基于多场耦合方法的厚截面复合材料固化过程的多目标优化

元振毅; 许英杰; 杨癸庚; 冯雨; 杨振朝; 同新星; 宋丹龙; 高达敬; 李言

doi:10.13801/j.cnki.fhclxb.20200603.004

基于多场耦合方法的厚截面复合材料固化过程的多目标优化

doi: 10.13801/j.cnki.fhclxb.20200603.004

元振毅^1, ,,
许英杰^2,,
杨癸庚^1,,
冯雨^1,,
杨振朝^1,,
同新星^1,,
宋丹龙^1,,
高达敬^1,,
李言^1,

1.
西安理工大学　机械与精密仪器工程学院，西安 710072
2.
西北工业大学　机电学院，西安 710072

基金项目: 国家自然科学基金(51805429)；陕西省自然科学基础研究计划(2019JQ-183；2019JQ-728)

详细信息

通讯作者:
元振毅，博士，讲师，研究方向为先进复合材料成型　E-mail：yuanzhenyi2007cs@163.com

中图分类号: TB330.1
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- 被引次数: 0
出版历程
- 收稿日期: 2020-04-07
- 录用日期: 2020-06-02
- 网络出版日期: 2020-06-03
- 刊出日期: 2021-02-15

Multi-objective optimization for curing process of thick composite based on multi-physics coupling method

YUAN Zhenyi^{1
, ,},
XU Yingjie^2
,,
YANG Guigeng^1
,,
FENG Yu^1
,,
YANG Zhenchao^1
,,
TONG Xinxing^1
,,
SONG Danlong^1
,,
GAO Dajing^1
,,
LI Yan^1
,

1.
School of Mechanical and Instrument Engineering, Xi’an University of Technology, Xi′an 710072, China
2.
School of Mechanical Engineering, Northwestern Polytechnical University, Xi′an 710072, China

摘要

摘要: 针对厚截面复合材料固化过程温度峰值过大所引起的材料力学性能降低及残余应力过大等问题，建立了基于多场耦合方法的复合材料固化过程多目标优化模型，用以降低固化温度峰值和缩短固化时间。首先建立包含热化学子模型、树脂黏度子模型和流动压实子模型的固化温度多场耦合模型，用以准确描述固化过程复合材料内部温度及构件厚度的演化规律。通过与文献中已有实验结果比较，证明所建立的多场耦合模型的有效性。在该多场耦合模型基础上，引入径向基(RBF)神经网络作为代理模型，利用多目标优化方法，对固化工艺参数进行最佳组合匹配。研究表明，温度峰值与保温平台温度变化呈明显非线性关联，这与复合材料固化过程的非线性特性有很大关系。在保温温度层面，为了降低温度峰值，需要提高第一阶段的保温温度，降低第二阶段的保温温度，同时在保温平台的时间上进行调整，以缩短固化时长。相比较于原有固化工艺制度，本文提出的优化方法可以显著降低厚截面复合材料层合板的固化时长和温度峰值。
- 复合材料 /
- 固化过程 /
- 代理模型 /
- 优化 /
- 多场耦合
Abstract: In order to reduce the mechanical properties and the curing residual stress of the thick composite caused by the excessive temperature peak during the curing process, a multi-objective optimization model based on the multi-physics coupling characteristics was developed to reduce the maximum curing temperature peak and the curing time. Firstly, a three-dimensional model which incorporated three typical sub-models including thermo-chemical model, resin viscosity model and resin flow model was established to investigate the development of temperature and thickness of laminate during curing process. The results of numerical model were compared with experiment data in reference and good accordance was obtained. Then, a multi-objective optimization method was applied to optimize curing process parameters by using a radial basis function neural network model (RBF) as the surrogate model. It is shown that the curing temperature peak has a nonlinear relationship with the first and second dwell temperature, which is related to the nonlinear characteristics of the curing process. In order to reduce the temperature peak, it is necessary to increase the first dwell temperature and reduce the second dwell temperature. Meanwhile, the dwell time should also be adjusted to shorten the total curing time. Compared to standard cure profiles, the proposed optimization method can significantly reduce the curing time and temperature peak for thick composite laminates.
- composite /
- curing process /
- surrogate model /
- optimization /
- multi-physics coupling

HTML全文

图 1 AS4/3501-6碳纤维/环氧树脂预浸料固化工艺曲线

Figure 1. Cure cycle curve of AS4/3501-6 carbon fiber/epoxy prepregs

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图 2 AS4/3501-6层合板中心处温度和厚度计算结果

Figure 2. Calculated temperature and thickness results of AS4/3501-6 laminates

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图 3 固化过程多目标优化方法流程图

Figure 3. Flow diagram of multi-objective optimization methodology

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图 4 多目标优化得到的帕累托解前沿

Figure 4. Pareto front of multi-objective optimization

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图 5 固化工艺参数对温度峰值和固化时长的影响

Figure 5. Effect of curing parameters on the temperature peak and curing time

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图 6 两种不同模型的AS4/3501-6层合板中心温度和计算结果比较

Figure 6. Comparison of left temperature and cure degree calculated results of AS4/3501-6 laminates using two different models

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表 1 3501-6环氧树脂和AS4碳纤维的材料性能

Table 1. Properties of 3501-6 epoxy resin and AS4 carbon fiber

Parameter		Value	Resource
Resin density ρ_r/(kg·m⁻³)		90α+1 232(α ≤ 0.45) 1 272 (α＞0.45)	[27]
Resin specific heat C_r/(J·(kg·K)⁻¹)		4 184[0.468+5.975×10⁻⁴T−0.141α]	[27]
Resin thermal conductivity λ_r/(W·(m·K)⁻¹)		0.04184[3.85+(0.035T−0.141)α]	[27]
Fiber density ρ_f/(kg·m⁻³)		1 790	[24]
Fiber specific heat variation with cure C_f/(J·(kg·K)⁻¹)		750+2.05×T(℃)	[24]
Fiber conductivity in the longitudinal direction $\lambda _{\rm{f}}^{\rm{L}} $/(W·(m·K)⁻¹)		7.69+0.0156×T(℃)	[24]
Fiber conductivity in the transverse direction $\lambda _{\rm{f}}^{\rm{T}} $/(W·(m·K)⁻¹)		2.4+0.00507×T(℃)	[24]
Resin viscosity constant η_∞/(Pa·s)		7.93×10⁻¹⁴	[23]
Activation energy of viscous flow U/(J·mol⁻¹)		9.08×10⁴	[23]
Constant irrelevant with temperature η_β		14.1	[23]
Preexponential factor of autocatalysis model	A₁/min⁻¹	2.101×10⁹	[23]
	A₂/min⁻¹	−2.014×10⁹	[23]
	A₃/min⁻¹	1.96×10⁵	[23]
Activity energy of autocatalysis model	∆E₁/(J·mol⁻¹)	8.07×10⁴	[23]
	∆E₂/(J·mol⁻¹)	7.78×10⁴	[23]
	∆E₃/(J·mol⁻¹)	5.66×10⁴	[23]
Notes: ρ_r—Density of resin; C_r—Specific heat of resin; λ_r—Heat conduction coefficient of resin; ρ_f—Density of fiber; C_f—Specific heat of fiber; $\lambda _{\rm{f}}^{\rm{L}} $—Heat conduction coefficient of fiber along the fiber direction; $\lambda _{\rm{f}}^{\rm{T}} $ — Heat conduction coefficient of fiber perpendicular the fiber direction; k_x and k_y—Permeability of composite along x direction and y direction; η_∞—Viscosity constant; U—Activation energy of viscose flow; η_β—Constant irrelevant with temperature; A₁, A₂ and A₃—Frequency factor of autocatalysis model; ∆E₁, ∆E₂ and ∆E₃—Activation energy of autocatalysis model.

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表 2 AS4/3501-6预浸料固化工艺参数设计区间

Table 2. Design space of curing process parameters of AS4/3501-6 prepregs

Parameter	Maximum value	Minimum value
C_T₁/℃	100	150
C_T₂/℃	155	220
r₁/(℃·min⁻¹)	0.5	3
r₂/(℃·min⁻¹)	0.5	3
t₁/min	30	120
t₂/min	30	120
Notes: C_T1—First holding-stage temperature; C_T2—Second holding-stage temperature; r₁—First heating rate; r₂—Second heating rate; t₁—Duration of first holding-stage; t₂—Duration of second holding-stage.

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