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目录 contents

    摘要

    采用三维Hashin准则作为纤维束损伤判据,根据材料不同损伤模式制定相应的材料性能退化方案,并考虑应变率效应对材料的强度性能进行修正,建立含孔复合材料层合板的渐进损伤分析模型,模拟材料在不同应变率下的损伤破坏过程。通过动态拉伸试验,获得材料在不同应变率下的载荷-位移关系及孔边不同位置的时间-应变关系,讨论了应变率对材料拉伸性能的影响及试件孔边的应力集中情况。有限元分析结果与试验数据相一致,证明了本文所提出分析模型的正确性和有效性。

    Abstract

    Three‑dimensional Hashin criterion is used as the damage criterion for fiber bundle, and the corresponding material degradation programme is formulated according to the different damage modes of the material. Morever, the strength performance of the material is modified considering the strain rate effect. The progressive damage analysis model of the composite laminate with hole is established to simulate the damage failure process of the material under different strain rates. Through dynamic tensile tests, the load-displacement curves of the material at different strain rates and the time-strain curves at different positions of the hole edge are obtained. The influence of strain rate on the tensile properties of the material and the stress concentration at the hole edge of the specimen are discussed. The finite element analysis results are consistent with the experimental data, which proves the correctness and validity of the analysis model proposed in this paper.

    纤维增强树脂基复合材料凭借高比强度、高比模量、耐高温以及可设计性强等出色的综合性能,已被大量运用于航空航天、国防军工以及交通运输、化工和建筑等领[1,2,3,4]。在实际应用中,出于结构连接的需要,不可避免地对层合板进行开孔等操作,这破坏了材料自身的连续性,降低了结构强[5,6,7]。研究显示,开孔使某船用层合板的强度下降了40%~60%[8]。而运用在航空航天、国防军工以及交通领域的结构,往往在很短的时间内承受极大的应力,由于复合材料存在应变率效应的问题,其破坏形式与应变率密切相[9,10]。因此,同时考虑以上两个方面的因素,准确地预测开孔复合材料在不同应变率下的应力分布和失效情况,对其工程应用有着重要的应用价值。

    自Hayes和Harding[11,12]发现多数情况下复合材料的力学性能与应变率相关,国内外一些研究工作者便致力于不同应变率下复合材料力学性能研究。Kawata和Harding[13,14]分别对玻璃纤维和碳纤维织物进行了冲击拉伸试验,结果表明材料的力学性能有显著的应变率强化效应。Wang[15]结合单向玻璃纤维增强复合材料在准静态约80 s-1下的应变率测试结果提出了一种粘弹性本构模型。Hansun[16]采用高速测试系统研究了玻璃纤维平纹布增强复合材料在中等应变率下的力学行为。吴健[17]通过恒定应变率下的面内剪切性能试验研究,建立了一种单向玻璃纤维增强环氧树脂基复合材料在中等应变率下的剪切本构模型。

    渐进失效分析的方法最先由Petit和Waddoups[18]提出来计算复合材料层合板的失效载荷,他们采用经典层合板理论计算应力分布,通过刚度矩阵出现奇异或对角线项为负来判断层合板出现损伤,但没有使用失效准则和刚度退化。随后不少研究工作者开始采用渐进失效的方法。Sleight[19]利用NASA的有限元软件COMET建立二维有限元模型,只考虑纤维断裂和基体开裂,分别使用二维的Hashin准则和Christensen准则,计算了石墨环氧树脂基层合板,并与试验值进行了比较;Chang[20]采用Yamada-Sun失效准则,建立二维模型计算对称铺层的带孔层合板失效载荷,但和试验值相比误差较大。后来,Tolson和Reddy[21,22]采用三维渐进失效的方法预测不含损伤的复合材料层合板的静强度,但对某个方向的应力进行了简化或对损伤模式的探讨不够深入。石晓朋[23]基于Hashin损伤准则建立了一种复合材料加筋壁板低速冲击模型,有效分析了接触力、加筋壁板吸收能量和损伤散逸能对冲击响应的影响。昌磊[24]结合改进的三维Hashin准则提出了适用于三维模型的刚度退化方案,但没有考虑应变率的影响。

    本文借助ABAQUS软件,采用三维Hashin准则作为纤维束的损伤起始判据,同时考虑4种失效模式,即纤维拉伸损伤、纤维压缩损伤、基体拉伸损伤以及基体压缩损伤,根据不同损伤模式引入相应的刚度折减方案,并考虑应变率效应对材料的强度性能进行修正,通过嵌入自行编写的用户定义材料子程序VUMAT,建立带孔复合材料层合板的渐进损伤有限元分析模型,模拟材料在不同加载速率下的拉伸损伤及破坏过程,并通过3种不同加载速率下的冲击拉伸试验对模拟结果进行验证。

  • 1 动态拉伸有限元模拟

    1
  • 1.1 本构模型

    1.1

    典型的层合复合材料属于正交各向异性材料,当用1,2,3轴分别表示xyz轴并把应力应变分量简写后,其材料满足的本构关系[25]

    σxσyσzσyzσzxσxy=σ1σ2σ3σ4σ5σ6=
    C11C12C13000C21C22C23000C31C32C33000000C44000000C55000000C66ε1ε2ε3ε4ε5ε6
    (1)

    式中:Cij表示刚度矩形分量;i,j = 1~6;σ1 ~ σ6为应力分量;ε1 ~ ε6为应变分量。

    C11=1-ν23ν32E2E3ΔC12=ν12+ν13ν32E2E3Δ=ν21+ν31ν23E1E3ΔC13=ν13+ν12ν23E2E3Δ=ν31+ν21ν32E1E2ΔC22=1-ν13ν31E1E3ΔC23=ν23+ν21ν13E1E3Δ=ν32+ν12ν31E1E2ΔC33=1-ν12ν21E1E2ΔC44=G23,C55=G13,C66=G12Δ=1-ν12ν21-ν23ν32-ν13ν31-2ν12ν23ν31E1E2E3
    (2)

    式中:E1E2E3分别为x轴,y轴,z轴方向的拉压模量;G12G13G23分别为xy方向,xz方向,yz方向的剪切模量;ν12ν13ν23分别为xy方向,xz方向,yz方向的泊松比。

  • 1.2 损伤判据

    1.2

    相关研究表[26,27]:复合材料某些破坏形式(如纤维断裂、层间分层和纤基脱粘等)在动载荷和静载荷下具有相同的特征,即复合材料的失效机制与应变率不相关。因此在考虑应变率效应的分析中可以借鉴准静态分析下的失效准则。

    三维Hashin失效准[28]已被众多科研工作[29,30,31]成功发展并应用于复合材料层合板的损伤破坏分析。其基本思想是将损伤分为纤维损伤和基体损伤,考虑以下几种典型的失效模式。

    纤维拉伸破坏(σ11 ≥ 0)

    FfT=σ11XT2+σ122+σ132SC2=1
    (3)

    纤维压缩破坏(σ11<0)

    FfC=σ11XC2=1
    (4)

    基体拉伸破坏(σ2233 ≥ 0)

    FmT=σ22+σ33YT2+σ232-σ22σ33ST2+σ122+σ132SC2=1
    (5)

    基体压缩破坏(σ2233<0)

    FmC=σ22+σ332ST2+YC2SC2-1σ22+σ33YC+σ232-σ22σ33ST2+σ122+σ132SC2=1
    (6)

    式中:XTXCYTYCSTSC分别为轴向拉伸、轴向压缩、横向拉伸、横向压缩、横向剪切和轴向剪切强度。

    单向复合材料的极限强度会随应变率的增加而增[32,33],本文考虑应变率效应通过式(7)对玻璃纤维/环氧树脂单向复合材料各项强度指标进行修正,即有

    S=S01+Clnε˙ε˙0
    (7)

    式中:S0为参考应变率下的参考强度值;S为当前应变率下的强度值;C为应变率硬化修正系数。

  • 1.3 损伤模型

    1.3

    复合材料在发生损伤到完全破坏失效是一个逐渐累积的过程,经Hashin损伤判据判断失效之后,再借鉴Matzenmiller[34]的研究成果,引入损伤因子,相应的损伤刚度矩阵C(d)可表示为

    C(d)=1Δ
    dfC11dfdmC12dfdmC13000dmC22dmC23000C33000dmC4400dfC550dfdmC66
    (8)

    式中:ΔCiji,j = 1~6)同第1小节;df=(1-dft)(1-dfc)为纤维破坏的全局损伤变量,dftdfc 分别为纤维拉伸和纤维压缩对应的损伤因子;dm=(1-dmt)(1-dmc)为基体破坏的全局损伤变量,dmtdmc分别为基体拉伸和基体压缩对应的损伤因子。

  • 1.4 分析流程

    1.4

    ABAQUS为用户提供了UMAT和VUMAT两种用户材料子程序接口,分别适用于隐式和显示求解模块。本文研究的是应变率对复合材料层合板拉伸性能的影响,所以采用ABAQUS/EXPLICIT求解器比较合适。根据上述的本构模型、损伤判据、刚度退化方案以及应变率修正编写VUMAT子程序的流程图如图1所示。

    图1
                            分析流程

    图1 分析流程

    Fig.1 Analysis flow of VUMAT

  • 1.5 有限元模型

    1.5

    层合板采用三维变形体(3D deformable),单元类型采用8节点减缩积分实体单元C3D8R,如图2所示,铺层方向通过Matreial Orientation实现。

    施加载荷时,模型左端固支,右端施加轴向位移载荷,不同应变率条件通过调整分析步步长来实现。

    图2
                            有限元模型

    图2 有限元模型

    Fig.2 Finite element model

  • 2 冲击拉伸试验

    2

    试验在英国英斯特朗公司的INSTRON VHS 80/20高速率试验机上进行。该设备的最高加载速率可达20 m/s。开始时,驱动器下降并加速同时试件可在夹具内侧面之间自由通过,如图3所示。当达到所需速度时,穿过楔形块的两个垂直分离杆到达行程终点时,楔形块被拉出,夹具突然夹紧试件下拉,直至试件被拉断。

    图3
                            动态拉伸试验测试系统

    图3 动态拉伸试验测试系统

    Fig.3 Dynamic tensile test system

    试件材料委托深圳市某公司,选用E-玻璃纤维按照(0°/90°)5铺设,并浸以环氧树脂,在高温下压制而成,组分材料性能参照表1,纤维体积含量约为55%。

    由于高速试验机使用特殊的夹具,参考国家拉伸试验试件标准,设计试件的几何尺寸如图4所示。为防止夹具夹坏试件,在试件左右两端设计了0.5 mm厚的加强片,材料选用与试件相同的材料。

    图4
                            试件尺寸

    图4 试件尺寸

    Fig.4 Size of the specimen

    在高速拉伸试验中,设定3种不同的加载速率,分别为0.05,0.5和5 m/s。试件均拉伸至断裂。

  • 3 结果与讨论

    3

    本文有限元模拟与试验中所用组分材料玻璃纤维及树脂基体的性能参数如表1所示,单向复合材料力学性能通过混合率计算获[35],如表2所示。

    表1 组分材料力学性能

    Tab.1 Mechanical properties of component materials

    材料性能E⁃玻璃纤维环氧树脂
    杨氏模量/GPa731.16
    剪切模量/GPa300.67
    泊松比0.220.35
    拉伸强度/MPa2 760112
    压缩强度/MPa2 000241
    剪切强度/MPa89.6

    表2 单向复合材料力学性能

    Tab.2 Mechanical properties of unidirectional composite

    材料性能参数数值材料性能参数数值
    ρ / (kg·m-3)1 900XT / MPa1 104
    E11 / GPa31.3XC / MPa800
    E22E33 / GPa7.68YT / MPa87.2
    ν12ν130.298YC / MPa187.7
    ν230.341ST / MPa69.7
    G12G13 / GPa2.86SC / MPa57.3
    G23 / GPa3.28C0.1

    INSTRON高应变率试验机通过控制加载速率来达到不同应变率的条件。本试验选择的3种加载速率的载荷位移关系如图5所示。随着应变率的增加,极限载荷有明显的增大趋势,与0.05 m/s相比,0.5 m/s的极限载荷增大了8.6%,5 m/s的极限载荷增大了10.1%。加载初期,每条曲线均呈现出明显的线性特征,而后进入非线性阶段,但其非线性表现并不明显,当达到极限载荷后材料随即失去承载能力,发生脆性断裂。3种速度下的曲线在初始线性阶段几乎保持平行,故本文认为该种复合材料层合板的纵向模量对应变率不敏感。

    图5
                            不同加载速率下载荷-位移关系试验结果

    图5 不同加载速率下载荷-位移关系试验结果

    Fig.5 Test results of load-displacement curves under different loading rates

    为了分析试件在冲击拉伸过程中的孔边应力集中现象,试验前在每个试件沿宽度方向和长度方向分别粘贴两个应变片,如图6所示,所测应变方向均与拉伸方向一致,其中宽度方向应变片型号为BE120-03AA(11)-X30,尺寸为2.7 mm×2.7 mm,长度方向应变片型号为BE120-3AA(11),尺寸为6.4 mm×3.5 mm,两者所能测的极限应变均为3%。图7中(a)和(b)分别给出0.05 m/s和5 m/s下的时间应变关系。通过比较不同位置的应变值可以发现,相同时刻下,宽度方向靠近孔边的应变值最大,长度方向靠近孔边的应变值最小,两者相差约为4倍;远离孔的两处应变值相近,宽度方向的略大于长度方向,这说明在拉伸过程中存在明显的应力集中现象。比较图7(a)和(b)两图宽度方向靠近孔边的应变值,5 m/s的有明显的增大趋势,也说明该层板对应变率敏感,且随应变率的增大而增大。

    图6
                            应变片位置分布

    图6 应变片位置分布

    Fig.6 Position distribution of strain gauges

    图7
                            孔边不同位置时间-应变关系

    图7 孔边不同位置时间-应变关系

    Fig.7 Time-strain curves at different positions of hole edge

    采用ABAQUS/Explicit进行有限元仿真分析,加载速率分别为0.05, 0.25, 0.5, 2.5和5 m/s,其载荷位移关系如图8所示。由模拟结果可以看出:随着加载速率即应变率的增大,极限载荷也伴随着明显的增大趋势;在加载初始阶段,每条曲线均呈现出明显的线性特征,而后过渡到非线性阶段,但其非线性表现并不明显,当达到极限载荷后材料随即失去承载能力,发生脆性断裂;5种速度下的曲线在初始线性阶段几乎重合,说明应变率对轴向模量的影响不大,这与试验结果相一致。

    图8
                            不同加载速率下载荷-位移关系有限元结果

    图8 不同加载速率下载荷-位移关系有限元结果

    Fig.8 Simulation results of load-displacement curves under different loading rates

    9同时给出了5 m/s下试验和有限元的载荷位移关系,通过对比,两者在断前吻合较好,证明了有限元模型的正确性及有效性。

    图9
                            5 m/s加载速率下试验及有限元载荷-位移关系对比

    图9 5 m/s加载速率下试验及有限元载荷-位移关系对比

    Fig.9 Experimental and simulative load-displacement curv-es under 5 m/s

    10为5 m/s下试件破坏过程及应力分布。整个分析步长400 μs,从266~330.4 μs完全破坏可以看出,层合板的破坏是一个逐渐损伤的过程。由图10(b)第180 μs的云图可以看出,最大应力发生在垂直于拉伸方向的孔边,最小应力发生在沿拉伸方向的孔边,而和试验相对应的两个远端位置处的应力相近,这与试验结果相吻合。结合图10(d)第291.2 μs和图10(e)第312 μs的云图可以得到:层板最先在垂直于拉伸方向的孔边发生破坏,然后裂纹沿宽度方向扩展,并最终至整块层板断裂,如图10(f)所示。裂纹形状同试验现象相吻合,如图11所示。

    图10
                            5 m/s加载速率下试件破坏过程及应力分布

    图10 5 m/s加载速率下试件破坏过程及应力分布

    Fig.10 Failure process and stress distribution of the specimen under 5 m/s

    图11
                            5 m/s加载速率下破坏试件表面形貌

    图11 5 m/s加载速率下破坏试件表面形貌

    Fig.11 Surface morphology of specimen under 5 m/s after failure

  • 4 结 论

    4

    (1) 对带孔玻璃纤维增强复合材料层合板进行不同应变率的拉伸试验,结果表明该种材料的极限强度随着应变率的上升有明显的增大趋势,而纵向模量随应变率的增加变化不明显。

    (2) 不同应变片的应变记录结果表明,同一试验条件下的试件存在明显的应力集中现象,表现为垂直于拉伸方向的孔边应力最大,而沿拉伸方向的孔边应力最小;同一位置的极限应变随应变率的上升有明显的变大趋势。

    (3) 基于各向异性材料本构模型,通过强度修正、Hashin失效准则以及刚度退化方案,并利用Fortran程序语言编写ABAQUS用户材料子程序VUMAT,模拟出损伤起始、扩展直至最终破坏的整个过程,其结果与试验吻合较好。

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荆臻

机 构:江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 无锡, 214122

Affiliation:Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, China

田常录

机 构:江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 无锡, 214122

Affiliation:Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, China

吴健

机 构:中国船舶科学研究中心, 无锡, 214082

Affiliation:China Ship Scientific Research Center, Wuxi, 214082, China

王纬波

机 构:中国船舶科学研究中心, 无锡, 214082

Affiliation:China Ship Scientific Research Center, Wuxi, 214082, China

赵军华

机 构:江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 无锡, 214122

Affiliation:Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, China

孙琎

机 构:江南大学机械工程学院江苏省食品先进制造装备技术重点实验室, 无锡, 214122

Affiliation:Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, China

角 色:通讯作者

Role:Corresponding author

邮 箱:sunjin@jiangnan.edu.cn

作者简介:孙琎,男,讲师,E-mail:sunjin@jiangnan.edu.cn。

刘彦东

角 色:中文编辑

Role:Editor

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材料性能E⁃玻璃纤维环氧树脂
杨氏模量/GPa731.16
剪切模量/GPa300.67
泊松比0.220.35
拉伸强度/MPa2 760112
压缩强度/MPa2 000241
剪切强度/MPa89.6
材料性能参数数值材料性能参数数值
ρ / (kg·m-3)1 900XT / MPa1 104
E11 / GPa31.3XC / MPa800
E22E33 / GPa7.68YT / MPa87.2
ν12ν130.298YC / MPa187.7
ν230.341ST / MPa69.7
G12G13 / GPa2.86SC / MPa57.3
G23 / GPa3.28C0.1
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图1 分析流程

Fig.1 Analysis flow of VUMAT

图2 有限元模型

Fig.2 Finite element model

图3 动态拉伸试验测试系统

Fig.3 Dynamic tensile test system

图4 试件尺寸

Fig.4 Size of the specimen

表1 组分材料力学性能

Tab.1 Mechanical properties of component materials

表2 单向复合材料力学性能

Tab.2 Mechanical properties of unidirectional composite

图5 不同加载速率下载荷-位移关系试验结果

Fig.5 Test results of load-displacement curves under different loading rates

图6 应变片位置分布

Fig.6 Position distribution of strain gauges

图7 孔边不同位置时间-应变关系

Fig.7 Time-strain curves at different positions of hole edge

图8 不同加载速率下载荷-位移关系有限元结果

Fig.8 Simulation results of load-displacement curves under different loading rates

图9 5 m/s加载速率下试验及有限元载荷-位移关系对比

Fig.9 Experimental and simulative load-displacement curv-es under 5 m/s

图10 5 m/s加载速率下试件破坏过程及应力分布

Fig.10 Failure process and stress distribution of the specimen under 5 m/s

图11 5 m/s加载速率下破坏试件表面形貌

Fig.11 Surface morphology of specimen under 5 m/s after failure

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    • 2

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      BAO Jianwen, JIANG Shicai, ZHANG Daijun. Current status and trends of aeronautical resin matrix composites reinforced by carbon fiber[J]. Science & Technology Review, 2018,36(19):52-63.

    • 3

      拓宏亮, 马晓平, 卢智先. 基于连续介质损伤力学的复合材料层合板低速冲击损伤模型[J]. 复合材料学报, 2018, 35(7):1878-1888.

      TUO Hongliang, MA Xiaoping, LU Zhixian. A model for low velocity impact damage analysis of composite laminates based on continuum damage mechanics[J]. Acta Materiae Compositae Sinica, 2018, 35(7): 1878-1888.

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