数字图像相关方法辅助的IM7/8552碳纤维/环氧树脂复合材料单向带层合板沿厚度方向非线性本构参数识别

贺体人; 刘刘; 徐吉峰

doi:10.13801/j.cnki.fhclxb.20200316.001

数字图像相关方法辅助的IM7/8552碳纤维/环氧树脂复合材料单向带层合板沿厚度方向非线性本构参数识别

doi: 10.13801/j.cnki.fhclxb.20200316.001

贺体人^1,,
刘刘^2, ,,
徐吉峰^1,

1.
中国商用飞机有限责任公司　北京民用飞机技术研究中心　民用飞机结构与复合材料北京市重点实验室，北京 102211
2.
北京理工大学　宇航学院，北京 100081

基金项目: 中国博士后科学基金面上资助(2019M651629)

详细信息

通讯作者:
刘刘，博士，副教授，博士生导师，研究方向为复合材料力学响应行为的实验　E-mail：liuliu@bit.edu.cn

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2020-01-07
- 录用日期: 2020-03-04
- 网络出版日期: 2020-03-16
- 刊出日期: 2021-01-15

Digital image correlation aided method for identification of nonlinear constitutive parameters of IM7/8552 carbon fiber/epoxy composite unidirectional laminate along thickness directionction

HE Tiren^1
,,
LIU Liu^{2
, ,},
XU Jifeng^1
,

1.
Beijing Key Laboratory of Commercial Aircraft Structures and Composite Materials, BASTRI, COMAC, Beijing 102211, China
2.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 提出了采用数字图像相关(DIC)方法和有限元模型修正(FEMU)技术相结合，通过短梁剪切(SBS)试验获得碳纤维增强环氧树脂(IM7/8552)正交各向异性复合材料单向带层合板沿厚度方向压缩本构关系参数的试验方法。该方法根据假设材料初始本构，采用3D有限元模型(FEM)计算获得主平面压头下方沿厚度方向的应力和应变分布，以DIC实测应变和有限元计算应变之间的方差建立目标函数，并在FEM中进行迭代更新，收敛后获得材料本构参数。由于选择的试样加载形式近似静定结构，试样表面的应力分布对材料本构关系及参数弱相关，上述迭代过程进一步转化为通过全场有限元计算应力和DIC实测应变之间的最小二乘回归识别假设本构关系及参数。因此，该方法具有以下优点：迭代过程中不需要建立针对识别参数的显式敏感度矩阵，识别效率高；识别过程对初始材料本构参数不敏感。
- 正交各向异性 /
- 压缩本构参数 /
- 数字图像相关(DIC) /
- 有限元模型修正(FEMU) /
- 复合材料
Abstract: A digital image correlation (DIC) aided method combined with finite element model updating (FEMU) technique was proposed to identify the compressive constitutive parameters along the thickness direction for carbon fiber/epoxy (IM7/8552) orthotropic composite unidirectional laminate through short beam shear (SBS) test. The stress and strain distributions on the loading plane along the thickness direction under the loading nose were calculated by 3D finite element model (FEM) with the initial trial parameters. A cost function of the square difference between DIC-measured and FEM-calculated strains was given accordingly and unknown constitutive parameters were determined iteratively through minimization of it. The stress distribution is weakly sensitive to the constitutive parameters since the SBS test configuration is nearly statically determinate. Thus minimization of the cost function can be achieved by the least squared linear regression between FEM-calculated stress and DIC-measured strain. The advantages of the proposed method include that an explicit sensitivity matrix is not required in the iterative procedure, the efficiency of the parameter identification is high, and it is not sensitive to the initial trial parameters.
- orthotropic /
- compressive constitutive parameters /
- digital image correlation (DIC) /
- finite element model updating (FEMU) /
- composite

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图 1 改进短梁剪切试验(SBS)装置

Figure 1. Equipment setup of custom short-beam shear (SBS) test

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图 2 碳纤维/环氧树脂(IM7/8552)复合材料单向带层合板材料方向示意图

Figure 2. Schematic diagram of material directions of carbon fiber/epoxy (IM7/8552) composite unidirectional belt laminate

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图 3 IM7/8552复合材料单向带层合板压头下方挤压失效

Figure 3. Compressive failure of IM7/8552 composite unidirectional belt laminate under loading nose

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图 4 数字图像相关(DIC)方法实测IM7/8552复合材料单向带层合板应变云图

Figure 4. Cloud images of strain of IM7/8552 composite unidirectional belt laminate from digital image correlation (DIC) aided method ((a) Normal axial strain; (b) Interlaminar strain; (c) Shear strain)

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图 5 SBS试验的IM7/8552复合材料单向带层合板3D有限元模型(FEM)的全局模型和子模型

Figure 5. 3D global and sub finite element model (FEM) of IM7/8552 composite unidirectional belt laminate of SBS test

ROI—Region of interest; L, w, h—Length, width and height of specimen, respectively

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图 6 开展本构参数识别感兴趣区域(ROI)

Figure 6. Region of interest(ROI) of identification process

P—External load of SBS test

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图 7 有限元模型修正(FEMU)法沿厚度方向压缩本构参数识别流程图

Figure 7. Flowchart of thickness compressive constitutive parameters identification process using finite element model updating (FEMU) method

ε₃₃—Interlaminar compressive stress-strain; B.C.—Boundary conditions

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图 8 IM7/8552复合材料单向带层合板横向压缩应力-应变数据和最小二乘回归结果

Figure 8. Interlaminar compressive stress-strain data and least-square convergence results of IM7/8552 composite unidirectional belt laminate

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图 9 IM7/8552复合材料单向带层合板沿厚度方向压缩正应力-应变关系识别结果(a)及目标函数值(b)随迭代次数的变化

Figure 9. Variation of constitutive curves (a) and objective function results (b) with iterations of IM7/8552 composite unidirectional belt laminate

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图 10 不同本构参数初值识别前和识别收敛后的应力-应变曲线

Figure 10. Stress-strain curves of different initial approximation before and after identification

A—Linear elastic initial approximation; B—Over inelastic initial approximation

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表 1 IM7/8552复合材料单向带层合板厚度方向本构参数识别结果

Table 1. Convergence results of compressive constitutive parameters along thickness direction of IM7/8552 composite unidirectional belt laminate

	E_33C/MPa⁻¹	K_33C/MPa⁻¹	n_33C
1	8 603.86	786.50	3.59
2	8 879.12	861.30	3.54
3	8 688.18	794.21	3.63
4	8 592.68	785.48	3.59
5	8 418.64	717.23	3.66
AVG	8 636.49	788.94	3.60
COV/%	1.94	6.48	1.26
Notes: E_33C—Compressive elastic modulus in thickness direction; K_33C—Secant modulus in thickness direction; n_33C—Index number; COV—Coefficient of variation.

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