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SiC pyramidal lattice core sandwich panels
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Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels Lu Zhang Investigation; Methodology , Yanfei Chen , Rujie He , Xuejian Bai , Keqiang Zhang , Shigang Ai , Yazheng Yang , Daining Fang PII: DOI: Reference:
S0020-7403(19)33067-X https://doi.org/10.1016/j.ijmecsci.2019.105409 MS 105409
To appear in:
International Journal of Mechanical Sciences
Received date: Revised date: Accepted date:
17 August 2019 20 December 2019 23 December 2019
Please cite this article as: Lu Zhang Investigation; Methodology , Yanfei Chen , Rujie He , Xuejian Bai , Keqiang Zhang , Shigang Ai , Yazheng Yang , Daining Fang , Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels, International Journal of Mechanical Sciences (2019), doi: https://doi.org/10.1016/j.ijmecsci.2019.105409
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Highlights
C/SiC pyramidal LCSPs are designed and fabricated.
Bending tests are conducted and bonds failure is commonly observed.
The mechanism maps are constructed to determine the bending failure mode.
FEA method is applied to study the bending response and failure behavior.
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Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels
Lu Zhang a, b, Yanfei Chen a, c *, Rujie He a, c *, Xuejian Bai a, b, Keqiang Zhang a, c, Shigang Ai a , c *, Yazheng Yang a, c, Daining Fang a, c
a
Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
b
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
c
Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Beijing Institute of Technology, Beijing 100081, China
* Corresponding authors: [email protected] (Yanfei Chen); [email protected] (Rujie He); [email protected] (Shigang Ai).
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Abstract Due to the excellent mechanical and chemical properties at ultra-high temperature, ceramic matrix composite structures have potential applications for thermal protection systems of hypersonic vehicles. This paper presented a PIP method to fabricate C/SiC pyramidal lattice core sandwich panels (LCSPs). Their bending behaviors with different core angles were experimentally studied firstly. Then the critical failure loads of different failure modes, including facesheet crushing or wrinkling, core member crushing, core shear failure and interlayer delamination, were theoretically established to construct the failure mechanism maps. The influence of geometric parameters, such as the length and the core angle of the core strut, and the thickness of the facesheet, on the failure mode was also analyzed. In addition, further failure process under bending load was investigated by finite element analysis (FEA) method. Elastic-damage constitutive model and cohesive element were applied to modelling the behavior of C/SiC composite and interlayer delamination between the sheet of the core and the facesheet. Theoretical and FEA results agreed well with experimental data. This work is believed to be helpful to understand the bending mechanism C/SiC pyramidal LCSPs.
Keywords: C/SiC composite; Pyramidal lattice core sandwich panel; Bending behavior; Finite element analysis
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1 Introduction Hypersonic flight vehicles have already become the highlight direction of aerospace engineering applications in various countries. A novel thermal protection system (TPS) is required with high importance and urgent necessity, because hypersonic fight vehicles have the characteristics of high speed, longtime flight and reuse [1, 2]. On one hand, the TPS undergoes severe aerodynamic heat during service. To maintain a good aerodynamic configuration, the TPS should keep certain satisfactory strength and chemical resistance at high temperatures and cannot produce a significant ablation. On the other hand, the lightweight design of the TPS makes the aircraft have higher specific working load. Hence, finding a material or structure that can meet the demands of lightweight and high-temperature resistance simultaneously is the major challenge faced by TPS. Tradiational TPSs were fabricated using refractory alloy and ceramic tile. For the former, the temperature limit, mass and high-temperature strength restrict its development. For the latter, high-temperature brittleness and low damage tolerance make their impact resistance very poor. Further, traditional TPSs are difficult to overcome the thermal short effect. Owing to the high specific modulus and strength, low thermal expansion coefficient, oxidation and ablation resistance, ceramic matrix composite (CMC) is the ideal candidate for TPS [3-5]. Among various CMCs, C/SiC composite can work at high temperatures above 1600 oC due to higher fracture toughness, damage tolerance, and oxidation resistance [6]. However, it is still a challenge to realize the lightweight application of C/SiC composite for the TPS. This is because the
fibers are easily damage at ultra-high temperature and the sandwich panel is
also easily layered due to the thermal strain mismatch. In previous studies, foam, honeycomb and sandwich panels have been regarded as promising structures to realize lightweight C/SiC composite. Among these lightweight structures, lattice core sandwich panel (LCSP) is a kind
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of composite structure, which consists of rigid skeleton and fillers. The skeleton of the LCSP is made of the material with low density and high stiffness, such as metallic, ceramic and polymer [7-11]. Usually the skeleton is a structure with a periodic lattice core between two facesheets to maximize the panel bearing capacity. We can also fill the sandwich panel space with flame retardant materials, absorbing materials and electronic components [12]. Therefore, compared with monolithic plates, LSCP has superior strength and shock resistance [13]. In the past few years, researches on LSCP mainly focused on metal or resin materials [14, 15]. In addition, the carbon nanotube reinforced sandwich plate structure under the influence of the mehcnaical loading and thermal field was investigated numerically and experimentally [16-19]. However, the study on C/SiC composite LSCP is rare. Gererally, C/SiC composite was usually prepared by using chemical vapor infiltration (CVI) [20], precursor infiltration and pyrolysis (PIP) [21], reactive melting infiltration (RMI) [22] and other mixing processing methods[23]. Among these technologies, PIP is a suitable method for preparing C/SiC LCSPs with large sizes and complex shapes. In our previous works [24, 25], C/SiC LCSPs with different geometrical configurations were designed and fabricated. The heat transferring mechanism of the C/SiC LCSPs was analyzed by experimental, theoretical and finite element analysis (FEA) methods [26, 27]. Chen et al. reported the out-of-plane compressive performance at ultra-high temperature and investigated the failure mechanisms of C/SiC corrugated lattice core sandwich panels [28, 29]. In addition, a structural efficiency concept was proposed to assess the thermal-mechanical comprehensive performance of lattice core ITPSs [27]. Recently, C/SiC ITPSs, consisting of C/SiC composite corrugated core sandwich plane, insulated aerogel filling in the core and insulated aerogel adhering onto the down surface of the down facesheet, was fabricated and its thermal insulation performance was tested by simulated atmospheric re-entry wind tunnel test [24].
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However, the intrinsic relationships between the geometrical configurations of facesheet and lattice core and the mechanical properties have not been clearly studied and understood. Especially, previous work mostly focused on characterizing the compressive behavior rather than the bending behavior. For the TPS application of the C/SiC LCSPs, their bending behavior is so important that it needs to be investigated in detail. Thus, this work focuses on studying the bending behavior of lightweight C/SiC pyramidal LCSPs. In Section 2, The C/SiC pyramidal LCSPs with different core angles were fabricated by PIP method and their bending properties were characterized mechanically by three-point bending test. In Section 3, the analytical critical failure loads of different failure modes were theoretically derived in detail. In Section 4, three-point bending finite element model was established and the bending behaivor were simulated. In Section 5, the bending performance and failure behaivor of the C/SiC pyramidal LCSPs were experimentally, theoretically and numerically discussed. It is believed that this work is helpful to further understand the bending behavior and engineering application of the C/SiC pyramidal LCSPs.
2 Experimental 2.1 Fabrication of C/SiC pyramidal LCSPs The raw materials for preparing C/SiC pyramidal LCSPs were commercial 2D T300 carbon fiber clothes (thickness: 0.25 mm, Yixing Feizhou High-Tech. Co., Ltd., China). Commercial solid polycarbosilane (PCS, Suzhou Saifei Group Co., Ltd., China) was used as the precursor for precursor infiltration and pyrolysis (PIP) fabrication of C/SiC pyramidal LCSPs. And Di-Vinyl-Benzene (DVB, Sinopharm Chemical Reagent Co., Ltd., China) was used as the solvent of the PCS. The lightweight C/SiC pyramidal LCSPs were fabricated by PIP method. The fabrication
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procedure of the lightweight C/SiC pyramidal LCSPs is illustrated in Fig. 1. The fabrication procedure was described as follows: (i) 2D T300 carbon fiber cloth was cut into designed shapes, including corresponding carbon fiber cores and facesheets; (ii) the cut carbon fiber cores and facesheets were put into the steel mold layer by layer, then fixed by trapezoid blocks, and finally compressed by steel sheets, , and cured at 120 oC to obtain the stacking carbon fiber preform, as shown in Fig. 1a; (iii) the fixed structure was soaked in PCS/DVB solution with a mass ratio of 2:1 at 60 oC for 5h. After that, as-immersed carbon fiber sandwich panels were obtained; (iv) the as-immersed carbon fiber sandwich panels were subsequently pyrolyzed at 1200 oC for 6 cycles and 1600 oC for 2 cycles in argon. Finally, three C/SiC pyramidal LCSPs with different core angles (45°, 60° and 75°) were obtained. Fig. 1b shows a typical C/SiC pyramidal LCSP prepared in this study. After each PIP cycle, the weight of C/SiC composite was weighed using an analytical balance. The porosity and density were determined by the Archimedes method with distilled water as the immersion medium. The microstructure was observed using a scanning electron microscopy. 2.2 Bending test For the bending test, the as-prepared C/SiC pyramidal LCSPs were cut into samples with 1×4 cells by using wire-cut electrical discharge machining. An Instron Legend 2367 testing system was used to conduct the bending tests based on the ASTM standard (C393-00) [30]. For the sandwich construction, the depth of the specimen shall be equal to the thickness of the sandwich construction, and the width shall be not less than twice the total thickness, not less than three times the dimension of a core cell, nor greater than one half the span length. The specimen length shall be equal to the span length plus 50 mm or plus one half the sandwich thickness. The geometric parameters of the prepared C/SiC pyramidal LCSPs were given in
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Table 1. We can see that all the specimens satisfy the ASTM standard. As shown in Fig. 2, a rectangle-shape indenter was machined to prevent local crushing failure of facesheet, and the rubber pad was used to distribute the load. The bending test was performed with a heading speed of 0.5 mm/min. The displacement-load curves and failures mode were recorded.
3 Theoretical analysis There may be four possible failure modes of C/SiC pyramidal LCSP under three-point bending load, as illustrated in Fig. 3b and 3c: (i) facesheet crushing or wrinkling; (ii) core member crushing; (iii) core shear failure; (iv) interlayer delamination. The failure modes of the LCSPs are determined by the competing mechanisms of the geometries and material properties of the facesheets and core members. The theoretical models of metallic sandwich panel presented in Refs [31, 32] were adopted for the prediction of failure modes of C/SiC pyramidal LCSPs in this work. Assume that the transverse shear load was carried by the core members and the bending moment is carried by the facesheets. The sketch of the unit cell is shown in Fig. 3a and the fixed geometrical parameters are given in Table 1. In this paper, the core angle was referred to . 3.1 Facesheet crushing or winkling The facesheet failure modes are determined by the bending moment. Facesheet crushing occurs when in-plane stress reaches the fracture strength. Therefore, the critical load for facesheet crushing can be estimated from [33]:
P
4 ct f l cos sin 2t t f lw ll
(facesheet crushing)
(1)
where P and c 55 MPa are the applied load and the failure strength of C/SiC composite. ll 3L 6 l cos cos 2b t / sin and lw 2 d l sin are the span between the
outer supports and the width of the lattice core sandwich beam.
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The sufficiently large ratio of length to thickness of the facesheet and the strain mismatch between the facesheet and the core possibly result in facesheet wrinkles with a short wavelength, a form of buckling instability. The facesheet buckles elastically as colume between the bonds of the lattice core. Therefore, the critical load of the facesheet wrinkling is calculated by following expression:
4lw l cos sin 2t t f t f k12 2 E tf P 2 ll 12 1 v l cos sin 2b 2t sin (2)
2
(facesheet wrinkling )
where E and v are the elastic modulus and Poisson’s ratio of C/SiC composite. 3.2 Core member crushing or buckling The failure mode of the core member is determined by the transverse shear load. Therefore, the critical loads of each failure mode of the core member are given as follows: 4 cbtlw cos sin L 2 k2 Ebt 3lw P 2 3l L cos sin P
core member crushing
(3) core member buckling
where k 2 is determined by the end constraint condition of the strut. Euler buckling model is used to predict the buckling form. The mutual coupling effect between the facesheet and the core is ignored. The connection between the core strut and facesheet is considered as a pinned connection. Therefore, k1 k2 1 is assumed. 3.3 Core shear failure The shear deformation can be ignored for the lattice core sandwich panel with good enough shear stiffness. However, when the sandwich panels that are short or the compliance is large with a low-density core, the shear deformation is significant. Bond fails when the shear
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stress exceeds the bond adhesion strength. Therefore, the critical load is written as:
P 2lwl s cos sin
(4)
where s is the effective in-plane shear strength of the sandwich panel. 3.4 Interlayer delamination Interlayer delamination possibly takes place at the location between the sheet of the lattice core and the facesheets or intra facesheet resulting from the weak bonding strength. Herein Ye delamination criterion is used to predict the interlayer delamination: Tensile delamination failure ( 33 0 ) 2
2
f 33T 31 32 1 0 Z S31 S32 2
T d
(5)
Compressive delamination failure ( 33 0 ) 2
2
f 31 32 1 0 S31 S32 C d
(6)
where 33 , 31 and 32 are the normal and shear stress components in the out-of-plane direction, respectively, and Z T , S31 and S32 are corresponding failure strengths.
4 Numerical simulation 4.1 Finite element model As shown in Fig. 4, the finite element model of the C/SiC pyramidal LCSP was built to model the bending behavior according to the real geometrical dimensions using commercial ABAQUS software package (version 6.13) [34]. Two analytical rigid semi-cylinder shells and one discrete rigid block with rounded corners were used to model the supports and indenter of experimental setups. Local material orientation was applied to the lattice core struts due to the angle change between the core struts and core sheet. Surface-to-surface contacts were used
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between the facesheets and rigid bodies. The sliding behavior was finite sliding. The displacement boundaries of the rigid bodies were constrained by referring points. The displacement and rotation of the supports were fixed according to the experimental setups. The supports were fixed according to the experimental setups. For the indenter, all the displacement/rotation conditions, except the displacement in z-axis direction which was loaded, were constrained, too. To keep the deformation symmetry, the displacements of the middle plane of the sandwich panel in x-axis and y-axis directions were constrained. The sandwich panel and supports were meshed with C3D8R element and R3D4 element, respectively. The mesh independency was studied firstly to ensure accuracy. Finally, the suitable mesh sizes of the face sheet and the lattice core were 1.0 and 2.0, respectively. 4.2 Material models In general, C/SiC composite was taken as a linear elastic damage material [35-37]. In this work, an elastic-damage constitutive model was adopted for C/SiC composite:
1 1 d1 C11 C 12 2 3 C13 12 13 23
C12 1 d 2 C22 C23
C13 C23 1 d3 C33
1 d 4 G12
1 d5 G13
1 2 3 12 13 1 d6 G23 23
(7) where di i 1,...6 and Cij , Gij i, j 1,...,3 were damage tensor and stiffness tensor, respectively. It was assumed that the d 4 , d 5 and d 6 are not independent and could be written as: d 4 =1 1 d1 1 d 2 d5 =1 1 d 2 1 d3 d 6 =1 1 d3 1 d1
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(8)
To model the failure behavior of C/SiC pyramidal LCSP, the maximum stress failure criteria were used:
1T C 1 T 2 C 2 T 3 3C
XT XC YT YC
(9)
ZT ZC
where X T , X C , YT , YC , ZT and Z C were the tensile and compressive strengths of the C/SiC composite in the x-axis, y-axis, and z-axis directions, respectively. The principle stress of every integration point was calculated by a VUMAT subroutine to judge whether the material fails or not. If the stress was less than the stress strength, the value of damage variable was zero; otherwise, the value of damage variable updated to be one. The interlayer delamination behavior occurred between the sheet of the core and the facesheet observed in the experiment, would be simulated using COH3D8 element. The cohesive crack approach was used to consider the interface failure. Mixed-mode traction separation law is used to model the delamination process [29].
5 Results and discussion 5.1 Experimental results 5.1.1 C/SiC composite Fig. 5 shows the relationship between the density, porosity and of weight gain rate (WGR) of C/SiC composite and PIP cycle. Both WGR and porosity both decreased with PIP cycle, but the density is the opposite. In the seventh cycle, increasing pyrolytic temperature leads to the transformation of amorphous silicon carbide into silicon carbide crystal (α-SiC and β-SiC phases), which penetrates into the interfibrous pores. The decrease of the WGR and
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density and the increase of the porosity is due to the pyrolysis reaction occurred during the seventh cycle. Finally, the WGR, the porosity, and density were measured to be about 1.5%, 20%, and 2 g/cm3, respectively, after 8 PIP cycles. Fig. 6 shows the SEM microstructure of the PIP-prepared C/SiC composite after 8 PIP cycles. The SiC matrix fills most of the interfibrous pores, but there are still some holes in the matrix, which is caused by insufficient penetration of the impregnation solution. 5.1.2 Bending performance of C/SiC pyramidal LCSPs The bending displacement-load curves are presented in Fig. 7a. All the curves had a similar process of initial nonlinearity, then linear dominance and final failure. The initial nonlinear was possibly due to the imperfect contact between the facesheets and indenter and supports. Because the lattice sandwich panel finally failed due to the fracture of facesheet, the expression of the bending strength was derived as follow:
f
Pll 4lwt f l cos sin t
(10)
where f was bending strength. Besides, the bending strengths of C/SiC pyramidal LCSPs are given in Fig. 7b. The bending strengths of the LCSPs with the core angles of 45, 60 and 75o were 18.4, 16.1 and 15.1 MPa, respectively. With the core angle increasing from 45 to 75o, the bending strength decreased from the maximum value to 87.5% of the maximum ( 60 ) and 83.2% of the maximum ( 75 ). It had the highest value for the LCSP with 45o core angle. To study the failure mechanism of the LCSPs under three-point bending load, their deformation process were observed and shown in Fig. 8. Bonds crushing failure of the core was observed for all C/SiC pyramidal LCSPs with different core angles. However, for the C/SiC pyramidal LCSPs with 60o core angle, multiple failure modes were observed. With the
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load increasing, the nearly simultaneous crushing of facesheet and bonds followed the interlayer delamination between the sheet of the core and facesheet, which failed attributing to the weak bonding strength. 5.2 Mechanism maps This subsection provides predictive failure mechanism maps for the C/SiC pyramidal LCSPs based on the geometric parameters and material properties (Elastic modulus and Poisson’s ratio). The dimensions of the core, including the length, width, thickness, and angle, etc. have significant influence on the bending behavior and failure modes of lattice sandwich panel. In constructing the mechanism maps, the length of the core l , determining the height of the core, and the face sheet thickness t f are varied. Herein the study was limited to the configurations with three different core angles. It was assumed that the failure mechanism maps were operated with lowest criterial loads derived in Section 3. Because interlayer delamination mode was predicted by stress components (Eqs. 5 and 6) rather than load and the effective in-plane shear strength of the sandwich panel was not determined, only facesheet crushing or winkling and core member crushing or buckling were illustrated in the failure mechanism maps. The results were plotted in Fig. 9 in terms of normalized parameters of l ll and t f ll . The specific experimental data for each specimen was marked by red pentagrams. Although the core angle varied, the distribution patterns of failure mechanism maps were similar. For the C/SiC pyramidal LCSPs, core member buckling (CB) was a difficult thing to achieve, because it required l ll greater than 0.463. That was to say, core buckling only took place in very thickness lattice sandwich panels. When the face sheet thickness was enough small, face sheet wrinkling (FW) dominated the deformation and failure behaviors of the panels. The probability of face sheet crushing (FC) was small, it needed l ll little than
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0.01001 45 , 0.01164 60 , 0.116 75 , corresponding t f ll
was
(0.007,0.017), (0.008,0.021) and (0.009,0.024), respectively. As illustrated in Fig.9, core crushing (CC) was most likely to take place, for the dimensions of bending experiments of lattice sandwich panel. The analytical predictions showed well agreement with experimental observation in Fig.8. 5.3 Numerical results Fig. 10 shows the numerically simulated results compared with experimental data. It showed that the numerical simulations gave satisfactory results and agreed well with experimental data. For the LCSPs with core angles of 60 and 75 , the simulated curves could model the mechanical behavior and capture the strength. However, for the LCSP with 45o core angle, we could see that the simulated curve fell off a cliff after reaching a peak value while the experimental curve underwent a rapid fall followed by a rise. The ongoing rising behavior was due to the continuous carrying capacity of the facesheet after the core member fail. In addition, the initial nonlinear behavior of experimental curves was modeled using surface-to-surface contact technique between the facesheets and indenter and supports. The load was borne by the core struts on both sides of the indenters. The maximum von Mises stress occurred near the bonds, due to stress concentration resulting from the geometrical mismatch and deformation incongruity. For the LCSP with a core angle of 45 , interlayer delamination occurred at the bonding location between the sheet of the core and facesheet followed by the failure of bonds. The interlayer delamination occurred firstly at lower right location and then moved to other locations. Therefore, its delamination level was worse than other locations. Similar failure processes were seen for the LCSPs with core angles of 60 and 75 . The difference was that the delamination level was weaker than that of the C/SiC pyramidal LCSP with 45o core angle. In the simulated process, the interlayer delamination
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behavior only took place at some middle elements but not total destruction of cohesive elements. Therefore, this was why we could not observe obvious interlayer delamination in experiments. The final failure took place at the bonds on the core strut for all lattice sandwich panels. However, further fracture failure in the middle of the facesheet was modeled for the C/SiC pyramidal LCSP with 60o core angle, which agreed with experimental observation.
6. Ashby chart for different materials Fig. 11 presents the Ashby chart of the bending strengths versus density for different materials [38-41], such as metal materials, bulk ceramics, ceramic foams, porous ceramics, metal LCSP and C/SiC LCPS. Aboviously, the bending strength of bulk ceramics are commonly greater than other materials except some alloys. Although the bending strength of C/SiC LCSP is lower than that of bulk ceramics, their density is much higher. Ceramic foams are lighter than C/SiC LCPS, but their bending strengths are also smaller, which makes them only be used for thermal insulation, but not for carrying load. For metla LCPS, their density and bending strength vary greatly. The reason is that metal materials can be 3D printed into lattice structures. However, the strength of these printed materials is weak due to the immature technology. Although some metal LCSP possesses higher bending strength using traditional technology, the density of metal materials is much higher than that of C/SiC composite. In addition, metallic service temperature is lower that C/SiC composites. In summary, C/SiC LCSP provides an effective approach to balance the load bearing capacity and the weight for different materials.
7. Conclusions The bending mechanical behavior of the C/SiC pyramidal LCSPs was investigated in this paper using experimental, theoretically and numerically simulating approaches. The conclusions were summarized as follows:
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(1) C/SiC pyramidal LCSPs with three different core angles were fabricated by the PIP method and tested under three-point bending load. For C/SiC composite, SiC matrix penetrated into most of the interfibrous pores and the final density reached above 2.0 g/cm3. For C/SiC pyramidal LCSPs, the failure of bonds of the core was commonly observed for all panels. In addition, interlayer delamination between the sheet of the core and facesheet, and facesheet crushing took place for the lattice sandwich panel with 60 inclination angle. (2) Analytical models, including facesheet crushing or wrinkling, core member crushing, core shear failure and interlayer delamination, were established to predict the critical bending load. Failure mechanism maps predicting the relationship between failure mode and dimensionless geometrical parameters were constructed based on these analytical models. The predicted failure modes agreed well with experimental results. We can design the C/SiC pyramidal LCSPs based on the failure mechanism maps. (3) FEA method was used to model the bending response and failure behavior. In the simulated process, the elastic-damage constitutive model was adopted to describe the mechanical behavior of C/SiC composite. The cohesive crack approach was used to model the interlayer delamination behavior between the sheet of the core and the facesheet. Simulated results agreed well with experimental results, and the interlayer delamination behavior occurred before bond failure. The facesheet crushing behavior observed on the LCSP with a core angle of 60 was exactly modeled. Form this work, it is believed that it can help to understand the bending behavior C/SiC pyramidal LCSPs, and to give further insights into the design of lightweight C/SiC structures for thermal protection system application.
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Author contributions Lu Zhang: Investigation; Methodology, Formal analysis, Writing - original draft; Yanfei Chen: Conceptualization, Methodology, Validation, Formal analysis, Funding acquisition, Writing - review & editing; Rujie He: Investigation, Project administration, Formal analysis, Supervision, Funding acquisition; Xuejian Bai: Resources, Data curation; Keqiang Zhang: Resources, Data curation; Shigang Ai: Software, Supervision; Yazheng: Supervision, Project administration; Daining Fang: Conceptualization, Supervision, Project administration .
Conflict of interest form The authors declared that there is no conflict of interest.
Acknowledgments This study was financially supported by the National Natural Science Foundation of China (51772028, 11902034), the Beijing Natural Science Foundation (2182064, 1204035), and the China Postdoctoral Science Foundation (Nos. 2019M650500).
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nanotube‐ reinforced composite plate: Experimental, numerical, and simulation, Advances in Polymer Technology, 37 (2018) 1643-1657. [18] K. Mehar, S.K. Panda, T.R. Mahapatra, Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure, International Journal of Mechanical Sciences, 133 (2017) 319-329. [19] K. Mehar, S.K. Panda, B.K. Patle, Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach, Polymer Composites, 39 (2018) 3792-3809. [20] J. Wang, X. Chen, K. Guan, L. Cheng, L. Zhang, Y. Liu, Effects of channel modification on microstructure and mechanical properties of C/SiC composites prepared by LA-CVI process, Ceramics International, 44 (2018) 16414-16420. [21] H. Zhong, Z. Wang, H. Zhou, D. Ni, Y. Kan, Y. Ding, S. Dong, Properties and microstructure evolution of Cf/SiC composites fabricated by polymer impregnation and pyrolysis (PIP) with liquid polycarbosilane, Ceramics International, 43 (2017) 7387-7392. [22] A. Abdollahi, N. Ehsani, Z. Valefi, Thermal shock resistance and isothermal oxidation behavior of C/SiC-SiC nano functionally gradient coating on graphite produced via reactive melt infiltration (RMI), Materials Chemistry and Physics, 182 (2016) 49-61. [23] S. Fan, C. Yang, L. He, J. Deng, L. Zhang, L. Cheng, The effects of phosphate coating on friction performance of C/C and C/SiC brake materials, Tribology International, 114 (2017) 337-348. [24] Y. Li, L. Zhang, R. He, Y. Ma, K. Zhang, X. Bai, B. Xu, Y. Chen, Integrated thermal protection system based on C/SiC composite corrugated core sandwich plane structure, Aerospace Science and Technology, (2019). [25] L. Zhang, D. Yin, R. He, Z. Yu, K. Zhang, Y. Chen, X. Bai, Y. Yang, D. Fang, Lightweight C/SiC Ceramic Matrix Composite Structures with High Loading Capacity, Advanced Engineering Materials, (2019) 1801246. [26] Y. Li, L. Zhang, R. He, Y. Ma, K. Zhang, X. Bai, B. Xu, Y. Chen, Integrated thermal protection system based on C/SiC composite corrugated core sandwich plane structure, Aerospace Science and Technology, 91 (2019) 607-616. [27] Y. Chen, Y. Tao, B. Xu, S. Ai, D. Fang, Assessment of thermal-mechanical performance with structural efficiency concept on design of lattice-core thermal protection system, Applied Thermal Engineering, 143 (2018) 200-208. [28] Y. Chen, S. Ai, R. He, K. Wei, D. Fang, A Study on the Compressive Performance of C/SiC Lattice Sandwich Panel at High Temperature, International Journal of Applied Mechanics, 9 (2017) 1750120. [29] Y. Chen, L. Zhang, Y. Zhao, R. He, S. Ai, L. Tang, D. Fang, Mechanical behaviors of C/SiC pyramidal lattice core sandwich panel under in-plane compression, Composite Structures, 214 (2019) 103-113. [30] A. C393-00, Standard Test Method for Flexural Properties of Sandwich Constructions, ASTM International, West Conshohocken, PA, (2000). [31] F.W. Zok, H.J. Rathbun, Z. Wei, A.G. Evans, Design of metallic textile core sandwich panels, International Journal of Solids and Structures, 40 (2003) 5707-5722. [32] J. Xiong, L. Ma, S. Pan, L. Wu, J. Papadopoulos, A. Vaziri, Shear and bending 20
performance of carbon fiber composite sandwich panels with pyramidal truss cores, Acta Materialia, 60 (2012) 1455-1466. [33] Q. Sun, G. Zhou, Z. Meng, H. Guo, Z. Chen, H. Liu, H. Kang, S. Keten, X. Su, Failure criteria of unidirectional carbon fiber reinforced polymer composites informed by a computational micromechanics model, Composites Science and Technology, 172 (2019) 81-95. [34] D.S. Inc, Abaqus Standard Manual (Version 6.13), (2013). [35] G. Camus, Modelling of the mechanical behavior and damage processes of fibrous ceramic matrix composites: application to a 2-D SiC/SiC, International Journal of solids and Structures, 37 (2000) 919-942. [36] P. Ladevèze, A. Gasser, O. Allix, Damage mechanisms modeling for ceramic composites, Journal of Engineering Materials and Technology, 116 (1994) 331-336. [37] J. Maire, J. Chaboche, A new formulation of continuum damage mechanics (CDM) for composite materials, Aerospace Science and Technology, 1 (1997) 247-257. [38] S. Alimirzaei, M. Mohammadimehr, A. Tounsi, Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions, Structural Engineering and Mechanics, 71 (2019) 485-502. [39] L.A. Chaabane, F. Bourada, M. Sekkal, S. Zerouati, F.Z. Zaoui, A. Tounsi, A. Derras, A.A. Bousahla, A. Tounsi, Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation, Structural Engineering and Mechanics, 71 (2019) 185-196. [40] B. Karami, M. Janghorban, A. Tounsi, Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions, Engineering with Computers, 35 (2019) 1297-1316. [41] D. Zarga, A. Tounsi, A.A. Bousahla, F. Bourada, S. Mahmoud, Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory, Steel and Composite Structures, 32 (2019) 389-410.
Figures
21
Fig. 1. (a) The assembly process of pyramidal LCSP using 2D T300 carbon fiber cloth: the carbon fiber pyramidal core was fixed by trapezoid blocks on one carbon fiber plate, then the other one was placed on the core, and finally the carbon fiber pyramidal LCSP was pressed by two metal plates; (b) prepared C/SiC pyramidal LCSP, including 6 4 cells.
Fig. 2. Bending test of the C/SiC pyramidal LCSPs with three different inclination angles,
.
22
Fig. 3. Schematic diagrams of (a) the unit cell of pyramidal LCSP; (b) bending test; and (c) failure modes, including facesheet crushing, facesheet wrinkling, core member crushing, core shear failure and interlayer delamination.
Fig. 4. Finite element model of bending test of C/SiC pyramidal LCSP.
23
Fig. 5. The relationship between the density, porosity and of weight gain rate (WGR) of prepared C/SiC composite and PIP cycle.
24
Fig. 6. Microstructure of the C/SiC composite: (a) low magnification, and (b) high magnification.
Fig. 7. Bending test of the C/SiC pyramidal LCSPs: (a) displacement-load curves, and (b) bending strength.
25
Fig. 8. Failure modes of the C/SiC pyramidal LCSPs with three different core angles.
26
Fig. 9. Failure mechanism maps for the C/SiC pyramidal LCSPs with three different core angles. [FW=face sheet wrinkling; FC=face sheet crushing; CB= core member buckling;
27
CC=core member crushing.]
Fig. 10. Numerical simulated results compared with experimental data for the C/SiC pyramidal LCSPs with three different core angles.
28
Fig. 11. Ashby chart of the bending properties versus density for the different materials.
29
Table Table 1. Geometric parameters of the C/SiC pyramidal LCSP.
Length
Width
Thickness
Span length
Thickness of the
(mm)
(mm)
(mm)
(mm)
core (mm)
45
139.1
35.2
15.2
104.3
8.2
60
120
35.2
17.0
90.0
10.0
75
96.3
35.2
18.1
72.2
11.1
l (mm)
b (mm)
d (mm)
t (mm)
t f (mm)
16.3
3.8
3.5
1.5
2.0
45
30
GRAPHICAL ABSTRACT
31
Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels Lu Zhang Investigation; Methodology , Yanfei Chen , Rujie He , Xuejian Bai , Keqiang Zhang , Shigang Ai , Yazheng Yang , Daining Fang PII: DOI: Reference:
S0020-7403(19)33067-X https://doi.org/10.1016/j.ijmecsci.2019.105409 MS 105409
To appear in:
International Journal of Mechanical Sciences
Received date: Revised date: Accepted date:
17 August 2019 20 December 2019 23 December 2019
Please cite this article as: Lu Zhang Investigation; Methodology , Yanfei Chen , Rujie He , Xuejian Bai , Keqiang Zhang , Shigang Ai , Yazheng Yang , Daining Fang , Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels, International Journal of Mechanical Sciences (2019), doi: https://doi.org/10.1016/j.ijmecsci.2019.105409
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Highlights
C/SiC pyramidal LCSPs are designed and fabricated.
Bending tests are conducted and bonds failure is commonly observed.
The mechanism maps are constructed to determine the bending failure mode.
FEA method is applied to study the bending response and failure behavior.
1
Bending behavior of lightweight C/SiC pyramidal lattice core sandwich panels
Lu Zhang a, b, Yanfei Chen a, c *, Rujie He a, c *, Xuejian Bai a, b, Keqiang Zhang a, c, Shigang Ai a , c *, Yazheng Yang a, c, Daining Fang a, c
a
Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, China
b
School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
c
Beijing Key Laboratory of Lightweight Multi-functional Composite Materials and Structures, Beijing Institute of Technology, Beijing 100081, China
* Corresponding authors: [email protected] (Yanfei Chen); [email protected] (Rujie He); [email protected] (Shigang Ai).
2
Abstract Due to the excellent mechanical and chemical properties at ultra-high temperature, ceramic matrix composite structures have potential applications for thermal protection systems of hypersonic vehicles. This paper presented a PIP method to fabricate C/SiC pyramidal lattice core sandwich panels (LCSPs). Their bending behaviors with different core angles were experimentally studied firstly. Then the critical failure loads of different failure modes, including facesheet crushing or wrinkling, core member crushing, core shear failure and interlayer delamination, were theoretically established to construct the failure mechanism maps. The influence of geometric parameters, such as the length and the core angle of the core strut, and the thickness of the facesheet, on the failure mode was also analyzed. In addition, further failure process under bending load was investigated by finite element analysis (FEA) method. Elastic-damage constitutive model and cohesive element were applied to modelling the behavior of C/SiC composite and interlayer delamination between the sheet of the core and the facesheet. Theoretical and FEA results agreed well with experimental data. This work is believed to be helpful to understand the bending mechanism C/SiC pyramidal LCSPs.
Keywords: C/SiC composite; Pyramidal lattice core sandwich panel; Bending behavior; Finite element analysis
3
1 Introduction Hypersonic flight vehicles have already become the highlight direction of aerospace engineering applications in various countries. A novel thermal protection system (TPS) is required with high importance and urgent necessity, because hypersonic fight vehicles have the characteristics of high speed, longtime flight and reuse [1, 2]. On one hand, the TPS undergoes severe aerodynamic heat during service. To maintain a good aerodynamic configuration, the TPS should keep certain satisfactory strength and chemical resistance at high temperatures and cannot produce a significant ablation. On the other hand, the lightweight design of the TPS makes the aircraft have higher specific working load. Hence, finding a material or structure that can meet the demands of lightweight and high-temperature resistance simultaneously is the major challenge faced by TPS. Tradiational TPSs were fabricated using refractory alloy and ceramic tile. For the former, the temperature limit, mass and high-temperature strength restrict its development. For the latter, high-temperature brittleness and low damage tolerance make their impact resistance very poor. Further, traditional TPSs are difficult to overcome the thermal short effect. Owing to the high specific modulus and strength, low thermal expansion coefficient, oxidation and ablation resistance, ceramic matrix composite (CMC) is the ideal candidate for TPS [3-5]. Among various CMCs, C/SiC composite can work at high temperatures above 1600 oC due to higher fracture toughness, damage tolerance, and oxidation resistance [6]. However, it is still a challenge to realize the lightweight application of C/SiC composite for the TPS. This is because the
fibers are easily damage at ultra-high temperature and the sandwich panel is
also easily layered due to the thermal strain mismatch. In previous studies, foam, honeycomb and sandwich panels have been regarded as promising structures to realize lightweight C/SiC composite. Among these lightweight structures, lattice core sandwich panel (LCSP) is a kind
4
of composite structure, which consists of rigid skeleton and fillers. The skeleton of the LCSP is made of the material with low density and high stiffness, such as metallic, ceramic and polymer [7-11]. Usually the skeleton is a structure with a periodic lattice core between two facesheets to maximize the panel bearing capacity. We can also fill the sandwich panel space with flame retardant materials, absorbing materials and electronic components [12]. Therefore, compared with monolithic plates, LSCP has superior strength and shock resistance [13]. In the past few years, researches on LSCP mainly focused on metal or resin materials [14, 15]. In addition, the carbon nanotube reinforced sandwich plate structure under the influence of the mehcnaical loading and thermal field was investigated numerically and experimentally [16-19]. However, the study on C/SiC composite LSCP is rare. Gererally, C/SiC composite was usually prepared by using chemical vapor infiltration (CVI) [20], precursor infiltration and pyrolysis (PIP) [21], reactive melting infiltration (RMI) [22] and other mixing processing methods[23]. Among these technologies, PIP is a suitable method for preparing C/SiC LCSPs with large sizes and complex shapes. In our previous works [24, 25], C/SiC LCSPs with different geometrical configurations were designed and fabricated. The heat transferring mechanism of the C/SiC LCSPs was analyzed by experimental, theoretical and finite element analysis (FEA) methods [26, 27]. Chen et al. reported the out-of-plane compressive performance at ultra-high temperature and investigated the failure mechanisms of C/SiC corrugated lattice core sandwich panels [28, 29]. In addition, a structural efficiency concept was proposed to assess the thermal-mechanical comprehensive performance of lattice core ITPSs [27]. Recently, C/SiC ITPSs, consisting of C/SiC composite corrugated core sandwich plane, insulated aerogel filling in the core and insulated aerogel adhering onto the down surface of the down facesheet, was fabricated and its thermal insulation performance was tested by simulated atmospheric re-entry wind tunnel test [24].
5
However, the intrinsic relationships between the geometrical configurations of facesheet and lattice core and the mechanical properties have not been clearly studied and understood. Especially, previous work mostly focused on characterizing the compressive behavior rather than the bending behavior. For the TPS application of the C/SiC LCSPs, their bending behavior is so important that it needs to be investigated in detail. Thus, this work focuses on studying the bending behavior of lightweight C/SiC pyramidal LCSPs. In Section 2, The C/SiC pyramidal LCSPs with different core angles were fabricated by PIP method and their bending properties were characterized mechanically by three-point bending test. In Section 3, the analytical critical failure loads of different failure modes were theoretically derived in detail. In Section 4, three-point bending finite element model was established and the bending behaivor were simulated. In Section 5, the bending performance and failure behaivor of the C/SiC pyramidal LCSPs were experimentally, theoretically and numerically discussed. It is believed that this work is helpful to further understand the bending behavior and engineering application of the C/SiC pyramidal LCSPs.
2 Experimental 2.1 Fabrication of C/SiC pyramidal LCSPs The raw materials for preparing C/SiC pyramidal LCSPs were commercial 2D T300 carbon fiber clothes (thickness: 0.25 mm, Yixing Feizhou High-Tech. Co., Ltd., China). Commercial solid polycarbosilane (PCS, Suzhou Saifei Group Co., Ltd., China) was used as the precursor for precursor infiltration and pyrolysis (PIP) fabrication of C/SiC pyramidal LCSPs. And Di-Vinyl-Benzene (DVB, Sinopharm Chemical Reagent Co., Ltd., China) was used as the solvent of the PCS. The lightweight C/SiC pyramidal LCSPs were fabricated by PIP method. The fabrication
6
procedure of the lightweight C/SiC pyramidal LCSPs is illustrated in Fig. 1. The fabrication procedure was described as follows: (i) 2D T300 carbon fiber cloth was cut into designed shapes, including corresponding carbon fiber cores and facesheets; (ii) the cut carbon fiber cores and facesheets were put into the steel mold layer by layer, then fixed by trapezoid blocks, and finally compressed by steel sheets, , and cured at 120 oC to obtain the stacking carbon fiber preform, as shown in Fig. 1a; (iii) the fixed structure was soaked in PCS/DVB solution with a mass ratio of 2:1 at 60 oC for 5h. After that, as-immersed carbon fiber sandwich panels were obtained; (iv) the as-immersed carbon fiber sandwich panels were subsequently pyrolyzed at 1200 oC for 6 cycles and 1600 oC for 2 cycles in argon. Finally, three C/SiC pyramidal LCSPs with different core angles (45°, 60° and 75°) were obtained. Fig. 1b shows a typical C/SiC pyramidal LCSP prepared in this study. After each PIP cycle, the weight of C/SiC composite was weighed using an analytical balance. The porosity and density were determined by the Archimedes method with distilled water as the immersion medium. The microstructure was observed using a scanning electron microscopy. 2.2 Bending test For the bending test, the as-prepared C/SiC pyramidal LCSPs were cut into samples with 1×4 cells by using wire-cut electrical discharge machining. An Instron Legend 2367 testing system was used to conduct the bending tests based on the ASTM standard (C393-00) [30]. For the sandwich construction, the depth of the specimen shall be equal to the thickness of the sandwich construction, and the width shall be not less than twice the total thickness, not less than three times the dimension of a core cell, nor greater than one half the span length. The specimen length shall be equal to the span length plus 50 mm or plus one half the sandwich thickness. The geometric parameters of the prepared C/SiC pyramidal LCSPs were given in
7
Table 1. We can see that all the specimens satisfy the ASTM standard. As shown in Fig. 2, a rectangle-shape indenter was machined to prevent local crushing failure of facesheet, and the rubber pad was used to distribute the load. The bending test was performed with a heading speed of 0.5 mm/min. The displacement-load curves and failures mode were recorded.
3 Theoretical analysis There may be four possible failure modes of C/SiC pyramidal LCSP under three-point bending load, as illustrated in Fig. 3b and 3c: (i) facesheet crushing or wrinkling; (ii) core member crushing; (iii) core shear failure; (iv) interlayer delamination. The failure modes of the LCSPs are determined by the competing mechanisms of the geometries and material properties of the facesheets and core members. The theoretical models of metallic sandwich panel presented in Refs [31, 32] were adopted for the prediction of failure modes of C/SiC pyramidal LCSPs in this work. Assume that the transverse shear load was carried by the core members and the bending moment is carried by the facesheets. The sketch of the unit cell is shown in Fig. 3a and the fixed geometrical parameters are given in Table 1. In this paper, the core angle was referred to . 3.1 Facesheet crushing or winkling The facesheet failure modes are determined by the bending moment. Facesheet crushing occurs when in-plane stress reaches the fracture strength. Therefore, the critical load for facesheet crushing can be estimated from [33]:
P
4 ct f l cos sin 2t t f lw ll
(facesheet crushing)
(1)
where P and c 55 MPa are the applied load and the failure strength of C/SiC composite. ll 3L 6 l cos cos 2b t / sin and lw 2 d l sin are the span between the
outer supports and the width of the lattice core sandwich beam.
8
The sufficiently large ratio of length to thickness of the facesheet and the strain mismatch between the facesheet and the core possibly result in facesheet wrinkles with a short wavelength, a form of buckling instability. The facesheet buckles elastically as colume between the bonds of the lattice core. Therefore, the critical load of the facesheet wrinkling is calculated by following expression:
4lw l cos sin 2t t f t f k12 2 E tf P 2 ll 12 1 v l cos sin 2b 2t sin (2)
2
(facesheet wrinkling )
where E and v are the elastic modulus and Poisson’s ratio of C/SiC composite. 3.2 Core member crushing or buckling The failure mode of the core member is determined by the transverse shear load. Therefore, the critical loads of each failure mode of the core member are given as follows: 4 cbtlw cos sin L 2 k2 Ebt 3lw P 2 3l L cos sin P
core member crushing
(3) core member buckling
where k 2 is determined by the end constraint condition of the strut. Euler buckling model is used to predict the buckling form. The mutual coupling effect between the facesheet and the core is ignored. The connection between the core strut and facesheet is considered as a pinned connection. Therefore, k1 k2 1 is assumed. 3.3 Core shear failure The shear deformation can be ignored for the lattice core sandwich panel with good enough shear stiffness. However, when the sandwich panels that are short or the compliance is large with a low-density core, the shear deformation is significant. Bond fails when the shear
9
stress exceeds the bond adhesion strength. Therefore, the critical load is written as:
P 2lwl s cos sin
(4)
where s is the effective in-plane shear strength of the sandwich panel. 3.4 Interlayer delamination Interlayer delamination possibly takes place at the location between the sheet of the lattice core and the facesheets or intra facesheet resulting from the weak bonding strength. Herein Ye delamination criterion is used to predict the interlayer delamination: Tensile delamination failure ( 33 0 ) 2
2
f 33T 31 32 1 0 Z S31 S32 2
T d
(5)
Compressive delamination failure ( 33 0 ) 2
2
f 31 32 1 0 S31 S32 C d
(6)
where 33 , 31 and 32 are the normal and shear stress components in the out-of-plane direction, respectively, and Z T , S31 and S32 are corresponding failure strengths.
4 Numerical simulation 4.1 Finite element model As shown in Fig. 4, the finite element model of the C/SiC pyramidal LCSP was built to model the bending behavior according to the real geometrical dimensions using commercial ABAQUS software package (version 6.13) [34]. Two analytical rigid semi-cylinder shells and one discrete rigid block with rounded corners were used to model the supports and indenter of experimental setups. Local material orientation was applied to the lattice core struts due to the angle change between the core struts and core sheet. Surface-to-surface contacts were used
10
between the facesheets and rigid bodies. The sliding behavior was finite sliding. The displacement boundaries of the rigid bodies were constrained by referring points. The displacement and rotation of the supports were fixed according to the experimental setups. The supports were fixed according to the experimental setups. For the indenter, all the displacement/rotation conditions, except the displacement in z-axis direction which was loaded, were constrained, too. To keep the deformation symmetry, the displacements of the middle plane of the sandwich panel in x-axis and y-axis directions were constrained. The sandwich panel and supports were meshed with C3D8R element and R3D4 element, respectively. The mesh independency was studied firstly to ensure accuracy. Finally, the suitable mesh sizes of the face sheet and the lattice core were 1.0 and 2.0, respectively. 4.2 Material models In general, C/SiC composite was taken as a linear elastic damage material [35-37]. In this work, an elastic-damage constitutive model was adopted for C/SiC composite:
1 1 d1 C11 C 12 2 3 C13 12 13 23
C12 1 d 2 C22 C23
C13 C23 1 d3 C33
1 d 4 G12
1 d5 G13
1 2 3 12 13 1 d6 G23 23
(7) where di i 1,...6 and Cij , Gij i, j 1,...,3 were damage tensor and stiffness tensor, respectively. It was assumed that the d 4 , d 5 and d 6 are not independent and could be written as: d 4 =1 1 d1 1 d 2 d5 =1 1 d 2 1 d3 d 6 =1 1 d3 1 d1
11
(8)
To model the failure behavior of C/SiC pyramidal LCSP, the maximum stress failure criteria were used:
1T C 1 T 2 C 2 T 3 3C
XT XC YT YC
(9)
ZT ZC
where X T , X C , YT , YC , ZT and Z C were the tensile and compressive strengths of the C/SiC composite in the x-axis, y-axis, and z-axis directions, respectively. The principle stress of every integration point was calculated by a VUMAT subroutine to judge whether the material fails or not. If the stress was less than the stress strength, the value of damage variable was zero; otherwise, the value of damage variable updated to be one. The interlayer delamination behavior occurred between the sheet of the core and the facesheet observed in the experiment, would be simulated using COH3D8 element. The cohesive crack approach was used to consider the interface failure. Mixed-mode traction separation law is used to model the delamination process [29].
5 Results and discussion 5.1 Experimental results 5.1.1 C/SiC composite Fig. 5 shows the relationship between the density, porosity and of weight gain rate (WGR) of C/SiC composite and PIP cycle. Both WGR and porosity both decreased with PIP cycle, but the density is the opposite. In the seventh cycle, increasing pyrolytic temperature leads to the transformation of amorphous silicon carbide into silicon carbide crystal (α-SiC and β-SiC phases), which penetrates into the interfibrous pores. The decrease of the WGR and
12
density and the increase of the porosity is due to the pyrolysis reaction occurred during the seventh cycle. Finally, the WGR, the porosity, and density were measured to be about 1.5%, 20%, and 2 g/cm3, respectively, after 8 PIP cycles. Fig. 6 shows the SEM microstructure of the PIP-prepared C/SiC composite after 8 PIP cycles. The SiC matrix fills most of the interfibrous pores, but there are still some holes in the matrix, which is caused by insufficient penetration of the impregnation solution. 5.1.2 Bending performance of C/SiC pyramidal LCSPs The bending displacement-load curves are presented in Fig. 7a. All the curves had a similar process of initial nonlinearity, then linear dominance and final failure. The initial nonlinear was possibly due to the imperfect contact between the facesheets and indenter and supports. Because the lattice sandwich panel finally failed due to the fracture of facesheet, the expression of the bending strength was derived as follow:
f
Pll 4lwt f l cos sin t
(10)
where f was bending strength. Besides, the bending strengths of C/SiC pyramidal LCSPs are given in Fig. 7b. The bending strengths of the LCSPs with the core angles of 45, 60 and 75o were 18.4, 16.1 and 15.1 MPa, respectively. With the core angle increasing from 45 to 75o, the bending strength decreased from the maximum value to 87.5% of the maximum ( 60 ) and 83.2% of the maximum ( 75 ). It had the highest value for the LCSP with 45o core angle. To study the failure mechanism of the LCSPs under three-point bending load, their deformation process were observed and shown in Fig. 8. Bonds crushing failure of the core was observed for all C/SiC pyramidal LCSPs with different core angles. However, for the C/SiC pyramidal LCSPs with 60o core angle, multiple failure modes were observed. With the
13
load increasing, the nearly simultaneous crushing of facesheet and bonds followed the interlayer delamination between the sheet of the core and facesheet, which failed attributing to the weak bonding strength. 5.2 Mechanism maps This subsection provides predictive failure mechanism maps for the C/SiC pyramidal LCSPs based on the geometric parameters and material properties (Elastic modulus and Poisson’s ratio). The dimensions of the core, including the length, width, thickness, and angle, etc. have significant influence on the bending behavior and failure modes of lattice sandwich panel. In constructing the mechanism maps, the length of the core l , determining the height of the core, and the face sheet thickness t f are varied. Herein the study was limited to the configurations with three different core angles. It was assumed that the failure mechanism maps were operated with lowest criterial loads derived in Section 3. Because interlayer delamination mode was predicted by stress components (Eqs. 5 and 6) rather than load and the effective in-plane shear strength of the sandwich panel was not determined, only facesheet crushing or winkling and core member crushing or buckling were illustrated in the failure mechanism maps. The results were plotted in Fig. 9 in terms of normalized parameters of l ll and t f ll . The specific experimental data for each specimen was marked by red pentagrams. Although the core angle varied, the distribution patterns of failure mechanism maps were similar. For the C/SiC pyramidal LCSPs, core member buckling (CB) was a difficult thing to achieve, because it required l ll greater than 0.463. That was to say, core buckling only took place in very thickness lattice sandwich panels. When the face sheet thickness was enough small, face sheet wrinkling (FW) dominated the deformation and failure behaviors of the panels. The probability of face sheet crushing (FC) was small, it needed l ll little than
14
0.01001 45 , 0.01164 60 , 0.116 75 , corresponding t f ll
was
(0.007,0.017), (0.008,0.021) and (0.009,0.024), respectively. As illustrated in Fig.9, core crushing (CC) was most likely to take place, for the dimensions of bending experiments of lattice sandwich panel. The analytical predictions showed well agreement with experimental observation in Fig.8. 5.3 Numerical results Fig. 10 shows the numerically simulated results compared with experimental data. It showed that the numerical simulations gave satisfactory results and agreed well with experimental data. For the LCSPs with core angles of 60 and 75 , the simulated curves could model the mechanical behavior and capture the strength. However, for the LCSP with 45o core angle, we could see that the simulated curve fell off a cliff after reaching a peak value while the experimental curve underwent a rapid fall followed by a rise. The ongoing rising behavior was due to the continuous carrying capacity of the facesheet after the core member fail. In addition, the initial nonlinear behavior of experimental curves was modeled using surface-to-surface contact technique between the facesheets and indenter and supports. The load was borne by the core struts on both sides of the indenters. The maximum von Mises stress occurred near the bonds, due to stress concentration resulting from the geometrical mismatch and deformation incongruity. For the LCSP with a core angle of 45 , interlayer delamination occurred at the bonding location between the sheet of the core and facesheet followed by the failure of bonds. The interlayer delamination occurred firstly at lower right location and then moved to other locations. Therefore, its delamination level was worse than other locations. Similar failure processes were seen for the LCSPs with core angles of 60 and 75 . The difference was that the delamination level was weaker than that of the C/SiC pyramidal LCSP with 45o core angle. In the simulated process, the interlayer delamination
15
behavior only took place at some middle elements but not total destruction of cohesive elements. Therefore, this was why we could not observe obvious interlayer delamination in experiments. The final failure took place at the bonds on the core strut for all lattice sandwich panels. However, further fracture failure in the middle of the facesheet was modeled for the C/SiC pyramidal LCSP with 60o core angle, which agreed with experimental observation.
6. Ashby chart for different materials Fig. 11 presents the Ashby chart of the bending strengths versus density for different materials [38-41], such as metal materials, bulk ceramics, ceramic foams, porous ceramics, metal LCSP and C/SiC LCPS. Aboviously, the bending strength of bulk ceramics are commonly greater than other materials except some alloys. Although the bending strength of C/SiC LCSP is lower than that of bulk ceramics, their density is much higher. Ceramic foams are lighter than C/SiC LCPS, but their bending strengths are also smaller, which makes them only be used for thermal insulation, but not for carrying load. For metla LCPS, their density and bending strength vary greatly. The reason is that metal materials can be 3D printed into lattice structures. However, the strength of these printed materials is weak due to the immature technology. Although some metal LCSP possesses higher bending strength using traditional technology, the density of metal materials is much higher than that of C/SiC composite. In addition, metallic service temperature is lower that C/SiC composites. In summary, C/SiC LCSP provides an effective approach to balance the load bearing capacity and the weight for different materials.
7. Conclusions The bending mechanical behavior of the C/SiC pyramidal LCSPs was investigated in this paper using experimental, theoretically and numerically simulating approaches. The conclusions were summarized as follows:
16
(1) C/SiC pyramidal LCSPs with three different core angles were fabricated by the PIP method and tested under three-point bending load. For C/SiC composite, SiC matrix penetrated into most of the interfibrous pores and the final density reached above 2.0 g/cm3. For C/SiC pyramidal LCSPs, the failure of bonds of the core was commonly observed for all panels. In addition, interlayer delamination between the sheet of the core and facesheet, and facesheet crushing took place for the lattice sandwich panel with 60 inclination angle. (2) Analytical models, including facesheet crushing or wrinkling, core member crushing, core shear failure and interlayer delamination, were established to predict the critical bending load. Failure mechanism maps predicting the relationship between failure mode and dimensionless geometrical parameters were constructed based on these analytical models. The predicted failure modes agreed well with experimental results. We can design the C/SiC pyramidal LCSPs based on the failure mechanism maps. (3) FEA method was used to model the bending response and failure behavior. In the simulated process, the elastic-damage constitutive model was adopted to describe the mechanical behavior of C/SiC composite. The cohesive crack approach was used to model the interlayer delamination behavior between the sheet of the core and the facesheet. Simulated results agreed well with experimental results, and the interlayer delamination behavior occurred before bond failure. The facesheet crushing behavior observed on the LCSP with a core angle of 60 was exactly modeled. Form this work, it is believed that it can help to understand the bending behavior C/SiC pyramidal LCSPs, and to give further insights into the design of lightweight C/SiC structures for thermal protection system application.
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Author contributions Lu Zhang: Investigation; Methodology, Formal analysis, Writing - original draft; Yanfei Chen: Conceptualization, Methodology, Validation, Formal analysis, Funding acquisition, Writing - review & editing; Rujie He: Investigation, Project administration, Formal analysis, Supervision, Funding acquisition; Xuejian Bai: Resources, Data curation; Keqiang Zhang: Resources, Data curation; Shigang Ai: Software, Supervision; Yazheng: Supervision, Project administration; Daining Fang: Conceptualization, Supervision, Project administration .
Conflict of interest form The authors declared that there is no conflict of interest.
Acknowledgments This study was financially supported by the National Natural Science Foundation of China (51772028, 11902034), the Beijing Natural Science Foundation (2182064, 1204035), and the China Postdoctoral Science Foundation (Nos. 2019M650500).
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Figures
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Fig. 1. (a) The assembly process of pyramidal LCSP using 2D T300 carbon fiber cloth: the carbon fiber pyramidal core was fixed by trapezoid blocks on one carbon fiber plate, then the other one was placed on the core, and finally the carbon fiber pyramidal LCSP was pressed by two metal plates; (b) prepared C/SiC pyramidal LCSP, including 6 4 cells.
Fig. 2. Bending test of the C/SiC pyramidal LCSPs with three different inclination angles,
.
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Fig. 3. Schematic diagrams of (a) the unit cell of pyramidal LCSP; (b) bending test; and (c) failure modes, including facesheet crushing, facesheet wrinkling, core member crushing, core shear failure and interlayer delamination.
Fig. 4. Finite element model of bending test of C/SiC pyramidal LCSP.
23
Fig. 5. The relationship between the density, porosity and of weight gain rate (WGR) of prepared C/SiC composite and PIP cycle.
24
Fig. 6. Microstructure of the C/SiC composite: (a) low magnification, and (b) high magnification.
Fig. 7. Bending test of the C/SiC pyramidal LCSPs: (a) displacement-load curves, and (b) bending strength.
25
Fig. 8. Failure modes of the C/SiC pyramidal LCSPs with three different core angles.
26
Fig. 9. Failure mechanism maps for the C/SiC pyramidal LCSPs with three different core angles. [FW=face sheet wrinkling; FC=face sheet crushing; CB= core member buckling;
27
CC=core member crushing.]
Fig. 10. Numerical simulated results compared with experimental data for the C/SiC pyramidal LCSPs with three different core angles.
28
Fig. 11. Ashby chart of the bending properties versus density for the different materials.
29
Table Table 1. Geometric parameters of the C/SiC pyramidal LCSP.
Length
Width
Thickness
Span length
Thickness of the
(mm)
(mm)
(mm)
(mm)
core (mm)
45
139.1
35.2
15.2
104.3
8.2
60
120
35.2
17.0
90.0
10.0
75
96.3
35.2
18.1
72.2
11.1
l (mm)
b (mm)
d (mm)
t (mm)
t f (mm)
16.3
3.8
3.5
1.5
2.0
45
30
GRAPHICAL ABSTRACT
31