J. Xue (*) .J.
Appl Compos Mater DOI 10.1007/s10443-014-9419-y
Experimental and Numerical Study on the Tensile Behaviour of UACS/Al Fibre Metal Laminate Jia Xue & Wen-Xue Wang & Jia-Zhen Zhang & Su-Jun Wu & Hang Li
Received: 6 August 2014 / Accepted: 2 September 2014 # Springer Science+Business Media Dordrecht 2014
Abstract A new fibre metal laminate fabricated with aluminium sheets and unidirectionally arrayed chopped strand (UACS) plies is proposed. The UACS ply is made by cutting parallel slits into a unidirectional carbon fibre prepreg. The UACS/Al laminate may be viewed as aluminium laminate reinforced by highly aligned, discontinuous carbon fibres. The tensile behaviour of UACS/Al laminate, including thermal residual stress and failure progression, is investigated through experiments and numerical simulation. Finite element analysis was used to simulate the onset and propagation of intra-laminar fractures occurring within slits of the UACS plies and delamination along the interfaces. The finite element models feature intralaminar cohesive elements inserted into the slits and inter-laminar cohesive elements inserted at the interfaces. Good agreement are obtained between experimental results and finite element analysis, and certain limitations of the finite element models are observed and discussed. The combined experimental and numerical studies provide a detailed understanding of the tensile behaviour of UACS/Al laminates. Keywords Fibre metal laminate . Discontinuous reinforcement . Tensile test . Finite element analysis . Cohesive zone modelling
1 Introduction Formability of carbon fibres during fabrication is important for applications involving complex shaped components for carbon fibre reinforced polymer (CFRP) [1]. J. Xue (*) : J. > < t ¼ ð1−DÞKδ; > > > > : t ¼ 0;
D¼0
if 0≤δ ≤δ0
ðIntactÞ
δ δ−δ D ¼ f 0 δ δ −δ
if δ0 ≤δ ≤δ f
ðSoftening Þ
D¼1
if δ > δ f
ðFailed Þ
f
0
ð1Þ
In a real structure, mixed-mode loading is usually present at the crack front, and the onset of delamination may occur before any of the tractions reach their corresponding interfacial strength. In consideration of mixed-mode loading, a quadratic nominal stress criterion, given below, was used in this study to simulate the onset of delamination.
t Intact
htzz i toZZ
2
þ
tzx tozx
2
D=0
þ
tzy tozy
!2 ¼1
Softening
ð2Þ
D=1
Failed
tzzo Kzz GIC
δzzo
δzzf
δ
Fig. 3 Bilinear traction-relative displacement cohesive law for mode I loading (mode II and III are similar)
Appl Compos Mater
where the Macauley bracket, 〈tzz〉, is defined as 〈tzz〉=0 if tzz ≤0 and 〈tzz〉=tzz if tzz >0. The Benzeggagh-Kennane Law was used to simulate the mixed-mode delamination propagation. The mixed-mode interfacial facture toughness, Gc is given as 8 π GS > > < Gc ¼ Gic þ ðGIIC −GIC Þ GT ð3Þ G ¼ Gt zz þ Gt zy > > : S Gr ¼ Gs þ Gt zz where is the work done by two shear tractions and their corresponding relative displacements, while is the total work done. The mixed-mode parameter η, is a constant. The material properties of the cohesive element are summarized in Table 2. There is no consensus within the literature about the initial stiffness of cohesive elements; however, the value of 106 is most commonly accepted. We took the values of fracture toughness and interfacial strength from [7]. For the cohesive element density, we used a low artificial density value to minimize inertial effects to allow explicit analysis. 3.2 Finite Element Model As discussed in section 2.1, the entire UACS/Al laminate may be treated as a series of repeating unit cells, as shown in Fig. 2b. In this study, we constructed the finite element model based on these single repeating unit cells, which is similar to [9] but with different slit patterns. In a previous study [22], we built the model based on three consecutive repeating unit cells in the directions of the fibre and normal to the fibre. We found that the damage propagation pattern, which develops with an increasing load until a maximum load is reached, is nearly the same for each single repeating unit cell. Therefore, it is reasonable and computationally economical to build finite element models with single repeating unit cells that still yield an accurate characterization of the bulk material. Fig. 4 shows the exploded view of the UACS/Al finite element model with a slit angle of 31°. Five layers of inter-laminar cohesive elements were inserted into the interfaces, including three layers of inter-laminar cohesive elements, which are inserted into the interfaces between four UACS plies, and two layers of inter-laminar cohesive elements inserted into the interfaces between the aluminium and the UACS layer. Four strips of intra-laminar cohesive elements were inserted into the slits of the UACS plies to simulate the epoxy-rich region separating from the carbon fibre. No fibre breakage was observed in the tensile tests; therefore, for simplicity, no failure criteria was defined for the CFRP. The failure behaviour of the UACS/Al model was simulated using only the cohesive elements. In the UACS finite element model by Li et al. [9], identical mesh was used for each of the layers through the thickness of the laminate, including both UACS plies and the interface layers. The drawback to a uniform mesh is that a reduction in the mesh size of the cohesive elements comes at a cost of unnecessarily raising the overall number of solid elements, which Table 2 Material properties of the cohesive element
106
Initial stiffness Kzz = Kzx = Kzy [N/mm] 2
Fracture toughness in mode I GIC [N mm/mm ]
0.2
Fracture toughness in mode II and III GIIC ¼ GIIIC [N mm/mm2] 0.6 Interfacial strength in mode I tzzo [N/mm2]
30
Interfacial strength in mode II and III tzxo = tzyo [N/mm2] Mixed mode parameter η
60 1.8
Density [10−9 g/mm3]
1.2
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Aluminium Inter-laminar cohesive CFRP Intra-laminar cohesive Z Y
X
Fig. 4 Exploded view of the 31 UACS/Al finite element model
may cause severe distortion in the solid elements and unacceptable computational cost. In this study, we employ an optimized discretization method that uses relatively coarse mesh to model the aluminium and the UACS plies, but uses refined mesh for the interface cohesive layers, as shown in Fig. 5. Figure 6 shows a detailed illustration of the finite element model with cohesive elements inserted into solid elements. The nodes of the refined inter-laminar cohesive elements are shared by the neighbouring solid elements. The thickness of the inter-laminar cohesive elements is 0.001 mm. For a small, finite thickness, it is more convenient to define and check the “tie” constraint between the inter-laminar cohesive elements and neighbouring solid elements. The slit cohesive elements inserted in the UACS plies share nodes with the neighbouring solid elements. The slit cohesive elements have zero thickness to avoid having severely distorted solid elements above and below the slit cohesive elements. Mesh dependency can be a problem for the cohesive zone modelling [23]. However, with this optimized discretization method, it is very convenient to re-mesh only the inter-laminar cohesive layers with only a few changes needed to the whole model, so the model is immediately ready to recalculate again. Therefore, the interface cohesive layers can be gradually refined to make sure that there is a sufficient number of cohesive elements in the cohesive zone and that the results are not mesh dependent. Three-dimensional eight-node reduced-integration solid elements, C3D8R from ABAQUS, were used to model the aluminium and the UACS plies with finer mesh used around the slits and delamination-prone area. The material properties of CFRP and aluminium are shown in Table 3. Because the maximum load is well above the yield point of aluminium, it is necessary to define plastic behaviour for the aluminium sheet. The plastic properties of aluminium alloy are shown in Table 4. The data are obtained from tensile tests of monolith 2024-T3 coupons with the same dimensions as that of the UACS/Al laminate coupons. The left edge of the model is fixed in X direction (fibre direction), while the right edge is under tensile load in X direction. The nodes under tensile loading were subjected to displacements in increments until a maximum displacement of 0.25 mm was reached, which corresponds to a maximum of 1 % strain in the fibre direction. Appropriate boundary conditions were defined for the centre nodes at the left edges to remove rigid motion. It should be noted that cohesive elements are excluded from all boundary conditions.
Appl Compos Mater
Z Y
X
(a) Finite element mesh for aluminium and UACS plies
Z Y
X
(b) Refined mesh for inter-laminar cohesive layers Fig. 5 Optimized modelling method with refined inter-laminar cohesive elements
Thermal residual stress [20] is considered in this model. A thermal load was imposed before the tensile loading, defined as a uniform temperature change from the cure temperature of 127 °C to ambient temperature, 25 °C. 3.3 Explicit Solver Due to the softening behaviour and degradation in stiffness during the damage evolution of cohesive elements, numerical analyses often encounter convergence difficulties if an implicit solver is used [24]. Even with the optimized discretization method, we find that using an implicit solver for the UACS/Al simulations employing both intra-laminar and inter-laminar
Appl Compos Mater
Fig. 6 Detailed illustration of the cohesive elements inserted into solid elements
cohesive elements yields severe convergence difficulties, especially the UACS/Al models with small slit angles in which case the mesh quality cannot be guaranteed near the sharp corners. Therefore, in this study, we used an explicit solver to overcome the convergence difficulties. The stability of explicit solvers allows for modelling of fast transient events occurring in dynamic analyses; however, explicit solvers require a large number of small time steps. In each increment, the calculation proceeds without iteration and without requiring the tangent stiffness matrices to be formed [25]. To reduce computational cost, we artificially reduced the duration of loading to accelerate the simulations. The thermal loading time was set to 10−4 s, while the tensile loading time was set to 10−3 s, and no noticeable inertial effect was observed. Table 3 Material properties of the CFRP and aluminium alloy PYROFIL#350(TR50S)
2024-T3
Longitudinal Young’s modulus [GPa]
142
71
Transverse Young’s modulus [GPa]
8.8
71 –
In-plane shear modulus [GPa]
4.2
Out-of-plane shear modulus [GPa]
3.7
–
In-plane Poisson’s ratio
0.27
0.33
Out-of-plane Poisson’s ratio Longitudinal tensile strength [MPa]
0.32 2,950
0.33 -
Longitudinal thermal expansion coefficient [10−6/°C]
0.3
26
Transverse thermal expansion coefficient [10−6/°C]
36.5
26
Volume fraction of fibers [%]
60
–
Density [10−9 g/mm3]
2.1*
3*
*artificially reduced to minimize inertial effect
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Table 4 Plastic properties of aluminium alloy
Yield stress [MPa]
Plastic strain [%]
305
0
309 320
0.001125 0.013996
331
0.118731
340
0.281615
350
0.481607
360
0.78642
370
1.18941
4 Results and Discussion The experimental results and finite element analysis results are presented in Figs. 7 to 13. 4.1 Tensile Strength and Thermal Residual Stresses Results for the tensile strength of the UACS/Al laminates and the thermal residual stress in the Al layers are presented in Figs. 7 and 8, respectively, both as a function of slit angle. The values reported for the UACS/Al laminate tensile tests are averaged from at least three test coupons, and the error bars for each value indicate the upper and lower limits of the measured results. From Fig. 7, it is clear that a small slit angle leads to large tensile strength, which is a reflection of a low stress concentration at the interface around the slit, which subsequently increases with the increasing slit angle [6]. For the case of 45°, the strength value is less than 400 MPa, which is less than the strength of the 2024-T3 Al layer. Conversely, the strength values measured for small slit angles exceed that of the Al layer despite all fibres having been cut to the same length, 25 mm. In contrast to tensile strength, thermal residual stress in the Al layer demonstrates different behaviour, as shown in Fig. 8. The thermal residual stresses for all slit angles are lower than the value corresponding to the case without slits (slit angle =0°), which indicates that the short fibre based FML can reduce the thermal residual stress in the Al layers. A low thermal residual stress is expected to improve the fatigue strength of UACS/Al laminates. In the present study, the angles of 11.3° and 16.7° are recommended. Smaller or larger slit angles lead to relatively high thermal residual stress due to the interaction between
Fig. 7 Effect of the slit angle on the strength of UACS/Al laminate
Appl Compos Mater Fig. 8 Effect of the slit angle on the thermal residual stress
the stress concentration and the number of slits in the specimen. For the case of the smaller slit angle, the total number of slits within the specimen volume is higher than in the larger slit angle specimen, and consequently, the UACS layer with small slit angle has better formability. However, a larger slit angle induces a larger stress concentration at the interface around the slit, which leads to relatively large expansion of the UACS layer caused by the thermal expansion of the Al layer. Furthermore, the stress–strain results presented in section 4.3 conforms well to the finite element analysis results. 4.2 Damage Progression Pattern The damage variable D defined in Eqs. (1), also known as the scalar stiffness degradation variable (SDEG) in ABAQUS, is plotted in Figs. 9, 10 and 11. As mentioned in section 3.1, the D value, which ranges from “0” to “1”, indicates the damage of cohesive elements; “0” corresponds to no damage, while “1” corresponds to full damage. Fully damaged elements have no load carrying capability and thus represent a crack in the model. The slit (intra-laminar) crack initiation and propagation in the UACS plies is similar for the different UACS/Al laminates with various slit angles, and thus, only the 31° UACS/Al laminate is shown in Fig. 9. For the intra-laminar cohesive elements plotted in Fig. 9, fully damaged elements are removed from the model to visualize the crack growth. Fig. 7a shows that at a tensile strain of 0.361 %, the crack first initiated at the crossing point of the slits where the stress concentration is the largest. Fig. 7b shows that at a tensile strain of 0.373 %, cracks propagate into all four slits through the thickness and that the crack starts to propagate towards the corners. Fig. 7c shows that nearly all of the intra-laminar cohesive elements in the centre part of the model are fully damaged at a tensile strain of 0.516 %. Figure 10 shows delamination onset and propagation at the interfaces of the 31° UACS/Al laminate. The three layers of inter-laminar cohesive elements inserted in the UACS layer, which are in contact with the two slits, all show similar damage patterns. Therefore, only the middle layer of the inter-laminar cohesive elements is shown in the left column in Fig. 8 to represent the damage pattern formed at the interfaces between the UACS plies. Similarly, the two layers of inter-laminar cohesive elements inserted between the aluminium and the UACS layer, which are in contact with only one slit, also show similar damage patterns. In this case, the top layer is shown in the right column of Fig. 10 to represent the damage pattern at the interfaces between the aluminium and the UACS layer. Fully damaged cohesive elements plotted in red are kept at the interfaces to avoid interpenetration of the neighbouring delaminated layers.
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(a) Crack initiation at 0.361% tensile strain
(b) Crack propagation at 0.373% tensile strain
(c) Crack propagation at 0.516% tensile strain Fig. 9 Slit (intra-laminar) crack initiation and propagation in the UACS plies of 31 UACS/Al laminate
Appl Compos Mater
(a)
(b)
(c) Fig. 10 Delamination onset and propagation at the interfaces of 31 UACS/Al laminate
Figure 10a shows the delamination onset in the centre of the model at the crossing point of the slits in the interface layer at a tensile strain of 0.516 %, that is, when the majority of the intra-laminate cohesive elements in the centre part of the model are fully damaged, as shown in
(a)
(b) Fig. 11 Damage propagation pattern at the interfaces of 5.7 UACS/Al laminate
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Figs. 9c and 10b shows the delamination propagation when the maximum load is reached at a tensile strain of 0.706 %. At this moment, only the cohesive elements near the crossing point of the slits are fully damaged, but the over-all stiffness in the laminate model begins to reduce quickly. Full delamination occurred at tensile strain of 0.824 %, as shown in Fig. 10.c, when all cohesive elements in the load carrying region were fully damaged. At this stage, the UACS layer was completely fractured and only the remaining aluminium layer could carry some load. For the finite element models of UACS/Al laminates with slit angles ranging from 11.3° to 45°, delamination initiated at the crossing point of the slits and propagated towards the edges. However, in the case of UACS/Al laminate with extremely small slit angles, for example, the 5.7° case shown in Fig. 11, delamination initiated at corners of the model and then propagated towards the centre. Fig. 11a shows the delamination region in the right corner at maximum load, and Fig. 11b shows large delamination regions forming in the four corners just before full delamination. In our understanding, the unusual damage pattern observed for the extremely small slit angle of 5.7° may be caused the unit cell model approach as the free boundary conditions around the two side edges parallel to the fibre direction have physical boundary conditions that are not exactly periodic. The stress concentration at the interfaces of the two sides due to the boundary effect becomes larger than that occurring at the centre point of the model when the slit angle is very small. Therefore, the delamination initiates from the two sides instead of at the centre point, which is not physically correct. Thus, for the case of a very small slit angle, more unit cells should be included in the model to obtain better simulation results. 4.3 Comparison of experimental results and FEA results The strength values obtained from experiments and FEA analysis are presented in Fig. 12. FEA prediction of tensile strength is reasonably accurate with less than 10 % error in most cases, except the 5.7° UACS/Al laminate, which underestimates the tensile strength by 16 % due to the reasons discussed in preceding subsection. Therefore, the results suggest that the present numerical simulation using a simplified unit cell model and two types of cohesive
Fig. 12 Experimental and FEA results of the tensile strength of UACS/Al for various slit angles
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elements may indeed be implemented for reasonably accurate prediction of UACS/Al laminate strength as long as the slit angle is not excessively small. Figure 13 shows the stress–strain curves of UACS/Al laminates with various slit angles obtained from experiments and FEA. The curves obtained from FEA generally agree well with those from tensile tests up to the maximum stress values, except for the case of the smallest slit angle. Different post-peak behaviour between test results and FEA predictions is observed in the case of larger slit angles. The stress–strain curves with small slit angles obtained from FEA show abrupt reduction of stress after the maximum stress level, which is similar to tensile test behaviour. However, the stress–strain curves with large slit angles slit angles obtained with FEA show a gradual reduction of tensile stress after the maximum stress level. We speculate that
Fig. 13 Stress–strain curves of UACS/Al laminate for various slit angles obtained from experimental and FEA results
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one of the reasons for this post-peak behaviour is due to the low yield stress employed in the FEA analysis. From the stress–strain curves of Fig. 13, it is observed that the yield stress values obtained from FEA are always lower than those obtained from tensile tests. In the case of large slit angle, large plastic deformation in the Al layers occurs due to the decrease in load bearing capability of the UACS layers because large delamination occurs predominantly at the interfaces of the UACS/Al laminate. Another explanation may be inaccurate boundary conditions on the two sides parallel to the fibre direction, as mentioned previously, which leads underestimation of delamination propagation. Further study is needed to clarify this issue.
5 Conclusions A new short carbon fibre reinforced metal laminate, known as UACS/Al laminate, is proposed. The tensile behaviour of UACS/Al laminate with various slit angles is investigated by tensile tests and FEA simulation. Based on the results from experiments and FEA simulations, the following conclusions are drawn. 1. Short fibre reinforced metal laminate with a proper slit angle leads to low thermal residual stress in the Al layers, which may improve the fatigue strength of FML. 2. Tensile tests show that UACS/Al laminates with smaller slit angles have relatively higher tensile strength. FEA can predict the tensile strength accurately, that is, with less than 10 % error, for most cases. Stress–strain curves predicted by FEA generally agree well with test results. 3. FEA shows that the delamination initiates at the crossing points of the slits and propagates towards the edges. The finite element model with an extremely small slit angle revealed an unusual damage pattern, likely due to the simplified boundary conditions imposed on the two sides parallel to the fibre direction. In addition, the post-peak behaviour predicted by FEA for relatively large slit angles had a relatively large error compared to the experimental results. Further investigation into the FEA modelling approach is needed to improve the accuracy of the FEA simulations. 4. An explicit solver can be used to simulate the finite element models using both intralaminar and inter-laminar cohesive elements with reasonable accuracy and computational cost, which avoids the severe convergence problems found with implicit solvers.
Acknowledgments This study was partially supported by Grant-in Aid for Scientific Research (B) (22360052) of Japan.
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