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epoxy composite after lightning strike
Aerospace Science and Technology 75 (2018) 304–314
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Experimental and numerical study on residual strength of aircraft carbon/epoxy composite after lightning strike F.S. Wang a,∗ , X.S. Yu b , S.Q. Jia a , P. Li a a b
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, PR China Shanghai Naichao Aviation Technology Ltd, Shanghai 201100, PR China
a r t i c l e
i n f o
Article history: Received 25 September 2017 Received in revised form 3 January 2018 Accepted 29 January 2018 Available online 6 February 2018 Keywords: Lightning strike Composite laminate Axial compression Residual strength Failure criterion
a b s t r a c t Mechanical properties of aircraft composite laminate after lightning strike are predicted and verified based on the combination of experiment and numerical simulation. Axial compression experiment of composite laminate containing lightning strike damage is carried out and failure modes of experimental samples under three kinds of electrical current waveforms are evaluated. The main failure modes include fiber fracture, matrix cracking and delamination. The final failure load decreases with the increase of actual integral action of lightning strike. Compression failure process of composite laminate is simulated using progressive damage analysis methods such as Hashin criterion, Maximum stress criterion and TSERPES criterion, respectively. Numerical simulation and experiment results are compared and coincided well. Percentage error of Hashin criterion is the minimum compared with those of TSERPES criterion and Maximum stress criterion. Stress concentration mainly appears in both angle sides on the fixed end and lightning damage regions of composite laminate. © 2018 Elsevier Masson SAS. All rights reserved.
1. Introduction Aircraft carbon/epoxy composite materials have been widely used in fuselage, wing and tail structures because of their excellent mechanical properties and low specific weight. But Carbon/epoxy composite material is sensitive to lightning current and its conductive property is poor, which causes larger damage probability and serious threat to flight safety when suffered from lightning strike [1]. According to the relevant reports, a commercial aircraft may suffer one lightning strike about once a year [2]. Lightning strike damage mainly displays as thermal ablation and mechanical damage around attachment points, which will greatly reduce the bearing capacity of aircraft structures [3]. So, it has great engineering significance to study the mechanical properties of composite material such as residual strength after lightning strike damage. At present, study on residual strength of composite laminate is mainly related with damage induced by the common low-velocity impact. For mechanical properties study on damage contained in composite laminate, the main methods include the softening inclusion method, sub-layer buckling method, opening equivalence method and progressive damage method [4]. At the same time, a variety of failure criteria have appeared gradually, which are suitable for failure analysis of composite laminate [5–8]. The com-
*
Corresponding author. E-mail address: [email protected] (F.S. Wang).
https://doi.org/10.1016/j.ast.2018.01.029 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.
mon failure criteria suitable for composite laminate include threedimensional Hashin failure criterion, Maximum stress failure criterion, Lee failure criterion and Chang–Chang failure criterion, etc. Feraboli P. et al. [9] carried out residual strength experiment of the damaged composite laminate after lightning strike. The results showed that tensile strength was not significantly reduced, but compression strength was weakened obviously. At the same time, Feraboli P. et al. [10] compared the lightning strike with lowvelocity impact experiment of T700S/2510 composite laminates. The results showed that the damage caused by low-velocity impact was larger than that of lightning strike. But decrease progress of compression residual strength was so complex that the general impact dynamical theory cannot be adopted to analyze the lightning strike problem and the influence of thermal effect needs to be considered. Gou J.H. et al. [11] developed a kind of tissue paper made of nanometer fiber and nickel to pave on the composite surface used for lightning protection design. Lightning strike experiment results showed that this protection method can reduce the damage area and depth effectively. But the bending experiment after lightning strike showed that residual strength of composite structure was not reduced obviously. Hirano Y. et al. [12] also carried out the axial compression experiment of the damaged composite laminate after lightning strike and compared compression experiment results with those of low-velocity impact damage contained in composite laminate. Kawakami H. et al. [13] adopted four-point bending experiment to study the bending strength of metal mesh protected composite laminate with patch repair after lightning
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Table 1 Lightning electrical current waveforms and experimental data. Waveform number
Sample number
Integral action/A2 /S
Lightning zone
Current peak/kA
Compression failure load/kN
1 2 3
1–0–1 1–0–2 1–0–3
2 × 106 (A wave) 2.25 × 106 (A wave + D wave) 0.25 × 106 (D wave)
IA IB IIB
88.4 93.7 31.3
29.7 29.6 30.6
Fig. 1. Experiment fixture and assembly pattern.
strike. The results showed that a good repair performed as well as the pristine protected specimen, while a poor repair performed equally or worse than a fully unprotected specimen. Klaus M. et al. [14] adopted three-dimensional progressive damage theory to predict residual strength of sandwich panels by four-point bending experiment after low velocity impact, which can also be employed to predict residual strength in compression after impact. Cestino E. [15] adopted numerical and experiment methods to evaluate the buckling behavior and residual tensile strength of aerospace composite structure after low velocity impact. Tensile and buckling experiments were used to validate the present methodology and a good correlation is obtained for all the cases under investigation. The authors also studied the lightning strike damage and residual strength of composite laminates [16–18]. But it only adopted numerical simulation method to predict residual tensile strength of composite laminates and lack of necessary experiment verification [16]. In this paper, lightning strike experiments of composite samples under three kinds of lightning current waveforms are carried out and evaluated. Residual compression strength and failure modes of the damaged composite laminates after lightning strike are studied through experiment and numerical simulation. For each lightning current waveform, residual strength is also compared by different failure criteria such as three-dimensional Hashin criterion, Maximum stress criterion and TSERPES criterion, respectively. 2. Experiment Experimental sample is T700/3234 carbon fiber/epoxy resin matrix composite laminate. Its size is 500 mm × 250 mm × 2 mm and ply number is 16. The stacking sequence is [45/−45/02 /45/90/ −45/0]s and thickness of each ply is 0.125 mm. Current peak values are 88.4 kA, 93.7 kA and 31.3 kA and their serial numbers are denoted as 1, 2 and 3, respectively. The detail description is given in Table 1. Three experimental samples are used and their serial numbers are 1–0–1, 1–0–2 and 1–0–3, respectively. It needs to be illustrated specially that the stacking sequence is changed to [−45/45/02 /−45/90/45/0]s here because composite samples are
Fig. 2. Paste scheme of strain gauges (unit: mm).
all upside down on both sides by operator in lightning current strike experiment. But this change does not affect the method correctness to evaluate ablation damage and residual strength. CSS-WAW600 hydraulic testing machine is used and DH-3815 static strain collection device is adopted to collect strain data. Test fixture and assembly pattern is shown in Fig. 1. The FRP strengthening pieces with 3 mm thickness are pasted on both up and down ends of experimental sample in order to protect the clamped ends. The fixed constraint is adopted on the bottom end and displacement load with 1 mm/min is applied. Simply supported constraint is adopted by active blades on both sides. Displacement load is applied until composite samples loss the bearing capacity completely. The BE120-4 strain gauges with one-way resistance are pasted on the given positions of experimental sample and paste scheme of strain gauges is shown in Fig. 2. Strain gages are pasted on the face and back of experimental sample, respectively. There will have no strain gages pasted in the places where lightning damage appears. The damaged experimental sample after axial compression is shown in Fig. 3. The typical failure modes are shown in Fig. 4, which include fiber fracture, matrix cracking and delamination. Experimental results show that failure modes are almost the same for different experimental samples. Delamination damage is caused by the excessive stress between the layers as shown in Fig. 4(a).
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Fiber fracture causes the tear damage along the direction vertical to fiber as shown in Fig. 4(b). Matrix cracking causes the tear damage along the fiber direction as shown in Fig. 4(c). The summarization of experiment data is given in Table 1. It can be seen that compression failure load is related to actual lightning current peak and actual integral action. The larger actual current peak value and integral action, the more serious experimental sample damage and the smaller compression failure load. Because the difference of actual lightning current peaks and integral actions of sample 1–0–1 and 1–0–2 is not large, so the difference of final compression failure loads is also very small.
3. Numerical simulation 3.1. Failure criteria and material properties degradation Composite laminate is able to bear compression load continually when damage appears. Considering failure modes of composite material, progressive damage numerical methods have been widely used for damage analysis and failure strength prediction, which generally includes stress calculation, failure analysis and material properties degradation. These three steps are iterated until calculation results satisfy a certain condition or the overall composite laminate is failure, which cannot bear the load any more. Failure mechanism and process of composite laminate is very complex and failure criteria are also various. The main static failure criteria applied to unidirectional laminate are Maximum stress criterion, Maximum strain criterion, Tsai–Wu criteria, Tsai–Hill criterion and Hoffman failure criterion, etc. For three-dimensional failure analysis, delamination damage in the thickness direction is also need to be considered in composite laminate [19]. According to failure modes of composite laminate after lightning strike, threedimensional Hashin criterion and Maximum stress criterion are used, which are the most common failure criteria applied to static failure analysis of composite laminate. TSERPES failure criterion is also adopted in order to compare numerical results and further verify rationality of progressive damage methods. The detailed description of three-dimensional Hashin criterion is as following [20]. Tensile delamination failure:
σ33
2
+
Zt
τ13
2
+
S 13
τ23 S 23
2 ≥ 1,
σ33 ≥ 0
(1)
Compression delamination failure:
Fig. 3. Experimental sample after compression failure.
τ13 S 13
2
+
τ23 S 23
2 ≥ 1,
Fig. 4. Compression failure modes of experimental sample.
σ33 < 0
(2)
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Table 2 Initial mechanical properties of T700/3234 composite laminate. Mechanical property parameters
Value
Mechanical property parameters
Value
E 11 /GPa E 22 = E 33 /GPa v 12 = v 13 v 23 G 12 = G 13 /GPa G 23 /GPa
1.28 8.7 0.32 0.3 4.0 4.0
X t /GPa X c /GPa Y t = Z t /MPa Y c = Z c /MPa S 12 = S 13 /MPa S 23 /MPa
2.093 0.87 50 198 104 86
Table 3 Degradation method of element stiffness for three-dimensional Hashin criterion. Failure mode
Stiffness degradation method
Tensile delamination failure Compression delamination failure Matrix cracking failure Matrix compression failure Fiber fracture failure Fiber buckling failure
E 33 E 33 E 22 E 22 E 11 E 11
= 0.01E 33 , G 13 = 0.2G 13 , G 23 = 0.2G 23 , v 13 = 0.2v 13 , v 23 = 0.2v 23 = 0.01E 33 , G 13 = 0.2G 13 , G 23 = 0.2G 23 , v 13 = 0.2v 13 , v 23 = 0.2v 23 = 0.2E 22 , G 12 = 0.2G 12 , G 23 = 0.2G 23 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 = 0.05E 11 = 0.1E 11
Matrix cracking failure:
σ22 + σ33 Yt
+
τ12
2 +
2
S 12
σ33 ≤ 0
+
1 2 S 23
τ13
Delamination failure: 2 23
τ − σ22 σ33
(3)
≥ 1,
σ22 + σ33 ≥ 0
1 YC
YC
+
2
2
2S 23
σ33 ≤ 0
+
τ12
2
1 2 S 23
+
S 12
τ13 S 13
2 τ23 − σ22 σ33
2 ≥ 1,
σ11
(4)
Xt
+
τ12
2
S 12
+
τ13 S 13
σ11 Xc
≥ 1,
σ11 < 0
2 ≥ 1,
σ11 ≥ 0
(5)
(6)
The detailed description of Maximum stress criterion is as following [21]. Matrix tensile failure:
σ22 Yt
≥ 1,
σ22 < 0
(7)
Matrix compression failure:
σ22 Yc
≥ 1,
σ22 < 0
(8)
Fiber tensile failure:
σ11 Yt
≥ 1,
σ11 < 0
(9)
Fiber buckling failure:
σ22 Yc
≥ 1,
σ11 < 0
2
+
S 13
τ23
2
S 23
≥1
(11)
+
τ12
2
+
S 12
τ13
≥1
(12)
≥1
(13)
2
S 13
2
(10)
The detailed description of TSERPES criterion is as following [22].
+
τ12 S 12
2
+
τ23 S 23
2
Fiber fracture failure:
Xc
Fiber buckling failure:
−
σ22
σ11
σ22 + σ33 < 0
2
2
Yc
Fiber fracture failure:
τ13
Matrix cracking failure:
σ22 + σ33
σ11 Xc
− 1 (σ22 + σ33 ) +
2S 23
+
Matrix-fiber shear failure:
Matrix compression failure:
2
Zc
2
S 13
σ33
≥1
(14)
Where, σ11 , σ22 and σ33 are normal stress in longitudinal, transverse and thickness direction, respectively. τ12 , τ13 and τ23 are shear stress in plane and transverse direction, respectively. X t and X c are tensile and compression strength in longitudinal direction, respectively. Y t and Y c are tensile and compression strength in transverse direction, respectively. Z t and Z c are tensile and compression strength in thickness direction. S 12 , S 13 and S 23 are shear strength in plane and transverse direction, respectively. Finite elements of numerical simulation will be damaged when their stress of composite laminate satisfies failure criterion. Stress distribution in elements varies with the change of element stiffness. Composite laminate has the characteristics of bearing continually after damage and progressive degradation of material parameters is often adopted. Chang [23–25] and Tan et al. [26] both have put forward the parameter degradation method. Chang thought that material stiffness reduced to zero as long as finite elements are failure, while Tan thought that it needs a large number of experimental results to summarize the reduction rules of material stiffness according to elements’ damage status. The reduction coefficient is often determined by experiment or experience. At present, parameter degradation method proposed by Tan is believed more mature and reliable by researchers. The corresponding material stiffness coefficient is reduced when elements’ stress satisfies above certain failure criteria. Initial mechanical properties of composite laminate are given in Table 2. Degradation methods of element stiffness for three-dimensional Hashin criterion, Maximum stress criterion and TSERPES criterion are given in Table 3, Table 4 and Table 5, respectively. In these tables, E 11 , E 22 and E 33 are
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Table 4 Degradation method of element stiffness for Maximum stress criterion. Failure mode
Stiffness degradation method
Matrix tensile failure Matrix compression failure Fiber tensile failure Fiber buckling failure
E 22 E 22 E 11 E 11
= 0.2E 22 , G 12 = 0.2G 12 , G 23 = 0.2G 23 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 = 0.05E 11 = 0.1E 11
Table 5 Degradation method of element stiffness for TSERPES criterion. Failure mode
Stiffness degradation method
Matrix cracking failure Matrix-fiber shear failure Delamination failure Fiber fracture failure
E 22 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 G 12 = v 12 = 0 E 11 = G 12 = G 23 = v 12 = v 23 = 0 E 11 = 0.14E 11
Young’s modulus in longitudinal, transverse and thickness directions, respectively. G 12 , G 13 and G 23 are shear modulus in plane and transverse direction, respectively. v 12 , v 13 and v 23 are Poisson’s ratio in plane and transverse direction, respectively. 3.2. Description of initial finite element model The initial model is the ablation damaged composite laminate after lightning strike in our previous published paper [18]. The geometrical size and stacking sequence of composite laminate used in numerical simulation is the same with that of axial compression experiment. Transient temperature field of composite laminate suffered from lightning strike is obtained by the coupled thermal-electrical-structural analysis. Element deletion program is compiled by APDL development language of ANSYS software to realize ablation simulation. In our study, sublimation temperature is specified as ablation temperature. If average element temperature is less than ablation temperature, current load will continue to apply. While if average element temperature is greater than ablation temperature, the element will be considered to ablate and then delete. The deleted elements boundary will be used as a new boundary to apply lightning electrical current load for next time step. The rest elements and nodes are renumbered to generate a new finite element model. Different electrical and thermal properties of the elements that not ablated in new model are defined depending on different temperature condition. Current waveforms in lightning strike experiment and ablation simulation results of composite laminate are shown in Fig. 5. For axial compression simulation, element type is selected as SOLID45, which is a three-dimensional finite element and has eight nodes. For the initial model to simulate axial compression of composite laminate, it divides into four temperature ranges to define different levels of material ablation damage [16]. When ablation temperature is less than 260 ◦ C, there is considered no damage in composite elements, in which the material properties has no change and is still the initial properties of composite material. When ablation temperature reaches the ranges between 260 ◦ C and 600 ◦ C, the damage is defined as resin damage and reduction factor of material property is 0.6. It is considered delamination damage when ablation temperature reaches the ranges between 600 ◦ C and 3316 ◦ C, material property of composite material will be reduced to 0.1. It is defined as fiber damage when ablation temperature exceeds 3316 ◦ C. The finite elements will be deleted completely and material property will be reduced to 0. Material properties under different temperature are given in Table 6. Analysis procedure of residual strength for the damaged composite laminate after lightning strike is as following: Firstly, the corresponding element numbers of different temperature ranges are extracted from ablation calculation results of composite laminate. The initial model is established in ANSYS software and the
Table 6 Material properties under different ablation temperature. Ablation temperature/◦ C
Failure mode
Reduction factor
25–260 260–600 600–3316 > 3316
No damage Resin damage Delamination failure Fiber fracture
No reduction 0.6 0.1 0
corresponding element numbers and temperature values in each temperature range are imported to the model. Material properties are reduced correspondingly according to Table 6. At this time, the model after material coefficient reduction is regarded as the initial model. Secondly, stress components of composite elements in global coordinate system are calculated by applying compression displacement load and those in local coordinate system are calculated by the transition matrix. Then stress components in local coordinate system are imported to above three failure criteria. For three-dimensional Hashin criterion, failure criterion is expressed by the Eqs. (1)–(6) and represented by six failure modes of composite laminate. For Maximum stress criterion, failure criterion is expressed by the Eqs. (7)–(10) and represented by four failure modes of composite laminate. For TSERPES criterion, failure criterion is expressed by the Eqs. (11)–(14) and represented by four failure modes of composite laminate. Element stress of composite laminate is judged whether to satisfy failure condition or not. If element stress satisfies failure condition, its stiffness is reduced correspondingly. Otherwise, compression displacement load keeps on applying until satisfying the failure condition. Element stiffness is reduced according to Table 3, Table 4 and Table 5 for different failure criteria. The load is increased gradually with the increase of displacement and failure elements in composite laminate are also increased. When composite laminate is unable to bear compression load, the calculating program will terminate automatically. At this time, the final compression failure load can be got. 4. Results and discussion 4.1. Load-displacement relationships Load-displacement curves of experimental sample 1–0–1 under three kinds of failure criteria are shown in Fig. 6. The final failure loads through numerical simulation and experiment are given in Table 7. It can be seen that the experiment result of sample 1–0–1 is 29.7 kN and the difference of numerical simulation results under different failure criteria are larger. Numerical simulation result is close to experiment result when Hashin criterion is used. Its percentage error is 2.66%. Followed by Maximum stress criterion, percentage error is −5.69%. Percentage error of numerical simulation result is the largest when TSERPES criterion is used and its percentage error is 12.53%. Compression displacement is the largest when Maximum stress criteria is used and stiffness reduction is first to start. Displacement is about 0.14 mm when stiffness reduction starts and reduction degree is obvious. Obvious stiffness reduction is produced when compression displacement is about 0.22 mm for other both two kinds of failure criteria. Change trend of load-displacement curves are similar for Hashin criterion and TSERPES criterion, but reduction degree is smaller than that for Maximum stress criterion. It can be seen from Fig. 7 and Table 8 that experiment result of sample 1–0–2 is almost the same as that of sample 1–0–1. Numerical simulation results of sample 1–0–2 under different failure criteria are also similar with those of sample 1–0–1. Similarly, the percentage error is the smallest when Hashin criterion is used and its percentage error is the largest when TSERPES criterion is used. Compression displacement is also the largest when Maximum stress criterion is used and the maximum displacement is
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Fig. 5. Lightning current waveforms and ablation simulation results. Table 7 Failure loads of sample 1–0–1 under different failure criterion.
Table 8 Failure loads of sample 1–0–2 under different failure criteria.
Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Hashin criterion Maximum criterion TSERPES criterion
30.49 28.01 33.42
29.7 29.7 29.7
2.66% −5.69% 12.53%
Hashin criterion Maximum criterion TSERPES criterion
30.3 27.91 33.18
29.6 29.6 29.6
2.36% −5.71% 12.09%
0.61 mm. The displacement is about 0.15 mm when stiffness reduction starts and reduction degree is rather obvious. Stiffness reduction is produced when compression displacement is about 0.21 mm for other both kinds of failure criteria. But reduction degree is not obvious. Change trend of load-displacement curve is also similar with those of Hashin criterion and TSERPES criterion.
It can be seen from Fig. 8 and Table 9 that experiment result of sample 1–0–3 is larger than those of samples 1–0–1 and 1–0–2. Percentage errors of numerical simulation results under different failure criteria are larger than those of samples 1–0–1 and 1–0–2. The difference with samples 1–0–1 and 1–0–2 is that numerical simulation result is close to experiment result when Maximum
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Table 9 Failure loads of sample 1–0–3 under different failure criteria. Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Hashin criterion Maximum criterion TSERPES criterion
33.30 29.33 36.31
30.6 30.6 30.6
8.82% −4.15% 18.66%
Fig. 8. Load-displacement curves of sample 1–0–3 under different failure criteria.
Fig. 6. Load-displacement curves of sample 1–0–1 under different failure criteria.
Fig. 7. Load-displacement curves of sample 1–0–2 under different failure criteria.
stress criterion is used and its percentage error is −4.15%. But the minimum percentage error is still larger than that of samples 1–0–1 and 1–0–2. Percentage error between numerical simulation and experiment results is the largest when TSERPES criterion is used and its percentage error is 18.66%. But it is the same as samples 1–0–1 and 1–0–2 that compression displacement is also the largest when Maximum stress criterion is used and stiffness reduction is also the first to start. The other characteristics of the curves are also similar with 1–0–1 and 1–0–2. 4.2. Damage extension Because damage extension in the axial compression of composite laminate after lightning strike is similar for the above three kinds of lightning current peaks, so here experimental sample with 93.7 kA lightning current peak is used to analyze damage extension. In order to focus on studying damage condition of upper
layers, damage extension of the top eight layers is listed out only. Damage extension under Hashin criterion, Maximum stress criterion and TSERPES criterion is shown in Fig. 9, Fig. 10, Fig. 11, respectively. It can be seen that damage extension under three kinds of failure criteria is similar. In the first −45◦ layer and second 45◦ layer, stress concentration of the damaged composite laminate first appears in fiber direction on the fixed end and decreases gradually to the center along fiber direction. Stress increases gradually with the increase of time and the damaged area is very large. The regions for serious ablation damaged will no longer bear the load. For the third 0◦ layer and the fourth 0◦ layer, stress in the fixed end is symmetrical. Stress concentration mainly appears in the fixed end and decrease gradually from the end to center. Stress in lightning ablation area decreases significantly and stress concentration appears obvious around the damaged regions. For the fifth −45◦ layer, stress concentration mainly appears around lightning ablation regions and the fixed end along fiber direction. The stress of the sixth 90◦ layer is symmetrical. But it is smaller than that of other layers and stress concentration mainly occurs in the regions damaged by lightning strike. The seventh 45◦ layer is similar with the fifth layer, where stress concentration mainly appears around lightning ablation regions and the fixed end along fiber direction. Stress of the eighth 0◦ layer in the fixed end is symmetrical. It is appears obvious stress concentration in the lightning damaged area. Under these three kinds of failure criteria, stress concentration in axial compression mainly appears in both angles on the fixed end and lightning damaged area of composite laminate. Stress concentration in both angles of the fixed end is the main reason to cause fiber fracture and matrix cracking along fiber direction. While stress difference in lightning damaged regions is the main reason to cause delamination of composite laminate. It is consistent with compression failure mode of experimental sample shown in Fig. 4. 5. Conclusions Using progressive damage analysis method, axial compression strength of composite laminates after lightning strike is simulated. The final residual strength is predicted by adopting Hashin criterion, TSERPES criterion and Maximum stress criterion, respectively. Experiment and numerical simulation results are compared. The following main conclusions can be got. 1. When composite laminates are suffered from lightning strike, the larger integral action of lightning electrical current, more
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Fig. 9. Damage extension of top eight layers under Hashin criterion.
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Fig. 10. Damage extension of top eight layers under Maximum stress criterion.
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Fig. 11. Damage extension of top eight layers under TSERPES criterion.
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serious the damage of composite laminate and the smaller compression failure load. 2. Numerical simulation result is larger than experiment result by Hashin criterion and TSERPES criterion, while it is smaller by Maximum stress criterion. Percentage error by Hashin criterion is relatively small and within the reasonable range. The numerical simulation and experimental results coincide well. 3. Stress concentration of axial compression mainly appears on both angles in the fixed end and lightning ablation regions of composite laminate. Stress concentration on two angles in the fixed end is the main reason to cause fiber fracture and matrix cracking along fiber direction, while stress difference in lightning damaged regions is the main reason to cause delamination of composite laminate. Conflict of interest statement There is no conflict of interest. Acknowledgements This study is supported by the National Natural Science Foundation of China (No.: 51475369). References [1] M. Gagné, D. Therriault, Lightning strike protection of composites, Prog. Aerosp. Sci. 64 (2013) 1–16. [2] A. Larsson, The interaction between a lightning flash and an aircraft in flight, C. R. Phys. 3 (10) (2002) 1423–1444. [3] P.G. Slattery, C.T. Mccarthy, R.M. O’Higgins, Assessment of residual strength of repaired solid laminate composite materials through mechanical testing, Compos. Struct. 147 (2016) 122–130. [4] Z.Y. Lin, X.W. Xu, Residual compressive strength of composite laminates after low-velocity impact, Acta Mater. Compos. Sin. 1 (25) (2008) 140–146 (in Chinese). [5] A. Puck, H. Schürmann, Failure analysis of FRP laminates by means of physically based phenomenological models, Compos. Sci. Technol. 58 (7) (2002) 1633–1662. [6] D. Zhang, J. Ye, D. Lam, Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading, Compos. Struct. 75 (2006) 121–131. [7] A.C. Orifici, I. Herszberg, R.S. Thomson, Review of methodologies for composite material modelling incorporating failure, Compos. Struct. 86 (2008) 194–210.
[8] P.F. Liu, J.Y. Zheng, Recent developments on damage modeling and finite element analysis for composite laminates: a review, Mater. Des. 31 (2010) 3825–3834. [9] P. Feraboli, M. Miller, Damage resistance and tolerance of carbon/epoxy composite coupons subjected to simulated lightning strike, Composites, Part A 40 (6–7) (2009) 954–967. [10] P. Feraboli, H. Kawakami, Damage of carbon/epoxy composite plates subjected to mechanical impact and simulated lightning, J. Aircr. 47 (3) (2010) 999–1012. [11] J.H. Gou, Y. Tang, F. Liang, et al., Carbon nanofiber paper for lightning strike protection of composite materials, Composites, Part B 41 (2010) 192–198. [12] Y. Hirano, S. Katsumata, Y. Iwahori, et al., Fracture behavior of CFRP specimen after lightning strike, in: 17th International Conference on Composite Materials, Edinburgh, UK, 2009. [13] H. Kawakami, P. Feraboli, Lightning strike damage resistance and tolerance of scarf-repaired mesh-protected carbon fiber composites, Composites, Part A, Appl. Sci. Manuf. 42 (9) (2011) 1247–1262. [14] M. Klaus, H.G. Reimerdes, N.K. Gupta, Experimental and numerical investigations of residual strength after impact of sandwich panels, Int. J. Impact Eng. 44 (2012) 50–58. [15] E. Cestino, G. Romeo, P. Piana, et al., Numerical/experimental evaluation of buckling behaviour and residual tensile strength of composite aerospace structures after low velocity impact, Aerosp. Sci. Technol. 54 (2016) 1–9. [16] F.S. Wang, N. Ding, Z.Q. Liu, et al., Ablation damage characteristic and residual strength prediction of carbon fiber/epoxy composite suffered from lightning strike, Compos. Struct. 117 (2014) 222–233. [17] Z.Q. Liu, Z.F. Yue, F.S. Wang, et al., Combining analysis of coupled electricalthermal and BLOW-OFF impulse effects on composite laminate induced by lightning strike, Appl. Compos. Mater. 22 (2) (2015) 189–207. [18] F.S. Wang, Y.Y. Ji, X.S. Yu, et al., Ablation damage assessment of aircraft carbon fiber epoxy composite and its protection structures suffered from lightning strike, Compos. Struct. 145 (2016) 226–241. [19] P.Y. Wang, F.S. Wang, Z.T. Zhu, et al., 3D numerical calculation of damage accumulation for composite single bolted joint, J. Mech. Strength 32 (5) (2010) 124–128 (in Chinese). [20] Z. Hashin, Failure criteria for unidirectional fiber composites, J. Appl. Mech. 47 (2) (1980) 329–334. [21] I.M. Daniel, Yield and failure criteria for composite materials under static and dynamic loading, Prog. Aerosp. Sci. 81 (2016) 18–25. [22] K.I. Tserpes, G. Labeas, P. Papanikos, et al., Strength prediction of bolted joints in graphite/epoxy composite laminates, Composites, Part B 33 (7) (2002) 521–529. [23] F.K. Chang, K.Y. Chang, A progressive damage model for laminated composites containing stress concentrations, J. Compos. Mater. 21 (9) (1987) 834–855. [24] F.K. Chang, K.Y. Chang, Post-failure analysis of bolted composite joints in tension or shear-out mode failure, J. Compos. Mater. 21 (9) (1987) 809–833. [25] K.Y. Chang, S. Liu, F.K. Chang, Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings, J. Compos. Mater. 25 (3) (1991) 274–301. [26] S.C. Tan, J. Perez, Progressive failure of laminated composites with a hole under compressive loading, J. Reinf. Plast. Compos. 12 (10) (1993) 1043–1057.
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Aerospace Science and Technology www.elsevier.com/locate/aescte
Experimental and numerical study on residual strength of aircraft carbon/epoxy composite after lightning strike F.S. Wang a,∗ , X.S. Yu b , S.Q. Jia a , P. Li a a b
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, PR China Shanghai Naichao Aviation Technology Ltd, Shanghai 201100, PR China
a r t i c l e
i n f o
Article history: Received 25 September 2017 Received in revised form 3 January 2018 Accepted 29 January 2018 Available online 6 February 2018 Keywords: Lightning strike Composite laminate Axial compression Residual strength Failure criterion
a b s t r a c t Mechanical properties of aircraft composite laminate after lightning strike are predicted and verified based on the combination of experiment and numerical simulation. Axial compression experiment of composite laminate containing lightning strike damage is carried out and failure modes of experimental samples under three kinds of electrical current waveforms are evaluated. The main failure modes include fiber fracture, matrix cracking and delamination. The final failure load decreases with the increase of actual integral action of lightning strike. Compression failure process of composite laminate is simulated using progressive damage analysis methods such as Hashin criterion, Maximum stress criterion and TSERPES criterion, respectively. Numerical simulation and experiment results are compared and coincided well. Percentage error of Hashin criterion is the minimum compared with those of TSERPES criterion and Maximum stress criterion. Stress concentration mainly appears in both angle sides on the fixed end and lightning damage regions of composite laminate. © 2018 Elsevier Masson SAS. All rights reserved.
1. Introduction Aircraft carbon/epoxy composite materials have been widely used in fuselage, wing and tail structures because of their excellent mechanical properties and low specific weight. But Carbon/epoxy composite material is sensitive to lightning current and its conductive property is poor, which causes larger damage probability and serious threat to flight safety when suffered from lightning strike [1]. According to the relevant reports, a commercial aircraft may suffer one lightning strike about once a year [2]. Lightning strike damage mainly displays as thermal ablation and mechanical damage around attachment points, which will greatly reduce the bearing capacity of aircraft structures [3]. So, it has great engineering significance to study the mechanical properties of composite material such as residual strength after lightning strike damage. At present, study on residual strength of composite laminate is mainly related with damage induced by the common low-velocity impact. For mechanical properties study on damage contained in composite laminate, the main methods include the softening inclusion method, sub-layer buckling method, opening equivalence method and progressive damage method [4]. At the same time, a variety of failure criteria have appeared gradually, which are suitable for failure analysis of composite laminate [5–8]. The com-
*
Corresponding author. E-mail address: [email protected] (F.S. Wang).
https://doi.org/10.1016/j.ast.2018.01.029 1270-9638/© 2018 Elsevier Masson SAS. All rights reserved.
mon failure criteria suitable for composite laminate include threedimensional Hashin failure criterion, Maximum stress failure criterion, Lee failure criterion and Chang–Chang failure criterion, etc. Feraboli P. et al. [9] carried out residual strength experiment of the damaged composite laminate after lightning strike. The results showed that tensile strength was not significantly reduced, but compression strength was weakened obviously. At the same time, Feraboli P. et al. [10] compared the lightning strike with lowvelocity impact experiment of T700S/2510 composite laminates. The results showed that the damage caused by low-velocity impact was larger than that of lightning strike. But decrease progress of compression residual strength was so complex that the general impact dynamical theory cannot be adopted to analyze the lightning strike problem and the influence of thermal effect needs to be considered. Gou J.H. et al. [11] developed a kind of tissue paper made of nanometer fiber and nickel to pave on the composite surface used for lightning protection design. Lightning strike experiment results showed that this protection method can reduce the damage area and depth effectively. But the bending experiment after lightning strike showed that residual strength of composite structure was not reduced obviously. Hirano Y. et al. [12] also carried out the axial compression experiment of the damaged composite laminate after lightning strike and compared compression experiment results with those of low-velocity impact damage contained in composite laminate. Kawakami H. et al. [13] adopted four-point bending experiment to study the bending strength of metal mesh protected composite laminate with patch repair after lightning
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Table 1 Lightning electrical current waveforms and experimental data. Waveform number
Sample number
Integral action/A2 /S
Lightning zone
Current peak/kA
Compression failure load/kN
1 2 3
1–0–1 1–0–2 1–0–3
2 × 106 (A wave) 2.25 × 106 (A wave + D wave) 0.25 × 106 (D wave)
IA IB IIB
88.4 93.7 31.3
29.7 29.6 30.6
Fig. 1. Experiment fixture and assembly pattern.
strike. The results showed that a good repair performed as well as the pristine protected specimen, while a poor repair performed equally or worse than a fully unprotected specimen. Klaus M. et al. [14] adopted three-dimensional progressive damage theory to predict residual strength of sandwich panels by four-point bending experiment after low velocity impact, which can also be employed to predict residual strength in compression after impact. Cestino E. [15] adopted numerical and experiment methods to evaluate the buckling behavior and residual tensile strength of aerospace composite structure after low velocity impact. Tensile and buckling experiments were used to validate the present methodology and a good correlation is obtained for all the cases under investigation. The authors also studied the lightning strike damage and residual strength of composite laminates [16–18]. But it only adopted numerical simulation method to predict residual tensile strength of composite laminates and lack of necessary experiment verification [16]. In this paper, lightning strike experiments of composite samples under three kinds of lightning current waveforms are carried out and evaluated. Residual compression strength and failure modes of the damaged composite laminates after lightning strike are studied through experiment and numerical simulation. For each lightning current waveform, residual strength is also compared by different failure criteria such as three-dimensional Hashin criterion, Maximum stress criterion and TSERPES criterion, respectively. 2. Experiment Experimental sample is T700/3234 carbon fiber/epoxy resin matrix composite laminate. Its size is 500 mm × 250 mm × 2 mm and ply number is 16. The stacking sequence is [45/−45/02 /45/90/ −45/0]s and thickness of each ply is 0.125 mm. Current peak values are 88.4 kA, 93.7 kA and 31.3 kA and their serial numbers are denoted as 1, 2 and 3, respectively. The detail description is given in Table 1. Three experimental samples are used and their serial numbers are 1–0–1, 1–0–2 and 1–0–3, respectively. It needs to be illustrated specially that the stacking sequence is changed to [−45/45/02 /−45/90/45/0]s here because composite samples are
Fig. 2. Paste scheme of strain gauges (unit: mm).
all upside down on both sides by operator in lightning current strike experiment. But this change does not affect the method correctness to evaluate ablation damage and residual strength. CSS-WAW600 hydraulic testing machine is used and DH-3815 static strain collection device is adopted to collect strain data. Test fixture and assembly pattern is shown in Fig. 1. The FRP strengthening pieces with 3 mm thickness are pasted on both up and down ends of experimental sample in order to protect the clamped ends. The fixed constraint is adopted on the bottom end and displacement load with 1 mm/min is applied. Simply supported constraint is adopted by active blades on both sides. Displacement load is applied until composite samples loss the bearing capacity completely. The BE120-4 strain gauges with one-way resistance are pasted on the given positions of experimental sample and paste scheme of strain gauges is shown in Fig. 2. Strain gages are pasted on the face and back of experimental sample, respectively. There will have no strain gages pasted in the places where lightning damage appears. The damaged experimental sample after axial compression is shown in Fig. 3. The typical failure modes are shown in Fig. 4, which include fiber fracture, matrix cracking and delamination. Experimental results show that failure modes are almost the same for different experimental samples. Delamination damage is caused by the excessive stress between the layers as shown in Fig. 4(a).
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Fiber fracture causes the tear damage along the direction vertical to fiber as shown in Fig. 4(b). Matrix cracking causes the tear damage along the fiber direction as shown in Fig. 4(c). The summarization of experiment data is given in Table 1. It can be seen that compression failure load is related to actual lightning current peak and actual integral action. The larger actual current peak value and integral action, the more serious experimental sample damage and the smaller compression failure load. Because the difference of actual lightning current peaks and integral actions of sample 1–0–1 and 1–0–2 is not large, so the difference of final compression failure loads is also very small.
3. Numerical simulation 3.1. Failure criteria and material properties degradation Composite laminate is able to bear compression load continually when damage appears. Considering failure modes of composite material, progressive damage numerical methods have been widely used for damage analysis and failure strength prediction, which generally includes stress calculation, failure analysis and material properties degradation. These three steps are iterated until calculation results satisfy a certain condition or the overall composite laminate is failure, which cannot bear the load any more. Failure mechanism and process of composite laminate is very complex and failure criteria are also various. The main static failure criteria applied to unidirectional laminate are Maximum stress criterion, Maximum strain criterion, Tsai–Wu criteria, Tsai–Hill criterion and Hoffman failure criterion, etc. For three-dimensional failure analysis, delamination damage in the thickness direction is also need to be considered in composite laminate [19]. According to failure modes of composite laminate after lightning strike, threedimensional Hashin criterion and Maximum stress criterion are used, which are the most common failure criteria applied to static failure analysis of composite laminate. TSERPES failure criterion is also adopted in order to compare numerical results and further verify rationality of progressive damage methods. The detailed description of three-dimensional Hashin criterion is as following [20]. Tensile delamination failure:
σ33
2
+
Zt
τ13
2
+
S 13
τ23 S 23
2 ≥ 1,
σ33 ≥ 0
(1)
Compression delamination failure:
Fig. 3. Experimental sample after compression failure.
τ13 S 13
2
+
τ23 S 23
2 ≥ 1,
Fig. 4. Compression failure modes of experimental sample.
σ33 < 0
(2)
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Table 2 Initial mechanical properties of T700/3234 composite laminate. Mechanical property parameters
Value
Mechanical property parameters
Value
E 11 /GPa E 22 = E 33 /GPa v 12 = v 13 v 23 G 12 = G 13 /GPa G 23 /GPa
1.28 8.7 0.32 0.3 4.0 4.0
X t /GPa X c /GPa Y t = Z t /MPa Y c = Z c /MPa S 12 = S 13 /MPa S 23 /MPa
2.093 0.87 50 198 104 86
Table 3 Degradation method of element stiffness for three-dimensional Hashin criterion. Failure mode
Stiffness degradation method
Tensile delamination failure Compression delamination failure Matrix cracking failure Matrix compression failure Fiber fracture failure Fiber buckling failure
E 33 E 33 E 22 E 22 E 11 E 11
= 0.01E 33 , G 13 = 0.2G 13 , G 23 = 0.2G 23 , v 13 = 0.2v 13 , v 23 = 0.2v 23 = 0.01E 33 , G 13 = 0.2G 13 , G 23 = 0.2G 23 , v 13 = 0.2v 13 , v 23 = 0.2v 23 = 0.2E 22 , G 12 = 0.2G 12 , G 23 = 0.2G 23 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 = 0.05E 11 = 0.1E 11
Matrix cracking failure:
σ22 + σ33 Yt
+
τ12
2 +
2
S 12
σ33 ≤ 0
+
1 2 S 23
τ13
Delamination failure: 2 23
τ − σ22 σ33
(3)
≥ 1,
σ22 + σ33 ≥ 0
1 YC
YC
+
2
2
2S 23
σ33 ≤ 0
+
τ12
2
1 2 S 23
+
S 12
τ13 S 13
2 τ23 − σ22 σ33
2 ≥ 1,
σ11
(4)
Xt
+
τ12
2
S 12
+
τ13 S 13
σ11 Xc
≥ 1,
σ11 < 0
2 ≥ 1,
σ11 ≥ 0
(5)
(6)
The detailed description of Maximum stress criterion is as following [21]. Matrix tensile failure:
σ22 Yt
≥ 1,
σ22 < 0
(7)
Matrix compression failure:
σ22 Yc
≥ 1,
σ22 < 0
(8)
Fiber tensile failure:
σ11 Yt
≥ 1,
σ11 < 0
(9)
Fiber buckling failure:
σ22 Yc
≥ 1,
σ11 < 0
2
+
S 13
τ23
2
S 23
≥1
(11)
+
τ12
2
+
S 12
τ13
≥1
(12)
≥1
(13)
2
S 13
2
(10)
The detailed description of TSERPES criterion is as following [22].
+
τ12 S 12
2
+
τ23 S 23
2
Fiber fracture failure:
Xc
Fiber buckling failure:
−
σ22
σ11
σ22 + σ33 < 0
2
2
Yc
Fiber fracture failure:
τ13
Matrix cracking failure:
σ22 + σ33
σ11 Xc
− 1 (σ22 + σ33 ) +
2S 23
+
Matrix-fiber shear failure:
Matrix compression failure:
2
Zc
2
S 13
σ33
≥1
(14)
Where, σ11 , σ22 and σ33 are normal stress in longitudinal, transverse and thickness direction, respectively. τ12 , τ13 and τ23 are shear stress in plane and transverse direction, respectively. X t and X c are tensile and compression strength in longitudinal direction, respectively. Y t and Y c are tensile and compression strength in transverse direction, respectively. Z t and Z c are tensile and compression strength in thickness direction. S 12 , S 13 and S 23 are shear strength in plane and transverse direction, respectively. Finite elements of numerical simulation will be damaged when their stress of composite laminate satisfies failure criterion. Stress distribution in elements varies with the change of element stiffness. Composite laminate has the characteristics of bearing continually after damage and progressive degradation of material parameters is often adopted. Chang [23–25] and Tan et al. [26] both have put forward the parameter degradation method. Chang thought that material stiffness reduced to zero as long as finite elements are failure, while Tan thought that it needs a large number of experimental results to summarize the reduction rules of material stiffness according to elements’ damage status. The reduction coefficient is often determined by experiment or experience. At present, parameter degradation method proposed by Tan is believed more mature and reliable by researchers. The corresponding material stiffness coefficient is reduced when elements’ stress satisfies above certain failure criteria. Initial mechanical properties of composite laminate are given in Table 2. Degradation methods of element stiffness for three-dimensional Hashin criterion, Maximum stress criterion and TSERPES criterion are given in Table 3, Table 4 and Table 5, respectively. In these tables, E 11 , E 22 and E 33 are
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Table 4 Degradation method of element stiffness for Maximum stress criterion. Failure mode
Stiffness degradation method
Matrix tensile failure Matrix compression failure Fiber tensile failure Fiber buckling failure
E 22 E 22 E 11 E 11
= 0.2E 22 , G 12 = 0.2G 12 , G 23 = 0.2G 23 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 = 0.05E 11 = 0.1E 11
Table 5 Degradation method of element stiffness for TSERPES criterion. Failure mode
Stiffness degradation method
Matrix cracking failure Matrix-fiber shear failure Delamination failure Fiber fracture failure
E 22 = 0.4E 22 , G 12 = 0.4G 12 , G 23 = 0.4G 23 G 12 = v 12 = 0 E 11 = G 12 = G 23 = v 12 = v 23 = 0 E 11 = 0.14E 11
Young’s modulus in longitudinal, transverse and thickness directions, respectively. G 12 , G 13 and G 23 are shear modulus in plane and transverse direction, respectively. v 12 , v 13 and v 23 are Poisson’s ratio in plane and transverse direction, respectively. 3.2. Description of initial finite element model The initial model is the ablation damaged composite laminate after lightning strike in our previous published paper [18]. The geometrical size and stacking sequence of composite laminate used in numerical simulation is the same with that of axial compression experiment. Transient temperature field of composite laminate suffered from lightning strike is obtained by the coupled thermal-electrical-structural analysis. Element deletion program is compiled by APDL development language of ANSYS software to realize ablation simulation. In our study, sublimation temperature is specified as ablation temperature. If average element temperature is less than ablation temperature, current load will continue to apply. While if average element temperature is greater than ablation temperature, the element will be considered to ablate and then delete. The deleted elements boundary will be used as a new boundary to apply lightning electrical current load for next time step. The rest elements and nodes are renumbered to generate a new finite element model. Different electrical and thermal properties of the elements that not ablated in new model are defined depending on different temperature condition. Current waveforms in lightning strike experiment and ablation simulation results of composite laminate are shown in Fig. 5. For axial compression simulation, element type is selected as SOLID45, which is a three-dimensional finite element and has eight nodes. For the initial model to simulate axial compression of composite laminate, it divides into four temperature ranges to define different levels of material ablation damage [16]. When ablation temperature is less than 260 ◦ C, there is considered no damage in composite elements, in which the material properties has no change and is still the initial properties of composite material. When ablation temperature reaches the ranges between 260 ◦ C and 600 ◦ C, the damage is defined as resin damage and reduction factor of material property is 0.6. It is considered delamination damage when ablation temperature reaches the ranges between 600 ◦ C and 3316 ◦ C, material property of composite material will be reduced to 0.1. It is defined as fiber damage when ablation temperature exceeds 3316 ◦ C. The finite elements will be deleted completely and material property will be reduced to 0. Material properties under different temperature are given in Table 6. Analysis procedure of residual strength for the damaged composite laminate after lightning strike is as following: Firstly, the corresponding element numbers of different temperature ranges are extracted from ablation calculation results of composite laminate. The initial model is established in ANSYS software and the
Table 6 Material properties under different ablation temperature. Ablation temperature/◦ C
Failure mode
Reduction factor
25–260 260–600 600–3316 > 3316
No damage Resin damage Delamination failure Fiber fracture
No reduction 0.6 0.1 0
corresponding element numbers and temperature values in each temperature range are imported to the model. Material properties are reduced correspondingly according to Table 6. At this time, the model after material coefficient reduction is regarded as the initial model. Secondly, stress components of composite elements in global coordinate system are calculated by applying compression displacement load and those in local coordinate system are calculated by the transition matrix. Then stress components in local coordinate system are imported to above three failure criteria. For three-dimensional Hashin criterion, failure criterion is expressed by the Eqs. (1)–(6) and represented by six failure modes of composite laminate. For Maximum stress criterion, failure criterion is expressed by the Eqs. (7)–(10) and represented by four failure modes of composite laminate. For TSERPES criterion, failure criterion is expressed by the Eqs. (11)–(14) and represented by four failure modes of composite laminate. Element stress of composite laminate is judged whether to satisfy failure condition or not. If element stress satisfies failure condition, its stiffness is reduced correspondingly. Otherwise, compression displacement load keeps on applying until satisfying the failure condition. Element stiffness is reduced according to Table 3, Table 4 and Table 5 for different failure criteria. The load is increased gradually with the increase of displacement and failure elements in composite laminate are also increased. When composite laminate is unable to bear compression load, the calculating program will terminate automatically. At this time, the final compression failure load can be got. 4. Results and discussion 4.1. Load-displacement relationships Load-displacement curves of experimental sample 1–0–1 under three kinds of failure criteria are shown in Fig. 6. The final failure loads through numerical simulation and experiment are given in Table 7. It can be seen that the experiment result of sample 1–0–1 is 29.7 kN and the difference of numerical simulation results under different failure criteria are larger. Numerical simulation result is close to experiment result when Hashin criterion is used. Its percentage error is 2.66%. Followed by Maximum stress criterion, percentage error is −5.69%. Percentage error of numerical simulation result is the largest when TSERPES criterion is used and its percentage error is 12.53%. Compression displacement is the largest when Maximum stress criteria is used and stiffness reduction is first to start. Displacement is about 0.14 mm when stiffness reduction starts and reduction degree is obvious. Obvious stiffness reduction is produced when compression displacement is about 0.22 mm for other both two kinds of failure criteria. Change trend of load-displacement curves are similar for Hashin criterion and TSERPES criterion, but reduction degree is smaller than that for Maximum stress criterion. It can be seen from Fig. 7 and Table 8 that experiment result of sample 1–0–2 is almost the same as that of sample 1–0–1. Numerical simulation results of sample 1–0–2 under different failure criteria are also similar with those of sample 1–0–1. Similarly, the percentage error is the smallest when Hashin criterion is used and its percentage error is the largest when TSERPES criterion is used. Compression displacement is also the largest when Maximum stress criterion is used and the maximum displacement is
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Fig. 5. Lightning current waveforms and ablation simulation results. Table 7 Failure loads of sample 1–0–1 under different failure criterion.
Table 8 Failure loads of sample 1–0–2 under different failure criteria.
Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Hashin criterion Maximum criterion TSERPES criterion
30.49 28.01 33.42
29.7 29.7 29.7
2.66% −5.69% 12.53%
Hashin criterion Maximum criterion TSERPES criterion
30.3 27.91 33.18
29.6 29.6 29.6
2.36% −5.71% 12.09%
0.61 mm. The displacement is about 0.15 mm when stiffness reduction starts and reduction degree is rather obvious. Stiffness reduction is produced when compression displacement is about 0.21 mm for other both kinds of failure criteria. But reduction degree is not obvious. Change trend of load-displacement curve is also similar with those of Hashin criterion and TSERPES criterion.
It can be seen from Fig. 8 and Table 9 that experiment result of sample 1–0–3 is larger than those of samples 1–0–1 and 1–0–2. Percentage errors of numerical simulation results under different failure criteria are larger than those of samples 1–0–1 and 1–0–2. The difference with samples 1–0–1 and 1–0–2 is that numerical simulation result is close to experiment result when Maximum
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Table 9 Failure loads of sample 1–0–3 under different failure criteria. Failure criterion
Failure load/kN
Experiment result/kN
Percentage error
Hashin criterion Maximum criterion TSERPES criterion
33.30 29.33 36.31
30.6 30.6 30.6
8.82% −4.15% 18.66%
Fig. 8. Load-displacement curves of sample 1–0–3 under different failure criteria.
Fig. 6. Load-displacement curves of sample 1–0–1 under different failure criteria.
Fig. 7. Load-displacement curves of sample 1–0–2 under different failure criteria.
stress criterion is used and its percentage error is −4.15%. But the minimum percentage error is still larger than that of samples 1–0–1 and 1–0–2. Percentage error between numerical simulation and experiment results is the largest when TSERPES criterion is used and its percentage error is 18.66%. But it is the same as samples 1–0–1 and 1–0–2 that compression displacement is also the largest when Maximum stress criterion is used and stiffness reduction is also the first to start. The other characteristics of the curves are also similar with 1–0–1 and 1–0–2. 4.2. Damage extension Because damage extension in the axial compression of composite laminate after lightning strike is similar for the above three kinds of lightning current peaks, so here experimental sample with 93.7 kA lightning current peak is used to analyze damage extension. In order to focus on studying damage condition of upper
layers, damage extension of the top eight layers is listed out only. Damage extension under Hashin criterion, Maximum stress criterion and TSERPES criterion is shown in Fig. 9, Fig. 10, Fig. 11, respectively. It can be seen that damage extension under three kinds of failure criteria is similar. In the first −45◦ layer and second 45◦ layer, stress concentration of the damaged composite laminate first appears in fiber direction on the fixed end and decreases gradually to the center along fiber direction. Stress increases gradually with the increase of time and the damaged area is very large. The regions for serious ablation damaged will no longer bear the load. For the third 0◦ layer and the fourth 0◦ layer, stress in the fixed end is symmetrical. Stress concentration mainly appears in the fixed end and decrease gradually from the end to center. Stress in lightning ablation area decreases significantly and stress concentration appears obvious around the damaged regions. For the fifth −45◦ layer, stress concentration mainly appears around lightning ablation regions and the fixed end along fiber direction. The stress of the sixth 90◦ layer is symmetrical. But it is smaller than that of other layers and stress concentration mainly occurs in the regions damaged by lightning strike. The seventh 45◦ layer is similar with the fifth layer, where stress concentration mainly appears around lightning ablation regions and the fixed end along fiber direction. Stress of the eighth 0◦ layer in the fixed end is symmetrical. It is appears obvious stress concentration in the lightning damaged area. Under these three kinds of failure criteria, stress concentration in axial compression mainly appears in both angles on the fixed end and lightning damaged area of composite laminate. Stress concentration in both angles of the fixed end is the main reason to cause fiber fracture and matrix cracking along fiber direction. While stress difference in lightning damaged regions is the main reason to cause delamination of composite laminate. It is consistent with compression failure mode of experimental sample shown in Fig. 4. 5. Conclusions Using progressive damage analysis method, axial compression strength of composite laminates after lightning strike is simulated. The final residual strength is predicted by adopting Hashin criterion, TSERPES criterion and Maximum stress criterion, respectively. Experiment and numerical simulation results are compared. The following main conclusions can be got. 1. When composite laminates are suffered from lightning strike, the larger integral action of lightning electrical current, more
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Fig. 9. Damage extension of top eight layers under Hashin criterion.
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Fig. 10. Damage extension of top eight layers under Maximum stress criterion.
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Fig. 11. Damage extension of top eight layers under TSERPES criterion.
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serious the damage of composite laminate and the smaller compression failure load. 2. Numerical simulation result is larger than experiment result by Hashin criterion and TSERPES criterion, while it is smaller by Maximum stress criterion. Percentage error by Hashin criterion is relatively small and within the reasonable range. The numerical simulation and experimental results coincide well. 3. Stress concentration of axial compression mainly appears on both angles in the fixed end and lightning ablation regions of composite laminate. Stress concentration on two angles in the fixed end is the main reason to cause fiber fracture and matrix cracking along fiber direction, while stress difference in lightning damaged regions is the main reason to cause delamination of composite laminate. Conflict of interest statement There is no conflict of interest. Acknowledgements This study is supported by the National Natural Science Foundation of China (No.: 51475369). References [1] M. Gagné, D. Therriault, Lightning strike protection of composites, Prog. Aerosp. Sci. 64 (2013) 1–16. [2] A. Larsson, The interaction between a lightning flash and an aircraft in flight, C. R. Phys. 3 (10) (2002) 1423–1444. [3] P.G. Slattery, C.T. Mccarthy, R.M. O’Higgins, Assessment of residual strength of repaired solid laminate composite materials through mechanical testing, Compos. Struct. 147 (2016) 122–130. [4] Z.Y. Lin, X.W. Xu, Residual compressive strength of composite laminates after low-velocity impact, Acta Mater. Compos. Sin. 1 (25) (2008) 140–146 (in Chinese). [5] A. Puck, H. Schürmann, Failure analysis of FRP laminates by means of physically based phenomenological models, Compos. Sci. Technol. 58 (7) (2002) 1633–1662. [6] D. Zhang, J. Ye, D. Lam, Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading, Compos. Struct. 75 (2006) 121–131. [7] A.C. Orifici, I. Herszberg, R.S. Thomson, Review of methodologies for composite material modelling incorporating failure, Compos. Struct. 86 (2008) 194–210.
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