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Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells
Journal Pre-proofs Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells Jin-Shui Yang, Wei-Ming Zhang, Fang Yang, Si-Yuan Chen, Rüdiger Schmidt, Kai-Uwe Schröder, Li Ma, Lin-Zhi Wu PII: DOI: Reference:
S0263-8223(19)33282-9 https://doi.org/10.1016/j.compstruct.2020.112027 COST 112027
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
30 August 2019 24 December 2019 29 January 2020
Please cite this article as: Yang, J-S., Zhang, W-M., Yang, F., Chen, S-Y., Schmidt, R., Schröder, K-U., Ma, L., Wu, L-Z., Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct.2020.112027
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Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells Jin-Shui Yang a, b, c, d, Wei-Ming Zhang a, Fang Yang a, Si-Yuan Chena, Rüdiger Schmidt e, Kai-Uwe Schröder e, Li Ma d, Lin-Zhi Wu a, d a Key
Laboratory of Advanced Ship Materials and Mechanics, College of Aerospace
and Civil Engineering, Harbin Engineering University, Harbin 150001, PR China b State
Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China
c State
Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
d National
Key Laboratory of Science and Technology on Advanced Composites in
Special Environments, Harbin Institute of Technology, Harbin 150001, PR China e Institute
of Structural Mechanics and Lightweight Design, RWTH Aachen
University, Wüllnerstraße 7, D-52062, Aachen, Germany Abstract Composite thin-walled curved structures are widely used in aerospace, marine, automotive and building engineering application. In this paper we design and fabricate a series of carbon fibre composite axial and circular corrugated sandwich cylindrical panels (ACSCPs and CCSCPs) by an in-house hot press moulding method. Low velocity impact tests are carried out to evaluate the impact resistance and failure mechanisms of such structures. Furthermore, validated finite element analysis (FEA) models based on the Hashin failure criteria are adopted to study the effects of the
Corresponding authors. E-mail addresses: [email protected] ((J.-S. Yang) 1
relative density, impact energy and impact position on their impact responses. It is observed that generally the peak forces and absorbed energies of the specimens ascend with the increase of the relative density. The impact responses, especially the ultimate loads of the present structures are particularly dependent on the impact position, but insensitive to the increase of the impact energy. By comparison, the ACSCPs generally have a more excellent impact resistance and energy absorption properties than that of CCSCPs. In addition, the corresponding energy contribution of the components for the ACSCPs and CCSCPs under different impact energy is also revealed, which could be useful for the multifunctional design of such kinds of composite curved sandwich structures. Keywords: Composite; Corrugated sandwich; Curved shells; Low velocity impact; Finite element analysis (FEA) 1. Introduction Composite sandwich structures comprised of two highly stiff face sheets and a low density core layer have attracted great interest in many engineering field in aerospace, marine, automotive and building industrials due to their higher specific stiffness, strength, excellent vibration damping, corrosion resistance and fabrication flexibility [1-9]. Compared with traditional porous foam, honeycomb and other complex lattice sandwiches, corrugated sandwich structures have generally emerged as preferred structures, due to the advantage of their simple configurations, mature fabrication technologies, low fabrication cost and considerable impact resistance [10-15]. However, it has been found that composite sandwich structures are very sensitive to the local impact damage such that a minor damage could even cause significant decrease of the structural stiffness and strength [16-17]. Therefore, more attention 2
should be paid to understanding the local impact responses and failure mechanism that would be of critical importance to reliable application of composite corrugated sandwich structures. Over decades, a large number of research work on the low velocity impact response of corrugated sandwich structures have been reported, and most are focused on metallic structures [13-17]. To name a few, Radford et al. [18] compared the dynamic response of metal corrugated, pyramidal and aluminum foam core sandwich beams subjected to shock loading. It was observed that the corrugated and metal foam core sandwich beams showed the highest shock resistance. Zhang et al. [19] analytically and numerically investigated the compressive strength and dynamic response of empty and foam-filled corrugated sinusoidal plate core sandwich plates, and it was found that the effect of the filled foam on the dynamic response of corrugated core sandwich plates was not evident as expected. Hou et al. [20] numerically and experimentally studied the dynamic response of aluminum corrugated sandwich panels with trapezoidal and triangular cores under low velocity local impact and planar impact and it was found that the triangular configuration had better performance. K ı l ı çaslan et al. [21] investigated the impact response of metallic multi-layered corrugated sandwich panels in a drop weight tower using spherical, flat and conical end striker tips. The results showed that the panels tested with spherical and flat striker tips were not penetrated and experienced slightly higher deformation forces and energy absorptions in 0o/90o corrugated layer orientation than in 0o/0o orientation. Zhang et al. [22] studied the dynamic response of sandwich plates with different configurations of graded corrugated cores using a SHPB testing to maximize mitigation of blast load effects onto the structure. Yazici et al. [23] investigated the influence of foam infill on the blast resistivity of steel corrugated sandwich panels 3
using a shock tube facility and high speed photography. To improve the impact resistance of ships in the event of a collision, St-Pierre et al. [24] proposed and investigated the low speed impact responses of simply-supported and clamped sandwich beams with corrugated and Y-frame cores. It was observed that no significant rate effects occur at impact speeds representative of ship collisions. Recently, Boonkong et al. [25] studied the low velocity impact response of lightweight aluminium curvilinear corrugated sandwich panels to evaluate their energy-absorbing capacities. The results showed that, among seven different all-metal sandwich structures, the aluminium alloy possessed the highest specific perforation resistance under conditions of low velocity impact loading. Qin et al. [26] analytically and numerically investigated the low-velocity impact response of fully clamped corrugated sandwich beams with metal foam-filled folded plate core. It was revealed that strain hardening of the face sheets and corrugated core had slight effects on the dynamic response of the foam-filled corrugated sandwich beams. More recently, some investigations have payed much attention to replace metallic corrugated core structures with face sheets and corrugated core of composite materials. For instance, the mechanical behaviour of sandwich structures with textile reinforced composite foldcores and carbon/epoxy skins under compression, shear and impact loads was evaluated both experimentally and numerically by Heimbs et al. [27]. It was found that foldcores made of woven aramid fibres possessed a considerable ductile behaviour, but carbon foldcores with their brittle nature absorb energy by crushing. Kazemahvazi et al. [28] investigated the dynamic compressive response of carbon fibre composite corrugated cores using a Kolsky-bar set-up. Significant inertial rate sensitivity of the corrugated composite sandwich cores subjected to blast
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loading has been revealed. Fan et al. [29] revealed the failure mechanism and the energy absorption capacity of the integrated woven sandwich composite by low-velocity dynamic compression tests. It was found that the dynamic strength and energy absorption capacity was much greater than that of quasi-static compression tests. Schneider et al. [30] developed and investigated the dynamic out-of-plane compression response of a fully recycable corrugated sandwich structure made from self-reinforced polyethylene terephthalate (SrPET) composites. It was found that the corrugated SrPET cores had similar quasi-static performance, but possessed superior dynamic compression properties compared to the commercial polymeric foams. He et al. [31] experimentally and numerically investigated the low velocity impact behavior of corrugated core sandwich panels with carbon fiber face sheets and aluminum alloy cores in order to improve the energy absorption capability of such structures. It should be noted that most of research about low velocity dynamic response of composite corrugated sandwich structures mainly focuses on sandwich beams and flat panels. It is generally known that curved shells are more likely candidates than flat panels for sandwich constructions in aerospace, marine, automotive and building engineering application. The reason is that both hoop and axial stresses can be exploited, which significantly improve the total mechanical properties [32]. However, to the authors’ knowledge, little or even no paper was reported for composite curved corrugated sandwich shells. In this contribution, a series of carbon fibre composite corrugated sandwich cylindrical panels (CSCPs) are fabricated. Low velocity impact tests are carried out to evaluate the impact resistance of such structures. In order to further investigate the failure mechanisms of such structures, the finite element analysis (FEA) is conducted based on the Hashin failure criteria that has been developed in our previous work
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[16]. Then the results from the experiments and FEA are presented, and the parametric analyses are conducted in the end. 2. Low-velocity impact experiments 2.1 Materials and fabrication In this section, an in-house hot press moulding method [7] is developed to manufacture carbon fibre composite axial and circular corrugated sandwich cylindrical panels (ACSCPs and CCSCPs) by using a carbon fiber reinforced orthogonal woven fabric composite with thickness 0.25 mm. The macro mechanical properties of the used material listed in Table 1 are tested by ourselves using an Instron 5505 Material Testing Sytsem in accordance with the ASTM D695-96 and ISO 527-4 guidelines. For comparison purposes, under the premise of ensuring basically equality of total mass, we have designed several kinds of specimens for ACSCPs and CCSCPs with different relative densities. Table 2 gives the related specifications of the composite sandwich cylindrical panels tested in the present work. Herein at least two identical specimens of each configuration are assured to guarantee the reliability of the experimental results. The sample images of each component and the ACSCPs and CCSCPs are presented in Fig. 1. The whole constructions and representative unit cells for axial corrugated and circular corrugated cores are shown in Fig. 2. The corresponding geometrical parameters H, R and represent the total height, outer radius and central angle of the sandwich cylindrical panel, respectively. t f and tc represent the thickness of the inner, outer curve shells and corrugated core,
respectively. Thus, the relative density of the axial corrugated core a and circle corrugated core c can be expressed as 6
a
2tc ( f a
d ) sin a
2 2 R t f R t f d
na
c
(1)
2tc ( f c
d ) sin c
H d nc
(2)
where na and nc are the number of axial and circular corrugated cores, respectively. It should be noted that different relative densities of the ACSCPs and CCSCPs are obtained by adjusting t f and tc in the present work. In addition, other geometrical parameters maintain constant listed as R=71.0 mm, d=11.0 mm, h=39.0 mm,
fa
=5.91 mm, f c =6.98 mm, =120o, =24o, a =53.5o, c =41.5o. 2.2 Testing procedure The low velocity impact response of carbon fibre composite ACSCPs and CCSCPs are investigated by using the Instron Dynatup 9250HV impact testing machine, as shown in Fig. 3. Firstly, according to the external dimensions of the present structures, the specimens are clamped by a self-designed clamping fixture with a 145 mm 105 mm rectangular impacting area. We used a steel impactor with a hemispherical head of 12mm in diameter, 36mm in length and 8.37 kg in weight during the experiment. Different impact energies can be set by adjusting the drop height. According to the different sizes and load capacities of the specimens we made, to reduce redundant specimens as much as possible without loss of generality, we choose one of the typical impact energy （ 15J ） in experimental research. A force transducer is connected to the impactor to measure the contact load between the
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impactor and specimen. Then the relevant results including force, energy, velocity and displacement can be finally obtained and stored by computer using data acquisition software. For comparison, the impact position is located on the middle point of the outer curve shell, as shown in Fig. 4. 3. FE models FE analyses for the low-velocity impact responses of composite ACSCPs and CCSCPs are performed using a commercial finite element code ABAQUS/Explicit. The inner, outer curve shell and corrugated core members are modeled as solid bodies and meshed as C3D8R elements (8-node linear brick, reduced-integration element). Perfect bonding of the interfaces between the curve shells and corrugated cores is assumed by a surface-based tie constraint during the numerical simulation. A mesh convergence study is carried out to ensure that the selected mesh strategies are precise enough. The impactor is simulated using a discrete rigid coupled together with a reference point on the outer curve shell, and the boundary conditions can be achieved by setting the rigid reference point with free translation along the 3-direction and fixed other degrees of freedom. For convenience, the specimen with four edges fixed is adopted to approximately simulate the experimental boundary condition, which is due to the fact that little unavoidable deviations of the boundary conditions between in the experiment and simulation can be negligible for the local response of low velocity impacts. As shown in Fig. 5, a displacement load with a velocity around 2.00 mm/s is applied in the downward 3-direction on the reference point, which is below the rate at which dynamic effects become important.
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To further reveal the damage mechanisms of carbon fiber composite ACSCPs and CCSCPs under low-velocity impact loading, a progressive damage model based on the Hashin failure criteria [16, 31] is implemented in ABAQUS/Explicit by embedding a user subroutine VUMAT, which have been developed for the composite pyramidal truss sandwich flat panels under low-velocity impact loading in our previous work [16]. To avoid the element distortion caused by the local stiffness reduction in the simulation, we delete the element in the next iterative calculation when the maximum strain value of the element exceeds 0.9 or the minimum strain value is lower than -0.9. Furthermore, by using the verified FE models, the influences of impact energy and impact position on the impact resistance properties of the present structures are systematically carried out. 4. Results and discussion 4.1 Comparison between experimental and FEA results Fig. 6 shows the experimental impact velocity-time curves, load-time curves and absorbed energy-time curves of A-3-N and C-3-M under the impact energy of 15J. It is also shown that the curves of specimens with the same specification all have good consistency, especially for the velocity and energy-time curves, which indicate that the present experimental results are repeatability and reliable. Furthermore, the corresponding velocity, load and energy versus contact time curves of the ACSCPs and CCSCPs under the impact energy of 15J are plotted in Fig. 7 (a)-(b), (c)-(d) and (e)-(f), respectively. It should be noted that the central position of the outer curve shell for all the specimens is selected as their impact location in our impact experiments, that is to say, the impact positions of ACSCP and CCSCP are located in the node A-N and the middle point of two nodes C-M, respectively. Generally, the 9
peak values of the impact loads and the impact energies of all the specimens increase with the increase of the relative density, which is due to the fact that the specimen with higher relative density would be much stiffer to sustain higher impact load. For the specimens A-N with different relative density, the impactor has completely penetrated the outer and inner curve shells of the specimens A-1 and A-2, and there is an almost linear ascent for the impact load-time curves after the load reaches the first peak point, and then a sharp drop occurs, following a fluctuant load plateau region until the load reaches the second peak, which indicates that the impactor firstly perforates the outer curve shell, and then the corrugated core through the corresponding upper node, and finally the inner curve shell, as shown in Fig. 8 (a)-(c) and Fig. 9 (a). However, there is no damage occurring for the inner curve shell of specimen A-3, which means that all the impact energy has been almost absorbed by the specimen A-3. The corresponding ultimate loads of the specimens A-1, A-2 and A-3 are 0.59 kN, 1.39 kN and 2.07kN, respectively. Furthermore, we have given the size of the failure areas of the corresponding specimens with scale bars shown in Fig. 8 and Fig. 9. For example, the failure areas for the specimens A-1-N, A-2-N and A-3-N under the impact energy of 15J are around 106.4mm2, 163.2mm2 and193.2mm2, respectively. For the specimens C-M with different relative density, the impactor has completely penetrated the outer and inner curve shell of the specimens C-1 and C-2, while it partially penetrates the inner curve shell of specimen C-3 shown in Fig.8 (d)-(f) and Fig. 9 (c). Compared with the specimen A-N, it is noted that the first peak of the impact load-time curves of specimen C-M is much lower but the corresponding second peak is slightly higher. The reason is that the impactor firstly penetrates the single outer curve shell, and then through the lower node of corrugated core, and finally the inner curve shell. The corresponding
10
ultimate loads of the specimens C-1, C-2 and C-3 are 1.04 kN, 1.50 kN and 2.25kN, respectively. The impact damage of specimens A-3-N and C-3-M under the impact energy of 15J are revealed in Fig. 9. A generally good agreement between experimental and numerical failure modes can be obtained in the present study. As shown in Fig. 10, there is an excellent consistency between the experimental and numerical results for the impact velocity-time curves and the absorbed energy-time curves of A-3-N and C-3-M. It can also be found that there is a certain deviation between the predicted and measured peaks of the load-time curves of A-3-N and C-3-M, which indicate the largest predicted error are 14.56% and 20.44%, respectively. The reason is mainly that the errors from fabrication and performance testing of the actual specimens between the numerical models are inevitable. However, both two variation tendencies are basically consistent, which indicates that the present numerical models can be adopted and developed for the further investigation. 4.2 Parametric analysis Based on the numerical models validated by experiments in Section 4.1, a series of parametric analyses is conducted to investigate the effects of the impact energy and position on damage resistance and energy absorption properties of the present structures. According to the different sizes and load capacities of the specimens we made, the impact responses of the specimens A-3-N and C-3-M under impact energy of 15J, 20J and 25J without loss of generality are plotted in Fig. 11. It is obvious that the velocity increases with the increase of the impact energy, and nonlinear relationships between the velocity, absorbed energy and the time can be found. It is also interesting to note that the ultimate loads for the present specimens are insensitive to the increase of the impact energies. As shown in Fig. 11 (c) and (d), a
11
few drops of the loads occur from the peaks for the specimen A-3-N (0-5ms) and C-3-M (0-8ms) under impact energy of 15J, which are attributed to the complete penetration of the outer curve shell and corrugated core, but no damage in the inner curve shell for specimen A-3-N, and partial penetration of the inner curve shell for specimen C-3-M shown in Fig.12 (a) and (d). Under the impact energy of 20J, the sharp drops in the load-time curves of specimen A-3-N (5-12ms) and C-3-M (8-16ms) are attributed to the partial penetration of the inner curve shell for specimen A-3-N, and complete penetration of the inner curve shell for specimen C-3-M, as depicted in Fig. 12 (b) and (e), respectively. Under the impact energy of 25J, the similar sharp drops in the load-time curves of specimen A-3-N (5-12ms) and C-3-M (8-16ms) also can be observed, which are attributed to the complete penetration of the inner curve shell for both two specimens, as depicted in Fig. 12 (c) and (f), respectively. To reveal the influences of the impact position on the impact resistance properties of the present structures, the impact responses of specimen A-3-M and C-3-N under different impact energy are displayed in Fig. 13. Similar phenomena of the load-time curves between the specimen A-3-M and C-3-M, specimen A-3-N and C-3-N can be observed. The result of comparison shows that, no matter the impact positions are located in the node N or the middle point of two nodes M, the corresponding ultimate loads of the specimen ACSCPs are generally little higher than that of the specimen CCSCPs. This also suggests that the ACSCPs have a more excellent impact resistance and energy absorption properties than that of CCSCPs. For the impact position located in the node N, Fig. 15 compares the energy contribution of the specimen A-3-N and C-3-N under different impact energy. The results show that the outer curve shell and corrugated core play a dominant role in the energy absorption, which approximately account for 96.70%, 83.64%, 76.68% for specimen A-3-N, and
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90.31%, 75.62%, 73.61% for specimen C-3-N under the impact energy of 15J, 20J and 25J, respectively. Generally, the energy contribution of the inner curve shell of the present structures would increase with the increase of the impact energy. For the impact position located in the middle point of two nodes M, the energy contribution of the specimen A-3-M and C-3-M under different impact energy is depicted in Fig. 16. In the case of low impact energy of 15J shown in Fig. 16 (a)-(b), it is found that the energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 42.80%, 28.60%, 28.60% for specimen A-3-M, and 39.50%, 31.13%, 29.37% for specimen C-3-M, respectively. The results indicate that the outer curve shell and corrugated core still play a dominant role in the energy absorption. Moreover, in the case of low impact energy of 20J shown in Fig. 16 (c)-(d), the corresponding energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 33.41%, 29.79%, 36.80% for specimen A-3-M, and 27.68%, 30.23%, 42.09% for specimen C-3-M, respectively. Similarly, in the case of low impact energy of 25J shown in Fig. 16 (e)-(f), the corresponding energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 30.84%, 29.15%, 40.01% for specimen A-3-M, and 27.10%, 30.56%, 42.34% for specimen C-3-M, respectively. From the results, it can be seen that with the increase of the impact energy, the inner curve shells gradually play a decisive role in the energy absorption of the whole structures. 5. Conclusions In this paper, the low velocity impact behavior of carbon fibre composite ACSCPs and CCSCPs is investigated experimentally and numerically. An in-house hot press moulding method is adopted to fabricate the specimens for ACSCPs and CCSCPs with different relative densities. Then a range of low velocity impact tests are
13
conducted to investigate the impact resistance of such structures, which consider the effects of impact force, impact velocity, absorbed energy and failure modes. Furthermore, FEA models based on the Hashin failure criteria are carried out, and the parametric analyses are conducted. The numerical results show fairly consistent with experimental tests. Combined with the experimental and numerical results, it is observed that generally the peak forces and the absorbed energies of the specimens ascend with the increase of the relative density. The impact responses are particularly dependent on the impact position, and the corresponding impact process and damage modes revealed. It is found that no matter the impact positions are located in the node N or the middle point of two nodes M, the ACSCPs generally have a more excellent impact resistance and energy absorption properties than that of CCSCPs. However, it is noted that the ultimate loads for the present specimens are insensitive to the increase of the impact energies. Finally, the corresponding energy contribution of the components for the ACSCPs and CCSCPs under different impact energy is also revealed, which could be useful for the multifunctional design of such kinds of composite curved sandwich structures. Acknowledgement The present work is supported by the National Science Foundation of China under Grant No. 11802070, the China Postdoctoral Science Foundation under Grant No. 2017M620110, the Hei Long Jiang Postdoctoral Foundation under Grant No. LBH-Z17043, the Open Foundation for the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body under Grant No. 31815007, the State Key Laboratory for Strength and Vibration of Mechanical Structures under Grant No. SV2019-KF-09 and the Fundamental Research Funds for the Central Universities
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cores. Compos struct 2012, 94(11): 3300-3308. [29] Fan H, Zhao L, Chen H, et al. Dynamic compression failure mechanisms and dynamic effects of integrated woven sandwich composites. J Compos Mater 2014, 48(4):427-437. [30] Schneider C, Kazemahvazi S, Zenkert D, et al. Dynamic compression response of self-reinforced poly (ethylene terephthalate) composites and corrugated sandwich cores. Compos Part A-Appl S 2015, 77: 96-105. [31] He W, Liu J, Tao B, et al. Experimental and numerical research on the low velocity impact behavior of hybrid corrugated core sandwich structures. Compos Struct 2016, 158: 30-43. [32] Rahmani O, Khalili SMR, Malekzadeh K. Free vibration response of composite sandwich cylindrical shell with flexible core. Compos Struct 2010, 92(5): 1269-1281.
Figures Fig. 1 The sample images of (a) ACSCP, (b) CCSCP, (c) axial corrugated core, (d) circular corrugated core, (e) outer curve shell and (f) inner curve shell. Fig. 2 The representative unit cell geometry of (a) axial corrugated and (b) circular corrugated core. Fig. 3 (a) The Instron Dynatup 9250HV impact testing apparatus, (b) the specimen and the clamping fixture. Fig. 4 Impact location of ACSCP (a) on the node A-N and (b) on the middle point of two nodes A-M; CCSCP (c) on the middle point of two nodes C-M and (d)on the node C-N. Fig. 5 Typical FE models of the low velocity impact test for (a) ACSCP and (b) CCSCP. Fig. 6 Experimental impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J. Fig. 7 Experimental impact velocity-time curves of (a) ACSCPs-N, (b) CCSCPs-M; the impact load-time curves of (c) ACSCPs-N, (d) CCSCPs-M; the absorbed 18
energy-time curves of (e) ACSCPs-N, (f) CCSCPs-M under the impact energy of 15J. Fig. 8 The impact damage of specimens (a) A-1-N, (b) A-2-N, (c) A-3-N, (d) C-1-M, (e) C-2-M, (f) C-3-M under the impact energy of 15J. Fig. 9 Comparison of the impact damage of specimen A-3-N by (a) experiment, (b) simulation and C-3-M by (c) experiment, (d) simulation under the impact energy of 15J. Fig. 10 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J. Fig. 11 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M obtained numerically under different impact energy. Fig. 12 The predicted impact damage of specimen A-3-N under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-M under the impact energy of (d) 15J, (e) 20J, (f) 25J. Fig. 13 Comparison of the impact velocity-time curves of (a) A-3-M, (b) C-3-N; the impact load-time curves of (c) A-3-M, (d) C-3-N; the absorbed energy-time curves of (e) A-3-M, (f) C-3-N obtained numerically under different impact energy. Fig. 14 The predicted impact damage of specimen A-3-M under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-N under the impact energy of (d) 15J, (e) 20J, (f) 25J. Fig. 15 Energy contribution of (a) A-3-N, (b) C-3-N under the impact energy of 15J; (c) A-3-N, (d) C-3-N under the impact energy of 20J; (e) A-3-N, (f) C-3-N under the impact energy of 25J. Fig. 16 Energy contribution of (a) A-3-M, (b) C-3-M under the impact energy of 15J; (c) A-3-M, (d) C-3-M under the impact energy of 20J; (e) A-3-M, (f) C-3-M under the impact energy of 25J.
(c)
(d)
(e)
(f)
(b)
(a)
19
Fig. 1 The sample images of (a) ACSCP, (b) CCSCP, (c) axial corrugated core, (d) circular corrugated core, (e) outer curve shell and (f) inner curve shell.
(a)
fa
tf
R
tc
d
a tf
(b) R fc tf
d
tc
c h
tf
Fig. 2 The representative unit cell geometry of (a) axial corrugated and (b) circular corrugated core.
20
(a)
(b)
Impactor
Specimen
Clamping fixture
Fig. 3 (a) The Instron Dynatup 9250HV impact testing apparatus, (b) the specimen and the clamping fixture.
(a)
(b)
(c)
(d)
21
Fig. 4 Impact location of ACSCP (a) on the node A-N and (b) on the middle point of two nodes A-M; CCSCP (c) on the middle point of two nodes C-M and (d) on the node C-N.
(a)
(b)
Fig. 5 Typical FE models of the low velocity impact test for (a) ACSCP and (b) CCSCP.
(b)
(a)
22
(c)
(d)
(e)
(f)
23
Fig. 6 Experimental impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J.
(a)
(b)
(c)
(d)
24
(e)
(f)
Fig. 7 Experimental impact velocity-time curves of (a) ACSCPs-N, (b) CCSCPs-M; the impact load-time curves of (c) ACSCPs-N, (d) CCSCPs-M; the absorbed energy-time curves of (e) ACSCPs-N, (f) CCSCPs-M under the impact energy of 15J. 25
(a)
(d) 20 mm
(b)
20 mm
(e)
20 mm
(c)
20 mm
(f) 20 mm
20 mm
Fig. 8 The impact damage of specimens (a) A-1-N, (b) A-2-N, (c) A-3-N, (d) C-1-M, (e) C-2-M, (f) C-3-M under the impact energy of 15J
26
(a)
(c)
20 mm
20 mm
(b)
(d)
20 mm
20 mm
Fig. 9 Comparison of the impact damage of specimen A-3-N by (a) experiment, (b) 27
simulation and C-3-M by (c) experiment, (d) simulation under the impact energy of 15J.
(b)
(a)
(d)
(c)
(e)
28
(f)
Fig. 10 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J.
(a)
29
(b)
(d)
(f)
30
Fig. 11 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M obtained numerically under different impact energy.
(a)
20 mm
(b)
(c)
20 mm
31
20 mm
(d)
20 mm
(e)
(f)
20 mm
20 mm
Fig. 12 The predicted impact damage of specimen A-3-N under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-M under the impact energy of (d) 15J, (e) 20J, (f) 25J.
32
(a)
(b)
(c)
(d)
(e)
(f)
33
Fig. 13 Comparison of the impact velocity-time curves of (a) A-3-M, (b) C-3-N; the impact load-time curves of (c) A-3-M, (d) C-3-N; the absorbed energy-time curves of (e) A-3-M, (f) C-3-N obtained numerically under different impact energy.
34
(a)
20 mm
(b)
(c)
20 mm
20 mm
(f)
(d)
20 mm
(e)
20 mm
20 mm
35
Fig. 14 The predicted impact damage of specimen A-3-M under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-N under the impact energy of (d) 15J, (e) 20J, (f) 25J.
(a)
(b)
(c)
(d)
(e)
(f)
36
Fig. 15 Energy contribution of (a) A-3-N, (b) C-3-N under the impact energy of 15J; (c) A-3-N, (d) C-3-N under the impact energy of 20J; (e) A-3-N, (f) C-3-N under the impact energy of 25J. 37
(a)
(b)
(c)
(d)
(e)
(f)
38
Fig. 16 Energy contribution of (a) A-3-M, (b) C-3-M under the impact energy of 15J; (c) A-3-M, (d) C-3-M under the impact energy of 20J; (e) A-3-M, (f) C-3-M under the impact energy of 25J.
[33] Table 1 Macro mechanical properties of orthogonal woven fabric composites Symbol
Value
Property
E11
63.8GPa
Longitudinal Young’s modulus
E22
63.8GPa
Transverse modulus
E33
11.0GPa
Out-of-plane modulus
39
12 ,13
0.064
Poisson’s ratio
23
0.32
Poisson’s ratio
G 12 , G 13
4.2GPa
Shear modulus
G 23
4.2GPa
Shear modulus
Xt
756MPa
Longitudinal tensile strength
Xc
557MPa
Longitudinal compressive strength
Yt
756MPa
Transverse tensile strength
Yc
557MPa
Transverse compressive strength
Zt
60MPa
Out-of-plane tensile strength
Zc
198MPa
Out-of-plane compressive strength
S12 , S13
118MPa
Shear strength
S 23
86MPa
Shear strength
1523kg / m3
Density
Table 2 Specifications of the composite sandwich cylindrical panels tested H (mm)
t f tc (mm)
M (g)
Relative density (%)
A-1
160.0±1.0
0.50
58.3±1.1
6.5
A-2
158.0±0.0
0.75
76.5±1.3
9.9
A-3
158.5±0.5
1.00
101.3±0.9
13.2
C-1
160.0±1.0
0.50
53.6±0.3
5.6
C-2
159.0±1.0
0.75
76.5±0.4
8.5
C-3
158.0±1.0
1.00
96.4±1.7
11.3
Specimen Symbol
ACSCP
CCSCP
[34]
Conflict of interest The authors declared that they have no conflicts of interest to this work 40
titled” Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells”. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. [35]
Author Statement We declare that all persons who have substantial contributions to the present work are listed in the manuscript. Dr. Jin-Shui Yang is the corresponding author and has made substantial contributions to the conception and design of the work; Mr. Wei-Ming Zhang designed experiments; Mr. Fang Yang carried out experiments; Mr. Si-Yuan Chen carried out simulations; Prof. Rüdiger Schmidt and Prof. Kai-Uwe Schröder revised the manuscript; Prof. Li Ma and Prof. Lin-Zhi Wu guided and given advices for this work. [36]
41
S0263-8223(19)33282-9 https://doi.org/10.1016/j.compstruct.2020.112027 COST 112027
To appear in:
Composite Structures
Received Date: Revised Date: Accepted Date:
30 August 2019 24 December 2019 29 January 2020
Please cite this article as: Yang, J-S., Zhang, W-M., Yang, F., Chen, S-Y., Schmidt, R., Schröder, K-U., Ma, L., Wu, L-Z., Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells, Composite Structures (2020), doi: https://doi.org/10.1016/j.compstruct.2020.112027
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© 2020 Published by Elsevier Ltd.
Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells Jin-Shui Yang a, b, c, d, Wei-Ming Zhang a, Fang Yang a, Si-Yuan Chena, Rüdiger Schmidt e, Kai-Uwe Schröder e, Li Ma d, Lin-Zhi Wu a, d a Key
Laboratory of Advanced Ship Materials and Mechanics, College of Aerospace
and Civil Engineering, Harbin Engineering University, Harbin 150001, PR China b State
Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China
c State
Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
d National
Key Laboratory of Science and Technology on Advanced Composites in
Special Environments, Harbin Institute of Technology, Harbin 150001, PR China e Institute
of Structural Mechanics and Lightweight Design, RWTH Aachen
University, Wüllnerstraße 7, D-52062, Aachen, Germany Abstract Composite thin-walled curved structures are widely used in aerospace, marine, automotive and building engineering application. In this paper we design and fabricate a series of carbon fibre composite axial and circular corrugated sandwich cylindrical panels (ACSCPs and CCSCPs) by an in-house hot press moulding method. Low velocity impact tests are carried out to evaluate the impact resistance and failure mechanisms of such structures. Furthermore, validated finite element analysis (FEA) models based on the Hashin failure criteria are adopted to study the effects of the
Corresponding authors. E-mail addresses: [email protected] ((J.-S. Yang) 1
relative density, impact energy and impact position on their impact responses. It is observed that generally the peak forces and absorbed energies of the specimens ascend with the increase of the relative density. The impact responses, especially the ultimate loads of the present structures are particularly dependent on the impact position, but insensitive to the increase of the impact energy. By comparison, the ACSCPs generally have a more excellent impact resistance and energy absorption properties than that of CCSCPs. In addition, the corresponding energy contribution of the components for the ACSCPs and CCSCPs under different impact energy is also revealed, which could be useful for the multifunctional design of such kinds of composite curved sandwich structures. Keywords: Composite; Corrugated sandwich; Curved shells; Low velocity impact; Finite element analysis (FEA) 1. Introduction Composite sandwich structures comprised of two highly stiff face sheets and a low density core layer have attracted great interest in many engineering field in aerospace, marine, automotive and building industrials due to their higher specific stiffness, strength, excellent vibration damping, corrosion resistance and fabrication flexibility [1-9]. Compared with traditional porous foam, honeycomb and other complex lattice sandwiches, corrugated sandwich structures have generally emerged as preferred structures, due to the advantage of their simple configurations, mature fabrication technologies, low fabrication cost and considerable impact resistance [10-15]. However, it has been found that composite sandwich structures are very sensitive to the local impact damage such that a minor damage could even cause significant decrease of the structural stiffness and strength [16-17]. Therefore, more attention 2
should be paid to understanding the local impact responses and failure mechanism that would be of critical importance to reliable application of composite corrugated sandwich structures. Over decades, a large number of research work on the low velocity impact response of corrugated sandwich structures have been reported, and most are focused on metallic structures [13-17]. To name a few, Radford et al. [18] compared the dynamic response of metal corrugated, pyramidal and aluminum foam core sandwich beams subjected to shock loading. It was observed that the corrugated and metal foam core sandwich beams showed the highest shock resistance. Zhang et al. [19] analytically and numerically investigated the compressive strength and dynamic response of empty and foam-filled corrugated sinusoidal plate core sandwich plates, and it was found that the effect of the filled foam on the dynamic response of corrugated core sandwich plates was not evident as expected. Hou et al. [20] numerically and experimentally studied the dynamic response of aluminum corrugated sandwich panels with trapezoidal and triangular cores under low velocity local impact and planar impact and it was found that the triangular configuration had better performance. K ı l ı çaslan et al. [21] investigated the impact response of metallic multi-layered corrugated sandwich panels in a drop weight tower using spherical, flat and conical end striker tips. The results showed that the panels tested with spherical and flat striker tips were not penetrated and experienced slightly higher deformation forces and energy absorptions in 0o/90o corrugated layer orientation than in 0o/0o orientation. Zhang et al. [22] studied the dynamic response of sandwich plates with different configurations of graded corrugated cores using a SHPB testing to maximize mitigation of blast load effects onto the structure. Yazici et al. [23] investigated the influence of foam infill on the blast resistivity of steel corrugated sandwich panels 3
using a shock tube facility and high speed photography. To improve the impact resistance of ships in the event of a collision, St-Pierre et al. [24] proposed and investigated the low speed impact responses of simply-supported and clamped sandwich beams with corrugated and Y-frame cores. It was observed that no significant rate effects occur at impact speeds representative of ship collisions. Recently, Boonkong et al. [25] studied the low velocity impact response of lightweight aluminium curvilinear corrugated sandwich panels to evaluate their energy-absorbing capacities. The results showed that, among seven different all-metal sandwich structures, the aluminium alloy possessed the highest specific perforation resistance under conditions of low velocity impact loading. Qin et al. [26] analytically and numerically investigated the low-velocity impact response of fully clamped corrugated sandwich beams with metal foam-filled folded plate core. It was revealed that strain hardening of the face sheets and corrugated core had slight effects on the dynamic response of the foam-filled corrugated sandwich beams. More recently, some investigations have payed much attention to replace metallic corrugated core structures with face sheets and corrugated core of composite materials. For instance, the mechanical behaviour of sandwich structures with textile reinforced composite foldcores and carbon/epoxy skins under compression, shear and impact loads was evaluated both experimentally and numerically by Heimbs et al. [27]. It was found that foldcores made of woven aramid fibres possessed a considerable ductile behaviour, but carbon foldcores with their brittle nature absorb energy by crushing. Kazemahvazi et al. [28] investigated the dynamic compressive response of carbon fibre composite corrugated cores using a Kolsky-bar set-up. Significant inertial rate sensitivity of the corrugated composite sandwich cores subjected to blast
4
loading has been revealed. Fan et al. [29] revealed the failure mechanism and the energy absorption capacity of the integrated woven sandwich composite by low-velocity dynamic compression tests. It was found that the dynamic strength and energy absorption capacity was much greater than that of quasi-static compression tests. Schneider et al. [30] developed and investigated the dynamic out-of-plane compression response of a fully recycable corrugated sandwich structure made from self-reinforced polyethylene terephthalate (SrPET) composites. It was found that the corrugated SrPET cores had similar quasi-static performance, but possessed superior dynamic compression properties compared to the commercial polymeric foams. He et al. [31] experimentally and numerically investigated the low velocity impact behavior of corrugated core sandwich panels with carbon fiber face sheets and aluminum alloy cores in order to improve the energy absorption capability of such structures. It should be noted that most of research about low velocity dynamic response of composite corrugated sandwich structures mainly focuses on sandwich beams and flat panels. It is generally known that curved shells are more likely candidates than flat panels for sandwich constructions in aerospace, marine, automotive and building engineering application. The reason is that both hoop and axial stresses can be exploited, which significantly improve the total mechanical properties [32]. However, to the authors’ knowledge, little or even no paper was reported for composite curved corrugated sandwich shells. In this contribution, a series of carbon fibre composite corrugated sandwich cylindrical panels (CSCPs) are fabricated. Low velocity impact tests are carried out to evaluate the impact resistance of such structures. In order to further investigate the failure mechanisms of such structures, the finite element analysis (FEA) is conducted based on the Hashin failure criteria that has been developed in our previous work
5
[16]. Then the results from the experiments and FEA are presented, and the parametric analyses are conducted in the end. 2. Low-velocity impact experiments 2.1 Materials and fabrication In this section, an in-house hot press moulding method [7] is developed to manufacture carbon fibre composite axial and circular corrugated sandwich cylindrical panels (ACSCPs and CCSCPs) by using a carbon fiber reinforced orthogonal woven fabric composite with thickness 0.25 mm. The macro mechanical properties of the used material listed in Table 1 are tested by ourselves using an Instron 5505 Material Testing Sytsem in accordance with the ASTM D695-96 and ISO 527-4 guidelines. For comparison purposes, under the premise of ensuring basically equality of total mass, we have designed several kinds of specimens for ACSCPs and CCSCPs with different relative densities. Table 2 gives the related specifications of the composite sandwich cylindrical panels tested in the present work. Herein at least two identical specimens of each configuration are assured to guarantee the reliability of the experimental results. The sample images of each component and the ACSCPs and CCSCPs are presented in Fig. 1. The whole constructions and representative unit cells for axial corrugated and circular corrugated cores are shown in Fig. 2. The corresponding geometrical parameters H, R and represent the total height, outer radius and central angle of the sandwich cylindrical panel, respectively. t f and tc represent the thickness of the inner, outer curve shells and corrugated core,
respectively. Thus, the relative density of the axial corrugated core a and circle corrugated core c can be expressed as 6
a
2tc ( f a
d ) sin a
2 2 R t f R t f d
na
c
(1)
2tc ( f c
d ) sin c
H d nc
(2)
where na and nc are the number of axial and circular corrugated cores, respectively. It should be noted that different relative densities of the ACSCPs and CCSCPs are obtained by adjusting t f and tc in the present work. In addition, other geometrical parameters maintain constant listed as R=71.0 mm, d=11.0 mm, h=39.0 mm,
fa
=5.91 mm, f c =6.98 mm, =120o, =24o, a =53.5o, c =41.5o. 2.2 Testing procedure The low velocity impact response of carbon fibre composite ACSCPs and CCSCPs are investigated by using the Instron Dynatup 9250HV impact testing machine, as shown in Fig. 3. Firstly, according to the external dimensions of the present structures, the specimens are clamped by a self-designed clamping fixture with a 145 mm 105 mm rectangular impacting area. We used a steel impactor with a hemispherical head of 12mm in diameter, 36mm in length and 8.37 kg in weight during the experiment. Different impact energies can be set by adjusting the drop height. According to the different sizes and load capacities of the specimens we made, to reduce redundant specimens as much as possible without loss of generality, we choose one of the typical impact energy （ 15J ） in experimental research. A force transducer is connected to the impactor to measure the contact load between the
7
impactor and specimen. Then the relevant results including force, energy, velocity and displacement can be finally obtained and stored by computer using data acquisition software. For comparison, the impact position is located on the middle point of the outer curve shell, as shown in Fig. 4. 3. FE models FE analyses for the low-velocity impact responses of composite ACSCPs and CCSCPs are performed using a commercial finite element code ABAQUS/Explicit. The inner, outer curve shell and corrugated core members are modeled as solid bodies and meshed as C3D8R elements (8-node linear brick, reduced-integration element). Perfect bonding of the interfaces between the curve shells and corrugated cores is assumed by a surface-based tie constraint during the numerical simulation. A mesh convergence study is carried out to ensure that the selected mesh strategies are precise enough. The impactor is simulated using a discrete rigid coupled together with a reference point on the outer curve shell, and the boundary conditions can be achieved by setting the rigid reference point with free translation along the 3-direction and fixed other degrees of freedom. For convenience, the specimen with four edges fixed is adopted to approximately simulate the experimental boundary condition, which is due to the fact that little unavoidable deviations of the boundary conditions between in the experiment and simulation can be negligible for the local response of low velocity impacts. As shown in Fig. 5, a displacement load with a velocity around 2.00 mm/s is applied in the downward 3-direction on the reference point, which is below the rate at which dynamic effects become important.
8
To further reveal the damage mechanisms of carbon fiber composite ACSCPs and CCSCPs under low-velocity impact loading, a progressive damage model based on the Hashin failure criteria [16, 31] is implemented in ABAQUS/Explicit by embedding a user subroutine VUMAT, which have been developed for the composite pyramidal truss sandwich flat panels under low-velocity impact loading in our previous work [16]. To avoid the element distortion caused by the local stiffness reduction in the simulation, we delete the element in the next iterative calculation when the maximum strain value of the element exceeds 0.9 or the minimum strain value is lower than -0.9. Furthermore, by using the verified FE models, the influences of impact energy and impact position on the impact resistance properties of the present structures are systematically carried out. 4. Results and discussion 4.1 Comparison between experimental and FEA results Fig. 6 shows the experimental impact velocity-time curves, load-time curves and absorbed energy-time curves of A-3-N and C-3-M under the impact energy of 15J. It is also shown that the curves of specimens with the same specification all have good consistency, especially for the velocity and energy-time curves, which indicate that the present experimental results are repeatability and reliable. Furthermore, the corresponding velocity, load and energy versus contact time curves of the ACSCPs and CCSCPs under the impact energy of 15J are plotted in Fig. 7 (a)-(b), (c)-(d) and (e)-(f), respectively. It should be noted that the central position of the outer curve shell for all the specimens is selected as their impact location in our impact experiments, that is to say, the impact positions of ACSCP and CCSCP are located in the node A-N and the middle point of two nodes C-M, respectively. Generally, the 9
peak values of the impact loads and the impact energies of all the specimens increase with the increase of the relative density, which is due to the fact that the specimen with higher relative density would be much stiffer to sustain higher impact load. For the specimens A-N with different relative density, the impactor has completely penetrated the outer and inner curve shells of the specimens A-1 and A-2, and there is an almost linear ascent for the impact load-time curves after the load reaches the first peak point, and then a sharp drop occurs, following a fluctuant load plateau region until the load reaches the second peak, which indicates that the impactor firstly perforates the outer curve shell, and then the corrugated core through the corresponding upper node, and finally the inner curve shell, as shown in Fig. 8 (a)-(c) and Fig. 9 (a). However, there is no damage occurring for the inner curve shell of specimen A-3, which means that all the impact energy has been almost absorbed by the specimen A-3. The corresponding ultimate loads of the specimens A-1, A-2 and A-3 are 0.59 kN, 1.39 kN and 2.07kN, respectively. Furthermore, we have given the size of the failure areas of the corresponding specimens with scale bars shown in Fig. 8 and Fig. 9. For example, the failure areas for the specimens A-1-N, A-2-N and A-3-N under the impact energy of 15J are around 106.4mm2, 163.2mm2 and193.2mm2, respectively. For the specimens C-M with different relative density, the impactor has completely penetrated the outer and inner curve shell of the specimens C-1 and C-2, while it partially penetrates the inner curve shell of specimen C-3 shown in Fig.8 (d)-(f) and Fig. 9 (c). Compared with the specimen A-N, it is noted that the first peak of the impact load-time curves of specimen C-M is much lower but the corresponding second peak is slightly higher. The reason is that the impactor firstly penetrates the single outer curve shell, and then through the lower node of corrugated core, and finally the inner curve shell. The corresponding
10
ultimate loads of the specimens C-1, C-2 and C-3 are 1.04 kN, 1.50 kN and 2.25kN, respectively. The impact damage of specimens A-3-N and C-3-M under the impact energy of 15J are revealed in Fig. 9. A generally good agreement between experimental and numerical failure modes can be obtained in the present study. As shown in Fig. 10, there is an excellent consistency between the experimental and numerical results for the impact velocity-time curves and the absorbed energy-time curves of A-3-N and C-3-M. It can also be found that there is a certain deviation between the predicted and measured peaks of the load-time curves of A-3-N and C-3-M, which indicate the largest predicted error are 14.56% and 20.44%, respectively. The reason is mainly that the errors from fabrication and performance testing of the actual specimens between the numerical models are inevitable. However, both two variation tendencies are basically consistent, which indicates that the present numerical models can be adopted and developed for the further investigation. 4.2 Parametric analysis Based on the numerical models validated by experiments in Section 4.1, a series of parametric analyses is conducted to investigate the effects of the impact energy and position on damage resistance and energy absorption properties of the present structures. According to the different sizes and load capacities of the specimens we made, the impact responses of the specimens A-3-N and C-3-M under impact energy of 15J, 20J and 25J without loss of generality are plotted in Fig. 11. It is obvious that the velocity increases with the increase of the impact energy, and nonlinear relationships between the velocity, absorbed energy and the time can be found. It is also interesting to note that the ultimate loads for the present specimens are insensitive to the increase of the impact energies. As shown in Fig. 11 (c) and (d), a
11
few drops of the loads occur from the peaks for the specimen A-3-N (0-5ms) and C-3-M (0-8ms) under impact energy of 15J, which are attributed to the complete penetration of the outer curve shell and corrugated core, but no damage in the inner curve shell for specimen A-3-N, and partial penetration of the inner curve shell for specimen C-3-M shown in Fig.12 (a) and (d). Under the impact energy of 20J, the sharp drops in the load-time curves of specimen A-3-N (5-12ms) and C-3-M (8-16ms) are attributed to the partial penetration of the inner curve shell for specimen A-3-N, and complete penetration of the inner curve shell for specimen C-3-M, as depicted in Fig. 12 (b) and (e), respectively. Under the impact energy of 25J, the similar sharp drops in the load-time curves of specimen A-3-N (5-12ms) and C-3-M (8-16ms) also can be observed, which are attributed to the complete penetration of the inner curve shell for both two specimens, as depicted in Fig. 12 (c) and (f), respectively. To reveal the influences of the impact position on the impact resistance properties of the present structures, the impact responses of specimen A-3-M and C-3-N under different impact energy are displayed in Fig. 13. Similar phenomena of the load-time curves between the specimen A-3-M and C-3-M, specimen A-3-N and C-3-N can be observed. The result of comparison shows that, no matter the impact positions are located in the node N or the middle point of two nodes M, the corresponding ultimate loads of the specimen ACSCPs are generally little higher than that of the specimen CCSCPs. This also suggests that the ACSCPs have a more excellent impact resistance and energy absorption properties than that of CCSCPs. For the impact position located in the node N, Fig. 15 compares the energy contribution of the specimen A-3-N and C-3-N under different impact energy. The results show that the outer curve shell and corrugated core play a dominant role in the energy absorption, which approximately account for 96.70%, 83.64%, 76.68% for specimen A-3-N, and
12
90.31%, 75.62%, 73.61% for specimen C-3-N under the impact energy of 15J, 20J and 25J, respectively. Generally, the energy contribution of the inner curve shell of the present structures would increase with the increase of the impact energy. For the impact position located in the middle point of two nodes M, the energy contribution of the specimen A-3-M and C-3-M under different impact energy is depicted in Fig. 16. In the case of low impact energy of 15J shown in Fig. 16 (a)-(b), it is found that the energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 42.80%, 28.60%, 28.60% for specimen A-3-M, and 39.50%, 31.13%, 29.37% for specimen C-3-M, respectively. The results indicate that the outer curve shell and corrugated core still play a dominant role in the energy absorption. Moreover, in the case of low impact energy of 20J shown in Fig. 16 (c)-(d), the corresponding energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 33.41%, 29.79%, 36.80% for specimen A-3-M, and 27.68%, 30.23%, 42.09% for specimen C-3-M, respectively. Similarly, in the case of low impact energy of 25J shown in Fig. 16 (e)-(f), the corresponding energy contribution of the outer curve shell, corrugated core and inner curve shell approximately account for 30.84%, 29.15%, 40.01% for specimen A-3-M, and 27.10%, 30.56%, 42.34% for specimen C-3-M, respectively. From the results, it can be seen that with the increase of the impact energy, the inner curve shells gradually play a decisive role in the energy absorption of the whole structures. 5. Conclusions In this paper, the low velocity impact behavior of carbon fibre composite ACSCPs and CCSCPs is investigated experimentally and numerically. An in-house hot press moulding method is adopted to fabricate the specimens for ACSCPs and CCSCPs with different relative densities. Then a range of low velocity impact tests are
13
conducted to investigate the impact resistance of such structures, which consider the effects of impact force, impact velocity, absorbed energy and failure modes. Furthermore, FEA models based on the Hashin failure criteria are carried out, and the parametric analyses are conducted. The numerical results show fairly consistent with experimental tests. Combined with the experimental and numerical results, it is observed that generally the peak forces and the absorbed energies of the specimens ascend with the increase of the relative density. The impact responses are particularly dependent on the impact position, and the corresponding impact process and damage modes revealed. It is found that no matter the impact positions are located in the node N or the middle point of two nodes M, the ACSCPs generally have a more excellent impact resistance and energy absorption properties than that of CCSCPs. However, it is noted that the ultimate loads for the present specimens are insensitive to the increase of the impact energies. Finally, the corresponding energy contribution of the components for the ACSCPs and CCSCPs under different impact energy is also revealed, which could be useful for the multifunctional design of such kinds of composite curved sandwich structures. Acknowledgement The present work is supported by the National Science Foundation of China under Grant No. 11802070, the China Postdoctoral Science Foundation under Grant No. 2017M620110, the Hei Long Jiang Postdoctoral Foundation under Grant No. LBH-Z17043, the Open Foundation for the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body under Grant No. 31815007, the State Key Laboratory for Strength and Vibration of Mechanical Structures under Grant No. SV2019-KF-09 and the Fundamental Research Funds for the Central Universities
14
under Grant No. 3072019CFM0202. References [1] Vaziri A, Hutchinson JW. Metal sandwich plates subject to intense air shocks. Int J Solid Struct 2007;44:2021–35. [2] Vasiliev VV, Barynin VA, Razin AF. Anisogrid composite lattice structures development and aerospace applications. Compos Struct 2012;94:1117–27. [3] Yan LL, Yu B, Han B, et al. Compressive strength and energy absorption of sandwich panels with aluminum foam-filled corrugated cores. Compos Sci Technol 2013;86:142–8. [4] Liu J, Zhu X, Zhou Z, et al. Effects of thermal exposure on mechanical behavior of carbon fiber composite pyramidal truss core sandwich panel. Compos B Eng 2014;60(60):82–90. [5] Yin S, Wu LZ, Yang JS, et al. Damping and low-velocity impact behavior of filled composite pyramidal lattice structures. J Compos Mater 2013;48(15):1789–800. [6] Yang JS, Xiong J, Ma L, et al. Vibration and damping characteristics of hybrid carbon fiber composite pyramidal truss sandwich panels with viscoelastic layers. Compos Struct 2013, 106: 570-580. [7] Yang JS, Xiong J, Ma L, et al. Modal response of all-composite corrugated sandwich cylindrical shells. Compos Sci Technol 2015;115:9–20. [8] Cai Z, Li Z, Ding Y, et al. Preparation and impact resistance performance of bionic sandwich structure inspired from beetle forewing. Compos Part B-Eng 2019, 161: 490-501. [9] Sun G, Chen D, Wang H, et al. High-velocity impact behaviour of aluminium honeycomb sandwich panels with different structural configurations. Int J Impact
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beams subjected to shock loading. Int J Impact Eng 2006, 32(6):968-987. [19] Zhang J, Qin Q, Wang TJ. Compressive strengths and dynamic response of corrugated metal sandwich plates with unfilled and foam-filled sinusoidal plate cores. Acta Mech 2013, 224(4): 759-775. [20] Hou S, Zhao S, Ren L, et al. Crashworthiness optimization of corrugated sandwich panels. Mater Des 2013, 51: 1071-1084. [21] Kılıçaslan C, Güden M, Odacı İK, et al. The impact responses and the finite element modeling of layered trapezoidal corrugated aluminum core and aluminum sheet interlayer sandwich structures. Mater Des 2013, 46: 121-133. [22] Zhang L, Hebert R, Wright JT, et al. Dynamic response of corrugated sandwich steel plates with graded cores. Int J Impact Eng 2014, 65: 185-194. [23] Yazici M, Wright J, Bertin D, et al. Experimental and numerical study of foam filled corrugated core steel sandwich structures subjected to blast loading. Compos struct 2014, 110: 98-109. [24] St-Pierre L, Deshpande VS, Fleck NA. The low velocity impact response of sandwich beams with a corrugated core or a Y-frame core. Int J Mech Sci 2015, 91: 71-80. [25] Boonkong T, Shen YO, Guan ZW, et al. The low velocity impact response of curvilinear-core sandwich structures. Int J Impact Eng 2016, 93: 28-38. [26] Qin Q, Zhang W, Liu S, et al. On dynamic response of corrugated sandwich beams with metal foam-filled folded plate core subjected to low-velocity impact. Compos Part A-Appl S 2018, 114: 107-116. [27] Heimbs S, Cichosz J, Klaus M, et al. Sandwich structures with textile-reinforced composite foldcores under impact loads. Compos Struct 2010, 92(6): 1485-1497. [28] Kazemahvazi S, Russell BP, Zenkert D. Impact of carbon fibre/epoxy corrugated 17
cores. Compos struct 2012, 94(11): 3300-3308. [29] Fan H, Zhao L, Chen H, et al. Dynamic compression failure mechanisms and dynamic effects of integrated woven sandwich composites. J Compos Mater 2014, 48(4):427-437. [30] Schneider C, Kazemahvazi S, Zenkert D, et al. Dynamic compression response of self-reinforced poly (ethylene terephthalate) composites and corrugated sandwich cores. Compos Part A-Appl S 2015, 77: 96-105. [31] He W, Liu J, Tao B, et al. Experimental and numerical research on the low velocity impact behavior of hybrid corrugated core sandwich structures. Compos Struct 2016, 158: 30-43. [32] Rahmani O, Khalili SMR, Malekzadeh K. Free vibration response of composite sandwich cylindrical shell with flexible core. Compos Struct 2010, 92(5): 1269-1281.
Figures Fig. 1 The sample images of (a) ACSCP, (b) CCSCP, (c) axial corrugated core, (d) circular corrugated core, (e) outer curve shell and (f) inner curve shell. Fig. 2 The representative unit cell geometry of (a) axial corrugated and (b) circular corrugated core. Fig. 3 (a) The Instron Dynatup 9250HV impact testing apparatus, (b) the specimen and the clamping fixture. Fig. 4 Impact location of ACSCP (a) on the node A-N and (b) on the middle point of two nodes A-M; CCSCP (c) on the middle point of two nodes C-M and (d)on the node C-N. Fig. 5 Typical FE models of the low velocity impact test for (a) ACSCP and (b) CCSCP. Fig. 6 Experimental impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J. Fig. 7 Experimental impact velocity-time curves of (a) ACSCPs-N, (b) CCSCPs-M; the impact load-time curves of (c) ACSCPs-N, (d) CCSCPs-M; the absorbed 18
energy-time curves of (e) ACSCPs-N, (f) CCSCPs-M under the impact energy of 15J. Fig. 8 The impact damage of specimens (a) A-1-N, (b) A-2-N, (c) A-3-N, (d) C-1-M, (e) C-2-M, (f) C-3-M under the impact energy of 15J. Fig. 9 Comparison of the impact damage of specimen A-3-N by (a) experiment, (b) simulation and C-3-M by (c) experiment, (d) simulation under the impact energy of 15J. Fig. 10 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J. Fig. 11 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M obtained numerically under different impact energy. Fig. 12 The predicted impact damage of specimen A-3-N under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-M under the impact energy of (d) 15J, (e) 20J, (f) 25J. Fig. 13 Comparison of the impact velocity-time curves of (a) A-3-M, (b) C-3-N; the impact load-time curves of (c) A-3-M, (d) C-3-N; the absorbed energy-time curves of (e) A-3-M, (f) C-3-N obtained numerically under different impact energy. Fig. 14 The predicted impact damage of specimen A-3-M under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-N under the impact energy of (d) 15J, (e) 20J, (f) 25J. Fig. 15 Energy contribution of (a) A-3-N, (b) C-3-N under the impact energy of 15J; (c) A-3-N, (d) C-3-N under the impact energy of 20J; (e) A-3-N, (f) C-3-N under the impact energy of 25J. Fig. 16 Energy contribution of (a) A-3-M, (b) C-3-M under the impact energy of 15J; (c) A-3-M, (d) C-3-M under the impact energy of 20J; (e) A-3-M, (f) C-3-M under the impact energy of 25J.
(c)
(d)
(e)
(f)
(b)
(a)
19
Fig. 1 The sample images of (a) ACSCP, (b) CCSCP, (c) axial corrugated core, (d) circular corrugated core, (e) outer curve shell and (f) inner curve shell.
(a)
fa
tf
R
tc
d
a tf
(b) R fc tf
d
tc
c h
tf
Fig. 2 The representative unit cell geometry of (a) axial corrugated and (b) circular corrugated core.
20
(a)
(b)
Impactor
Specimen
Clamping fixture
Fig. 3 (a) The Instron Dynatup 9250HV impact testing apparatus, (b) the specimen and the clamping fixture.
(a)
(b)
(c)
(d)
21
Fig. 4 Impact location of ACSCP (a) on the node A-N and (b) on the middle point of two nodes A-M; CCSCP (c) on the middle point of two nodes C-M and (d) on the node C-N.
(a)
(b)
Fig. 5 Typical FE models of the low velocity impact test for (a) ACSCP and (b) CCSCP.
(b)
(a)
22
(c)
(d)
(e)
(f)
23
Fig. 6 Experimental impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J.
(a)
(b)
(c)
(d)
24
(e)
(f)
Fig. 7 Experimental impact velocity-time curves of (a) ACSCPs-N, (b) CCSCPs-M; the impact load-time curves of (c) ACSCPs-N, (d) CCSCPs-M; the absorbed energy-time curves of (e) ACSCPs-N, (f) CCSCPs-M under the impact energy of 15J. 25
(a)
(d) 20 mm
(b)
20 mm
(e)
20 mm
(c)
20 mm
(f) 20 mm
20 mm
Fig. 8 The impact damage of specimens (a) A-1-N, (b) A-2-N, (c) A-3-N, (d) C-1-M, (e) C-2-M, (f) C-3-M under the impact energy of 15J
26
(a)
(c)
20 mm
20 mm
(b)
(d)
20 mm
20 mm
Fig. 9 Comparison of the impact damage of specimen A-3-N by (a) experiment, (b) 27
simulation and C-3-M by (c) experiment, (d) simulation under the impact energy of 15J.
(b)
(a)
(d)
(c)
(e)
28
(f)
Fig. 10 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M under the impact energy of 15J.
(a)
29
(b)
(d)
(f)
30
Fig. 11 Comparison of the impact velocity-time curves of (a) A-3-N, (b) C-3-M; the impact load-time curves of (c) A-3-N, (d) C-3-M; the absorbed energy-time curves of (e) A-3-N, (f) C-3-M obtained numerically under different impact energy.
(a)
20 mm
(b)
(c)
20 mm
31
20 mm
(d)
20 mm
(e)
(f)
20 mm
20 mm
Fig. 12 The predicted impact damage of specimen A-3-N under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-M under the impact energy of (d) 15J, (e) 20J, (f) 25J.
32
(a)
(b)
(c)
(d)
(e)
(f)
33
Fig. 13 Comparison of the impact velocity-time curves of (a) A-3-M, (b) C-3-N; the impact load-time curves of (c) A-3-M, (d) C-3-N; the absorbed energy-time curves of (e) A-3-M, (f) C-3-N obtained numerically under different impact energy.
34
(a)
20 mm
(b)
(c)
20 mm
20 mm
(f)
(d)
20 mm
(e)
20 mm
20 mm
35
Fig. 14 The predicted impact damage of specimen A-3-M under the impact energy of (a) 15J, (b) 20J, (c) 25J and C-3-N under the impact energy of (d) 15J, (e) 20J, (f) 25J.
(a)
(b)
(c)
(d)
(e)
(f)
36
Fig. 15 Energy contribution of (a) A-3-N, (b) C-3-N under the impact energy of 15J; (c) A-3-N, (d) C-3-N under the impact energy of 20J; (e) A-3-N, (f) C-3-N under the impact energy of 25J. 37
(a)
(b)
(c)
(d)
(e)
(f)
38
Fig. 16 Energy contribution of (a) A-3-M, (b) C-3-M under the impact energy of 15J; (c) A-3-M, (d) C-3-M under the impact energy of 20J; (e) A-3-M, (f) C-3-M under the impact energy of 25J.
[33] Table 1 Macro mechanical properties of orthogonal woven fabric composites Symbol
Value
Property
E11
63.8GPa
Longitudinal Young’s modulus
E22
63.8GPa
Transverse modulus
E33
11.0GPa
Out-of-plane modulus
39
12 ,13
0.064
Poisson’s ratio
23
0.32
Poisson’s ratio
G 12 , G 13
4.2GPa
Shear modulus
G 23
4.2GPa
Shear modulus
Xt
756MPa
Longitudinal tensile strength
Xc
557MPa
Longitudinal compressive strength
Yt
756MPa
Transverse tensile strength
Yc
557MPa
Transverse compressive strength
Zt
60MPa
Out-of-plane tensile strength
Zc
198MPa
Out-of-plane compressive strength
S12 , S13
118MPa
Shear strength
S 23
86MPa
Shear strength
1523kg / m3
Density
Table 2 Specifications of the composite sandwich cylindrical panels tested H (mm)
t f tc (mm)
M (g)
Relative density (%)
A-1
160.0±1.0
0.50
58.3±1.1
6.5
A-2
158.0±0.0
0.75
76.5±1.3
9.9
A-3
158.5±0.5
1.00
101.3±0.9
13.2
C-1
160.0±1.0
0.50
53.6±0.3
5.6
C-2
159.0±1.0
0.75
76.5±0.4
8.5
C-3
158.0±1.0
1.00
96.4±1.7
11.3
Specimen Symbol
ACSCP
CCSCP
[34]
Conflict of interest The authors declared that they have no conflicts of interest to this work 40
titled” Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells”. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. [35]
Author Statement We declare that all persons who have substantial contributions to the present work are listed in the manuscript. Dr. Jin-Shui Yang is the corresponding author and has made substantial contributions to the conception and design of the work; Mr. Wei-Ming Zhang designed experiments; Mr. Fang Yang carried out experiments; Mr. Si-Yuan Chen carried out simulations; Prof. Rüdiger Schmidt and Prof. Kai-Uwe Schröder revised the manuscript; Prof. Li Ma and Prof. Lin-Zhi Wu guided and given advices for this work. [36]
41