Belystchko-Tsay element formulation. CFRP layers were also modelled with the same type of Belystchko-Tsay shell elements. It should be noted here that the first (close to steel) CFRP layer is transverse layer and the second CFRP layer is longitudinal layer (top layer). A control type hourglass mode was used with hourglass coefficient equals to 0.3 for crash analysis to avoid zero energy modes during the simulation. The impactor was modelled as a moving-rigid-wall having an initial velocity of 6 ms−1 and a mass of 574 kg. The bottom of the steel tube was modelled as a fixed support by restraining all degrees of freedoms of the bottom nodes of steel tube. The stationary baseplate was modelled using another stationary type rigid wall at the lower part of the composite tube. In addition to geometry, meshing and material properties, the other important consideration for the computational model in this study is the definition of contact interface types between the

The material properties of steel under static loading cannot be used for dynamic simulations, and strain rate effects need to be considered. Therefore, steel was modelled using strain rate sensitive model [26] as it is capable of simulating the strain rate effects based on Cowper-Symonds model. The Cowper-Symonds model scales the yield stress of ε ́ 1/ p

()

steel by a factor of 1+ c where, έ is the strain rate and C, P are strain rate parameters. C= 40 and P = 5 are used in this simulation as suggested in the research literature [27–29]. CFRP was modelled using an enhanced composite material model. This material model considers the effects of directionality in the material stress–strain response by allowing different fibre orientations specified at each through-thickness integration point. Unidirectional laminated fibre composite shell thickness, each fibre orientation, and constitutive constants are required to input. This material model is built on a set of stress-based failure criteria for the fibre and matrix failure under tensile, compressive and/or in-plane shear loading. These failure 246

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strength taking values in the range between 0.0 and 1.0. 2

σ Compressive failure, fibre direction: ⎛ aa ⎞ ≥1 ⎝ XC ⎠ ⎜

⎟

(3) 2

2

σ τ Tensile failure, matrix direction: ⎛ bb ⎞ + ⎛ ab ⎞ ≥1 ⎝ YT ⎠ ⎝ SC ⎠ ⎜

⎟

⎜

⎟

(4) 2

Compressive failure, matrix direction:

(Y − YT ) σbb σbb2 τ + ⎛ ab ⎞ + C ≥1 YC YT S YC YT C ⎝ ⎠ (5) ⎜

⎟

where each value of each expression evaluated after each load step ≥ 1 implies the failure and the value < 1 implies the elastic behaviour of the material. σaa , σbb and τab are respectively the stress in direction a, stress in direction b and shear stress. XC , XT YT , YC are the strength values where X is strength in the a direction, Y is strength in b direction and Sc is the shear strength. Subscripts C and T are respectively for compression and tension. In this study, adhesive layers were not separately modelled, and both the CFRP and adhesive layers were modelled as a single composite layer. Composite properties were computed using Eq. (6) based on the thickness of the materials and individual material properties.

σ(eq) CFRP =

Table 1 Material properties. Steel

CFRP

Density Poisson's ratio Young's modulus Strength

7850 kg/m 0.3 210 GPa 350 MPa

Geometries Thickness

2 mm

3

1700 kg/m 0.2 230 GPa 3790 MPa

Epoxy 3

0.176 mm

1100 kg/m3 0.25 1900 MPa 36 MPa

3. FE modelling results

0.1 mm

The developed FE models were used to simulate the behaviour of CFRP strengthened hollow steel tubes under axial impact loading. The results obtained from the FE models were compared with the experimental results [24] as shown in Figs. 2 and 3. Comparison of the peak impact forces between FE results and experimental data are presented in Table 4, and FE results agreed well with the experimental data with a mean ratio of 1.017 and a coefficient of variation of 0.03. The models accurately predicted the peak impact force and the deflection behaviour of the bare steel tubes. Then these validated bare steel tube models were used to develop CFRP wrapped steel tubes. Three CFRP wrapped tubes were modelled, and FE modelling results are compared with experimental data as

Table 2 FE model definition and specimen dimensions. Type

Model identification

SHS column (mm)

Length (mm)

Bare steel tube models

ST50 ST65 ST75 FRP50 FRP65 FRP75

50 × 50 × 2 65 × 65 × 2 75 × 75 × 2 50 × 50 × 2 65 × 65 × 2 75 × 75 × 2

300 300 300 300 300 300

CFRP strengthened steel tube models

Table 3 CFRP composite material properties for FE simulation.

modes can be accounted for in shell theory where plane stress condition is assumed and the failure mechanisms of delamination response associated with a splaying mode of failure. The elastic material behaviour of the composite is calculated based on the Young's modulus, shear modulus and Poisson's ratio. Damage occurs as soon as one of the following four criteria by Chang-Chang [30] is met as expressed in Eqs. (2)–(5). 2

2

σ τ Tensile failure fibre direction: ⎛ aa ⎞ + β ⎛ ab ⎞ ≥1 ⎝ XT ⎠ ⎝ SC ⎠ ⎜

⎟

⎜

(6)

where, σ(eq) CFRP is the tensile strength of the composite, σCFRP , σad, tCFRP and tad are respectively the tensile strength of CFRP, tensile strength of adhesive, thickness of CFRP and adhesive. Similarly, Young's modulus was calculated by assuming an adhesive thickness of 0.1 mm. The basic material properties used for the FE simulation are shown in Table 3. The material properties listed in Table 3 are available from references [5,6,8,10,24,37]. It is impossible to find a single reference which contains all tested material properties. The transverse properties were obtained through a sensitivity analysis (trial and error) based on range of values reported in the literature mentioned above to determine the best combination. The set of material properties which provided best validation curves were listed in Table 3.

Fig. 1. The geometry and the FE mesh of the model.

Material properties

σCFRP tCFRP + σad tad tCFRP + tad

⎟

(2)

β is a weighting factor for the ratio of the shear stress to shear 247

Material parameter

Value

Density Longitudinal elastic modulus Transverse elastic modulus Longitudinal tensile strength Longitudinal compressive strength Transverse tensile strength Shear strength Transverse compressive strength Shear modulus Poisson's ratio

1700 kg/m3 147 GPa 9.2 GPa 2430 MPa 700 MPa 100 MPa 150 MPa 234 MPa 4.25 GPa 0.2

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(A)

250

Experiment LS-DYNA

ST50

Experiment LS-DYNA

ST65 200

Impact force (kN)

200

Impact force (kN)

(B)

250

150

100

150

100

50

50

0

0 0

20

40

60

80

100

120

0

140

20

40

60

80

100

120

140

Axial displacement (mm)

Axial displacement (mm)

(C)

250

Experiment LS-DYNA

ST75

Impact force (kN)

200

150

100

50

0 0

20

40

60

80

100

120

Axial displacement (mm) Fig. 2. Comparison of impact force vs axial displacement for bare steel tube models.

the wall thickness, yield strength and strain rate hardening of the steel. Steel material properties were kept at constant during the parametric study. Impact mass was varied from 150 to 650 kg, and the impact velocities were ranged from 2 to 8 ms−1. Adhesive strengths were ranged from 15 to 80 MPa. Three fibre types were modelled: (i) normal modulus CFRP (ii) high modulus CFRP and (iii) GFRP. Impact conditions and key parameters used for the parametric study are summarised in Table 5. Impact performance of bare and CFRP wrapped tubes is evaluated and presented in Table 6 and 7, respectively. In these Tables, where the average crushing force, Pave is defined as absorbed energy (Emax) divided by maximum axial deflection (Dmax). Subscripts st and f are for steel and CFRP wrapped tubes respectively. Specific energy absorption (SEA) is defined as absorbed energy (Emax) divided by mass of the axially crushed section.

shown in Fig. 3. The comparison of the FE results of axial impact force vs. axial displacement of CFRP wrapped models also showed that the developed FE models accurately predicted the peak impact force and the axial displacement. The failure modes obtained from FE analysis were compared with those obtained from experiments. Fig. 4 shows the failure mode of bare steel tube. Steel tube underwent a folding type of failure which is a common type of failure under axial dynamic loading [31–35]. Comparison of failure modes of CFRP wrapped models is shown in Fig. 5. The failure mode of the composite tube also followed a folding type of failure. Numerically-obtained failure mode is similar to the experimentally observed failure mode. The folding of the CFRP wrapped tubes was initialised from the top of the composite tubes in the FE models, and same failure mode was observed in the experiments. Fibre breakage is observed during the experiments, and similar type of CFRP failure was observed in FE models as shown in Fig. 6. Overall, the developed FE models accurately predicted the axial impact response of bare and CFRP wrapped steel tubes.

4.1. Effect of impact mass Four impact masses were selected (150, 450, 574 and 650 kg) to simulate different magnitude of impacts. Impact velocity was kept constant at 6 ms−1 for all the models as the experiment was conducted at same velocity. Variation of impact force vs. time, axial displacement vs. time and impact force vs. axial displacement responses are shown in Fig. 7. FE modelling results showed that peak impact force was generally around 268 kN and selected range of impact masses did not have a significant influence on peak impact force of the tube models as shown

4. Parametric study After validating the developed models, a parametric study was conducted to investigate the influence of impact mass, impact velocity, adhesive strength and fibre type on peak impact force, deflection behaviour, and energy absorption. It is well known that the structural behaviour of axially impacted steel hollow sections strongly depends on 248

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(A)

(B)

300

250

Experiment LS-DYNA

FRP50

Experiment LS-DYNA

FRP65

250

Impact force (kN)

Impact force (kN)

200

150

100

50

200

150

100

50

0

0 0

20

40

60

80

100

0

120

20

40

60

80

100

120

Axial displacement (mm)

Axial displacement (mm)

(C) 350

Experiment LS-DYNA

FRP75

300

Impact force (kN)

250 200 150 100 50 0 0

20

40

60

80

100

Axial displacement (mm) Fig. 3. Comparison of impact force vs axial displacement for FRP wrapped models. Table 4 Comparison of FE results with experimental results. Model

ST50 FRP50 ST65 FRP65 ST75 FRP75 Mean COV

Peak impact force (kN)

PFE/Pexp

Experimental (Pexp)

FE model (PFE)

201 221 208 256 233 315

198 226 213 268 244 308

0.985 1.023 1.024 1.047 1.047 0.978 1.017 0.03

in Fig. 7(A). However, axial deflection behaviour was significantly influenced by the impact mass. It was observed that the axial displacement increased with the increment of impact mass (Fig. 7(B)). Such behaviour may be further understood by studying internal energy absorption of the models. Lower impact mass (150 kg) contained less impact energy (2.7 kJ) during the impact. By increasing impact mass gradually, (450, 574 and 650 kg) higher impact energies were obtained (8.1, 10.3 and 11.7 kJ, respectively). Tubes absorbed higher impact energy by undergoing higher axial displacement and resulted in folding failure mechanism, which is a common failure mode for tubular structures under axial impact loading [36–38]. The number of folds increased with the increment of impact mass. Peak impact forces were increased almost up to 25% for all the cases compared to bare steel tubes. Axial deflections were reduced by 7, 17, 9 and 10 mm

Fig. 4. Failure mode of bare steel tube – FE analysis (a) side view (b) isometric view.

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Fig. 5. (A) Failure behaviour of FE model (B) failure behaviour of CFRP wrapped steel tube.

than those of the bare steel tubes. However, failure modes remained similar for both bare and CFRP wrapped tubes. The difference in ultimate axial displacement between bare and CFRP wrapped steel tubes could be mainly due to increased stiffness of the tubes as a result of CFRP wrapping. Due to the axial impact the CFRP wrapped tube deforms both axially and laterally (through bulging) while it crushes as seen in Figs. 4 and 5. During this process the CFRP contributes to reduce the deflection, especially the lateral deflection (bulging) and enhances the overall stiffness

respectively in CFRP wrapped tubes with impact masses of 150, 450, 574 and 650 kg respectively compared to bare steel tubes with same impact masses. 4.2. Effect of impact velocity Four impact velocities were evaluated with a constant impact mass of 574 kg. Obtained responses on impact force and axial displacement are presented in Fig. 8. The results showed that the peak impact force is sensitive to impact velocity (Fig. 8(A)). Peak impact force increased gradually with the increment of velocity. Unlike the peak impact force, the axial displacement increased proportionally to the impact velocity. Obtained axial displacements are recorded as 13.4, 88.1, 150.2 and 240 mm for four different impact velocities of 2, 5, 6 and 8 ms−1 respectively (Fig. 8(B)). A reduction in axial displacement in CFRP wrapped tubes was observed compared to the bare steel tubes with similar impact velocity. Axial displacement of 20 mm was observed for the bare steel tubes under the lowest impact velocity of 2 ms−1. It was about 262 mm under the highest impact velocity of 8 ms−1. Axial displacements of CFRP wrapped tubes modelled with similar impact velocities were 13.4 mm and 240.2 mm respectively, which were lower

4.3. Effect of adhesive strength The results presented in Fig. 9 indicate that the influence of adhesive strength on the axial impact behaviour of CFRP wrapped tubes was not significant. Peak impact forces and axial displacements were similar for the models with different adhesive strengths. Failure modes were also similar. The results indicated that the performance of the CFRP wrapped tube was not governed by the adhesive strength. Similar structural behaviour of all the models could be observed as a result of higher axial stress value applied to the models. Failure of CFRP layers may be attributed to the combination of several possible failure criteria 250

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Fig. 6. Fibre breakage during failure (A) experimental (B) FEM. Table 5 Key parameters for parametric study.

Table 6 Impact performance of bare steel tubes.

Model identification

Impact mass (kg)

Impact velocity (ms−1)

FRP type

Adhesive strength (MPa)

ST65M1V ST65M2V ST65M3V ST65M4V ST65MV1 ST65MV2 ST65MV3 ST65MV4 FRP65M1V FRP65M2V FRP65M3V FRP65M4V FRP65MV1 FRP65MV2 FRP65MV3 FRP65MV4 FRP65A1 FRP65A2 FRP65A3 FRP65A4 FRP65E1 FRP65E2

150 450 574 650 574 574 574 574 150 450 574 650 574

6 6 6 6 2 5 6 8 6 6 6 6 2 5 6 8 6 6 6 6 6 6

Normal modulus

60

FRP65E3

6

Model

Maximum peak impact force (Pmax,st) kN

Maximum axial deflection (Dmax) mm

Absorbed energy (Emax) kJ

Average crushing force (Pave,st) kN

SEA (kJ/ kg)

STM1V STM2V STM3V STM4V STMV1 STMV2 STMV3 STMV4

214 215 214 215 201 216 214 213

38.04 127.46 159.10 184.20 19.78 118.84 159.10 261.95

2.7 8.1 10.332 11.7 1.148 7.175 10.332 18.368

70.98 63.55 64.94 63.52 58.04 60.38 64.94 70.12

17.39 15.57 15.91 15.56 14.22 14.79 15.91 17.18

as discussed in Section 2.3. 4.4. Effect of fibre properties

High modulus GFRP

15 30 60 80 60 60

Three different fibre types were selected to study the effect of the fibre properties on the behaviour of the CFRP wrapped tubes under axial impact loads: (i) high modulus carbon fibres (ii) normal modulus carbon fibres and (iii) glass fibres. Fibre properties are presented in Table 8. Fig. 10(C) shows the impact force vs. axial displacement behaviour of the models with different CFRP properties. Peak impact force was higher in the models with high elastic modulus. Peak impact force increased from 214 to 292 kN with use of high modulus CFRP. The peak impact force increased up to 18%, 25% and 36% respectively when using GFRP, high modulus CFRP and normal modulus CFRP compared

60

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Table 7 Impact performance of CFRP wrapped steel tubes. Model

Maximum peak impact force (Pmax ,f) kN

Maximum axial deflection (Dmax) mm

Absorbed energy (Emax) kJ

Average crushing force (Pave) kN

Pmax,f/Pmax,st

Pave,f/Pave,st

SEA (kJ/kg)

FRPM1V FRPM2V FRPM3V FRPM4V FRPMV1 FRPMV2 FRPMV3 FRPMV4 FRPA1 FRPA2 FRPA3 FRPA4 FRPE1 FRPE2 FRPE3

266 268 268 267 253 262 268 267 267 264 268 269 268 292 253

31.40 110.12 150.12 174.01 13.41 88.12 150.12 240.17 135.42 139.51 150.12 143.34 150.12 141.12 147.32

2.7 8.1 10.3 11.7 1.2 7.2 10.3 18.3 10.3 10.3 10.3 10.3 10.3 10.3 10.3

85.99 73.64 68.82 67.24 85.67 81.44 68.82 76.48 76.53 74.33 68.82 72.25 68.82 73.28 70.29

1.24 1.25 1.25 1.24 1.25 1.21 1.25 1.25 1.25 1.23 1.25 1.26 1.25 1.36 1.18

1.19 1.15 1.05 1.04 1.46 1.32 1.05 1.08 1.17 1.13 1.05 1.10 1.05 1.11 1.08

19.88 17.02 15.91 15.54 19.80 18.83 15.91 17.68 17.69 17.18 15.91 16.70 15.91 16.94 16.25

to the bare steel tube. After the first impact, it was observed that the residual force of wrapped tubes increased. This increment indicates that the stiffness of the steel tube has been enhanced by either CFRP or GFRP. The increase in the peak impact force due to high modulus CFRP was greater than the normal modulus CFRP. This was most likely to occur because composite elastic modulus of high modulus CFRP was

greater than the composite elastic modulus of normal modulus CFRP which could enhance the initial stiffness of the tube. In GFRP wrapped models initial stiffness was lower than the normal modulus CFRP models. Due to this variation of the initial stiffness, the variation of the peak impact force was more likely to occur. After the initiation of failure, the same failure mode was observed for all the steel tubes, and

(B)

(A) 180

300

FRP65M1V FRP65M2V FRP65M3V FRP65M4V

160

Axial displacement (mm)

140

200

150

100

120 100

FRP65M1V FRP65M2V FRP65M3V FRP65M4V

80 60 40

50

20 0 0

10

20

30

40

50

60

0

70

0

10

20

30

Time (ms)

(C) FRP65M1V FRP65M2V FRP65M3V FRP65M4V

250

200

150

100

50

0 0

40

Time (ms)

300

Impact force (kN)

Impact force (kN)

250

20

40

60

80

100

120

140

160

Axial displacement (mm) Fig. 7. Impact behaviour under different impact masses. 252

180

50

60

70

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(A)

300

FRP65MV1 FRP65MV2 FRP65MV3 FRP65MV4

240

FRP65MV1 FRP65MV2 FRP65MV3 FRP65MV4

220 200

Axial displacement (mm)

250

Impact force (kN)

(B)

260

200

150

100

50

180 160 140 120 100 80 60 40 20

0

0

0

10

20

30

40

50

60

70

80

0

10

20

Time (ms)

30

40

50

60

70

80

Time (ms)

(C) 300

FRP65MV1 FRP65MV2 FRP65MV3 FRP65MV4

Impact force (kN)

250

200

150

100

50

0 0

20

40

60

80

100 120 140 160 180 200 220 240 260

Axial displacement (mm) Fig. 8. behaviour under different impact velocities.

Based on the peak impact force, axial displacement of the tubes and the velocity vs. time responses, it can be seen that the CFRP wraps have significant effect on the system performance. CFRP layers can provide a confinement effect in the hoop direction of the tube to the inner steel tube. The stiffness of the structure is also increased to a certain extent because of the longitudinal CFRP layer. The total stiffness of the structure has been enhanced due to the combined effect of the CFRP in both the directions. Hence, the wrapped steel tubes were capable of sustaining higher impact force and reduce the axial displacement. However, the peak impact force was found to be more sensitive to the impact velocity than the impact mass in this study. Fig. 11 illustrates the variation of peak impact force with the mass and the velocity. Table 6 and 7 show that peak impact force and average crushing force of the tubes were increased after wrapping with CFRP. About 25% increment of peak impact force was observed when using normal modulus CFRP. The use of normal modulus CFRP with different adhesive strengths also exhibited about 25% of peak impact force increment compared to the bare steel tube. The models with high modulus CFRP properties exhibited a greater percentage of peak impact force increment (36%) and greater average crushing force increment (11%) during the simulation. Other than that, the comparison of average crushing forces showed that there is no significant increment of the average crushing force for most of the CFRP wrapped models. Fig. 12 illustrates the stress distribution of longitudinal CFRP and

the failure mode is presented in Fig. 6. This change in the stiffness could lead to the variation of the average crushing forces. The increase in the modulus has resulted in an increase in the peak impact force and the average crushing force. Furthermore, the axial displacement of the steel tube also reduced with introducing the wrapping. It was found that using high modulus CFRP has resulted in 18 mm reduction in the axial displacement of the steel tube. The results showed that using normal modulus CFRP and GFRP could reduce axial displacement by and 9 and 12 mm, respectively. 4.5. Impact behaviour The relationships between impact forces vs. axial displacements indicated that the axial displacement of CFRP wrapped steel tubes was dependent on the folding mechanism which was directly related to the impact energy. This can be explained by the kinetic energy formula. With the increase of the mass and velocity, the kinetic energy of the impactor has been increased which leads CFRP wrapped steel tube to produce more folds and more severe deformation. This folding type of failure is common for tubular structures under axial impacts and reported in the research literature [37,39]. Both the bare steel tubes and CFRP wrapped tubes underwent same failure mode with absorbing the same amount of impact energy during the numerical simulation. Almost all the impact energy carried by the impactor was absorbed by the tube. 253

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160

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100 80 60 40 20

0 0

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Axial displacement (mm) Fig. 9. Impact behaviour under different adhesive strength.

been discussed. Following conclusions can be drawn based on the results and discussions presented in this paper.

Table 8 Properties of different types of fibres.

Normal modulus CFRP High modulus CFRP GFRP

Elastic modulus (GPa)

Tensile strength (MPa)

Density (kg m−3)

230

3800

1700

640 73

2600 3400

2100 2600

1. Effect of the impact mass considered within the study did not have a major effect on the peak impact force. However, both the axial displacement and absorbed internal energy were increased significantly with the increased in impact mass. 2. Impact velocity was found to be a dominant parameter when the tube was subjected to an axial impact load, and the peak impact force was sensitive up to a certain impact velocity (6 ms−1). Beyond such impact velocity, the peak impact force did not significantly vary with the speed of impact. 3. Adhesive strength did not significantly influence the structural response of CFRP wrapped steel square hollow tube under axial impact loading. 4. Fibre modulus was found to be a significant parameter for the CFRP wrapped steel tubes under axial impact loading. Depending on the fibre type, the peak impact force could rise up to 36%, and meanwhile, the axial displacement could be reduced. 5. Based on the results of peak impact force, axial displacement of the tubes and the velocity vs. time responses, it can be concluded that CFRP strengthening have significant positive effect on the system performance under impact loading. The total stiffness of the structure has been enhanced due to the combined effect of the CFRP in

transverse CFRP layers of the FRP65 model during the initialisation of the failure. The stress contours of CFRP layers showed that CFRP had not reached its ultimate tensile strength when the tube failed. It clearly indicated that the CFRP failure mode was not a tensile failure mode. 5. Conclusions In this paper, the behaviour of CFRP wrapped hollow square steel tubes under axial impact loading is investigated using numerical simulation validated using existing experimental data. The validated results are in good agreement with the experimental data. They were then used to carry out the parametric study. The influence of the impact mass, impact velocity, adhesive strength and the CFRP fibre modulus on the peak impact force, axial deflection and the internal energy have 254

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Axial displacement (mm) Fig. 10. Impact behaviour with different types of fibres.

(A)

(B)

274

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Peak impact force (kN)

270

266 264 262 260 258 256 254

264 262 260 258 256 254

252 250 100

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0

1

Impact mass

2

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Impact velocity (m/s) Fig. 11. Peak impact force variation. 255

6

7

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Fig. 12. Stress distribution of FRP65 model CFRP layers during failure initialisation (A) longitudinal CFRP layer (B) transverse CFRP layer.

both the directions.

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