三维机织复合材料残余应力/应变多尺度分析及工艺参数优化

王琦; 蒋秋梅; 杨旭锋; 任明法

doi:10.13801/j.cnki.fhclxb.20200720.002

三维机织复合材料残余应力/应变多尺度分析及工艺参数优化

doi: 10.13801/j.cnki.fhclxb.20200720.002

王琦^1,,
蒋秋梅^2,,
杨旭锋^1,,
任明法^1, ,

1.
大连理工大学　工程力学系，大连 116024
2.
西安航天动力技术研究所燃烧，热结构与内流场重点实验室，西安 710100

基金项目: 国家自然科学基金 (U1837204)

详细信息

通讯作者:
任明法，博士，教授，博士生导师，研究方向为复合材料力学及其结构分析　E-mail：renmf@dlut.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: 2020-05-21
- 录用日期: 2020-07-01
- 网络出版日期: 2020-07-21
- 刊出日期: 2021-04-08

Multiscale analysis and process parameters optimization of residual stress/strain of 3D woven composite

WANG Qi^1
,,
JIANG Qiumei^2
,,
YANG Xufeng^1
,,
REN Mingfa^{1
, ,}

1.
Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
2.
National Key Laboratory of Combustion, Thermal Structure and Flow, Xi’an Aerospace Propulsion Institute, Xi’an 710100, China

摘要

摘要: 为预测三维机织复合材料工艺引入的残余应力/应变，提出工艺制度优化方案，建立了一种工艺过程分析的多尺度模型。通过建立纤维尺度及纱线尺度代表体元(RVE)，计算了成型过程中纤维纱线及三维机织复合材料的模量演化历程。考虑固化过程中树脂的化学收缩效应，在纱线尺度上开展热-化学-力学耦合分析，预测了细观残余应力-应变及其演化规律。采用三维机织技术，实现了光纤布拉格光栅传感器(FBG)在三维机织预制体中的预埋，并对其树脂传递模塑(RTM)成型过程中的温度、应变历程进行监测，试验结果验证了有限元模型的准确性。采用基于空间信息、误差信息和优化结果的三种序列采样方法，建立了工艺过程分析代理模型，并开展工艺参数优化设计，结果显示采用优化后的工艺参数，残余应变降低了15.4%，工艺周期缩短了10.6%。
- 三维机织复合材料 /
- 多尺度 /
- 残余应力 /
- 代理模型 /
- 优化设计
Abstract: To predict the process-induced residual stress/strain of 3D woven composite and propose the optimal cure cycle, a multiscale model of the process analysis has been developed. Based on the representative volume elements (RVE) at the fiber and yarn scale, the modulus development of yarns and 3D woven composite was obtained. A thermal-chemical-mechanical coupling analysis was conducted on the yarn scale with the consideration of chemical shrinkage effect of resin, and the evolution of the microscopic stress-strain was calculated. The fiber Bragg grating (FBG) sensors were embedded in the 3D woven preform through the 3D weaving technique, and the evolutions of temperature and strain were monitored. The accuracy of the finite element model was validated by the experimental result. Three sequential sampling methods based on space, error and result were adopted to establish the surrogate model of the process analysis of 3D woven composite. Based on the surrogate model, the optimization of process parameters of 3D woven composite forming process was carried out. The results show that the residual strain is reduced by 15.4% and the cure cycle is shortened by 10.6%.
- 3D woven composite /
- multiscale /
- residual stress /
- surrogate model /
- optimization design

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图 1 纤维尺度代表性体积单元(RVE)

Figure 1. Fiber scale representative volume elemrnt (RVE)

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图 2 纱线尺度RVE

Figure 2. Yarn scale RVE

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图 3 典型固化工艺周期

Figure 3. Typical autoclave process cycle

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图 4 固化工艺优化流程

Figure 4. Flow chart of the optimization of the curing process

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图 5 纱线尺度RVE中心点温度和固化度曲线

Figure 5. Histories of temperature and degree of cure at the center of yarn scale RVE

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图 6 固化过程中树脂收缩应变和树脂模量演化规律

Figure 6. Evolutions of resin shrinkage strain and resin modulus during curing process

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图 7 126 min时三维机织复合材料纱线尺度RVE温度和固化度分布云图

Figure 7. Distribution of temperature and degree of cure of 3D woven composite yarn scale RVE at 126 min

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图 8 225 min时三维机织复合材料纱线尺度RVE温度和固化度分布云图

Figure 8. Distribution of temperature and degree of cure of 3D woven composite yarn scale RVE at 225 min

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图 9 三维机织复合材料纱线尺度RVE固化后各方向残余应变场分布

Figure 9. Distribution of residual strain field after curing of 3D woven composite yarn scale RVE

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图 10 三维机织预制体与模具

Figure 10. 3D woven perform and tool

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图 11 三维机织复合材料固化中内部温度曲线

Figure 11. Internal temperature history of 3D woven composites during curing

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图 12 三维机织复合材料固化过程残余应变演化仿真与试验结果对比

Figure 12. Comparison of simulation and experiment result of residual strain evolution of 3D woven composite during curing process

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表 1 3501-6环氧树脂热-化学性能^[7]

Table 1. Thermo-chemical properties of 3501-6 epoxy resin^[7]

Parameter	Value
${\rho _{\rm{r}}}/({\rm{kg}} \cdot {{\rm{m}}^{ - 3}})$	$90\alpha + 1\;232(\alpha \leqslant 0.45)\ \ \ \ 1\;272(\alpha > 0.45)$
${C_{\rm{r}}}/({\rm{J}} \cdot {{\rm{(kg}} \cdot {\rm{K)}}^{ - 1}})$	$4\;148(0.468 + 5.975 \times {10^{ - 4} }T - 0.141\alpha )$
${k_{\rm{r}}}/({\rm{W}} \cdot {{\rm{(m}} \cdot {\rm{K)}}^{ - 1}})$	$0.04184(3.85 + (0.035T - 0.141)\alpha )$
${H_{\rm{r}}}/\left( {{\rm{J}} \cdot {\rm{k}}{{\rm{g}}^{ - 1}}} \right)$	$473\;600$
${A_1}/{\min ^{ - 1}}$	$2.102 \times {10^9}$
${A_2}/{\min ^{ - 1}}$	$ - 2.104 \times {10^9}$
${A_3}/{\min ^{ - 1}}$	$1.960 \times {10^5}$
$\Delta {E_1}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$	$8.07 \times {10^4}$
$\Delta {E_2}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$	$7.78 \times {10^4}$
$\Delta {E_3}/\left( {{\rm{J}} \cdot {\rm{mo}}{{\rm{l}}^{ - 1}}} \right)$	$5.66 \times {10^4}$
Notes: ${\rho _{\rm{r}}}$—Density of the resin; ${C_{\rm{r}}}$—Specific heat capacity of the resin; ${k_{\rm{r}}}$—Thermal conductivity of the resin; A_i—Frequency factors; $\Delta {E_i}$—Activation energies.

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表 2 AS4碳纤维和3501-6环氧树脂力学性能^[10]

Table 2. Mechanical properties of AS4 carbon fiber and 3501-6 epoxy resin^[10]

Parameter	Value
$E_{\rm{r}}^\infty /{\rm{GPa}}$	3.447
$E_{\rm{r}}^0/{\rm{GPa}}$	3.447/1 000
$v_{\rm{r}}^\infty $	0.37
${\phi _{\rm{r}}}/℃{^{ - 1}} $	$57.6 \times {10^{ - 6}}$
${E_{{\rm{f}}1}}/{\rm{GPa}}$	206.8
${E_{{\rm{f}}2}}/{\rm{GPa}}$	20.7
${v_{{\rm{f}}12}}$	0.2
${v_{{\rm{f}}13}}$	0.2
${v_{{\rm{f}}23}}$	0.5
${G_{{\rm{f}}12}}/{\rm{GPa}}$	27.6
${G_{{\rm{f}}13}}/{\rm{GPa}}$	27.6
${G_{{\rm{f}}23}}/{\rm{GPa}}$	6.9
${\phi _{{\rm{f}}1}}/℃{^{ - 1}}$	$ - 9.0 \times {10^{ - 7}}$
${\phi _{{\rm{f}}2}}/℃{^{ - 1}}$	$7.2 \times {10^{ - 6}}$
Notes: E, v and G—Elastic modulus, Poisson’s ratio and shear modulus, respectively; $\phi $—Coefficient of thermal expansion; subscripts f and r represent fiber and resin respectively.

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表 3 AS4碳纤维热-力学性能^[26]

Table 3. Thermo-chemical properties of AS4 carbon fiber^[26]

Parameter	Value
${\rho _{\rm{f}}}/\left( {{\rm{kg}} \cdot {{\rm{m}}^{{\rm{ - 3}}}}} \right)$	1790
${C_{\rm{f}}}/\left( {{\rm{J}} \cdot {{\left( {{\rm{kg}} \cdot {\rm{K}}} \right)}^{ - 1}}} \right)$	$750 + 2.05T$
$k_{\rm{f}}^{\rm{L}}/\left( {{\rm{W}} \cdot {{\left( {{\rm{m}} \cdot {\rm{K}}} \right)}^{ - 1}}} \right)$	$ 0.04184 \times \left( {3.85 + \left( {0.035T - 0.141} \right)\alpha } \right) $
$k_{\rm{f}}^{\rm{T}}/\left( {{\rm{W}} \cdot {{\left( {{\rm{m}} \cdot {\rm{K}}} \right)}^{ - 1}}} \right)$	$2.4 + 0.00507T$
Notes: ${\rho _{\rm{f}}}$—Density of the fiber; ${C_{\rm{f}}}$—Specific heat capacity of the fiber; $k_{\rm{f}}^{\rm{L}}$, $k_{\rm{f}}^{\rm{T}}$—Longitudinal and transverse thermal conductivity of the fiber respectively.

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表 4 多岛遗传优化算法参数

Table 4. Parameters used for multi-island GA optimization

Parameter	Value
Number of generations	50
Number of islands	2
Rate of migration	0.25
Rate of mutation	0.01
Sub-population size	100
Elite size	2

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表 5 三维机织复合材料固化工艺参数优化结果

Table 5. Optimized results of process parameters for 3D woven composite curing

Parameter	Original value	Optimal value
h₁ /(℃·min⁻¹)	2	2.038
h₂ /(℃·min⁻¹)	2	1.794
c₁ /(℃·min⁻¹)	2	3.88
${t_{{\rm{cc}}}}$/min	340	303.7
${\bar \varepsilon _{{\textit{zz}}}}\left( x \right)$/10⁻⁶	−1 089	−921.2

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