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Effect of the interference fit on the stress distribution and failure mode of a flat-head riveted GLARE joint
Journal Pre-proofs Effect of the interference fit on the stress distribution and failure mode of a flathead riveted GLARE joint Kai Jin, Hao Wang, Jie Tao, Jingming Tian PII: DOI: Reference:
S0263-8223(19)31280-2 https://doi.org/10.1016/j.compstruct.2019.111788 COST 111788
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 April 2019 3 December 2019 9 December 2019
Please cite this article as: Jin, K., Wang, H., Tao, J., Tian, J., Effect of the interference fit on the stress distribution and failure mode of a flat-head riveted GLARE joint, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111788
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© 2019 Published by Elsevier Ltd.
Effect of the interference fit on the stress distribution and failure mode of a flat-head riveted GLARE joint
Kai Jin1, 4, Hao Wang2, Jie Tao2, 3* and Jingming Tian2
1College
of Mechanical and Electrical Engineering, Nanjing University of
Aeronautics and Astronautics, Nanjing 211106, P.R. China. 2College
of Material Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.R. China.
3Jiangsu
Collaborative Innovation Centre for Advanced Inorganic Function Composites, Nanjing 211816, P.R. China.
4
Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology,
Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China *Corresponding
author: Phone: +86 025-5211-2911, Fax: +86 025-5211-2911, E-mail: [email protected]
ABSTRACT Glass laminate aluminium reinforced epoxy (GLARE) is an ideal material for fuselage skin, and a rivet joint is the most reliable way to connect fuselage skin. Due to the complex deformation of the joints and the effects of the riveted residual stress, the tensile failure modes are complex and difficult to predict during the service stage. A 3D constitutive model was employed to analyse the mechanical and failure
behaviours of the flat-head rivet joints of GLARE during the entire process from riveting to stretching. Under different fibre orientations of GLARE, the effects of the riveting interference on the stress distribution during riveting, the residual stress and the failure mode were investigated. The compressive stress and bending stress when the fibres were in the 0° direction are the main load modes during riveting, but only the bending stress in the 0° direction becomes residual stress. If the bending stress is more highly concentrated in a fibre layer, there is greater damage accumulation in the layer. Since a high interference fit may also cause the shear fracture of the rivet and serious interface delamination, the riveting interference should be under strict control against the different fibre orientations of GLARE.
KEYWORDS: GLARE, constitutive model, rivet joint, residual stress, failure mode
1. INTRODUCTION: Glass laminate aluminium reinforced epoxy (GLARE) is a sandwich-structured material consisting of aluminium sheets and glass-fibre composites. The material has high specific static properties fracture and fatigue resistance
[1-4],
excellent impact resistance
[9-13].
[5-8],
and outstanding
As a lightweight hybrid material, GLARE has
been successfully utilized in the aviation industry fuselage skin structures of the Airbus 380
[16]
[14, 15],
especially for the upper
and the cargo floor of the Boeing 777
[17].
For most commercial aircrafts, the ambient pressure is designed for an altitude of
at least 2500 m, where the atmospheric pressure is approximately 0.075 MPa [18]. The fuselage skin mainly endures the circumferential pressure, which is caused by the pressure difference between the cabin pressure and atmospheric pressure, and the longitudinal tensile stress caused by aerodynamic loading. Therefore, the strength of the GLARE fuselage skin is vital. Currently, single-shear lap riveting is considered to be the most reliable way to longitudinally connect the fuselage skin [19]. However, the joint area, which contains multiple discontinuities, is typically a point of structural weakness. Due to the stress concentration, structural failures are more likely to occur at the riveted joint area. Sinke
[20]
introduced a riveting process between single metal and fibre metal
laminates (FMLs) and noted that delamination and fibre breakage were the major problems of the riveting process. Huang
[21]
provided feasible methods and analysed
potential failure modes. Some researchers focused on drilling technologies to improve the riveting quality. Giasin, et al.
[22]
studied the effect of the drilling parameters on
the thrust, torque and surface roughness. These authors found that the spindle speed and feed speed significantly affected the drilling force and the quality of the rivet hole. Pawer et al.
[23]
showed that the feed speed played a leading role in controlling
delamination and burr formation. In addition, burrs could be reduced if the minimum quantity lubrication (MQL) was applied
[24, 25].
Park et al.
[26]
analysed the failure
mechanism during the drilling process and found the relationship between the drilling parameters and delamination. For the riveting process, Pan et al.
[27]
developed a
method of using polyaniline modified epoxy to protect the riveting interface, which
improved the joint performance. Ryan and Monaghan
[28]
analysed the failure
mechanism during riveting through the finite element method. Linde and Boer
[29]
presented a model to describe the inter-rivet buckling behaviour when FMLs were bolted together. Due to the complex deformation of joints and the riveted residual stress effect, it is difficult to predict the failure behaviour under loading conditions. To improve the structural performance of riveted joints, a study should be conducted to analyse the deformation behaviour and the failure mechanism during loading. It is essential to develop an accurate constitutive model to characterize the deformation and to predict failures. In this study, a 3D constitutive model with damage criteria for fibre metal laminate was presented, and this model can describe the metal ductile fracture, fibre breakage, matrix cracking and interface delamination. The new model can analyse the stress distribution in riveting, the residual stress distribution and the failure modes under different fibre orientations. Meanwhile, to control the riveting quality, the effect of the riveting interference as a control variable for the deformation and failure modes was investigated through experiments and simulations.
2. EXPERIMENTAL 2.1. GLARE preparation The thickness of the prepreg was 0.125 mm with S4 glass fibre as the reinforcement phase and E302 epoxy as the matrix. The aluminium alloy 2024-T3 of 0.3 mm was used for the metal layers. To improve the contact area with the resin
matrix, the metal sheet was treated by anodizing before laying up. GLARE with a 3/2 structure, as listed in Table 1, was prepared by stacking layers of aluminium sheets and prepregs unidirectionally at 0° [Al/0°/0°/Al/0°/0°/Al] (GLARE 2A) and orthogonally
at
90°
[Al/0°/90°/Al/90°/0°/Al]
(GLARE
3).
An
autoclave moulding method was used to produce the FMLs. GLARE 2A has excellent tensile property, which is suitable for bearing a unidirectional load. GLARE 3 has excellent impact resistance and can bear the bending stress caused by the pressure load and the weight of the fuselage, which is suitable for the upper fuselage skin. Table 1 GLARE structures in this study 0° fibre
90° fibre
volume fraction
volume fraction
1.4 mm
35.7%
0%
1.4 mm
17.8%
17.8%
Name
Orientation
FMLs thickness
GLARE 2A-3/2
[0°/0°]sy
GLARE 3-3/2
[0°/90°]sy
Fig. 1 FMLs structure diagram: (a) GLARE 2A-3/2; (b) GLARE 3-3/2
2.2. Drilling and riveting The effectiveness of an FML connection depends on the drilling quality. Delamination is most likely to occur due to a weak interfacial strength. According to previous research [30, 31], a reduction in the axial thrust can avoid delamination during drilling. Meanwhile, the geometric parameters of the drill bit significantly affect the quality of the holes
[32, 33].
A TiAlN-coated carbide drill bit with two rows of crumbs
slots was adopted. The diameter (D) was 4.1 mm, the chisel edge width was 0.246
mm (0.06 D), the vertex angle was 120°, and the helix angle was 30°. The drilling process is shown in Fig. 2 (a), where MQL was used to remove the cutting heat. The spindle speed was 7500 rpm, and the feed speed was 0.1 mm/r. The drilled hole (Fig. 2 (b)) was smooth without defects, such as delamination and fibre pull-out.
Fig. 2 Images of the drilling process: (a) Equipment setup; (b) Surface appearance of the hole
Aluminium alloy 2024-T3 flat-head rivets (see Fig. 3 (a)) were used in this study. The nominal diameter (d) was 4.0 mm, the nominal length (l) was 8.0 mm, the flat-head thickness (k) was 2.0 mm, the flat-head diameter (dk) was 8.0 mm and the chamfering (r) was 0.1 mm. To prevent impact damage, the experiments used press riveting. A Type-C pneumatic squeeze riveter is shown in Fig. 3 (b). The pressure was controlled between 4.5 kg/mm2 and 5.0 kg/mm2. Since the axial compression and radial expansion of the rivet rod occur simultaneously, a stable hardening surface around the hole can be formed for a single metal. However, excessive expansion of the rivet may cause delamination due to the low interlaminar bonding strength of GLARE. Therefore, to avoid delamination, the riveting interference was set as a control variable and used to control the riveting process. The interplay between the fibre orientation and the riveting interference was also investigated.
(a)
(b)
Fig. 3 Images of the riveting process: (a) Flat-head rivet dimensioned drawing; (b) Type C pneumatic squeeze riveter
The riveting interference is controlled by the pressure of the riveting force, hole diameter and upsetting size and is used to evaluate the squeeze to the wall of the hole. Within a reasonable interference, the stress states and wall surface structure of a hole can be effectively improved through interference-fit riveting, which improves the fatigue life. To observe the interference after riveting, the sample was cut vertically along the centre line of the hole using a Struers secetom-15 precision cutting machine. The geometric data were measured by a Hirox RH-2000 3D video microscope.
Fig. 4 Schematic diagram of the interference calculation
Because of the cutting error, the measured flat-head diameter (d4) and measured rivet rod diameter (d2) were different from the real flat-head diameter (d3) and real rivet rod diameter (de), as shown in Fig. 4. The relative interference (he) is expressed in Eq. (1) and (2) using the initial hole diameter (d) and real rivet rod diameter (de). The height of the controlled rivet tail (H) and relative interference (he) are listed in Fig.
5. ℎ𝑒 =
𝑑𝑒 ― 𝑑 𝑑
𝑑𝑒 =
× 100% 𝑑2𝑑3 𝑑4
(1) (2)
Fig. 5 Geometry appearance of the cut section: (a) GLARE 2A; (b) GLARE 3
2.3. Tensile test According to ASTM D3552-17, tensile tests of the riveted GLARE were carried out using the SANS CMT5105 universal material testing machine. The tensile speed was set to 1.0 mm/min. The geometry of a test specimen and test setup are shown in Fig. 6. Since different riveting interferences cause different structural deformations, the loading capacity of the riveted joint components may be strengthened or weakened. For a single metal, greater expansion of the rivet rod and a smaller thickness of the rivet tail lead to greater compression on the wall of the hole. Therefore, the riveted joint components can theoretically bear more load under shear and tensile conditions. However, for GLARE, more expansion of the rivet rod may result in delamination or matrix cracks in the experiment. When the rivets are moderately extruded around the hole, the passivation effect of the local plastic zone can significantly reduce the stress concentration and effectively improve the tensile behaviours of riveted joints. The mechanisms of the deformation and failure modes are analysed in Section 4.
Fig. 6 Tensile test: (a) Test specimen; (b) Test equipment setup
3. NUMERICAL SIMULATION 3.1. 3D constitutive model In this study, an integrated 3D constitutive model was proposed to describe the mechanical behaviours of the aluminium alloy layers, glass fibre-reinforced plastic (GFRP) layers [34] and Al/GFRP interface layers. Ductile fracture of aluminium occurs under uniaxial tension. Therefore, a damage model for ductile fracture prediction should be considered. Using the Voce model
[35]
and Rice and Tracey model
[36],
the elasto-plastic model of metal layers is
expressed as: 𝜎𝑎 =
{(1 ―𝜎𝐷)𝜎
𝑦
𝑦
𝑖𝑓 𝐷 > 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑝
𝜎𝑦 = 𝜎𝑦0 + 𝑄(1 ― 𝑒 ―𝑏𝜀 )
𝑑𝐷 =
{
𝑑𝜀𝑝 𝜒𝑐𝑟 ∙ 𝑒
0
3 ― 𝜂 2
(3) (4)
1
𝑖𝑓 𝜂 > ― 3
(5)
𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where 𝜎𝑎 is the apparent flow stress; D is the accumulated damage; 𝜎𝑦 is the yield stress; 𝜎𝑦0 is the initial yield stress; 𝜀𝑝 is the effective plastic strain; 𝜂 is the stress triaxiality; and 𝑄, 𝑏 and 𝜒𝑐𝑟 are the model parameters.
The tensile behaviour of GFRP was described by Hooke's law, considering the damage criteria. Based on the model of Linde et al.
[29, 37],
a constitutive model with
3D damage criteria is presented as follows: (6)
𝝈𝑮𝑭𝑹𝑷 = 𝑪𝑫, 𝑮𝑭𝑹𝑷𝜺𝑮𝑭𝑹𝑷
𝑪𝑫, 𝑮𝑭𝑹𝑷 =
[
(1 ― 𝐷𝑓)𝐶11 (1 ― 𝐷𝑓)(1 ― 𝐷𝑚)𝐶12 (1 ― 𝐷𝑓)(1 ― 𝐷𝑧)𝐶13 (1 ― 𝐷𝑚)𝐶22 (1 ― 𝐷𝑚)(1 ― 𝐷𝑧)𝐶23 (1 ― 𝐷𝑧)𝐶33
(1 ― 𝐷𝑓)(1 ― 𝐷𝑧)𝐶55
𝑆𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐
𝜀𝑡11
𝜀𝑡22
( ― 𝐶22𝜀𝑡22(𝑓𝑚 ― 𝜀𝑡22)/𝐺𝑚)
(9)
𝜀𝑡33
( ― 𝐶33𝜀𝑡33(𝑓𝑧 ― 𝜀𝑡33)/𝐺𝑧)
𝑓𝑧 𝑒
(
𝜀𝑡11
2 𝑓𝑓 = 𝜀𝑐11(𝜀11) + 𝜀𝑡11 ―
(𝜀22) + 𝜀𝑐
𝑓𝑚 =
𝑓𝑧 =
𝜀𝑡33
22
2
(𝜀33) +
𝜀𝑐33
2
(
𝜀𝑡33
―
(
𝜀𝑡22
―
(𝜀𝑡22)2 𝜀𝑐22
(𝜀𝑡11)2 𝜀𝑐11
)
𝜀22 +
𝜀𝑡33 2
(𝜀𝑡33)2 𝜀𝑐33
(1 ― 𝐷𝑚)(1 ― 𝐷𝑧)𝐶66
(8)
𝑓𝑓 𝑒
𝐷𝑚 = 1 ― 𝑓𝑚 𝑒
𝜀𝑡22
(7)
( ― 𝐶11𝜀𝑡11(𝑓𝑓 ― 𝜀𝑡11)/𝐺𝑓)
𝐷𝑓 = 1 ―
𝐷𝑧 = 1 ―
]
0 (1 ― 𝐷𝑓)(1 ― 𝐷𝑚)𝐶44
)𝜀 + ( ) (𝜀 33
𝜀𝑠23
)𝜀
11
(10)
> 𝜀𝑡11
𝜀𝑡22 2
( ) (𝜀 𝜀𝑠12
23)
2
+
2 12)
𝜀𝑡33 2
(11)
> 𝜀𝑡22
( ) (𝜀 𝜀𝑠13
2 13)
> 𝜀𝑡33
(12)
(13)
where 𝑪𝑫, 𝑮𝑭𝑹𝑷 is the stiffness matrix; 𝐷𝑓, 𝐷𝑚 and 𝐷𝑧 are the fibre and matrix damages; 𝑓𝑓, 𝑓𝑚 and 𝑓𝑧 are the failure criteria; 𝐺𝑓, 𝐺𝑚 and 𝐺𝑧 are the fracture energies for fibre failure, matrix failure in the ply plane and matrix failure in the thickness direction, respectively; 𝜀𝑡11 and 𝜀𝑐11 are the fibre failure strains for tension and compression in the fibre direction, respectively; 𝜀𝑡22, 𝜀𝑐22 and 𝜀𝑠12, which are perpendicular to the fibre direction in the ply plane, are the matrix failure strains for tension, compression and shear, respectively; and 𝜀𝑡33 and 𝜀𝑐33, are the matrix failure strains for tension and compression, respectively. 𝜀𝑠13 and 𝜀𝑠23 are the matrix
shearing failures in the thickness direction. 𝜀𝑖𝑗 is the strain of GFRP layers. To predict the interlaminar fracture under the open mode (Mode Ⅰ), sliding mode (Mode Ⅱ) or tearing mode (Mode Ⅲ), a 3D cohesive model was developed, based on the study of Xu and Needleman [38] as follows:
𝛷(𝛥𝑛,𝛥𝑡,𝛥𝑠) = 𝛷𝑛 + 𝛷𝑛𝑒
{
―
𝛥𝑛
𝛷𝑛 ― 𝛿 𝛥𝑛
𝑇𝑛 = 𝛿𝑛 𝑒
𝑛
{
𝛥𝑛 𝛿𝑛
𝛿𝑛 𝑒
―
(1 ― 𝑟 + )( ) ― [𝑞 + ( ) ]𝑒
( )+ 2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
𝛥𝑛
1―𝑞
𝑟 ― 𝑞 𝛥𝑛
𝛿𝑛
𝑟―1
𝑟 ― 1 𝛿𝑛
[
1―𝑞 𝑟―1
―
1―𝑒
[ ( ) ]𝑒
𝛷𝑡𝛥𝑡
𝑇𝑡 = 2 𝛿𝑡 𝛿𝑡 𝑞 +
𝑟 ― 𝑞 𝛥𝑛
𝑟 ― 𝑞 𝛥𝑛
2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
―
𝛥𝑛 𝛿𝑛
―
―
𝛥𝑛 𝛿𝑛
―
𝑒
𝑟 ― 1 𝛿𝑛
[ ( ) ]𝑒
𝛷𝑠𝛥𝑠
𝑇𝑠 = 2 𝛿𝑠 𝛿𝑠 𝑞 +
( )
𝑟 ― 1 𝛿𝑛
𝑒
][
]
𝛥𝑛
𝑟 ― 𝛿𝑛
―
( ) 2 𝛥2 𝑡 + 𝛥𝑠 𝛿2 𝑡
}
( ) 2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
( ) 2 𝛥2 𝑡 + 𝛥𝑠 𝛿2 𝑡
𝛷𝑛 = 𝑒 ⋅ 𝜎𝑚𝑎𝑥 ⋅ 𝛿𝑛 𝛷𝑡 = 𝛷𝑠 =
𝑒 2
⋅ 𝜏𝑚𝑎𝑥 ⋅ 𝛿𝑡
}
(14)
(15)
(16)
(17) (18) (19)
where 𝛷 is the total potential failure energy; 𝛷𝑛, 𝛷𝑡 and 𝛷𝑠 are the work of separation of the potential failure energy in each direction; 𝑇𝑛 is the traction in the normal direction; 𝑇𝑡 and 𝑇𝑠 are the tractions in the tangential directions; 𝛥𝑛, 𝛥𝑡 and 𝛥𝑠 are the opening displacements in each direction; 𝛿𝑛, 𝛿𝑡 and 𝛿𝑠 are the characteristic length when debonding; 𝑞 and 𝑟 are the coupling parameters.
3.2. Finite element modelling
The aim of this study is to analyse the mechanical and failure behaviours of GLARE during the process chain. Using the user subroutine VUMAT, the presented 3D constitutive model was created in ABAQUS. Three aluminium alloy plies and four GFRP plies were built. Meanwhile, six individual plies of the cohesive elements were placed between the aluminium ply and the GFRP ply and between the two GFRP plies, to represent the interfacial behaviour. In this study, GLARE with unidirectional (0°/0°) and orthogonal (0°/90°) plies (see Table 1) was used to investigate the effects of the fibre orientation on the deformation and failure behaviours. The material properties of the AA2024-T3 and GFRP were obtained from a series of tests in our laboratory and are listed in Tables 2-4. According to the setups of the riveting test and tensile test, the FE model was built by meshing a hexahedral element (C3D8), as shown in Fig. 7. The deformation and damage accumulation during the riveting process, the residual stress distribution after riveting and the failure behaviours during the uniaxial tensile process were predicted by the presented constitutive model.
Fig. 7 FE simulation model for the process chain
Table 2 Material properties of AA2024-T3 Parameter
Value
Young’s Modulus
E
73.8 GPa
Poisson's ratio
ν
0.33
Yield strength
σY
305 MPa
Tensile strength
σT
450 MPa
Elongation
εF
0.19
Strain hardening coefficient
Q
142.5
Strain hardening index
b
16.4
Critical void growth index
𝜒𝑐𝑟
2.0
Critical strain
εD
0.05
Table 3 Material properties of GFRP Parameter
Value
Young’s Modulus
Poisson's ratio
Ultimate strength
E11
55.0 GPa
E22
9.5 GPa
E33
9.5 GPa
Ν12
0.33
Ν23
0.45
Ν13 𝜎𝑡11
0.33 2400 MPa
𝜎𝑐11 𝜎𝑡22 𝜎𝑐22
2000 MPa
𝜏12
75 MPa
𝜏23
50 MPa
𝜏13
75 MPa
50 MPa 150 MPa
Table 4 Parameters of the cohesive model Parameter Bonding strength
Characteristic length
4. RESULTS AND DISCUSSION 4.1. Stress analysis for riveting
Value
𝜎𝑚𝑎𝑥 𝜏𝑚𝑎𝑥 𝛿𝑛
26 MPa
𝛿𝑡
0.1
𝛿𝑠
0.1
75 MPa 0.2
By comparing the microscopic cross sections of the experiment and simulation, we found that when the axial compression of the nail rod was relatively large, the radial expansion of the rivet in GLARE 2A was relatively severe. The nail rod flowed towards the contact surfaces of two GLARE sheets, resulting in a clearance between the two sheets as shown in Figs. 8 (a) and (d). If the radial expansion of nail rod was small, the plastic flow of the nail rod tended to the easily deformed area and resulted in an uneven expansion as shown in Figs. 8 (b) and (e). If the interference was moderate, the radial expansion of nail rod was uniform as shown in Figs. 8 (c) and (f).
Fig. 8 Microscopic cross sections of the riveted GLARE 2A: (a) Rivet tail height (H) = 2.5 mm, relative interference (he) = 2.97%, in experiment; (b) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.95%, in experiment; (c) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.0%, in experiment; (d) Rivet tail height (H) = 2.5 mm, relative interference (he) = 2.97%, in simulation; (e) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.95%, in simulation; (f) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.0%, in simulation.
In GLARE 3 (see Fig. 9), when the radial expansion of nail rod was relatively small (he = 0.99%), the gap between the nail rod and hole was generated, which is different from the appearance of GLARE 2A. The formation of such gap was
attributed to the small amount of rivet interference, the weak adhesion between rivet and GLARE, and the slight external vibration, as shown in Figs. 9 (a) and (d). When the nail rod continued to compress in the axial direction, the radial extrusion of the nail rod to the hole increased as shown in Figs. 9 (b) and (e). When the nail rod fully squeezed the hole, the expansion of the nail rod (see Figs. 9 (c) and (f)) was completely uniform.
Fig. 9 Microscopic cross sections of the riveted GLARE 3: (a) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.99%, in experiment; (b) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.07%, in experiment; (c) Rivet tail height (H) = 2.5 mm, relative interference (he) = 3.05%, in experiment; (d) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.99%, in simulation; (e) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.07%, in simulation; (f) Rivet tail height (H) = 2.5 mm, relative interference (he) = 3.05%, in simulation.
During the riveting process, the deformations of the rivet and GLARE were generated together. The upper layer of GLARE was near the rivet tail, and the lower layer of GLARE was in contact with the flat-head. At 3.0% of the relative interference (he) and 2.5 mm rivet tail height (H), the stresses in each layer of GLARE 2A and GLARE 3 are shown in Fig. 10. For the GFRP layers, S11 denotes the stress parallel to
the fibre orientation, S22 denotes the stress perpendicular to the fibre orientation, and S33 denotes the stress along the thickness direction. For the Al layers, S11 is the stress along the roll direction of metal. As shown in Fig. 10 (a), the fibre layers (GFRP) mainly bear the rivet expansion force. Compared with the circumferential expansive force of the rivet, the pressing force in the direction of the thickness is very minor. The characteristics of the stress distribution can be analysed from two sections: 0° section and 90° section. For GLARE 2A (0°/0°), all the fibres in Line 1 are located in the 0° section (parallel to direction 1). When the rivet expanded, the fibres in Line 1 only suffered vertical compression. However, the fibres in Line 2 at the 90° section (parallel to direction 2) were bent due to the rivet expansion, presenting tension along the fibre orientation. For GLARE 3 (0°/90°), GFRP-1 and GFRP-4 are the 0° orientation layers; on the other hand, GFRP-2 and GFRP-3 are the 90° orientation layers. Fig. 10 (a) shows that the vertical pressures are more concentrated on the fibre layers (GFRP-1 and GFRP-4) that are parallel to the direction of the force. Moreover, the bending forces are more focused on the fibre layers (GFRP-2 and GFRP-3) that are perpendicular to the direction of the force. Two fibre layers in unidirectional placement can uniformly distribute the bending and compressive stresses, whereas two fibre layers with orthogonal placement may cause stress concentration, especially bending stress. To further study the characteristics of the stress distribution, the stresses in the metal layers and fibre layers are shown in Figs. 10 (b)-(g). For the metal layers, comparing Fig. 10 (b) with Figs. 10 (d) and (f), the stress distribution along the fibre
direction is different from those along the other two directions. This finding indicates that the stress of the aluminium alloy is affected by the fibre orientation. Since the fibres of GLARE 2A and GLARE 3 along their orientation provide enough support, the strains concentrate on this direction. Thus, the aluminium alloy layers also shoulder the responsibility. The compressive stress of the metal layers is directly proportional with the vertical pressures of the fibre layers. For the fibre layers, Figs. 10 (c), (e) and (g) show that the stresses of fibre and matrix change linearly. Due to a higher stress concentration of GLARE 3 in the fibre direction, the stress level is always higher than that of GLARE 2A. Conversely, the resin matrix shares the load with the metal. The matrix stress of GLARE 3 is more homogeneous, since the fibre orientation is orthogonal. In addition, GLARE 2A at Line 2 only has flexural load. The resin matrix and metal must share the increased vertical compressions, as shown in Figs. 10 (d) and (e). In the thickness direction (Figs. 10 (f) and (g)), the interface between two GLARE pieces affects the load transmission. In general, the stress distribution is controlled by the resin matrix and metal in the thickness direction.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Fig. 10 Stress distributions of Glare 2A and Glare 3: (a) Overall stress distribution; (b) Stress distribution of Al layers along the fibre direction; (c) Stress distribution of GFRP layers along the fibre direction; (d) Stress distribution of Al layers perpendicular to the fibre direction; (e) Stress distribution of GFRP layers perpendicular to the fibre direction; (f) Stress distribution of Al layers along the thickness direction; (g) Stress distribution of GFRP layers along the thickness direction
The constraints between the rivet devices and the riveted FMLs were relieved after riveting, and the residual stress was generated. Comparing the simulated contours of the rivet tail of GLARE 2A with the experimental results (see Fig. 11 (a)), we find the deformation behaviours under different relative interferences are accurately simulated. The residual stresses in each layer of GLARE 2A and GLARE 3 at 3.0% relative interference and 2.5 mm rivet tail height are shown in Figs. 11 (b) - (e). For GLARE 2A (0°/0°), the vertical pressures of the fibres were released in the 0° section (Fig. 11 (b)) due to the elastic recovery of 0° fibres and the rivet. However, only the partial bending stresses of the fibres in the 90° section (see Fig. 11 (c)) were released. The matrix stresses in the plane and thickness directions tended toward zero. A similar phenomenon emerged in GLARE 3 (0°/90°), which indicates that the bending stress of the fibres was a major mode of residual stress regardless of the fibre orientation. (a)
(b)
(d)
(c)
(e)
Fig. 11 Variation in the stresses after the riveting process: (a) Comparison of the contours of the upset head; (b) Comparison of the residual stress of GLARE 2A in Line 1; (c) Comparison of the residual stress of GLARE 2A in Line 2; (d) Comparison of the residual stress of GLARE 3 in Line 1; (e) Comparison of the residual stress of GLARE 3 in Line 2
The contribution of the interference on the residual stress parallel to the fibre orientation for the GFRP layers (S11) and along the metal rolling direction for the Al layers (S11) are shown in Fig. 12, since the residual stress is mainly reflected in the stress component (S11). The residual stresses of the layers along Line 1 (see Fig. 12 (a)) represent the stress distribution of the FML hole at the 0° section, while the residual stresses of the layers along Line 2 at the 90° section are shown in Fig. 12 (b). As shown in Fig. 12 (a), the compression of the fibres of GLARE 2A is not completely released if the relative interference is large (he = 2.97%), especially in the region near the rivet tail. If the relative interference is appropriate, the compression can be completely released. The fibre stress changed from compression stress to
tensile stress since the bending stresses transmitted to this region. For GLARE 3, the tensile force produced by bending in the 90° fibre orientation is a major residual stress. The stress decreased with the decreasing relative interference due to decreasing rivet nail rod expansion. Meanwhile, the residual stress concentrated in the region near the rivet tail. When GLARE 2A and GLARE 3 in Line 2 are compared (Fig. 12 (b)), it can be seen that the bending tension is still a main residual stress in GLARE 3. The variation trend in Line 2 is similar to that in Line 1. However, the bending force was shared by GFRP layers in GLARE 2A. Moreover, the residual stress was more concentrated on the GFRP layers near the rivet tail. The residual stress was evenly reduced in each GFPR layer with the reduced relative interference.
Fig. 12 Compression of the residual stresses after riveting: (a) Residual stress distribution in Line 1; (b) Residual stress distribution in Line 2
4.2. Failure analysis for riveted GLARE after the tensile test The tensile test results obtained from the experiments and simulations under the different relative interferences (see Fig. 13) indicate that GLARE 2A and GLARE 3 reached the maximum tensile peak force when the rivet tail height was 3.0 mm and 2.5 mm, respectively. Therefore, the tensile properties of riveted GLARE did not
change regularly with the interference variation. Riveting with different interferences changed the structure of riveted GLARE and enhanced or weakened the bearing capacity of the components. A smaller the height of the rivet tail corresponded to more plastic deformation and expansion of the rivet that squeezed the hole. During the riveting process, excessive extrusion of the rivet hole may cause excessive plastic deformation of the metal layers, fibre buckling fracture, matrix cracking or delamination. If the rivet is moderately squeezed around the hole using an appropriate interference, the passivation effect of the local plastic zone produced by the rivet to the hole wall can greatly reduce the stress concentration and effectively improve the tensile behaviour of the rivet joint.
Fig. 13 Load-displacement curves: (a) GLARE 2A; (b) GLARE 3
The failure of a rivet has two modes: rivet pull-out (Mode Ⅰ) and rivet shear fracture (Mode Ⅱ). The material constitutive model presented in the study accurately describes the failure behaviours, as shown in Fig. 14. To investigate the effect of the interference fit on the riveted GLARE failure behaviours, the damage and stress distributions of layers of GLARE 2A (H=3.5 mm and H=2.5 mm) and GLARE 3 (H=2.5 mm) are shown in Figs. 15 - 20. For Al layers, S11 is the stress in the X-axis, which is the tensile direction, and S22 is the stress in the Y-axis perpendicular to the
tensile direction. For GFRP layers, S11 is the in-plane stress parallel to the fibre orientation and S22 is the stress perpendicular to the fibre orientation.
Fig. 14 Failure modes of a rivet after tensile tests: (a) Failure mode of GLARE 2A (H=3.5 mm) in the experiment; (b) Failure mode of GLARE 2A (H=2.5 mm) in the experiment; (c) Failure mode of GLARE 2A (H=3.5 mm) in the simulation; (d) Failure mode of GLARE 2A (H=2.5 mm) in the simulation
For mode Ⅰ, the damage accumulation of each component is shown in Fig. 15. Damage was slightly accumulated in the rivet and the Al-1 and Al-3 layers of the upper GLARE (Fig. 15 (a)) due to the compression of the rivet nail rod as shown in Fig. 16 (a) and (b). The fibres were slightly damaged (Fig. 15 (b)) in the region where the tensile and residual bending stresses were concentrated. The damage in the fibre layers may be caused by a synergistic effect of the drawing force generated by the uniaxial tension (Fig. 16 (c)) and residual bending tension (Fig. 12 (b)). The resin matrix suffered a penetrating fracture, which was generated by the rivet squeezing and was propagated along the fibre orientation. The region of damage (Fig. 15 (c)) was consistent with the region of rivet compression concentration (Fig. 16(d)). Therefore,
the matrix damage was mainly caused by rivet compression. Delamination emerged on the interface between the two GLARE sheets due to the two reversed relative strains near the interface of two GLAREs. During the tensile test, there was no transverse fibre constraint around the hole. The deformations of the metal and matrix could not cooperate with each other. The matrix damage and delamination in the layer rapidly expanded with the increasing compression load of the rivet. (a)
(b)
(c)
(d)
Fig. 15 Damage accumulation distributions of GLARE 2A (H=3.5 mm): (a) Metal damage; (b) Fibre damage; (c) Matrix damage; (d) Delamination
(a)
(b)
(c)
(d)
Fig. 16 In-plane stress distributions of GLARE 2A (H=3.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
For mode Ⅱ, the rivet was completely fractured by shear stress and caused the
riveting failure. There was minor damage to the metal distributed around the hole without buckling (Fig. 17 (a)), which was caused by the compression of the rivet tail on the Al-1 layer in the tensile direction as shown in Fig. 18 (a). The resin matrix damage (Fig. 17 (b)) was significantly affected by the compression force perpendicular to the fibre orientation (Fig. 18 (d)). Delamination was generated on the Al/GFRP interfaces near the two jointed GLAREs (Fig. 17 (c)) due to two reversed relative stresses as shown in Fig. 18. Moreover, the comparison of Figs. 18 (c) and 16 (c) shows that the fractured rivet did not generate a large drawing force. Therefore, there was no fibre damage if a larger interference fit was used. Thus, the fibres can still uniformly undertake rivet pressure, although the matrix cannot transmit the load. (a)
(b)
(c)
Fig. 17 Damage accumulation distributions of GLARE 2A (H=2.5 mm): (a) Metal damage; (b) Matrix damage; (c) Delamination
(a)
(b)
(c)
(d)
Fig. 18 In-plane stress distributions of GLARE 2A (H=2.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
By comparing GLARE 3 (H=2.5 mm) with GLARE 2A (H=2.5 mm), we observe that the damage of GLARE 3 in the Al layers and resin matrix (Figs. 19 (a) and (c)) was smaller than that of GLARE 2A due to the transverse fibre constraints of the 90° fibre layers perpendicular to the direction of the tensile load. During the extrusion damage expansion stage of GLARE 3, the resin matrix only bore a small load. The 0° fibre layers and 90° fibres layers were synergistically subjected to the compression stress of the rivet and the tensile stress around the hole (Figs. 20 (c) and (d)). The 0º fibres in the 90º section had severe damages due to the stress
concentration and bending residual stress (Fig. 12), as shown in Fig. 19 (b). Meanwhile, a large interlaminar shear stress between the 0° fibre layer and the 90° fibre layer was generated due to two concentrated stresses in two mutual vertical directions. Thus, the delamination in GLARE 3 was serious. The upper layer of GLARE was completely delaminated around the hole. (a)
(b)
(c)
(d)
Fig. 19 Damage accumulation distributions of GLARE 3 (H=2.5 mm): (a) Metal damage; (b) Fibre damage; (c) Matrix damage; (d) Delamination
(a)
(b)
(c)
(d)
Fig. 20 In-plane stress distributions of GLARE 3 (H=2.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
5. CONCLUSIONS (1) A constitutive model with damage criteria for FMLs was presented to describe the deformation behaviour during the riveting process and to predict progressive failure. By using the model, the stress distribution during the riveting process, the residual stress variation after riveting and the failure modes of the tensile test were predicted. (2) It was found that the stress distribution of metal layers is controlled by the fibre orientation during riveting. The orthogonal placement of the fibre layers cannot
more uniformly distribute stress. In contrast, the orthogonal placement of the fibre layers may cause a high stress gradient between the layers and a stress concentration during riveting. (3) After riveting, the stresses in the rivet, metal layers and matrix of fibre layers are almost released. Only the bending stresses on the fibres are converted into residual stress, which is a precipitating factor for fibre breakage. Furthermore, fibre breakage only appears at the areas of bending tension concentration. More residual bending stress may cause heavier fibre damage accumulation. (4) Rivet pull-out and rivet shear fracture are the main failure modes of the rivet. For GLARE 2A, the fibre breakage and metal ductile damage are slight. The major failure is a penetrating fracture of the matrix in the thickness direction. The growth direction is along the fibre direction. If a high relative interference is used, delamination in each interface may occur around the rivet hole. Therefore, the riveting quality should be controlled by the relative interference of the rivet according to the fibre orientation.
ACKNOWLEDGEMENTS This work is supported by the Fundamental Research Funds for the Central Universities (No. NS2018032).
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AUTHOR STATEMENT
Kai Jin: Conceptualization, Methodology, Software, Formal analysis, Writing-Original draft preparation and Writing-Reviewing and Editing
Hao Wang: Data curation and Visualization
Jie Tao: Supervision, Resources and Project administration
Jiming Tian: Investigation
S0263-8223(19)31280-2 https://doi.org/10.1016/j.compstruct.2019.111788 COST 111788
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
10 April 2019 3 December 2019 9 December 2019
Please cite this article as: Jin, K., Wang, H., Tao, J., Tian, J., Effect of the interference fit on the stress distribution and failure mode of a flat-head riveted GLARE joint, Composite Structures (2019), doi: https://doi.org/10.1016/ j.compstruct.2019.111788
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© 2019 Published by Elsevier Ltd.
Effect of the interference fit on the stress distribution and failure mode of a flat-head riveted GLARE joint
Kai Jin1, 4, Hao Wang2, Jie Tao2, 3* and Jingming Tian2
1College
of Mechanical and Electrical Engineering, Nanjing University of
Aeronautics and Astronautics, Nanjing 211106, P.R. China. 2College
of Material Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.R. China.
3Jiangsu
Collaborative Innovation Centre for Advanced Inorganic Function Composites, Nanjing 211816, P.R. China.
4
Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology,
Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China *Corresponding
author: Phone: +86 025-5211-2911, Fax: +86 025-5211-2911, E-mail: [email protected]
ABSTRACT Glass laminate aluminium reinforced epoxy (GLARE) is an ideal material for fuselage skin, and a rivet joint is the most reliable way to connect fuselage skin. Due to the complex deformation of the joints and the effects of the riveted residual stress, the tensile failure modes are complex and difficult to predict during the service stage. A 3D constitutive model was employed to analyse the mechanical and failure
behaviours of the flat-head rivet joints of GLARE during the entire process from riveting to stretching. Under different fibre orientations of GLARE, the effects of the riveting interference on the stress distribution during riveting, the residual stress and the failure mode were investigated. The compressive stress and bending stress when the fibres were in the 0° direction are the main load modes during riveting, but only the bending stress in the 0° direction becomes residual stress. If the bending stress is more highly concentrated in a fibre layer, there is greater damage accumulation in the layer. Since a high interference fit may also cause the shear fracture of the rivet and serious interface delamination, the riveting interference should be under strict control against the different fibre orientations of GLARE.
KEYWORDS: GLARE, constitutive model, rivet joint, residual stress, failure mode
1. INTRODUCTION: Glass laminate aluminium reinforced epoxy (GLARE) is a sandwich-structured material consisting of aluminium sheets and glass-fibre composites. The material has high specific static properties fracture and fatigue resistance
[1-4],
excellent impact resistance
[9-13].
[5-8],
and outstanding
As a lightweight hybrid material, GLARE has
been successfully utilized in the aviation industry fuselage skin structures of the Airbus 380
[16]
[14, 15],
especially for the upper
and the cargo floor of the Boeing 777
[17].
For most commercial aircrafts, the ambient pressure is designed for an altitude of
at least 2500 m, where the atmospheric pressure is approximately 0.075 MPa [18]. The fuselage skin mainly endures the circumferential pressure, which is caused by the pressure difference between the cabin pressure and atmospheric pressure, and the longitudinal tensile stress caused by aerodynamic loading. Therefore, the strength of the GLARE fuselage skin is vital. Currently, single-shear lap riveting is considered to be the most reliable way to longitudinally connect the fuselage skin [19]. However, the joint area, which contains multiple discontinuities, is typically a point of structural weakness. Due to the stress concentration, structural failures are more likely to occur at the riveted joint area. Sinke
[20]
introduced a riveting process between single metal and fibre metal
laminates (FMLs) and noted that delamination and fibre breakage were the major problems of the riveting process. Huang
[21]
provided feasible methods and analysed
potential failure modes. Some researchers focused on drilling technologies to improve the riveting quality. Giasin, et al.
[22]
studied the effect of the drilling parameters on
the thrust, torque and surface roughness. These authors found that the spindle speed and feed speed significantly affected the drilling force and the quality of the rivet hole. Pawer et al.
[23]
showed that the feed speed played a leading role in controlling
delamination and burr formation. In addition, burrs could be reduced if the minimum quantity lubrication (MQL) was applied
[24, 25].
Park et al.
[26]
analysed the failure
mechanism during the drilling process and found the relationship between the drilling parameters and delamination. For the riveting process, Pan et al.
[27]
developed a
method of using polyaniline modified epoxy to protect the riveting interface, which
improved the joint performance. Ryan and Monaghan
[28]
analysed the failure
mechanism during riveting through the finite element method. Linde and Boer
[29]
presented a model to describe the inter-rivet buckling behaviour when FMLs were bolted together. Due to the complex deformation of joints and the riveted residual stress effect, it is difficult to predict the failure behaviour under loading conditions. To improve the structural performance of riveted joints, a study should be conducted to analyse the deformation behaviour and the failure mechanism during loading. It is essential to develop an accurate constitutive model to characterize the deformation and to predict failures. In this study, a 3D constitutive model with damage criteria for fibre metal laminate was presented, and this model can describe the metal ductile fracture, fibre breakage, matrix cracking and interface delamination. The new model can analyse the stress distribution in riveting, the residual stress distribution and the failure modes under different fibre orientations. Meanwhile, to control the riveting quality, the effect of the riveting interference as a control variable for the deformation and failure modes was investigated through experiments and simulations.
2. EXPERIMENTAL 2.1. GLARE preparation The thickness of the prepreg was 0.125 mm with S4 glass fibre as the reinforcement phase and E302 epoxy as the matrix. The aluminium alloy 2024-T3 of 0.3 mm was used for the metal layers. To improve the contact area with the resin
matrix, the metal sheet was treated by anodizing before laying up. GLARE with a 3/2 structure, as listed in Table 1, was prepared by stacking layers of aluminium sheets and prepregs unidirectionally at 0° [Al/0°/0°/Al/0°/0°/Al] (GLARE 2A) and orthogonally
at
90°
[Al/0°/90°/Al/90°/0°/Al]
(GLARE
3).
An
autoclave moulding method was used to produce the FMLs. GLARE 2A has excellent tensile property, which is suitable for bearing a unidirectional load. GLARE 3 has excellent impact resistance and can bear the bending stress caused by the pressure load and the weight of the fuselage, which is suitable for the upper fuselage skin. Table 1 GLARE structures in this study 0° fibre
90° fibre
volume fraction
volume fraction
1.4 mm
35.7%
0%
1.4 mm
17.8%
17.8%
Name
Orientation
FMLs thickness
GLARE 2A-3/2
[0°/0°]sy
GLARE 3-3/2
[0°/90°]sy
Fig. 1 FMLs structure diagram: (a) GLARE 2A-3/2; (b) GLARE 3-3/2
2.2. Drilling and riveting The effectiveness of an FML connection depends on the drilling quality. Delamination is most likely to occur due to a weak interfacial strength. According to previous research [30, 31], a reduction in the axial thrust can avoid delamination during drilling. Meanwhile, the geometric parameters of the drill bit significantly affect the quality of the holes
[32, 33].
A TiAlN-coated carbide drill bit with two rows of crumbs
slots was adopted. The diameter (D) was 4.1 mm, the chisel edge width was 0.246
mm (0.06 D), the vertex angle was 120°, and the helix angle was 30°. The drilling process is shown in Fig. 2 (a), where MQL was used to remove the cutting heat. The spindle speed was 7500 rpm, and the feed speed was 0.1 mm/r. The drilled hole (Fig. 2 (b)) was smooth without defects, such as delamination and fibre pull-out.
Fig. 2 Images of the drilling process: (a) Equipment setup; (b) Surface appearance of the hole
Aluminium alloy 2024-T3 flat-head rivets (see Fig. 3 (a)) were used in this study. The nominal diameter (d) was 4.0 mm, the nominal length (l) was 8.0 mm, the flat-head thickness (k) was 2.0 mm, the flat-head diameter (dk) was 8.0 mm and the chamfering (r) was 0.1 mm. To prevent impact damage, the experiments used press riveting. A Type-C pneumatic squeeze riveter is shown in Fig. 3 (b). The pressure was controlled between 4.5 kg/mm2 and 5.0 kg/mm2. Since the axial compression and radial expansion of the rivet rod occur simultaneously, a stable hardening surface around the hole can be formed for a single metal. However, excessive expansion of the rivet may cause delamination due to the low interlaminar bonding strength of GLARE. Therefore, to avoid delamination, the riveting interference was set as a control variable and used to control the riveting process. The interplay between the fibre orientation and the riveting interference was also investigated.
(a)
(b)
Fig. 3 Images of the riveting process: (a) Flat-head rivet dimensioned drawing; (b) Type C pneumatic squeeze riveter
The riveting interference is controlled by the pressure of the riveting force, hole diameter and upsetting size and is used to evaluate the squeeze to the wall of the hole. Within a reasonable interference, the stress states and wall surface structure of a hole can be effectively improved through interference-fit riveting, which improves the fatigue life. To observe the interference after riveting, the sample was cut vertically along the centre line of the hole using a Struers secetom-15 precision cutting machine. The geometric data were measured by a Hirox RH-2000 3D video microscope.
Fig. 4 Schematic diagram of the interference calculation
Because of the cutting error, the measured flat-head diameter (d4) and measured rivet rod diameter (d2) were different from the real flat-head diameter (d3) and real rivet rod diameter (de), as shown in Fig. 4. The relative interference (he) is expressed in Eq. (1) and (2) using the initial hole diameter (d) and real rivet rod diameter (de). The height of the controlled rivet tail (H) and relative interference (he) are listed in Fig.
5. ℎ𝑒 =
𝑑𝑒 ― 𝑑 𝑑
𝑑𝑒 =
× 100% 𝑑2𝑑3 𝑑4
(1) (2)
Fig. 5 Geometry appearance of the cut section: (a) GLARE 2A; (b) GLARE 3
2.3. Tensile test According to ASTM D3552-17, tensile tests of the riveted GLARE were carried out using the SANS CMT5105 universal material testing machine. The tensile speed was set to 1.0 mm/min. The geometry of a test specimen and test setup are shown in Fig. 6. Since different riveting interferences cause different structural deformations, the loading capacity of the riveted joint components may be strengthened or weakened. For a single metal, greater expansion of the rivet rod and a smaller thickness of the rivet tail lead to greater compression on the wall of the hole. Therefore, the riveted joint components can theoretically bear more load under shear and tensile conditions. However, for GLARE, more expansion of the rivet rod may result in delamination or matrix cracks in the experiment. When the rivets are moderately extruded around the hole, the passivation effect of the local plastic zone can significantly reduce the stress concentration and effectively improve the tensile behaviours of riveted joints. The mechanisms of the deformation and failure modes are analysed in Section 4.
Fig. 6 Tensile test: (a) Test specimen; (b) Test equipment setup
3. NUMERICAL SIMULATION 3.1. 3D constitutive model In this study, an integrated 3D constitutive model was proposed to describe the mechanical behaviours of the aluminium alloy layers, glass fibre-reinforced plastic (GFRP) layers [34] and Al/GFRP interface layers. Ductile fracture of aluminium occurs under uniaxial tension. Therefore, a damage model for ductile fracture prediction should be considered. Using the Voce model
[35]
and Rice and Tracey model
[36],
the elasto-plastic model of metal layers is
expressed as: 𝜎𝑎 =
{(1 ―𝜎𝐷)𝜎
𝑦
𝑦
𝑖𝑓 𝐷 > 0 𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑝
𝜎𝑦 = 𝜎𝑦0 + 𝑄(1 ― 𝑒 ―𝑏𝜀 )
𝑑𝐷 =
{
𝑑𝜀𝑝 𝜒𝑐𝑟 ∙ 𝑒
0
3 ― 𝜂 2
(3) (4)
1
𝑖𝑓 𝜂 > ― 3
(5)
𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where 𝜎𝑎 is the apparent flow stress; D is the accumulated damage; 𝜎𝑦 is the yield stress; 𝜎𝑦0 is the initial yield stress; 𝜀𝑝 is the effective plastic strain; 𝜂 is the stress triaxiality; and 𝑄, 𝑏 and 𝜒𝑐𝑟 are the model parameters.
The tensile behaviour of GFRP was described by Hooke's law, considering the damage criteria. Based on the model of Linde et al.
[29, 37],
a constitutive model with
3D damage criteria is presented as follows: (6)
𝝈𝑮𝑭𝑹𝑷 = 𝑪𝑫, 𝑮𝑭𝑹𝑷𝜺𝑮𝑭𝑹𝑷
𝑪𝑫, 𝑮𝑭𝑹𝑷 =
[
(1 ― 𝐷𝑓)𝐶11 (1 ― 𝐷𝑓)(1 ― 𝐷𝑚)𝐶12 (1 ― 𝐷𝑓)(1 ― 𝐷𝑧)𝐶13 (1 ― 𝐷𝑚)𝐶22 (1 ― 𝐷𝑚)(1 ― 𝐷𝑧)𝐶23 (1 ― 𝐷𝑧)𝐶33
(1 ― 𝐷𝑓)(1 ― 𝐷𝑧)𝐶55
𝑆𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐
𝜀𝑡11
𝜀𝑡22
( ― 𝐶22𝜀𝑡22(𝑓𝑚 ― 𝜀𝑡22)/𝐺𝑚)
(9)
𝜀𝑡33
( ― 𝐶33𝜀𝑡33(𝑓𝑧 ― 𝜀𝑡33)/𝐺𝑧)
𝑓𝑧 𝑒
(
𝜀𝑡11
2 𝑓𝑓 = 𝜀𝑐11(𝜀11) + 𝜀𝑡11 ―
(𝜀22) + 𝜀𝑐
𝑓𝑚 =
𝑓𝑧 =
𝜀𝑡33
22
2
(𝜀33) +
𝜀𝑐33
2
(
𝜀𝑡33
―
(
𝜀𝑡22
―
(𝜀𝑡22)2 𝜀𝑐22
(𝜀𝑡11)2 𝜀𝑐11
)
𝜀22 +
𝜀𝑡33 2
(𝜀𝑡33)2 𝜀𝑐33
(1 ― 𝐷𝑚)(1 ― 𝐷𝑧)𝐶66
(8)
𝑓𝑓 𝑒
𝐷𝑚 = 1 ― 𝑓𝑚 𝑒
𝜀𝑡22
(7)
( ― 𝐶11𝜀𝑡11(𝑓𝑓 ― 𝜀𝑡11)/𝐺𝑓)
𝐷𝑓 = 1 ―
𝐷𝑧 = 1 ―
]
0 (1 ― 𝐷𝑓)(1 ― 𝐷𝑚)𝐶44
)𝜀 + ( ) (𝜀 33
𝜀𝑠23
)𝜀
11
(10)
> 𝜀𝑡11
𝜀𝑡22 2
( ) (𝜀 𝜀𝑠12
23)
2
+
2 12)
𝜀𝑡33 2
(11)
> 𝜀𝑡22
( ) (𝜀 𝜀𝑠13
2 13)
> 𝜀𝑡33
(12)
(13)
where 𝑪𝑫, 𝑮𝑭𝑹𝑷 is the stiffness matrix; 𝐷𝑓, 𝐷𝑚 and 𝐷𝑧 are the fibre and matrix damages; 𝑓𝑓, 𝑓𝑚 and 𝑓𝑧 are the failure criteria; 𝐺𝑓, 𝐺𝑚 and 𝐺𝑧 are the fracture energies for fibre failure, matrix failure in the ply plane and matrix failure in the thickness direction, respectively; 𝜀𝑡11 and 𝜀𝑐11 are the fibre failure strains for tension and compression in the fibre direction, respectively; 𝜀𝑡22, 𝜀𝑐22 and 𝜀𝑠12, which are perpendicular to the fibre direction in the ply plane, are the matrix failure strains for tension, compression and shear, respectively; and 𝜀𝑡33 and 𝜀𝑐33, are the matrix failure strains for tension and compression, respectively. 𝜀𝑠13 and 𝜀𝑠23 are the matrix
shearing failures in the thickness direction. 𝜀𝑖𝑗 is the strain of GFRP layers. To predict the interlaminar fracture under the open mode (Mode Ⅰ), sliding mode (Mode Ⅱ) or tearing mode (Mode Ⅲ), a 3D cohesive model was developed, based on the study of Xu and Needleman [38] as follows:
𝛷(𝛥𝑛,𝛥𝑡,𝛥𝑠) = 𝛷𝑛 + 𝛷𝑛𝑒
{
―
𝛥𝑛
𝛷𝑛 ― 𝛿 𝛥𝑛
𝑇𝑛 = 𝛿𝑛 𝑒
𝑛
{
𝛥𝑛 𝛿𝑛
𝛿𝑛 𝑒
―
(1 ― 𝑟 + )( ) ― [𝑞 + ( ) ]𝑒
( )+ 2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
𝛥𝑛
1―𝑞
𝑟 ― 𝑞 𝛥𝑛
𝛿𝑛
𝑟―1
𝑟 ― 1 𝛿𝑛
[
1―𝑞 𝑟―1
―
1―𝑒
[ ( ) ]𝑒
𝛷𝑡𝛥𝑡
𝑇𝑡 = 2 𝛿𝑡 𝛿𝑡 𝑞 +
𝑟 ― 𝑞 𝛥𝑛
𝑟 ― 𝑞 𝛥𝑛
2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
―
𝛥𝑛 𝛿𝑛
―
―
𝛥𝑛 𝛿𝑛
―
𝑒
𝑟 ― 1 𝛿𝑛
[ ( ) ]𝑒
𝛷𝑠𝛥𝑠
𝑇𝑠 = 2 𝛿𝑠 𝛿𝑠 𝑞 +
( )
𝑟 ― 1 𝛿𝑛
𝑒
][
]
𝛥𝑛
𝑟 ― 𝛿𝑛
―
( ) 2 𝛥2 𝑡 + 𝛥𝑠 𝛿2 𝑡
}
( ) 2 𝛥2 𝑡 + 𝛥𝑠 2 𝛿𝑡
( ) 2 𝛥2 𝑡 + 𝛥𝑠 𝛿2 𝑡
𝛷𝑛 = 𝑒 ⋅ 𝜎𝑚𝑎𝑥 ⋅ 𝛿𝑛 𝛷𝑡 = 𝛷𝑠 =
𝑒 2
⋅ 𝜏𝑚𝑎𝑥 ⋅ 𝛿𝑡
}
(14)
(15)
(16)
(17) (18) (19)
where 𝛷 is the total potential failure energy; 𝛷𝑛, 𝛷𝑡 and 𝛷𝑠 are the work of separation of the potential failure energy in each direction; 𝑇𝑛 is the traction in the normal direction; 𝑇𝑡 and 𝑇𝑠 are the tractions in the tangential directions; 𝛥𝑛, 𝛥𝑡 and 𝛥𝑠 are the opening displacements in each direction; 𝛿𝑛, 𝛿𝑡 and 𝛿𝑠 are the characteristic length when debonding; 𝑞 and 𝑟 are the coupling parameters.
3.2. Finite element modelling
The aim of this study is to analyse the mechanical and failure behaviours of GLARE during the process chain. Using the user subroutine VUMAT, the presented 3D constitutive model was created in ABAQUS. Three aluminium alloy plies and four GFRP plies were built. Meanwhile, six individual plies of the cohesive elements were placed between the aluminium ply and the GFRP ply and between the two GFRP plies, to represent the interfacial behaviour. In this study, GLARE with unidirectional (0°/0°) and orthogonal (0°/90°) plies (see Table 1) was used to investigate the effects of the fibre orientation on the deformation and failure behaviours. The material properties of the AA2024-T3 and GFRP were obtained from a series of tests in our laboratory and are listed in Tables 2-4. According to the setups of the riveting test and tensile test, the FE model was built by meshing a hexahedral element (C3D8), as shown in Fig. 7. The deformation and damage accumulation during the riveting process, the residual stress distribution after riveting and the failure behaviours during the uniaxial tensile process were predicted by the presented constitutive model.
Fig. 7 FE simulation model for the process chain
Table 2 Material properties of AA2024-T3 Parameter
Value
Young’s Modulus
E
73.8 GPa
Poisson's ratio
ν
0.33
Yield strength
σY
305 MPa
Tensile strength
σT
450 MPa
Elongation
εF
0.19
Strain hardening coefficient
Q
142.5
Strain hardening index
b
16.4
Critical void growth index
𝜒𝑐𝑟
2.0
Critical strain
εD
0.05
Table 3 Material properties of GFRP Parameter
Value
Young’s Modulus
Poisson's ratio
Ultimate strength
E11
55.0 GPa
E22
9.5 GPa
E33
9.5 GPa
Ν12
0.33
Ν23
0.45
Ν13 𝜎𝑡11
0.33 2400 MPa
𝜎𝑐11 𝜎𝑡22 𝜎𝑐22
2000 MPa
𝜏12
75 MPa
𝜏23
50 MPa
𝜏13
75 MPa
50 MPa 150 MPa
Table 4 Parameters of the cohesive model Parameter Bonding strength
Characteristic length
4. RESULTS AND DISCUSSION 4.1. Stress analysis for riveting
Value
𝜎𝑚𝑎𝑥 𝜏𝑚𝑎𝑥 𝛿𝑛
26 MPa
𝛿𝑡
0.1
𝛿𝑠
0.1
75 MPa 0.2
By comparing the microscopic cross sections of the experiment and simulation, we found that when the axial compression of the nail rod was relatively large, the radial expansion of the rivet in GLARE 2A was relatively severe. The nail rod flowed towards the contact surfaces of two GLARE sheets, resulting in a clearance between the two sheets as shown in Figs. 8 (a) and (d). If the radial expansion of nail rod was small, the plastic flow of the nail rod tended to the easily deformed area and resulted in an uneven expansion as shown in Figs. 8 (b) and (e). If the interference was moderate, the radial expansion of nail rod was uniform as shown in Figs. 8 (c) and (f).
Fig. 8 Microscopic cross sections of the riveted GLARE 2A: (a) Rivet tail height (H) = 2.5 mm, relative interference (he) = 2.97%, in experiment; (b) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.95%, in experiment; (c) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.0%, in experiment; (d) Rivet tail height (H) = 2.5 mm, relative interference (he) = 2.97%, in simulation; (e) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.95%, in simulation; (f) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.0%, in simulation.
In GLARE 3 (see Fig. 9), when the radial expansion of nail rod was relatively small (he = 0.99%), the gap between the nail rod and hole was generated, which is different from the appearance of GLARE 2A. The formation of such gap was
attributed to the small amount of rivet interference, the weak adhesion between rivet and GLARE, and the slight external vibration, as shown in Figs. 9 (a) and (d). When the nail rod continued to compress in the axial direction, the radial extrusion of the nail rod to the hole increased as shown in Figs. 9 (b) and (e). When the nail rod fully squeezed the hole, the expansion of the nail rod (see Figs. 9 (c) and (f)) was completely uniform.
Fig. 9 Microscopic cross sections of the riveted GLARE 3: (a) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.99%, in experiment; (b) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.07%, in experiment; (c) Rivet tail height (H) = 2.5 mm, relative interference (he) = 3.05%, in experiment; (d) Rivet tail height (H) = 3.5 mm, relative interference (he) = 0.99%, in simulation; (e) Rivet tail height (H) = 3.0 mm, relative interference (he) = 2.07%, in simulation; (f) Rivet tail height (H) = 2.5 mm, relative interference (he) = 3.05%, in simulation.
During the riveting process, the deformations of the rivet and GLARE were generated together. The upper layer of GLARE was near the rivet tail, and the lower layer of GLARE was in contact with the flat-head. At 3.0% of the relative interference (he) and 2.5 mm rivet tail height (H), the stresses in each layer of GLARE 2A and GLARE 3 are shown in Fig. 10. For the GFRP layers, S11 denotes the stress parallel to
the fibre orientation, S22 denotes the stress perpendicular to the fibre orientation, and S33 denotes the stress along the thickness direction. For the Al layers, S11 is the stress along the roll direction of metal. As shown in Fig. 10 (a), the fibre layers (GFRP) mainly bear the rivet expansion force. Compared with the circumferential expansive force of the rivet, the pressing force in the direction of the thickness is very minor. The characteristics of the stress distribution can be analysed from two sections: 0° section and 90° section. For GLARE 2A (0°/0°), all the fibres in Line 1 are located in the 0° section (parallel to direction 1). When the rivet expanded, the fibres in Line 1 only suffered vertical compression. However, the fibres in Line 2 at the 90° section (parallel to direction 2) were bent due to the rivet expansion, presenting tension along the fibre orientation. For GLARE 3 (0°/90°), GFRP-1 and GFRP-4 are the 0° orientation layers; on the other hand, GFRP-2 and GFRP-3 are the 90° orientation layers. Fig. 10 (a) shows that the vertical pressures are more concentrated on the fibre layers (GFRP-1 and GFRP-4) that are parallel to the direction of the force. Moreover, the bending forces are more focused on the fibre layers (GFRP-2 and GFRP-3) that are perpendicular to the direction of the force. Two fibre layers in unidirectional placement can uniformly distribute the bending and compressive stresses, whereas two fibre layers with orthogonal placement may cause stress concentration, especially bending stress. To further study the characteristics of the stress distribution, the stresses in the metal layers and fibre layers are shown in Figs. 10 (b)-(g). For the metal layers, comparing Fig. 10 (b) with Figs. 10 (d) and (f), the stress distribution along the fibre
direction is different from those along the other two directions. This finding indicates that the stress of the aluminium alloy is affected by the fibre orientation. Since the fibres of GLARE 2A and GLARE 3 along their orientation provide enough support, the strains concentrate on this direction. Thus, the aluminium alloy layers also shoulder the responsibility. The compressive stress of the metal layers is directly proportional with the vertical pressures of the fibre layers. For the fibre layers, Figs. 10 (c), (e) and (g) show that the stresses of fibre and matrix change linearly. Due to a higher stress concentration of GLARE 3 in the fibre direction, the stress level is always higher than that of GLARE 2A. Conversely, the resin matrix shares the load with the metal. The matrix stress of GLARE 3 is more homogeneous, since the fibre orientation is orthogonal. In addition, GLARE 2A at Line 2 only has flexural load. The resin matrix and metal must share the increased vertical compressions, as shown in Figs. 10 (d) and (e). In the thickness direction (Figs. 10 (f) and (g)), the interface between two GLARE pieces affects the load transmission. In general, the stress distribution is controlled by the resin matrix and metal in the thickness direction.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Fig. 10 Stress distributions of Glare 2A and Glare 3: (a) Overall stress distribution; (b) Stress distribution of Al layers along the fibre direction; (c) Stress distribution of GFRP layers along the fibre direction; (d) Stress distribution of Al layers perpendicular to the fibre direction; (e) Stress distribution of GFRP layers perpendicular to the fibre direction; (f) Stress distribution of Al layers along the thickness direction; (g) Stress distribution of GFRP layers along the thickness direction
The constraints between the rivet devices and the riveted FMLs were relieved after riveting, and the residual stress was generated. Comparing the simulated contours of the rivet tail of GLARE 2A with the experimental results (see Fig. 11 (a)), we find the deformation behaviours under different relative interferences are accurately simulated. The residual stresses in each layer of GLARE 2A and GLARE 3 at 3.0% relative interference and 2.5 mm rivet tail height are shown in Figs. 11 (b) - (e). For GLARE 2A (0°/0°), the vertical pressures of the fibres were released in the 0° section (Fig. 11 (b)) due to the elastic recovery of 0° fibres and the rivet. However, only the partial bending stresses of the fibres in the 90° section (see Fig. 11 (c)) were released. The matrix stresses in the plane and thickness directions tended toward zero. A similar phenomenon emerged in GLARE 3 (0°/90°), which indicates that the bending stress of the fibres was a major mode of residual stress regardless of the fibre orientation. (a)
(b)
(d)
(c)
(e)
Fig. 11 Variation in the stresses after the riveting process: (a) Comparison of the contours of the upset head; (b) Comparison of the residual stress of GLARE 2A in Line 1; (c) Comparison of the residual stress of GLARE 2A in Line 2; (d) Comparison of the residual stress of GLARE 3 in Line 1; (e) Comparison of the residual stress of GLARE 3 in Line 2
The contribution of the interference on the residual stress parallel to the fibre orientation for the GFRP layers (S11) and along the metal rolling direction for the Al layers (S11) are shown in Fig. 12, since the residual stress is mainly reflected in the stress component (S11). The residual stresses of the layers along Line 1 (see Fig. 12 (a)) represent the stress distribution of the FML hole at the 0° section, while the residual stresses of the layers along Line 2 at the 90° section are shown in Fig. 12 (b). As shown in Fig. 12 (a), the compression of the fibres of GLARE 2A is not completely released if the relative interference is large (he = 2.97%), especially in the region near the rivet tail. If the relative interference is appropriate, the compression can be completely released. The fibre stress changed from compression stress to
tensile stress since the bending stresses transmitted to this region. For GLARE 3, the tensile force produced by bending in the 90° fibre orientation is a major residual stress. The stress decreased with the decreasing relative interference due to decreasing rivet nail rod expansion. Meanwhile, the residual stress concentrated in the region near the rivet tail. When GLARE 2A and GLARE 3 in Line 2 are compared (Fig. 12 (b)), it can be seen that the bending tension is still a main residual stress in GLARE 3. The variation trend in Line 2 is similar to that in Line 1. However, the bending force was shared by GFRP layers in GLARE 2A. Moreover, the residual stress was more concentrated on the GFRP layers near the rivet tail. The residual stress was evenly reduced in each GFPR layer with the reduced relative interference.
Fig. 12 Compression of the residual stresses after riveting: (a) Residual stress distribution in Line 1; (b) Residual stress distribution in Line 2
4.2. Failure analysis for riveted GLARE after the tensile test The tensile test results obtained from the experiments and simulations under the different relative interferences (see Fig. 13) indicate that GLARE 2A and GLARE 3 reached the maximum tensile peak force when the rivet tail height was 3.0 mm and 2.5 mm, respectively. Therefore, the tensile properties of riveted GLARE did not
change regularly with the interference variation. Riveting with different interferences changed the structure of riveted GLARE and enhanced or weakened the bearing capacity of the components. A smaller the height of the rivet tail corresponded to more plastic deformation and expansion of the rivet that squeezed the hole. During the riveting process, excessive extrusion of the rivet hole may cause excessive plastic deformation of the metal layers, fibre buckling fracture, matrix cracking or delamination. If the rivet is moderately squeezed around the hole using an appropriate interference, the passivation effect of the local plastic zone produced by the rivet to the hole wall can greatly reduce the stress concentration and effectively improve the tensile behaviour of the rivet joint.
Fig. 13 Load-displacement curves: (a) GLARE 2A; (b) GLARE 3
The failure of a rivet has two modes: rivet pull-out (Mode Ⅰ) and rivet shear fracture (Mode Ⅱ). The material constitutive model presented in the study accurately describes the failure behaviours, as shown in Fig. 14. To investigate the effect of the interference fit on the riveted GLARE failure behaviours, the damage and stress distributions of layers of GLARE 2A (H=3.5 mm and H=2.5 mm) and GLARE 3 (H=2.5 mm) are shown in Figs. 15 - 20. For Al layers, S11 is the stress in the X-axis, which is the tensile direction, and S22 is the stress in the Y-axis perpendicular to the
tensile direction. For GFRP layers, S11 is the in-plane stress parallel to the fibre orientation and S22 is the stress perpendicular to the fibre orientation.
Fig. 14 Failure modes of a rivet after tensile tests: (a) Failure mode of GLARE 2A (H=3.5 mm) in the experiment; (b) Failure mode of GLARE 2A (H=2.5 mm) in the experiment; (c) Failure mode of GLARE 2A (H=3.5 mm) in the simulation; (d) Failure mode of GLARE 2A (H=2.5 mm) in the simulation
For mode Ⅰ, the damage accumulation of each component is shown in Fig. 15. Damage was slightly accumulated in the rivet and the Al-1 and Al-3 layers of the upper GLARE (Fig. 15 (a)) due to the compression of the rivet nail rod as shown in Fig. 16 (a) and (b). The fibres were slightly damaged (Fig. 15 (b)) in the region where the tensile and residual bending stresses were concentrated. The damage in the fibre layers may be caused by a synergistic effect of the drawing force generated by the uniaxial tension (Fig. 16 (c)) and residual bending tension (Fig. 12 (b)). The resin matrix suffered a penetrating fracture, which was generated by the rivet squeezing and was propagated along the fibre orientation. The region of damage (Fig. 15 (c)) was consistent with the region of rivet compression concentration (Fig. 16(d)). Therefore,
the matrix damage was mainly caused by rivet compression. Delamination emerged on the interface between the two GLARE sheets due to the two reversed relative strains near the interface of two GLAREs. During the tensile test, there was no transverse fibre constraint around the hole. The deformations of the metal and matrix could not cooperate with each other. The matrix damage and delamination in the layer rapidly expanded with the increasing compression load of the rivet. (a)
(b)
(c)
(d)
Fig. 15 Damage accumulation distributions of GLARE 2A (H=3.5 mm): (a) Metal damage; (b) Fibre damage; (c) Matrix damage; (d) Delamination
(a)
(b)
(c)
(d)
Fig. 16 In-plane stress distributions of GLARE 2A (H=3.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
For mode Ⅱ, the rivet was completely fractured by shear stress and caused the
riveting failure. There was minor damage to the metal distributed around the hole without buckling (Fig. 17 (a)), which was caused by the compression of the rivet tail on the Al-1 layer in the tensile direction as shown in Fig. 18 (a). The resin matrix damage (Fig. 17 (b)) was significantly affected by the compression force perpendicular to the fibre orientation (Fig. 18 (d)). Delamination was generated on the Al/GFRP interfaces near the two jointed GLAREs (Fig. 17 (c)) due to two reversed relative stresses as shown in Fig. 18. Moreover, the comparison of Figs. 18 (c) and 16 (c) shows that the fractured rivet did not generate a large drawing force. Therefore, there was no fibre damage if a larger interference fit was used. Thus, the fibres can still uniformly undertake rivet pressure, although the matrix cannot transmit the load. (a)
(b)
(c)
Fig. 17 Damage accumulation distributions of GLARE 2A (H=2.5 mm): (a) Metal damage; (b) Matrix damage; (c) Delamination
(a)
(b)
(c)
(d)
Fig. 18 In-plane stress distributions of GLARE 2A (H=2.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
By comparing GLARE 3 (H=2.5 mm) with GLARE 2A (H=2.5 mm), we observe that the damage of GLARE 3 in the Al layers and resin matrix (Figs. 19 (a) and (c)) was smaller than that of GLARE 2A due to the transverse fibre constraints of the 90° fibre layers perpendicular to the direction of the tensile load. During the extrusion damage expansion stage of GLARE 3, the resin matrix only bore a small load. The 0° fibre layers and 90° fibres layers were synergistically subjected to the compression stress of the rivet and the tensile stress around the hole (Figs. 20 (c) and (d)). The 0º fibres in the 90º section had severe damages due to the stress
concentration and bending residual stress (Fig. 12), as shown in Fig. 19 (b). Meanwhile, a large interlaminar shear stress between the 0° fibre layer and the 90° fibre layer was generated due to two concentrated stresses in two mutual vertical directions. Thus, the delamination in GLARE 3 was serious. The upper layer of GLARE was completely delaminated around the hole. (a)
(b)
(c)
(d)
Fig. 19 Damage accumulation distributions of GLARE 3 (H=2.5 mm): (a) Metal damage; (b) Fibre damage; (c) Matrix damage; (d) Delamination
(a)
(b)
(c)
(d)
Fig. 20 In-plane stress distributions of GLARE 3 (H=2.5 mm) after failure: (a) S11 of the aluminium layers; (b) S22 of the aluminium layers; (c) S11 of the GFRP layers; (d) S22 of the GFRP layers
5. CONCLUSIONS (1) A constitutive model with damage criteria for FMLs was presented to describe the deformation behaviour during the riveting process and to predict progressive failure. By using the model, the stress distribution during the riveting process, the residual stress variation after riveting and the failure modes of the tensile test were predicted. (2) It was found that the stress distribution of metal layers is controlled by the fibre orientation during riveting. The orthogonal placement of the fibre layers cannot
more uniformly distribute stress. In contrast, the orthogonal placement of the fibre layers may cause a high stress gradient between the layers and a stress concentration during riveting. (3) After riveting, the stresses in the rivet, metal layers and matrix of fibre layers are almost released. Only the bending stresses on the fibres are converted into residual stress, which is a precipitating factor for fibre breakage. Furthermore, fibre breakage only appears at the areas of bending tension concentration. More residual bending stress may cause heavier fibre damage accumulation. (4) Rivet pull-out and rivet shear fracture are the main failure modes of the rivet. For GLARE 2A, the fibre breakage and metal ductile damage are slight. The major failure is a penetrating fracture of the matrix in the thickness direction. The growth direction is along the fibre direction. If a high relative interference is used, delamination in each interface may occur around the rivet hole. Therefore, the riveting quality should be controlled by the relative interference of the rivet according to the fibre orientation.
ACKNOWLEDGEMENTS This work is supported by the Fundamental Research Funds for the Central Universities (No. NS2018032).
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AUTHOR STATEMENT
Kai Jin: Conceptualization, Methodology, Software, Formal analysis, Writing-Original draft preparation and Writing-Reviewing and Editing
Hao Wang: Data curation and Visualization
Jie Tao: Supervision, Resources and Project administration
Jiming Tian: Investigation