Damage to carbon fibre reinforced polymers (CFRP) in hole-clinched joints with aluminium alloy and CFRP

Journal Pre-proofs Damage to carbon fibre reinforced polymers (CFRP) in hole-clinched joints with aluminium alloy and CFRP Yang Liu, Weimin Zhuang, Shijie Wu PII: DOI: Reference:

S0263-8223(19)32082-3 https://doi.org/10.1016/j.compstruct.2019.111710 COST 111710

To appear in:

Composite Structures

Received Date: Revised Date: Accepted Date:

2 June 2019 20 October 2019 18 November 2019

Please cite this article as: Liu, Y., Zhuang, W., Wu, S., Damage to carbon fibre reinforced polymers (CFRP) in holeclinched joints with aluminium alloy and CFRP, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111710

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© 2019 Published by Elsevier Ltd.

Damage to carbon fibre reinforced polymers (CFRP) in hole-clinched joints with aluminium alloy and CFRP Yang Liua, Weimin Zhuanga,*, Shijie Wub a

State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China b

SAIC Volkswagen Automotive Co. Ltd., Shanghai 201800, China

Abstract: This study aimed to investigate the damage to carbon fibre reinforced polymers (CFRP) in hole-clinched joints composed of CFRP and aluminium alloy 5754. A continuous damage model (CDM) based on the modified Hashin failure criterion was proposed to predict the mechanical behaviour and damage evolution of the CFRP, and the CDM was validated using open hole tensile tests. The effect of the CFRP hole radius on the joint quality was investigated to obtain the optimal joining conditions. Furthermore, a numerical model for the hole-clinching process was developed to understand the forming mechanism of the joint and the damage patterns in the CFRP. The CFRP damage patterns with different ply angles in the hole clinching process were evaluated using numerical simulations. The proposed CDM can predict the mechanical behaviour and complex damage modes of CFRP. An increased hole radius generally corresponds to an increased neck thickness and a decreased undercut of the joints. Hole clinching cannot effectively join CFRP with a 0° ply, and delamination is most severe in joints with a complex angle ply. Keywords: Hole clinching; Carbon fibre reinforced polymers; Continuous damage model; Ply angle; Damage analysis

*Corresponding author: Tel. : +86-431-85095584-8508 E-mail address: [email protected]

1. Introduction To address issues of environmental pollution and energy shortages, increasing fuel efficiency, reducing production weight, and optimising vehicle performance have become attractive trends in the automotive industry. Hybrid metal–composite structures have been employed to construct lightweight automotive bodies [1]. The superior fatigue performance and high strength-to-density ratios of carbon fibre reinforced polymers (CFRP) have made these favoured materials in the automotive industry in recent years [2]. The use of multi-material structures presents challenges for joining methods. Mechanical clinching [3], self-piercing riveting (SPR) [4], friction stir welding [5], and adhesive bonding [6] have been applied to join composite sheets. Each of these various joining technologies have unique advantages. Mechanical fastening technologies, such as mechanical clinching and SPR, have been increasingly employed for body-in-white joining, owing to their superior ability to join materials with large differences in physical properties and the environmentally friendly nature of these joining processes. Mechanical clinching possesses additional advantages, such as not requiring additional fasteners, low cost, and excellent fatigue properties [7]. Clinching can be utilised to join similar or dissimilar metal sheets. Mucha [8] investigated the effects of clinching process parameters on the joinability of advanced high-strength steel. Abe et al. [9] joined ultra-high-strength steel sheets with different ductilities, using a clinching process. Steel with a high ductility was successfully joined with the help of modified dies. Furthermore, the joinability and tensile properties of clinched joints composed of similar and dissimilar titanium sheets were investigated by He et al. [10]. The joints were found to yield a better mechanical performance when titanium was utilised as the upper sheet. Xing et al. [11] discussed the suitability of clinching and SPR for joining the copper alloy H62. The fatigue properties of joints fabricated using different joining methods were compared by conducting mechanical tests. In addition, He et al. [12] simulated the joining of aluminium alloys using clinching, and the simulation results were validated experimentally. Lambiase et al. [13] investigated the feasibility of using clinching to join titanium with different aluminium alloys, and simulations and experiments were performed to analyse the forming quality and material flow for the resulting joints.

The results indicated that only aluminium AA7075 could be successfully joined to titanium. The static strength of clinched joints is relatively low, and thus some improved clinching processes have been proposed to enhance the mechanical properties of clinched joints. The clinch-bonded hybrid process has been widely applied, as the addition of an adhesive can significantly enhance the static strength and fatigue properties of clinched joints. Lei et al. [14] analysed the static performance of clinch-bonded hybrid joints for copper alloys, aluminium alloys, and galvanised steel sheets under tensile shear and cross-tension loading conditions. Chen et al. [15] introduced a new clinching reshaping method, using a special rivet to develop a reforming process to enhance the joint strength. The special rivet was helpful for guiding the material flow during the reforming process, which could improve the forming quality. The effect of the reshaping force on the geometric interlocking and mechanical properties of clinched joints was explored by Chen et al. [16]. A reshaping method using flat dies decreased the protrusion height and improved the strength of the joint. In addition, Zhang et al. [17] proposed a novel clinching–welding fastening method, and the load-bearing abilities and energy absorption performances of clinched joints were enhanced using the proposed joining method. Given its advantages, the use of mechanical clinching has been extended to the process of joining polymer materials. Lambiase [18] discussed the suitability of clinching for joining the aluminium alloy AA6082-T6 and polycarbonate sheets, and the effects of the tool shape and joining force on the forming quality and mechanical properties of the joints were analysed. The joints exhibited an optimal mechanical performance when round split dies were employed. Lambiase et al. [19] preheated the sheets before clinching, with the aim of joining the aluminium alloy AA5053 and polystyrene. The influence of the heating time, heating temperature, and forming pressure on the joint performance was investigated. Furthermore, Lin et al. [20] joined the aluminium alloy 5052 and thermoplastic CFRP using a preheated clinching process. The softened CFRP could withstand large deformations, and the resulting joints exhibited excellent properties when suitable clinching parameters were adopted. Lambiase et al. [21] investigated the joinability of aluminium and glass fibre reinforced polymers (GFRP), through clinching. Different tools and sheet thicknesses were adopted in the experiments to optimise the joint performance. In addition, Lambiase et al. [22] developed a two-step clinching process using reshaping tools.

This process could increase the undercut value, resulting in the enhancement of the mechanical behaviour of the joint. To decrease the damage to CFRP during clinching, a new process for joining CFRP and metal sheets, referred to as hole clinching, was presented by Lee et al. [23]. Lee et al. [24] conducted numerical analyses and experiments to investigate the influence of the tool shape on the joint performance. They reported that a sharp punch corner decreased the neck thickness of the joint and tended to result in neck fractures. Lambiase et al. [25] employed friction-assisted clinching to enhance the material formability, and the resulting joints exhibited good forming qualities, even with the use of sharp tools. Lee et al. [26] improved the hole clinching process using a spring die, which enhanced the formability of the metals and reduced the damage to the CFRP because of the increased hydrostatic stress during the clinching process. The damage evolution in the neck of the joint was also investigated using numerical simulations. However, these previous studies have mainly focused on damage and fracturing in the neck of the upper sheet during hole clinching. The constitutive model for the CFRP was assumed to be an elastic perfectly plastic material in the simulations [23, 24, 26], which cannot accurately predict the complex damage behaviour of CFRP. The damage to CFRP is crucial in determining the strength of hole-clinched joints. In this study, the damage to CFRP after hole clinching, is comprehensively explored. A continuous damage model (CDM) for CFRP is proposed to predict different damage patterns. Furthermore, open-hole tensile tests of CFRP with different ply angles and finite element (FE) analyses are performed to validate the CDM. In addition, the effect of the CFRP hole radius on the geometric interlocking parameters is investigated experimentally. An FE hole-clinching model is constructed, and the forming damage of the CFRP is evaluated through simulations.

2. Constitutive model of CFRP 2.1. Material degradation model A progressive damage analysis based on continuous damage mechanics has the capacity to predict the damage evolution of composites. In the three-dimensional (3D) stress state of composites, each ply is regarded as a homogeneous orthotropic material. Damage tensors are introduced to the model, and the CDM utilised in the study can be defined as follows [27]:

    11       22    33     12       23   13       

 12 E11  13 E11

-

0 0 0

 21 E22

 31 E33  32 E33

 0   1 0 0 0 (1  d 22) E22    23 1 0 0 0 E22 (1  d 33) E33   1 0 0 0 0  (1  d 12)G12   1 0 0 0 0  (1  d 23)G23   1 0 0 0 0  (1  d 13)G13 

1 (1  d 11) E11

-

-

0

0

 11    ,  22   33     12     23   13 

(1)

where dij are the damage variables, with the subscripts 1, 2, and 3 representing the fibre direction, perpendicular to the fibre direction in the ply, and perpendicular to the ply, respectively;  ij and  ij are the strain and stress tensors, respectively; E11 ,

E22 , and E33 are the Young’s moduli in the principal directions; G12 , G23 , and G23 are the shear moduli; and vij is the Poisson’s ratio. 2.2. Failure criterion and damage evolution 2.2.1. Failure criterion When damage occurs in composites, the local stress changes dramatically, while the strain changes gently. Thus, a failure criterion based on the equivalent strain is more suitable for determining the damage evolution of composites. The main failure modes of CFRP include fibre fracture, matrix cracking, fibre-matrix shear failure, and interlaminar delamination. The modified Hashin failure criterion was employed to determine the fibre and matrix damage, and interlaminar delamination was determined according to the Linde failure criterion [28]. The initial failure strain in each failure mode can be defined as follows:  ft0 

Xt X Y Y Z Z 0 0 ， fc0  c ， mt  t ， mc  c ， dt0  t ， dc0  c ， C11 C11 C22 C22 C33 C33

120 

(2)

S S S12 ， 230  23 ，130  13 2C44 2C55 2C66

where  ft0 and  fc0 are the initial tensile and compressive failure strains in the fibre 0 0 direction, respectively;  mt and  mc are the initial tensile and compressive failure

0 strains in the transverse matrix direction, respectively; 120 ,  23 , and 130 are the

initial shear failure strain components; X t , Yt , and Z t denote the tensile strength in the principal directions; X c , Yc , and Z c denote the compressive strength in the principal directions; S12 , S 23 , and S13 denote the shear strength components; and

Cij denotes the stiffness matrix components. The mathematical formulations of the proposed failure criterion are given as follows: 11 2 12 2 13 2 )  ( 0 )  ( 0 )  1 Fibre tension (11  0) ,  ft0 12 13  rfc  ( 110 )2  1 Fibre compression (11  0) ,  fc

rft  (

rmt  ( rmc 

 22   33 2  232   22 33 12 2 13 2 )   ( 0 )  ( 0 )  1 Matrix tension ( 22   33  0) , 0 2  mt0 ( 23 ) 12 13

0  22   33  mc  22   33 2  232   22 33 12 2 13 2 2 [( )  1]  ( )   ( 0 )  ( 0 ) 1 0  mc 2120 120 ( 230 )2 12 13

rfs  ( rfd 

(3) (4)

(5)

Matrix compression ( 22   33  0) (6)

11 2 12 2 13 2 )  ( 0 )  ( 0 )  1 Fibre-matrix shear (11  0) ,  fc0 12 13  332  1 1  ( 0  0 )  ( 130 )2  1 Interlaminar delamination. 0 0  dt dc  dt  dc 13

(7)

(8)

2.2.2. Damage evolution When the material meets the failure criterion, it will enter the damage evolution stage. The damage of the material is represented by a stiffness degradation, which results in a decrease in the loading capacity. Complete failure of the material occurs when the energy release rate reaches the fracture energy. The bilinear constitutive law was applied in the present study. This law is controlled by the intermediate damage variables, dI: dI 

 I f (   I 0 ) , I  ( ft，fc，mt，mc，dt，dc) ,  0     f , I I  ( I f   I 0 )

I f 

2GIc , I  ( ft，fc，mt，mc，dt，dc) ,  I max  ( X t , X c , Yt , Yc , Zt , Zc ) ,  I max Lc

(9)

(10)

where  I f represents the ultimate failure strain, GIc is the energy release rate, and

Lc is the characteristic length of an element. The damage variables dij in Eq. (1) can be defined as follows: d11  1  (1  d ft )(1  d fc ) , d22  1  (1  dmt )(1  dmc ) , d33  1  (1  ddt )(1  ddc ) ,

d12  1  (1  d f )(1  d m ) , d23  1  (1  dm )(1  dd ) , d13  1  (1  d f )(1  dd ) . (11) Furthermore, the damage variable in the fibre-matrix shear mode is assumed as follows:

d fs  1  (1  d11 )(1  d22 ) .

(12)

3. Validation of the constitutive model 3.1. Open-hole tensile experiments of CFRP CFRP composed of epoxy resin and T300 unidirectional fibre fabric was utilised in these experiments. The CFRP sheets were of the size 200 mm  36 mm  2.4 mm, and holes with radii of 3 mm were located in the centres of the sheets. The specimens were laminated in two different configurations: [0°]16 and [45°/-45°]4s. The material properties of the composite ply were provided by the manufacturer and are listed in Table 1. Table 1. Material properties of the composite ply Property

Symbol

Value

ρ

1530

Longitudinal Young’s modulus (GPa)

E11

127

Transverse Young’s modulus (GPa)

E22

8.41

Young’s modulus in the thickness direction (GPa)

E33

8.41

Shear modulus (GPa)

G12, G23, G13

4.41

Poisson’s ratio

v12

0.31

Longitudinal tensile strength (MPa)

Xt

2097

Longitudinal compressive strength (MPa)

Xc

1258

Transverse tensile strength (MPa)

Yt

42

Transverse compressive strength (MPa)

Yc

175

Tensile strength in the thickness direction (MPa)

Zt

42

Compressive strength in the thickness direction (MPa)

Zc

175

Shear strength (MPa)

S12, S23, S13

90

Density

(kg/m3)

Open-hole tensile tests were performed on the CFRP according to ASTM D5766/D 5766M-11, using a universal testing machine. The testing velocity was set to 2 mm/min. 3D digital image correlation (DIC) was utilised to obtain the strain fields of the specimens during the tensile tests, which required painting the specimen surfaces with randomly arranged white and black speckles before the tests. Two charge-coupled device (CCD) cameras were used to record images during the tensile tests. The CCD cameras had a lens focal length of 80 mm and spatial resolution of 3384 × 2704 pixels. Furthermore, the images were processed using VIC-3D software to display the strain field. Figure 1 shows the open-hole tensile test setup.

Fig. 1. Experimental setup used for DIC during the open-hole tensile tests

3.2. FE model The geometry of the 3D FE model was consistent with that of the specimens used in the tests. The model was partitioned in the direction of the sheet thickness, with each partition representing a ply. In addition, a material coordinate system was established to realise different layer angles in each ply. The CDM was implemented in ABAQUS 6.14/Explicit through a VUMAT user subroutine using the FORTRAN language. Element deletion was controlled by the intermediate damage variable, dI. When the damage variables dft or dfc were equal to 1, the element was automatically deleted from the model. The FE mesh and boundary conditions for the specimen are illustrated in Fig. 2. Because the damage was most likely to initiate around the circular hole, and considering the path of the crack propagation, the mesh was finest around the hole area. The element size increased smoothly from the hole, resulting in a gradient distribution along the length of the specimen, which reduced the computing resources required for the FE simulation. The smallest element size was approximately 0.2 mm, and the largest was 3 mm. There were 16 plies of elements through the thickness.

Fig. 2. Meshing and boundary conditions in the 3D FE model

As depicted in Fig. 2, one side of the specimen was completely constrained, while a displacement load was applied to the other side along the direction of the length. In an explicit analysis, the result of a quasi-static simulation is valid only if the kinetic energy does not exceed 10% of the internal energy. During this simulation, the kinetic energy exceeded the value of internal energy by 5%. 3.3. Comparison between the experimental and simulation results The load–displacement curves and failure modes obtained from the open-hole tensile tests and simulations are presented in Figs. 3 and 4. In the initial stages of tensile testing, the load of the [0°]16 CFRP sheet increased linearly. Finally, instant fracture occurred along the fibre direction near the hole, causing the load to decrease sharply. A similar trend is observed in the load–displacement curve of the [45/-45]4s CFRP, but the stiffness underwent an evident decline compared with the [0°]16 CFRP, and the specimen ultimately broke along the -45 fibre direction. The trends in the load–displacement curves and failure modes obtained from the simulations and experiments are similar. The simulation values for the failure load differed from the experimental values by a maximum of 9.6%.

Fig. 3. Comparison of the load–displacement curves obtained in the experiments and simulations

(a) [0°]16 CFRP (b) [45°/-45°]4s CFRP Fig. 4. Comparison of the failure modes obtained in the experiments and simulations

The strain field on the surface of the CFRP sheet before fracture was measured using DIC, and the results are compared with the simulation results in Fig. 5. The strain distributions obtained with the two methods are consistent, and the error of the strain component is less than 10%, confirming the effectiveness of the constitutive model. Simulation

DIC test

LE, LE12

(a) [0°]16 CFRP

LE, LE22

(b) [45°/-45°]4s CFRP Fig. 5. Comparison of the strain fields obtained with the DIC tests and simulations

3.4. Damage prediction of CFRP To verify the accuracy of the CDM for predicting the complex damage modes of CFRP, the progressive damage of the CFRP was analysed. The damage evolution of [0°]16 CFRP during the tensile test process is illustrated in Fig. 6, where S represents the total tensile displacement. Matrix tensile damage, shear damage, and slight delamination can be observed in the 0° layers, leading to the specimen fracturing along the fibre direction. No fibre damage occurred before the complete failure of the specimen. When the displacement was 0.1S, matrix tensile damage was first generated at the edge of the hole, resulting in microcracks in the matrix. The damage then propagated along the fibre direction from the upper and lower sides of the hole, and the cracks were parallel to the loading direction. As the displacement increased to 0.23S, shear damage occurred around the hole. As the displacement increased further, the shear damage extended along the fibre direction, and the resulting damage region surrounded the hole. Delamination was initiated between the layers as the displacement reached 0.5S, and the final damage area was only distributed on both sides of the hole. 0.1S Damage value

0.23S

0.5S

0° fibre

value

(a) Matrix tensile damage

0.99S

(b) Delamination

(c) Fibre-matrix shear damage Fig. 6. Damage evolution pattern of [0]16 CFRP

Figure 7 illustrates the damage evolution of the [45°/-45°]4s CFRP during the tensile testing process. It can be observed from the simulation results that the damage patterns in the 45° and -45° layers were distributed symmetrically, and thus the damage evolution in the 45° layer was analysed. During the tensile process, serious matrix damage, shear damage, and delamination in the ±45° layers occurred, resulting in the specimen fracturing along the fibre directions. At a displacement of 0.08S, matrix tensile damage could be observed around the hole, and matrix microcracks formed and propagated along the 45° fibre direction. Finally, the ultimate damage area penetrated the width of the sheet. As the displacement increased to 0.16S, delamination and shear damage occurred simultaneously, with the damage mainly extending along the 45° fibre direction. When the specimen failed, shear damage surrounded the hole, and the [45°/-45°]4s CFRP suffered more severe delamination than the [0°]16 CFRP. 0.08S Damage value

0.16S

0.5S

0° fibre

(a) Matrix tensile damage

0.99S

(b) Delamination

(c) Fibre-matrix shear damage Fig. 7. Damage evolution pattern of [45°/-45°]4s CFRP

Based on the above analysis, the damage variables obtained in the simulations can characterise the failure region of the CFRP. Therefore, the established CDM can accurately predict the progressive damage process for CFRP sheets under complex failure modes.

4. Hole-clinching experiments 4.1. Materials The sheet materials utilised in the hole-clinching experiments were CFRP and AA5754 aluminium alloy. The composition and mechanical properties of the CFRP are described in Section 3.1. The design of CFRP sheets in the hole-clinching referred to the reference [26]. The size of an AA5754 sheet was 95 mm  35 mm  1.5 mm, and a CFRP sheet had dimensions of 95 mm  35 mm  1 mm. Furthermore, the hole radii were 4 mm, 4.1 mm, and 4.2 mm, and the utilised CFRP lamination sequences were [0°]6, [0°/90°]3, [45°/-45°]3, and [45°/90°/-45°/0°/90°/45°], respectively. 4.2. Technological process A schematic representation of the hole-clinching process is presented in Fig. 8. A punch, die, and blank holder are required to join the sheets. Some parameters affect the formation of the joint, including the punch diameter and chamfer and the die diameter and depth. The design of the tool shape was adopted from reference [23]. The geometries of the tools used for clinching are presented in Fig. 9.

The clinching process was performed on a servo-driven riveting machine, manufactured by Wuhan Jiarui Riveting Equipment Co., Ltd. (China), and the sheets were clinched with a lap area of 35 mm × 35 mm using a clinching machine. The joints were produced with a bottom thickness of 0.4 mm by controlling the displacement of the punch. Furthermore, the downward velocity of the punch was set to 1 mm/s.

Fig. 8. Schematic representation of the hole-clinching process

(a) Punch

(b) Die

Fig. 9. Geometries of the tools (dimensions in mm)

4.3. Effect of the CFRP hole radius on the joint quality As shown in Fig. 10, the neck thickness TN, undercut TU and bottom thickness X are critical parameters in the cross-section of the joint, and represent the main factors influencing joint strength. The hole-clinched joints with different ply angles have the same cross-section parameters. Figure 11 shows the cross-sections of joints with different hole radii. Here, the joints had a neck thickness and undercut, and there were

no visible cracks in the AA5754 sheets. The variations in the neck thickness and undercut are illustrated in Fig. 12. Increasing the hole radius generally results in an increase in the neck thickness and a decrease in the undercut of a joint. An enlarged punch-hole clearance caused more material to remain in the neck and resulted in less material flow during the upsetting phase, leading to smaller undercuts in the joints. A comprehensive consideration of the neck thickness and undercut indicates that the optimal condition consists of a hole with a radius of 4.1 mm. Thus, a CFRP hole radius of 4.1 mm was adopted in the following hole-clinching simulations.

Fig. 10. Quality assessment criteria for the hole-clinched joint

(a) RH = 4 mm

(b) RH = 4.1 mm

(c) RH = 4.2 mm Fig. 11. Cross-sections of hole-clinched joints with different hole radii

Fig. 12. Variation in the neck thickness and undercut for different hole radii

5. Numerical hole-clinching simulations 5.1. FE model As shown in Fig. 13, a 3D FE model of the hole-clinching process was created to investigate the material flow and analyse the damage to the CFRP. Numerical simulations were implemented in ABAQUS 6.14 using the explicit solver. The punch, blank holder, and die were simulated as rigid bodies. Furthermore, an elastoplastic model was applied for the AA5754 sheet, and the mechanical properties of AA5754 are listed in Table 2. If the constitutive model is effective, it applicable to the CFRP sheets with different specimen sizes and ply angles. Thus, the CDM proposed in Section 2 was utilised to simulate the mechanical behaviour of the CFRP.

(a) Whole FE model

(b) Cross-section of the FE model Fig. 13. FE hole-clinching model Table 2. Mechanical properties of the AA5754 sheet Density

Elastic modulus

Tensile strength

Yield strength

(kg/m3)

(GPa)

(MPa)

(MPa)

2700

70

244.1

162.1

Poisson’s ratio 0.3

Solid elements with reduced integration (C3D8R) were employed for discretisation. Because the upper sheet undergoes significant deformation during the hole clinching process, an extremely fine mesh was employed in the joining region of the upper sheet. The element size in the upper sheet varied from 0.07 to 0.2 mm. To deal with the excessive mesh distortion, an arbitrary Lagrangian–Eulerian (ALE) adaptive mesh domain was utilised in the upper sheet during the simulations. An approximate mesh size of 0.166 mm was applied in the lower sheet, to realise the six element layers in the thickness of the CFRP. The definitions of the layer angles in each ply are introduced in Section 3.2. During the simulations, the punch followed a defined law to move downward with a displacement of 2.1 mm, while the die was fixed. Furthermore, the blank holder applied a force of 1000 N to clamp the substrate sheets. A surface-to-surface contact algorithm was selected to model the friction at the interface between the parts, and the following friction coefficients were adopted: μ = 0.2 at the interface between the punch and AA5754 [29], μ = 0.1 at the interface between the AA5754 and CFRP, μ = 0.2 at the interface between the blank holder and AA5754, μ = 0.1 at the interface between the CFRP and the die, and μ = 0.2 at the interface between the AA5754 and die.

5.2. Validation of the hole-clinching model The FE model was validated by comparing the cross-sectional geometries of the experimental and simulated specimens. As shown in Fig. 14, the FE model can accurately characterise the material flow of the joint. Comparisons between the key geometric features of the numerical and experimental tests are summarised in Table 3, and the maximum deviation is less than 10%.

Fig. 14. Comparison of the cross-sections obtained in the experiment and simulation Table 3. Comparison between the cross-sectional geometries of the joint TN (mm)

TU (mm)

X (mm)

Experiment

0.821

0.254

0.44

Simulation

0.805

0.264

0.40

Error

1.9%

3.9%

9.1%

The material flow and evolution of the strain distribution during hole clinching are depicted in Fig. 15, where D is the total displacement of the punch. First, the AA5754 was compressed by the punch, and the material flowed into the pilot hole. When the punch displacement reached 0.25D, the material near the punch corner became thinner under the tension force, gradually forming the joint neck. In addition, a larger strain appeared in the area in contact with the punch corner. As the punch displacement increased, the material flowed downward, resulting in a high hoop tensile stress in the neck of the joint. Here, the strain concentration in the neck was liable to lead to neck fracture. Meanwhile, the material under the punch came into contact with the die and flowed in the radial direction. This region was not liable to induce damage owing to the compressive hydrostatic stress. During the formation of the undercut, the material was compressed between the punch and the die, and it flowed in the radial direction to form an interlock with the lower sheet, during which the bottom thickness decreased. During the deformation of the AA5754, the composite near the hole region was slightly deformed by the dragging and extrusion

forces, which induced damage in the CFRP.

(a) 0.1D

(b) 0.25D

(c) 0.75D

(d) 1.0D

Fig. 15. Simulation of the hole clinching process

5.3. Damage analysis of CFRP sheets with different ply angles 5.3.1. Joint with [0°]6 CFRP Because the damage patterns in each layer of the [0°]6 CFRP sheet are similar, the damage distribution of one layer is presented in Fig. 16. The joint suffered serious matrix damage and shear damage, while slight fibre compression damage occurred at the hole edge. The matrix compression damage was mainly distributed along the 90° fibre direction near the hole edge. The region of matrix tensile and shear damage was widely distributed, mainly along the 0° fibre direction, and the damage variables around the hole edge reached the maximum value of 1. This damage resulted in longitudinal cracking of the CFRP on both sides of the hole, as shown in Fig. 17. Thus, it can be concluded that the [0°]6 CFRP is not suitable for use in hole clinching.

Fibre compression

Fibre tension Matrix compression Matrix tension Fibre-matrix shear

Fig. 16. Predicted damage pattern of [0°]6 CFRP

Fig. 17. Fractured joint with [0°]6 CFRP

5.3.2. Joint with [0°/90°]3 CFRP As the layers with the same ply orientation have similar damage modes, and the damage was greatest in the layers near the upper surface of the CFRP, the 0° layer on the upper surface of the CFRP and its adjacent 90° layer were selected for damage analysis, as shown in Fig. 18. During the clinching process, the CFRP did not suffer fibre damage, while matrix damage, shear damage, and delamination were observed in both layers. The hole surface was mainly subjected to hoop compression and shear stress owing to the material flow of AA5754, which resulted in more severe matrix tension and shear damage than matrix compression damage. Owing to the interlayer force, the corresponding damage propagated along the 0° and 90° fibre directions in both layers, resulting in a cross-shaped distribution around the hole. The damage variables in some areas reached a maximum, indicating that microcracks occurred around the hole. Overall, the damage degree in the 90° layer was less than that in the 0° layer. Fibre damage Matrix compression Matrix tension Fibre-matrix shear Delamination

(a) 0° layer

(b) 90° layer Fig. 18. Predicted damage pattern of [0°/90°]3 CFRP

5.3.3. Joint with [45°/-45°]3 CFRP The 45° layer on the upper surface of the CFRP and its adjacent -45° layer were selected for damage analysis, as shown in Fig. 19. Similar to the damage mode of the [0°/90°]3 CFRP, no fibre damage occurred, while matrix and shear damage with a cross-shaped distribution occurred near the hole in the ±45° fibre directions. The damage was more serious in the 45° fibre direction. However, the lengths of the microcracks caused by the matrix tensile damage and shear damage were less than those of the [0/90]3 CFRP. Slight delamination could be observed at the edge of the hole, and the damage value in most areas was less than the maximum threshold. Fibre damage Matrix compression Matrix tension Fibre-matrix shear Delamination

(a) 45° layer

(b) -45° layer Fig. 19. Predicted damage pattern of [45°/-45°]3 CFRP

5.3.4. Joint with [45°/90°/-45°/0°/90°/45°] CFRP Four different layers adjacent to the upper surface of the CFRP were selected for damage analysis, as shown in Fig. 20. In the hole-clinching process, different damage patterns were distributed around the hole, and slight fibre damage occurred in each layer. Compared to the other layers, the matrix tensile damage and shear damage were most severe in the 0° layer. Matrix compression damage and shear damage were both

present in the ±45° layers, with a corresponding failure occurring at edge of the hole toward the 45° fibre direction. In addition, the matrix compression damage and delamination tended to extend along the -45° fibre direction in the -45° layer. The principal failure modes in the 90° layer consisted of matrix tension damage, shear damage, and delamination. The damage areas were mainly distributed on both sides of the hole. Delamination in the [45°/90°/-45°/0°/90°/45°] CFRP spread over a large region around the hole, as delamination was liable to be induced between layers with different ply orientations. Fibre damage Matrix compression Matrix tension Fibre-matrix shear Delamination

(a) 0° layer

(c) -45° layer

(c) 90° layer

(d) 45° layer Fig. 20. Predicted damage pattern of [45°/90°/-45°/0°/90°/45°] CFRP

6. Conclusions A continuous CFRP damage model was proposed, and the constitutive model was validated using open-hole tensile tests for CFRP. The effect of the CFRP hole

radius on the joint quality was investigated experimentally, and the material flow and damage of the CFRP during the hole-clinching process were predicted using FE simulations. Based on these detailed experimental and numerical investigations, the following main conclusions can be drawn: (1) The proposed CDM can predict the mechanical behaviour and complex damage modes of CFRP, and there is a strong consistency between the experimental and numerical results for the open-hole tensile tests. (2) Using CFRP with a larger hole radius results in a lower undercut and larger neck thickness in the hole-clinched joint. (3) An excellent agreement between the experimental and numerical results can be achieved by utilizing the proposed FE model for the hole-clinching process. The forming mechanism and damage evolution of the joint could be better understood through the simulation results. (4) Hole clinching is unable to effectively join a [0°]6 CFRP sheet, owing to the large amount of matrix tension and shear damages that occur around the hole. The main damage patterns in the joints with [0°/90°]3 CFRP or [45°/-45°]3 CFRP consist of matrix tension damage and fibre-matrix shear damage along the fibre directions. Delamination is most severe in the joint with [45°/90°/-45°/0°/90°/45°] CFRP.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51775227＆51375201).

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