CFRP薄壁结构多尺度建模及耐撞性分析

朱国华, 竺森森, 胡珀, 王振, 赵轩

朱国华, 竺森森, 胡珀, 等. CFRP薄壁结构多尺度建模及耐撞性分析[J]. 复合材料学报, 2023, 40(6): 3626-3639. DOI: 10.13801/j.cnki.fhclxb.20220720.002
引用本文: 朱国华, 竺森森, 胡珀, 等. CFRP薄壁结构多尺度建模及耐撞性分析[J]. 复合材料学报, 2023, 40(6): 3626-3639. DOI: 10.13801/j.cnki.fhclxb.20220720.002
ZHU Guohua, ZHU Sensen, HU Po, et al. Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures[J]. Acta Materiae Compositae Sinica, 2023, 40(6): 3626-3639. DOI: 10.13801/j.cnki.fhclxb.20220720.002
Citation: ZHU Guohua, ZHU Sensen, HU Po, et al. Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures[J]. Acta Materiae Compositae Sinica, 2023, 40(6): 3626-3639. DOI: 10.13801/j.cnki.fhclxb.20220720.002

CFRP薄壁结构多尺度建模及耐撞性分析

基金项目: 国家重点研发计划(2021 YFB2501705);国家自然科学基金 (51905042);长安大学中央高校基础研究基金 (300102221201)National Key R&D Program of China (2021YFB2501705); National Natural Science Foundation of China (51905042); The Fundamental Research Funds for the Central Universities, CHD (300102221201)
详细信息
    通讯作者:

    朱国华,博士,副教授,硕士生导师,研究方向为汽车轻量化  E-mail: guohuazhu@chd.edu.cn

  • 中图分类号: TB332

Multi-scale modeling and crashworthiness analysis of CFRP thin-walled structures

  • 摘要: 碳纤维增强树脂基复合材料(CFRP)具有较高的比强度、比刚度及显著的轻量化效果,因此CFRP薄壁结构被作为能量吸收装置广泛应用于工程领域。以单向碳纤维复合材料为研究对象,利用扫描电镜获取其微观胞元结构参数及纤维体积分数,构建能够准确反映其微观形态的代表性体积单元(Representative volume element,RVE),通过加载周期性边界条件及单位载荷,获取材料宏观等效弹性参数,并开展实验验证。随后,开发基于微观力学的失效准则及损伤演化方程,并结合材料力学特点,构建CFRP宏观损伤模型,最终形成一套基于微观失效的多尺度损伤模型。在此基础上,对CFRP薄壁圆管在轴向准静态载荷下的压溃性能进行数值仿真,并与实验结果进行对比,验证了多尺度模型的仿真精度。最后,基于验证后的多尺度有限元模型,研究了碳纤维铺层角度及碳纤维体积分数对CFRP薄壁结构耐撞性的影响。结果表明:铺层角度和碳纤维体积分数对CFRP圆管耐撞性能具有较大影响。
    Abstract: Carbon fiber reinforced plastics (CFRP) are of high specific strength, specific stiffness and significant lightweight effect. Therefore, CFRP thin-walled structures are widely used as energy-absorbing devices in engineering fields. This paper took unidirectional CFRP as research object. The micro-scale structural parameters and fiber volume fraction were obtained by using scanning electron microscope. Then, a representative volume element (RVE) was established, which was capable to accurately reflect its micro morphology. By applying periodic boundary conditions and unit load, the macro equivalent elastic parameters were acquired and then verified by experimental tests. Subsequently, the failure criterion and damage evolution equation based on micromechanics were developed. Combined with the mechanical characteristics of unidirectional CFRP, the macro damage model was developed, and finally forming a set of multi-scale damage model based on micro failure. On this basis, the crashworthiness performance of CFRP thin-walled circular tube under axial quasi-static load was numerically explored, and the numerical results were verified through the crushing test. Based on the verified multi-scale finite element model, the effects of carbon fiber ply angle and carbon fiber volume fraction on the crashworthiness were investi-gated. The results show that the ply angle and carbon fiber volume fraction have great impact on the crashworthiness characteristics of CFRP thin-walled structures.
  • 重金属对水环境的污染是当今面临的最严重的一类环境污染,主要由采矿、冶金、电镀、石油化工和纺织业等行业的发展引起的[1-2]。与有机污染物不同,重金属污染具有不可降解性。未经处理的或未处理完全的含重金属废水排放到环境中,会通过生物累积危害到食物链的各环节,破坏生态平衡。Cd(II)是一种典型的毒性极大的重金属离子,美国环保署将其列为B1类致癌物,对人体的肾脏有极大的危害[3-4]。因此,工业废水中Cd(II)的去除是至关重要的。

    去除水中Cd(II)常用方法有混凝-絮凝、微生物、膜分离、吸附等。其中吸附法因其效果好、成本低、工艺简单等优点成为最常用的方法[5-8]。海藻酸钠(SA)是一种天然多糖,可与CaCl2溶液交联形成一种吸附性能极好的水凝胶材料—海藻酸钙CaAlg(CA)。以CA为基材的小球在重金属的吸附方面效果显著[9]。氧化石墨烯(GO)是石墨多次化学氧化后得到的含有大量羟基和羧基的常见改性材料。它具有极高的比表面积和电负性,这些特性也使其成为一种理想的重金属离子吸附材料[10]。将SA、致孔剂和GO混合后再与CaCl2交联,GO的含氧基团也能参与到交联过程,从而使三者形成有机统一的多孔材料,而且各组分间的相互作用更强,这对其吸附性能和力学性能都有很大的提升。

    在吸附过程,相对于球型吸附剂,膜上的吸附位点能够更准而快地捕捉重金属离子[11]。将GO与致孔剂共混在SA溶液中,与CaCl2交联制得的GO/CA水凝胶复合膜将会是一种优良的重金属离子吸附剂。由于SA良好的成膜性[12],此复合膜还可用作膜过滤技术。将其吸附性能与截留性能结合,从而可在实际水处理工程中达到更好的应用效果。目前还没有关于它对重金属离子吸附性能的相关公开报道。

    本文将制备一种新型的GO/CA复合膜材料,用于探究其对Cd(II)的吸附性能和吸附机制。将吸附前后的GO/CA水凝胶复合膜进行表征;并探究常见的变量因素对其吸附容量的影响。还将引入吸附动力学、吸附等温线来分析其吸附机制。

    海藻酸纳(Sodium alginate,分析纯)、硝酸镉(Cd(NO3)2,分析纯)、HNO3(分析纯),购于国药化学试剂有限公司;天然鳞片石墨,购于南京先丰纳米有限公司;尿素(Urea)、CaCl2、KMnO4、NaNO3 H2O2,分析纯,均购于天津科密欧化学试剂有限公司;浓HCl、浓H2SO4,分析纯,均购于成都科隆化学品有限公司。

    将2.5 g SA和2.5 g尿素加入100 mL超声均匀的GO(制备参考文献[13])溶液(0.3 wt%),室温下用磁力搅拌器以400 r/min的速率搅拌36 h。搅拌均匀的铸膜液在室温下静置36 h以脱除气泡。将铸膜液倒在玻璃板上,用刮膜棒将其铺平后将玻璃板平行地放入2.5 wt%的CaCl2溶液中交联。膜从玻璃板脱落后取出玻璃板。复合膜在48 h后取出,以达到交联完全和尿素溶出的目的。将交联完全的膜用去离子水洗脱后即可置于1 wt%的CaCl2溶液中保存备用。为制备纯CA水凝胶膜,将2.5 g SA和2.5 g尿素加入100 mL去离子水中,其余步骤同上。

    用扫描电镜(SEM,JMS6510LV, Japan)和透射电镜(TEM, JEM-2100, Japan)来表征GO/CA水凝胶复合膜是否制备成功;将GO/CA水凝胶复合膜裁成10 cm×1 cm的样本条,用拉力测定仪(电子单纱强力仪,HD021NS,南通宏大实验仪器有限公司)进行力学性能测试,每个样品测10次,取平均值;用称重法计算GO/CA水凝胶复合膜的平均孔径:先将膜片浸没在去离子水中24 h,取出后用滤纸擦干表面水分。将此湿膜片称重,通过称重法[13]确定其孔隙率ε,再用Guernout-Elford-Ferry公式[13]计算平均孔径r;两种复合膜的水通量使用小型平板纳滤错流过滤系统在25℃、0.1 MPa的条件下进行测定。试验前,在0.15 MPa的压力下用去离子水预压,用通量计算公式[13]计算通量;GO/CA水凝胶复合膜的表面官能团用傅里叶衰减全反射红外光谱仪(FTIR-ATR, Thermoelectroncorp, iS50, 美国)测定。

    本文将探究溶液pH、Cd(II)初始离子浓度、接触时间、温度等因素对GO/CA水凝胶复合膜吸附性能的影响。溶液的pH用0.1 mol/L HNO3溶液调节。每组实验均将300 mL Cd(NO3)2溶液置于500 ml的烧杯中,然后加入复合膜片0.06 g,用保鲜膜封存静置。在固定时间,每次从同一位置的上层溶液用滴管吸取5 mL的样品,并测定其Cd(II)浓度。达到吸附平衡后,用镊子将膜片夹出。Cd(II)在膜上的吸附量按下式计算:

    Vnt(i)=Vnt(i1)5
    (1)
    Qnt=ni=1(Cnt(i1)Cnt(i))Vnt(i1)m
    (2)

    式中:Qnt是在时间t的吸附容量(mg·g−1);Cnt是第i次采样时的Cd(II)浓度(mg·L−1);Vnt(i)是第i次取样时Cd(NO3)2溶液的体积(mL);m是用于吸附的GO/CA水凝胶复合膜的重量(g)。溶液中的Cd(II)浓度由电感耦合等离子体发射光谱仪(ICP-5000,聚光科技(杭州)股份有限公司)测定。

    为探究pH的影响,将溶液pH分别调至3、4、5、6、7,在初始离子浓度为80 mg·L−1、温度为318 K的条件下进行吸附;为探究GO的影响,在pH=7、288 K、初始离子浓度50 mg·L−1的条件下,分别将0.06 g的CA膜和GO/CA水凝胶复合膜加入Cd(NO3)2溶液进行静态吸附实验;为探究初始离子浓度的影响,在pH=7、318 K的条件下,配制梯度浓度(10、40、80 mg·L−1)的溶液进行静态吸附实验;为探究温度和接触时间的影响,在初始离子浓度为50 mg·L−1、pH=7的条件下,设置三组温度(288 K、303 K、318 K)的静态吸附实验;为探究GO/CA水凝胶复合膜的再生性,在pH=7,初始浓度为80 mg·L−1的条件下进行5个吸附-解吸循环。选取0.4 mol/L HCl溶液作为洗脱剂,洗脱后用去离子水冲洗。置于CaCl2溶液中12 h恢复强度后,进入下一循环。

    为探究吸附过程的动力学规律,引入伪一级、伪二级、Elovich动力学模型[1]和颗粒内扩散模型[2];引入Freundlich和Langmuir模型[2]对吸附过程进行拟合来探究Cd(II)在GO/CA水凝胶复合膜上的平衡吸附;由复合膜本身的性质及其对重金属离子的吸附特点可知,吸附过程存在离子交换。定量检测吸附平衡后的Cd(NO3)2溶液,确定溶液中Ca(II)的增加量,来判定Cd(II)与Ca(II)的离子交换在吸附中所占的比例。RLN分别为单独定义的一个无量纲常数和Freundlich液相吸附等温指数。

    用傅里叶红外衰减全反射红外光谱仪定性表征吸附Cd(II)前后的GO/CA水凝胶复合膜。对吸附Cd(II)前后的GO/CA水凝胶复合膜喷金处理后进行X射线能谱分析(XPS K-Alpha Thermo, AlKα)。

    GO/CA水凝胶复合膜的表面形貌和微观结构如图1(a)图1(b)所示。从图1(a)可以看出,GO/CA水凝胶复合膜表面平整,有烘干留下的褶皱。从图1(b)可以看出,在水凝胶均匀的网络骨架结构上有片层状的GO,两者均匀地结合,说明成功制备了GO/CA水凝胶复合膜。

    图  1  氧化石墨烯/海藻酸钙水凝胶( GO/CA)复合膜的表面形貌(a)、透视特征(b)及官能团的变化(c)
    Figure  1.  Surface morphology (a), perspective characteristics (b) and functional groups (c) of graphene oxide/calcium alginate hydrogel( GO/CA) hydrogel composite membrane

    纯CA膜和GO/CA水凝胶复合膜的红外光谱如图1(c)所示。可见,加入GO后,膜表面官能团的类型未发生变化。在3 300 cm−1附近的特征峰为—OH的伸缩振动峰,1 600和1 400 cm−1附近的特征峰为羧酸盐的反对称和对称伸缩峰,1 300 cm−1附近为C—H的伸缩振动峰,1 000 cm−1附近的峰为C—O的伸缩振动峰。而对于GO,羧基的特征峰位于1 723和1 618 cm−1。以上结果也说明了加入到铸膜液中的GO,参与了制膜过程的交联反应,从而使其由羧基状态转化成了羧酸盐状态。

    表1是CA和GO/CA水凝复合膜的渗透性能。可以看出,加入GO后,膜的孔隙率和平均孔径都明显地增大。这是由于加入GO使水凝胶骨架之间有更大的支撑空间,进而膜的内部结构更加立体。内部孔隙率的增加也提升了膜的输水性能,从而使膜的水通量增大。

    表  1  CA膜和GO/CA水凝复合膜的渗透性能
    Table  1.  Permeability of CA membrane and GO/CA hydrogel composite membrane
    MembraneMean pore size/nmPoriness/%Water flux/(L·m-2h-1)
    CA10.686.514.7
    GO/CA12.690.118.1
    下载: 导出CSV 
    | 显示表格

    CA膜和GO/CA水凝复合膜的力学性能如表2所示。可以看出GO的加入明显提升了其机械强度。这是由于GO加入后,三者相互交联,形成比CA膜更稳定的结构。

    表  2  CA膜和GO/CA水凝复合膜的力学性能
    Table  2.  Mechanical properties of the CA membrane and GO/CA hydrogel composite membrane
    MembraneElongation at break/%Fracture energy/(kJ·m−2)Stress/MPa
    CA9534914
    GO/CA143651 725
    下载: 导出CSV 
    | 显示表格

    图2(a)是CA膜和GO/CA水凝胶复合膜吸附性能的比较。可以看出,在添加GO后,膜的吸附性能明显提升。由于加入GO,膜表面有了更多的吸附位点(含氧基团),提高了膜的吸附能力。且加入GO会增大膜的孔隙率,为吸附提供更大的空间。

    图  2  GO (a)、pH ((b)、(c))、初始浓度(d)、温度(e)和循环次数(f)对GO/CA 膜吸附容量的影响
    Figure  2.  Effect of GO (a), pH ((b), (c)), initial concentration (d), temperature (e), cycle times (f) on adsorption capacity of GO/CA hydrogel composite membrane

    溶液初始pH值对GO/CA水凝胶复合膜吸附性能的影响如图2(b)所示。可以看出在低pH时,吸附效果较差。随pH升高,吸附容量逐渐增大,在pH为6~7时保持稳定。这是由于pH影响膜的表面电性。GO/CA水凝胶复合膜表面有大量羧基等含氧基团。在溶液中H+浓度较大时(pH<pKa (3.38~3.65)[14]),含氧基团被质子化,使膜表面带正电。这严重影响带正电的重金属离子与膜的静电吸引作用,阻碍了吸附反应。随着pH升高,膜表面质子化逐渐消失,负电性恢复,吸附容量也逐渐增加,在pH=6~7时达到稳定。从Cd(II)离子种类分布(图2(c))可看出,pH升到弱碱性时,Cd(II)的水解增强,形成氢氧化物甚至会出现沉淀,这会影响吸附反应的进行。因此pH=6~7是最适宜的条件。

    图2(d)为Cd(II)初始浓度不同时GO/CA水凝胶复合膜的吸附量。可以看出吸附量与浓度成正相关。由于离子浓度较大,溶液对金属离子会产生更强的驱动力[15]。较大的离子浓度,还会使离子与GO/CA水凝胶复合膜之间有更大的碰撞几率和接触密度[16]。这些是吸附的有利因素,因此Cd(II)初始浓度与吸附量呈正相关。

    图2(e)为不同温度下时间与吸附量的关系。可以看出,吸附量随时间先迅速增长后缓慢增长,最后趋于稳定。这是由于吸附初期离子浓度大且空余吸附位点多。随吸附位点逐渐被占据,吸附速度减缓,在20 h达到平衡。由此可认为吸附最佳时间为20 h。还可知,吸附量与温度正相关。但当温度上升到一定值后其影响变小,这是由于膜表面吸附位点数量固定,吸附位点达到饱和,吸附量就基本保持稳定,不会再随温度升高而增大。

    图2(f)所示,解吸次数对GO/CA水凝胶复合膜吸附Cd(II)有一定的影响,但在5次吸附-解吸循环后仍能保持70%的吸附量,说明复合膜具有可重复利用性。在经过吸附-解吸循环后,膜的吸附量下降的原因是:吸附过程中,不可逆吸附占据一定的比例,使这部分吸附位点难以循环利用;且解吸过程具有不完全性,这也使膜在再吸附过程失去一部分吸附能力,使吸附量下降。

    初始浓度C0不同时,GO/CA水凝胶复合膜吸附Cd(II)动力学拟合结果如图3(a)~3(d)表3所示。在低浓度下,吸附过程与伪一级动力学模型更一致。拟合优度R2更接近于1,平衡吸附量Qe拟合值更接近于实验数据。而Cd(II)浓度增加到40 mg·L−1以上时,吸附过程则更符合伪二级吸附动力学模型。图3(d)是颗粒内扩散模型结果,可以看出复合膜吸附Cd(II)明显地分为了三个阶段:表面吸附阶段、颗粒内部扩散阶段和吸附平衡阶段。其中表面吸附阶段的反应时长为4 h,颗粒内扩散阶段的反应时长为16 h,因此第二阶段被认为是吸附过程的速率控制阶段,说明此吸附过程是颗粒内扩散为主的三阶段吸附[17]

    图  3  GO/CA水凝复合膜吸附动力学((a)~(d))及等温线((e)、(f))模型拟合图
    Figure  3.  Adsorption kinetics((a)-(d))and isotherm ((e), (f)) model fitting diagram of GO/CA hydrogel composite membrane
    表  3  Cd(II)的初始浓度C0不同时GO/CA水凝复合膜吸附性能的动力学模型拟合参数
    Table  3.  Kinetic model parameters of GO/CA hydrogel composite membrane adsorption at different initial concentration C0 of Cd(II)
    C0/(mg·L−1)Pseudo-first order kinetic modelPseudo-second order kinetic modelElovich model
    k1/min−1Qe/(mg·g−1)R2k2/min−1Qe/(mg·g−1)R2ABR2
    100.1530 51.370.99990.0826 57.280.987434.53−4.4970.964 1
    400.3131140.00.99190.0116147.50.9993113.7−7.5790.9785
    800.4497211.90.98040.0066224.10.9993135.3−22.170.9714
    Notes: C0—Initial concentration of Cd(II); R2—Goodness; Qe—Adsorption capacity at adsorption equilibrium; k1, k2 and A—Constant of kinetic models, respectively; B—Coefficient of elovich kinetic models.
    下载: 导出CSV 
    | 显示表格

    图3(e)3(f)表4是不同温度下GO/CA水凝胶复合膜吸附Cd(II)等温线拟合结果。可以看出,此吸附过程更符合Langmuir模型,由于拟合优度R2更接近于1,说明吸附过程属于单层吸附[18]。计算得到在288、303和318 K时RL均在0~1范围内,说明GO/CA水凝胶复合膜吸附Cd(II)是有利吸附。Freundlich模型的R2都大于0.9,其参数有较大参考价值。通过拟合得到的N分别为1.79、2.77和3.15,可判断吸附过程属于物理吸附。

    表  4  GO/CA水凝胶复合膜吸附Cd(II)的吸附等温线模型参数
    Table  4.  Isothermal adsorption model parameters of Cd(II) adsorbed by GO/CA hydrogel composite membrane
    Temper-
    ature/K
    Freundlich isothermLangmuir isotherm
    kfNR2klQm/(mg·g−1)R2
    28813.811.7870.94450.176685.400.9914
    30347.992.7700.96180.2168161.80.9952
    31847.673.1470.95890.3146173.60.9981
    Notes: kf—Capacity factor of Freundlich; N—Liquid phase adsorption isotherm index of Freundlich; k1—Langmuir constant of affinity point; Qm—Adsorption capacity of single layer.
    下载: 导出CSV 
    | 显示表格

    在吸附达到平衡后,测定溶液中出现的Ca(II)的浓度为2.32 mg·L−1。由此可知离子交换作用在吸附过程占了较大的比重,经计算得到物理作用力吸附、离子交换作用及溶液中剩余的未被吸附的Cd(II)的比例分别是59.94%、32.33%、7.72%。

    图4是吸附Cd(II)前后GO/CA水凝胶复合膜的FTIR图谱。在3 232、1 586、1 407和1 019 cm−1处的四个特征峰分别代表—OH、羧基上的—C=O和—C—OH及C—O的伸缩振动峰。证明膜表面有大量羟基和羧基等亲水基团。吸附后,四个特征峰的位置分别移动到3 208、1 577、1 408和1 023 cm−1,强度也轻微地降低。没有新的特征峰出现,说明吸附过程发生了配位反应或离子交换[19-20]。这表明化学吸附可能占有一定的比重,但Cd(II)在GO/CA水凝胶复合膜上的吸附仍然以物理吸附作用为主。

    图  4  GO/CA水凝胶复合膜的FTIR图谱
    Figure  4.  FTIR spectra of GO/CA hydrogel composite membrane

    图5是GO/CA水凝胶复合膜吸附Cd(II)前后的XPS能谱。图5(a)为吸附前后复合膜的XPS全谱。可以看出,吸附重金属离子后,Ca2+的吸收峰强度减弱,且在405 eV出现新的吸收峰,即Cd 3d的吸收峰图5(b)。证明吸附反应发生,也证明了Ca2+与Cd2+发生了离子交换作用。图5(c)为吸附前后膜的C元素的XPS拟合分峰结果。吸附后,羧基和羟基的强度减弱,峰位置也发生变化,说明复合膜中的羟基、羧基等基团参与了吸附过程,与金属离子形成了配合物。

    图  5  GO/CA水凝胶复合膜吸附Cd(II)的XPS能谱
    Figure  5.  XPS spectra of GO/CA hydrogel composite membrane adsorption of Cd(II)

    (1)成功制备了氧化石墨烯(GO)/海藻酸钙(CA)水凝胶复合膜。加入GO提高了GO/CA复合膜的力学性能、平均孔径、水通量及吸附性能。复合膜对Cd(II)的吸附性能良好,拟合得到的最大吸附量为173.61 mg·g−1,平衡时间为20 h。最适pH为6~7,吸附量与初始离子浓度、接触时间、温度都成正相关。

    (2) GO/CA水凝胶复合膜对重金属离子Cd(II)的吸附过程符合Langmuir吸附等温线模型,属于单层有利的物理吸附。在低离子浓度,吸附过程遵循伪一级吸附动力学,在较高浓度遵循伪二级吸附动力学,是以颗粒内扩散为控速步骤的三阶段吸附。

    (3)经过5个吸附-解吸循环,GO/CA水凝胶复合膜对Cd(II)的吸附量仍能保持原吸附量的70%,证明了其可重复利用性。

  • 图  1   碳纤维增强树脂基复合材料(CFRP)薄壁管制造工艺流程图

    Figure  1.   Manufacturing process of carbon fiber reinforced plastics (CFRP) thin-walled tubes

    图  2   试验现场布置图

    Figure  2.   Experimental setup

    图  3   CFRP的截面SEM图像

    Figure  3.   SEM images of cross section for CFRP

    图  4   (a) 单向碳纤维复合材料六面体代表性体积单元(RVE)模型;(b) RVE参考点

    Figure  4.   (a) Hexagonal representative volume element (RVE) model of UD-CFRP; (b) Reference points at RVE

    F, M—Fiber and matrix, respectively; Number—Selection order of reference points; a=c=1; b= 3

    图  5   多尺度分析框架

    Figure  5.   Multiscale analysis framework

    图  6   多尺度模型的数值算法流程

    Figure  6.   Numerical calculation procedure for the multi-scale model

    SAFs—Stress amplification factors; RVEs—Representative volume elements

    图  7   CFRP薄壁结构单位应力施加

    Figure  7.   Application of unit macro stress for CFRP thin-walled structure

    图  8   CFRP薄壁结构RVE模型在宏观六工况下的微观应力分布

    Figure  8.   Microscopic stress distribution for RVEs of CFRP thin-walled structure under six loading cases

    图  9   CFRP薄壁结构0°拉伸试件试验结果

    Figure  9.   Experimental results of 0° samples of CFRP thin-walled structure

    图  10   CFRP薄壁结构90°拉伸试件试验结果

    Figure  10.   Experimental results of 90 ° samples of CFRP thin-walled structure

    图  11   CFRP薄壁结构有限元模型

    Figure  11.   Finite element model of CFRP thin-walled structure

    图  12   网格大小敏感性分析

    Figure  12.   Mesh size sensitivity analysis

    图  13   CFRP薄壁结构实验与仿真载荷-位移对比曲线

    Figure  13.   Comparison of load-displacement curves between experiment and simulation for CFRP thin-walled structure

    图  14   CFRP薄壁结构变形结果对比

    Figure  14.   Comparison of deformation modes for CFRP thin-walled structure

    图  15   不同铺层角度的CFRP圆管载荷-位移曲线

    Figure  15.   Comparison of load-displacement curves for CFRP tubes with different fiber orientations

    图  16   不同铺层角度CFRP薄壁圆管轴向压溃后的变形结果

    Figure  16.   Crushing process of CFRP tubes with different fiber orientations

    图  17   不同体积分数的CFRP薄壁圆管载荷-位移曲线

    Figure  17.   Comparison of load-displacement curves for CFRP tubes with different fiber volume fractions

    图  18   不同纤维体积分数CFRP薄壁圆管的变形过程

    Figure  18.   Deformation process of CFRP thin-walled circular tubes with different fiber volume fractions

    表  1   T300碳纤维力学性能

    Table  1   Mechanical properties of T300 carbon fiber

    Mechanical propertyValue
    Ef1/GPa185
    Ef2=Ef3/GPa13
    Gf12=Gf13/GPa15
    Gf23/GPa9
    νf12=νf130.28
    νf230.35
    Notes: Ef1, Ef2, Ef3, Gf12, Gf13, and G—Elastic moduli of T300 carbon fiber fibers in the 1, 2, 3, 12, 13, and 23 directions, respectively; vf12, vf13, and vf23—Poisson's ratios in the 12, 13, and 23 directions, respectively.
    下载: 导出CSV

    表  2   基体力学性能

    Table  2   Mechanical properties of matrix

    Mechanical propertyValue
    Em/GPa2.6
    ν0.33
    Note: Em and v—Micro elastic modulus and Poisson's ratio of the matrix, respectively.
    下载: 导出CSV

    表  3   CFRP薄壁结构宏观单位应力加载

    Table  3   Appling macro unit stress of CFRP thin-walled structure

    n¯σ1¯σ2¯σ3¯τ12¯τ23¯τ13
    1100000
    2010000
    3001000
    4000100
    5000010
    6000001
    Notes: ¯σ1, ¯σ2 and ¯σ3—Macro-stress in the 1, 2 and 3 direction of CFRP, respectively; ¯τ12 , ¯τ23, ¯τ13—Macro shear stress in the 12, 23 and 13 direction of CFRP, respectively.
    下载: 导出CSV

    表  4   CFRP薄壁结构宏观弹性参数计算方法

    Table  4   Calculation method of macro elastic parameters for CFRP thin-walled structure

    Loading caseLoading conditionCalculation formula
    1¯σ1=1E1=¯σ1ˉε1υ12=ˉε2ˉε1υ13=ˉε3ˉε1
    2¯σ2=1E2=¯σ2ˉε2υ21=ˉε1ˉε2υ23=ˉε3ˉε2
    3¯σ3=1E3=¯σ3ˉε3υ31=ˉε1ˉε3υ32=ˉε2ˉε3
    4¯τ12=1G12=¯τ12ˉγ12
    5¯τ23=1G23=¯τ23ˉγ23
    6¯τ13=1G13=¯τ13ˉγ13
    Notes: E1, E2 and E3—Macroscopic elastic modulus in the 1, 2 and 3 direction of CFRP, respectively; G12, G23 and G13—Macroscopic shear modulus in the 12, 23 and 13 direction of CFRP, respectively; ˉυij (i, j=1, 2, 3)—Poisson's ratio of CFRP in the ij direction; ˉεi(i=1, 2, 3)—Strain of CFRP in the i direction; ˉγij (i, j=1, 2, 3)—Strain of CFRP in the ij direction.
    下载: 导出CSV

    表  5   CFRP弹性参数预测结果与试验结果对比

    Table  5   Comparison of CFRP elastic parameters between numerical and experimental results

    PropertyE1
    /GPa
    E2=E3/GPaG12=G13/GPaG23
    /GPa
    υ12=υ13υ23
    Test131.57.60.29
    RVE132.67.54.33.50.290.39
    Error/%2.139.210
    下载: 导出CSV

    表  6   CFRP多尺度损伤模型输入参数

    Table  6   Input parameters of CFRP multi-scale damage model

    ParameterValueParameterValue
    E1/MPa 132600 Ef1/MPa 185000
    E2/MPa 7500 Ef2/MPa 13000
    E3/MPa 7500 X0,Tf/MPa 3470
    ν12 0.29 X0,Cf/MPa 2100
    ν13 0.29 Em/MPa 2600
    ν23 0.39 Y0,Tm/MPa 77
    G12/MPa 4300 Y0,Cm/MPa 121
    G13/MPa 4300 γ 1.5
    G23/MPa 3500 ρ/(t·mm−3) 1.4×10−9
    Notes: X0,Tf and X0,Cf —Longitudinal tensile strength and compressive strength of T300 fiber, respectively; Y0,Tm and Y0,Cm—Final tensile strength and compressive strength of matrix, respectively; γ—Damage shape parameter of matrix; p—Beta damping parameter of CFRP.
    下载: 导出CSV

    表  7   CFRP层间失效模型输入参数

    Table  7   Input parameters of CFRP inter-laminar failure model

    DescriptionVariableValue
    Damage initiation/MPat0n49.2
    t0s59.5
    t0t59.5
    Fracture energies/(J·m−2)GCn490
    GCs1060
    GCt1060
    BKη2.284
    Notes: t0n—Maximum nominal stress in the normal-only mode; t0s—Maximum nominal stress in the first shear direction (for a mode that involves separation only in this direction); t0t—Maximum nominal stress in the second shear direction (for a mode that involves separation only in this direction); GCn—Ttype I critical fracture energies in n direction; GCs— Type II critical fracture energies in n direction; GCt—Critical fracture energies in t direction; η—A bonding attribute parameter.
    下载: 导出CSV

    表  8   CFRP薄壁结构耐撞性能指标结果对比

    Table  8   Comparison of crashworthiness index results for CFRP thin-walled structure

    PropertyFp/kNWe/kJWs/(J·g−1)Fm/kNEc
    Experimental 35.0 2.230 48.02 27.88 0.80
    Simulation 37.8 2.218 47.76 27.73 0.73
    Error/% 8 0.54 0.54 0.5 7.9
    Notes: Fp—Maximum peak force that occurs during the entire crushing process; We—Total energy absorbed by the structural component during the impact process; Ws—Amount of energy absorbed by energy absorbing structure per unit mass; Fm—Average force is the energy absorbed during the impact process per unit distance; Ec—Ratio of the average force to the maximum peak force.
    下载: 导出CSV

    表  9   不同铺层角度的CFRP薄壁圆管耐撞性能指标结果

    Table  9   Crashworthiness index results of CFRP tubes with different fiber orientations

    Ply angleFp/kNWe/JWs/(J·g−1)Fm/kNEc
    [0°]831.6170336.721.30.674
    [±15°]432.9165335.620.70.629
    [±30°]433.4175437.821.90.656
    [±45°]434.7189940.923.70.683
    [±60°]438.3231649.929.00.757
    [±75°]442.9249653.731.20.727
    [90°]842.4223648.128.00.660
    下载: 导出CSV

    表  10   不同体积分数的CFRP薄壁圆管耐撞性能指标结果

    Table  10   Crashworthiness indicators of CFRP tubes with different volume fractions

    Volume fraction/vol%m/gFp/kNWe/JWs/(J·g−1)Fm/kNEc
    3038.9529.8164942.320.60.692
    5042.5234.8193345.524.20.694
    7246.4437.8221847.827.70.733
    8849.5639.9249450.331.20.781
    Note: m—Mass of carbon fiber.
    下载: 导出CSV
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  • 收稿日期:  2022-06-06
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