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基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测

杨凤祥 陈静芬 陈善富 刘志明

杨凤祥, 陈静芬, 陈善富, 等. 基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测[J]. 复合材料学报, 2020, 37(9): 2207-2222 doi:  10.13801/j.cnki.fhclxb.20200110.002
引用本文: 杨凤祥, 陈静芬, 陈善富, 等. 基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测[J]. 复合材料学报, 2020, 37(9): 2207-2222 doi:  10.13801/j.cnki.fhclxb.20200110.002
Fengxiang YANG, Jingfen CHEN, Shanfu CHEN, Zhiming LIU. Failure strength prediction of composite laminates using 3D damage constitutive model with nonlinear shear effects[J]. Acta Materiae Compositae Sinica, 2020, 37(9): 2207-2222. doi: 10.13801/j.cnki.fhclxb.20200110.002
Citation: Fengxiang YANG, Jingfen CHEN, Shanfu CHEN, Zhiming LIU. Failure strength prediction of composite laminates using 3D damage constitutive model with nonlinear shear effects[J]. Acta Materiae Compositae Sinica, 2020, 37(9): 2207-2222. doi: 10.13801/j.cnki.fhclxb.20200110.002

基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测

doi: 10.13801/j.cnki.fhclxb.20200110.002
基金项目: 国家自然科学基金青年项目(11502095);广东省自然科学基金博士启动项目(2015A030310306);中央高校基本科研业务费专项资金(暨南大学科研培育与创新基金)(21615306)
详细信息
    通讯作者:

    陈静芬,博士,副研究员,硕士生导师,研究方向为复合材料及其结构静动力非线性分析  E-mail:tjingfen.chen@jnu.edu.cn

Failure strength prediction of composite laminates using 3D damage constitutive model with nonlinear shear effects

  • 摘要: 基于连续损伤力学,建立了同时考虑复合材料剪切非线性效应和损伤累积导致材料属性退化的三维损伤本构模型。模型能够区分纤维损伤、基体损伤和分层损伤不同的失效模式,并定义了相应损伤模式的损伤变量。复合材料层合板层内纤维初始损伤采用最大应力准则判定,基体初始损伤采用三维Puck准则中的基体失效准则判定,分层初始损伤采用三维Hou准则中的分层破坏准则判定,为了计算Puck失效理论中的基体失效断裂面角度,本文提出了分区抛物线法,通过Matlab软件编写计算程序并进行分析。结果表明,与Puck遍历法和分区黄金分割法对比,本文提出的分区抛物线法有效地降低了求解断裂面角度的计算次数,提高了计算效率和计算精度。推导了本构模型的应变驱动显式积分算法以更新应力和解答相关的状态变量,开发了包含数值积分算法的用户自定义子程序VUMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著非线性效应的AS4碳纤维/3501-6环氧树脂复合材料层合板进行渐进失效分析,验证了本文提出的材料本构模型的有效性。结果显示,已提出的模型能够较准确地预测此类复合材料层合板的力学行为及其失效强度,为复合材料构件及其结构设计提供一种有效的分析方法。
  • 图  1  层合板子层应力状态与潜在断裂面的定义

    Figure  1.  Definition of stress state and potential fracture surface for composite layer

    图  2  基体应力危险系数含局部极大值点的搜索区间

    Figure  2.  Search region with local maximum value of matrix stress exposure

    图  3  三种应力状态下应力危险系数随旋转角度的变化曲线及Case 3的应力和应力危险系数随旋转角度的变化曲线

    Figure  3.  Variation of matrix stress exposure with rotation angle in three stress states and variation of stresses and matrix stress exposure for case 3

    图  4  材料属性退化模式

    Figure  4.  Material property degradation modes

    图  5  剪切损伤演化方案

    Figure  5.  Shear damage evolution program

    图  6  AS4碳纤维/3501-6环氧树脂复合材料偏轴压缩试件的几何形状及尺寸

    Figure  6.  Geometry and dimensions of AS4 carbon fiber/3501-6 epoxy composite specimen under off-axis compression

    图  7  准静态荷载下不同偏轴角度AS4碳纤维/3501-6环氧树脂复合材料层合板的试验和预测应力-应变曲线

    Figure  7.  Experimental and predicted stress-strain curves of off-axis AS4 carbon fiber/3501-6 epoxy unidirectional composite laminates under quasi-static load

    图  8  含缺口AS4碳纤维/3501-6环氧树脂复合材料层合板的几何尺寸

    Figure  8.  Geometry of notched ASAS4 carbon fiber/3501-6 epoxy composite

    图  9  [0°/90°/±45°]2S层合板达到破坏荷载时0°、45°和−45°单层的纤维断裂损伤变量${d_{\rm{f}}}$预测分布图(D=12.7 mm)

    Figure  9.  Predicted patterns of damage variables ${d_{\rm{f}}}$ in 0°, 45° and−45° plies of [0°/90°/±45°]2S laminates at maximum load(D=12.7 mm)

    图  10  [0°/90°/±45°]2S层合板达到破坏荷载时0°、90°、45°和−45°单层的基体断裂损伤变量${d_{\rm{m}}}$预测分布图(D=12.7 mm)

    Figure  10.  Predicted patterns of damage variables ${d_{\rm{m}}}$ in 0°, 90°, 45° and −45°plies of [0°/90°/±45°]2S laminates at maximum load(D=12.7 mm)

    图  11  [0°/90°/±45°]2S层合板达到破坏荷载时0°、90°、45°和−45°单层的分层损伤变量${d_{\rm{z}}}$预测分布图(D=12.7 mm)

    Figure  11.  Predicted patterns of damage variables ${d_{\rm{z}}}$ in 0°, 90°, 45° and −45° plies of [0°/90°/±45°]2S laminates at maximum load(D=12.7 mm)

    图  12  [0°/90°/±45°]2S层合板达到破坏荷载时0°/90°、90°/45°、45°/−45°层间粘结单元分层损伤预测分布图(D=12.7 mm)

    Figure  12.  Predicted patterns of delamination in 0°/90°, 90°/45°, 45°/ −45° interfaces of [0°/90°/±45°]2S laminates at maximum load using cohesive element method (D=12.7 mm)

    图  13  [±45°]4S层合板达到破坏荷载时,45°和−45°单层的基体断裂损伤变量${d_{\rm{m}}}$预测分布图(D=12.7 mm)

    Figure  13.  Predicted patterns of damage variables ${d_{\rm{m}}}$ in 45° and −45° plies of [±45°]4S laminates at maximum load(D=12.7 mm)

    图  14  [0°/90°/±45°]2S及[±45°]4S带孔层合板拉伸应力-应变预测曲线

    Figure  14.  Predicted tensile stress-strain curves of [0°/90°/±45°]2S and [±45°]4S laminates with holes

    表  1  三种典型的三维应力状态及材料参数

    Table  1.   Typical 3D stress states and material properties

    Material propertyStress state${\sigma _2}$/
    MPa
    ${\sigma _3}$/
    MPa
    ${\tau _{12}}$/
    MPa
    ${\tau _{13}}$/
    MPa
    ${\tau _{23}}$/
    MPa
    $R_ {\bot} ^{\rm{t}}/{\rm{MPa}}$ 25 Case 1 0 0 0 0 59.1
    $R_ {\bot} ^{\rm{c}}/{\rm{MPa}}$ 120 Case 2 −231.2 0 0 0 0
    $R_{ \bot \parallel }^{\rm{A}}/{\rm{MPa}}$ 70 Case 3 34.0 −87.0 22.0 46.0 29.0
    Notes: $R_ {\bot} ^{\rm{t}}$, $R_ {\bot} ^{\rm{c}}$—Tensile strength and compressive strength in the transverse direction,respectively; $R_{ \bot \parallel }^{\rm{A}}$—Strength of the fracture plane against failure due to longitudinal shear stress; ${\sigma _2}$, ${\sigma _3}$—Normal stresses in the transverse and through-thickness directions, respectively; ${\tau _{12}}$, ${\tau _{13}}$, ${\tau _{23}}$—Shear stresses for the 1-2, 1-3, 2-3 plane, respectively.
    下载: 导出CSV

    表  2  三种典型三维应力状态下断裂角计算精度和计算效率对比

    Table  2.   Comparison of accuracy and efficiency for fracture angle calculation under three typical 3D stress states

    Stress statePrecision/(°)Theoretical
    solution/(°)
    Puck’s algorithm[11]SRGSS[16]Proposed method
    θ/(°)NT/sθ/(°)NT/sθ/(°)NT/s
    Case 1 1 45.000 45.0 180 0.437 44.854 24 0.107 45.000 19 0.101
    0.1 45.0 1 800 4.160 44.985 29 0.148 45.000 19 0.101
    Case 2 1 ±51.137 51.0 180 0.428 51.245 31 0.109 51.044 21 0.104
    0.1 51.1 1 800 4.162 51.145 41 0.151 51.044 21 0.104
    Case 3 1 14.901 15.0 180 0.432 14.854 38 0.112 14.974 23 0.107
    0.1 14.9 1 800 4.187 14.916 53 0.156 14.974 23 0.107
    Notes: θ—Fracture angle; N—Number of state points; T—Calculated time by different search methods; SRGSS—Selective range golden section search algorithm.
    下载: 导出CSV

    表  3  AS4碳纤维/3501-6环氧树脂复合材料单向板材料属性

    Table  3.   Material properties of unidirectional AS4 carbon fiber/3501-6 epoxy composite laminate

    $\begin{aligned}&{E_1}/{\rm{GPa}}\end{aligned}$$\begin{aligned}&{E_2} = {E_3}/{\rm{GPa}}\end{aligned}$$\begin{aligned}&{S_{{\rm{fc}}}}/{\rm{MPa}}\end{aligned}$$\begin{aligned}&{S_{{\rm{ft}}}}/{\rm{MPa}}\end{aligned}$$\begin{aligned}&{G_{12}} = {G_{13}}/{\rm{GPa}}\end{aligned}$$\begin{aligned}&{G_{23}}/{\rm{GPa}}\end{aligned}$$\begin{aligned}{\nu _{23}}\end{aligned}$
    138 10.1 1690 1450 7.0 1.57 0.34
    $\begin{aligned}{\nu _{12}} = {\nu _{13}}\end{aligned}$ $\begin{aligned}R_ {\bot} ^{\rm{t}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}R_ {\bot} ^{\rm{c}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}{S_{{\rm{zt}}}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}{S_{{\rm{zc}}}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}{S_{13}} = {S_{23}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}A\end{aligned}$
    0.29 65 285 65 285 81 1.3
    $\begin{aligned}R_{ \bot \parallel }^{\rm{A}}/{\rm{MPa}}\end{aligned}$ $\begin{aligned}{G_{{\rm{ft}}}}\end{aligned}$/(N·mm−1) $\begin{aligned}{G_{{\rm{fc}}}}\end{aligned}$/(N·mm−1) $\begin{aligned}{G_{ {\simfont\text{Ⅰ} }\!\!\!{\rm{C} } } }\end{aligned}$/(N·mm−1) $\begin{aligned}{G_{ {\simfont\text{Ⅱ} }\!\!{\rm{C} } } }\end{aligned}$/(N·mm−1) ${G_{ {\simfont\text{Ⅲ} } {\rm{C} } } }$/(N·mm−1)
    81 220.6 220.6 0.22 0.65 0.65
    Notes: $\begin{aligned}{E_1}\end{aligned}$, $\begin{aligned}{E_2}\end{aligned}$, $\begin{aligned}{E_3}\end{aligned}$—Elastic moduli in the fiber, transverse and through-thickness directions; $\begin{aligned}{S_{{\rm{fc}}}}\end{aligned}$, $\begin{aligned}{S_{{\rm{ft}}}}\end{aligned}$—Tensile strength and compressive strength in the fiber direction; $\begin{aligned}{S_{{\rm{zt}}}}\end{aligned}$, $\begin{aligned}{S_{{\rm{zc}}}}\end{aligned}$— Tensile and compressive strengths in the through-thickness directions; $\begin{aligned}{\nu _{ij}}\end{aligned}$, $\begin{aligned}{G_{ij}}\end{aligned}$(ij=12, 13, 23)—Poisson’s ratios and shear moduli for 1-2, 1-3, 2-3 plane, respectively; $\begin{aligned}{S_{13}}\end{aligned}$, $\begin{aligned}{S_{23}}\end{aligned}$—Shear strengths for 1-3 and 2-3 planes; $\begin{aligned}{G_{{\rm{ft}}}}\end{aligned}$ and $\begin{aligned}{G_{{\rm{fc}}}}\end{aligned}$—Tensile and compressive fracture energies in the fiber direction; $\begin{aligned}{G_{ {\simfont\text{Ⅰ} }\!\!\!{\rm{C} } } }\end{aligned}$, $\begin{aligned}{G_{ {\simfont\text{Ⅱ} }\!\!{\rm{C} } } }\end{aligned}$, $\begin{aligned}{G_{ {\simfont\text{Ⅲ} }{\rm{C} } } }\end{aligned}$—Fracture energies for mode Ⅰ, Ⅱ and Ⅲ in the through-thickness direction, respectively; A—Parameter in the Soutis’ formula related to the composite material.
    下载: 导出CSV

    表  4  [0°/90°/±45°]2S及[±45°]4S带孔层合板拉伸破坏强度预测值与试验结果对比

    Table  4.   Comparison between predicted and experimental tensile failure strengths of [0°/90°/±45°]2S and [±45°]4S composite laminates

    Lay-upD/
    mm
    Test value/
    MPa
    Present modelLi model[9]Abaqus built-in model
    Predicted
    value/MPa
    Error/
    %
    Predicted
    value/MPa
    Error/
    %
    Predicted
    value/MPa
    Error/
    %
    6.35 420±25 416 −1.0 426 1.4 629 49.8
    [0°/90°/±45°]2S 12.70 340±13 338 −0.6 352 3.5 557 63.8
    25.40 262±3 253 −3.4 256 −2.3 458 74.8
    6.35 159±7 163 2.5 174 9.4 78 −50.9
    [±45°]4S 12.70 153±7 150 −2.0 148 −3.2 74 −51.6
    25.40 126±2 118 −6.3 130 3.2 63 −50.0
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-10-30
  • 录用日期:  2020-01-02
  • 网络出版日期:  2020-01-10
  • 刊出日期:  2020-09-17

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