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变厚度复合材料U型零件固化变形仿真预测与结构影响因素

孙立帅 刘闯 李玉军 赵志勇 王俊彪

孙立帅, 刘闯, 李玉军, 等. 变厚度复合材料U型零件固化变形仿真预测与结构影响因素[J]. 复合材料学报, 2022, 39(0): 1-14
引用本文: 孙立帅, 刘闯, 李玉军, 等. 变厚度复合材料U型零件固化变形仿真预测与结构影响因素[J]. 复合材料学报, 2022, 39(0): 1-14
Lishuai SUN, Chuang LIU, Yujun LI, Zhiyong ZHAO, Junbiao WANG. Prediction and analysis of cure-induced deformation of composite U-shaped parts with variable thickness[J]. Acta Materiae Compositae Sinica.
Citation: Lishuai SUN, Chuang LIU, Yujun LI, Zhiyong ZHAO, Junbiao WANG. Prediction and analysis of cure-induced deformation of composite U-shaped parts with variable thickness[J]. Acta Materiae Compositae Sinica.

变厚度复合材料U型零件固化变形仿真预测与结构影响因素

基金项目: 国家自然科学基金(11902256);陕西省自然科学基金(2019JQ-479)
详细信息
    通讯作者:

    刘闯,博士,副教授,硕士生导师,研究方向为复合材料数字化制造 E-mail: Liuchuang@mail.nwpu.edu.cn

  • 中图分类号: TB332

Prediction and analysis of cure-induced deformation of composite U-shaped parts with variable thickness

  • 摘要: 为了准确预测变厚度CCF800H/AC531碳纤维/环氧树脂复合材料U型零件的固化变形,并分析弯边以及变厚区参数对变形的影响。首先,利用自洽方法确定了单层复合材料力学性能,采用细观有限元方法预测了层合板的整体性能以避免仿真建模时复杂的铺层设置。而后结合固化硬化瞬时线弹性模型建立了零件的固化变形预测方法并进行了验证。变厚区对相邻区域的变形的影响规律由变厚区结构参数确定,与铺层方式和材料种类无关。运用Box-Behnken响应面方法,拟合了两个二次模型以分析弯边参数和变厚度结构参数对固化变形的影响规律。变厚区对较薄区域的影响较大,变形最大减小幅度达15%,而对较厚区域的影响可以忽略。采用方差分析比较了不同因素的影响,变厚区的宽度变化对变形的影响较小。当截面距变厚区的距离大于150 mm时,变厚区对较薄区域的影响接近为0。

     

  • 图  1  变厚度U型零件的结构参数与固化变形(CID)

    Figure  1.  Geometric parameters and cure-induced deformation (CID) of variable thickness U-shaped part

    图  2  变厚度U型零件残余应力的累计与释放

    Figure  2.  Stress accumulation and release of variable thickness U-shaped part

    图  3  变厚度U型零件CID:(a)剪切模量很小;(b)剪切模量很大

    Figure  3.  CID of variable thickness U-shaped part: (a) Shear modulus stiff; (b) Shear modulus flexible

    图  4  变厚度U型零件弯边CID:(a)变厚度弯边;(b)由A点到B点的CID

    Figure  4.  A flange’s CID of variable thickness U-shaped part: (a) A flange with a variable thickness area; (b) CID from A to B

    图  5  CCF800H/AC531预浸料固化制度

    Figure  5.  Curing scheme for the CCF800H/AC531

    图  6  层合板截面属性的赋予:(a)铺层划分与单层方向定义;(b)等效性能的赋予

    Figure  6.  Definition of section properties of laminates: (a) Layer division and direction definition; (b) Definition of equivalent properties

    图  7  代表性体积单元(RVE)的有限元模型

    Figure  7.  Numerical model of representative volume element (RVE)

    图  8  进行等效性能预测时RVE的位移云图

    Figure  8.  Displacement cloud maps of RVE for different equivalent properties

    图  9  变厚度U型零件不同厚度区域的网格划分与组装

    Figure  9.  Meshing and assembling elements of variable thickness U-shaped part

    图  10  变厚度U型零件固化变形变厚区仿真边界条件

    Figure  10.  Constraints on the variable thickness area of variable thickness U-shaped part

    图  11  变厚度U型件每个截面脱模前后施加的边界条件

    Figure  11.  Constraints applied to each cross-section of variable thickness U-shaped part before and after curing

    图  12  变厚度U型零件CID计算:(a)仿真结果;(b)变形角度

    Figure  12.  Calculation of CID of variable thickness U-shaped part: (a) FEA result; (b) Spring-in angle

    图  13  变厚度U型试验件的制造

    Figure  13.  Experiment for obtaining cure-induced deformation of variable thickness U-shaped part

    图  14  变厚度U型零件CID试验值与预测值:(a)弯边1;(b)弯边2

    Figure  14.  Experimental and predicted CID data for the variable thickness U-shaped part (a) No. 1 flange (b) No. 2 flange

    图  15  不同铺层的变厚度U型零件的CID

    Figure  15.  CID data for the variable thickness U-shaped parts with different lay-ups

    图  16  不同材料的变厚度U型零件的CID

    Figure  16.  CID data for the variable thickness U-shaped parts with different materials

    图  17  Box-Behnken响应面方法设计点

    Figure  17.  Design points of Box-Behnken response surface methodology

    图  18  CID分析流程

    Figure  18.  Process of CID analysis

    图  19  等厚度U型零件各弯边参数对CID影响的等高云图:(a) 厚度(t)和半径(r);(b) t和角度(θ);(c) θ和弯边长度(l)

    Figure  19.  Contour plot of the influence of flange parameters on CID of equal thickness U-shaped parts: (a) Thickness (t) and radius (r); (b) t and flange angle (θ); (c) θ and flange length (l)

    图  20  各变厚区参数对变厚度U型零件CID影响的等高云图:(a) tmin和Δt;(b) Δtd;(c) wd

    Figure  20.  Contour plot of the influence of variable thickness area parameters on CID of variable thickness U-shaped parts: (a) tmin and Δt; (b) Δt and d; (c) w and d

    表  1  AC531树脂固化动力学性能

    Table  1.   Cure kinetics parameters of AC531

    ParameterValue
    A1/s−13384
    A2/s−17536410
    m0.6062
    n13.6286
    n20.8712
    Q1/(J·mol−1)55575
    Q2/(J·mol−1)94596
    R/(J·(mol·K)−1)8.314
    Notes: A1 and A2 are the pre-exponential coefficients; Q1 and Q2 are the reaction activation energy; R is the universal gas constant; m is the first exponential constant; n1 and n2 are the second exponential constants.
    下载: 导出CSV

    表  2  AC531树脂与CCF800H碳纤维体系热机械性能

    Table  2.   Thermo-mechanical properties of the CCF800H/AC531 carbon/epoxy

    ParameterValue
    Tg(0)/K274.98
    ρ/(kg·m−3)1540
    ρr/(kg·m−3)1300
    g13.244
    g27.528
    Vf57.4%
    Notes: Tg is the glass transition temperature; ρ and ρr are the densities of the composite and resin. g1 and g2 are the are the fifitting coefficients; Vf is the volume fraction of the fiber.
    下载: 导出CSV

    表  3  AC531树脂与CCF800H碳纤维的性能[22]

    Table  3.   Mechanical properties of AC531 and CCF800H[22]

    Mechanical
    properties
    AC531 resinCCF800H fiber
    E11/GPa4.74294
    E22/GPa4.7414
    $v_{12} $0.380.2
    $v_{23} $0.380.5
    G12 /GPa1.7215
    G23 /GPa1.725.5
    $ M_{\text{1}}^{\text{T}} $/(10−6·°C−1)35−0.56
    $ M_{\text{2}}^{\text{T}} $ /(10−6·°C−1)3510.1
    $ M_{\text{1}}^{\text{S}} $−0.6%
    Notes: E11, E22 and E33 are elastic moduli; $v_{12} $, $v_{23} $—Poisson’s ratios; G12, G13 and G23 shear moduli; $ M_{\text{1}}^{\text{T}} $ and $ M_{\text{2}}^{\text{T}} $ are thermal expansion coefficients; $ M_{\text{1}}^{\text{S}} $ is chemical shrinkage coefficient.
    下载: 导出CSV

    表  4  边界条件

    Table  4.   Boundary conditions

    PlaneBC1PlaneBC2BC3BC4
    Y=−LSX=0SSS
    Y=LSX=LUzSS
    Z=−HRY\UZY=0SSS
    Z=HRY\RZY=LSUxS
    X=−LFZ=0SSS
    X=LFZ=HSSUy
    Notes: U denotes to apply a uniform displacement to the plane. S denotes to apply a symmetrical constraint to the plane; R denotes to limit the displacement of the plane; F denotes that no constraints are imposed.
    下载: 导出CSV

    表  5  [0,90]ns铺层CCF800H/AC531复合材料等效性能

    Table  5.   Equivalent material properties of CCF800H/AC531 composite with [0,90]ns layup

    PropertyValue
    E11/MPa91237
    E22/MPa18406
    G12 /MPa4597
    G23 /MPa3709
    v120.031
    v13=v230.566
    $ M_{\text{1}}^{\text{T}} $/(10−6·K−1)1.88
    $ M_{\text{2}}^{\text{T}} $ /(10−5·K−1)4.27
    $ M_{\text{1}}^{\text{S}} $0
    $ M_{\text{2}}^{\text{S}} $−0.76%
    下载: 导出CSV

    表  6  等厚度U型零件弯边参数的范围

    Table  6.   Range of flange parameters of equal thickness U-shaped parts

    Parametert/mmr/mm$\theta $/(°)l/mm
    Lower bound
    156050
    Upper bound
    425120500
    Notes: t is the part’s thickness; r is the flange radius; $ \theta $ is the flange angle; l is the flange length.
    下载: 导出CSV

    表  7  变厚度U型零件参数的范围

    Table  7.   Range of parameters of variable thickness U-shaped parts

    Parameterstmin/mmΔt/mmd/mmw/mm
    Lower bound
    1002
    Upper bound
    4435/15020
    Notes: tmin is the thickness of the thinner area; Δt is the value of variable thickness; d is the distance between the cross-section and the variable thickness area; w is the width of the variable thickness area.
    下载: 导出CSV
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  • 收稿日期:  2021-11-22
  • 录用日期:  2022-01-18
  • 修回日期:  2021-12-28
  • 网络出版日期:  2022-02-19

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