基于机器学习的短纤维增强复合材料弹性力学性能预测

王吉玲; 金浩; 郭瑞文; 史晨曦; 杨礼芳; 李梅娥; 周进雄

基于机器学习的短纤维增强复合材料弹性力学性能预测

1.
西安交通大学材料科学与工程学院金属材料强度国家重点实验室, 西安 710049
2.
西安交通大学航天航空学院, 西安 710049
3.
北京机电工程研究所, 北京 100074

详细信息

通讯作者:
李梅娥，博士，副教授，硕士生导师，研究方向为材料成型过程的模拟仿真　E-mail: limeie@mail.xjtu.edu.cn

中图分类号: TB332;TB333
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- 文章访问数: 151
- HTML全文浏览量: 82
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-18
- 修回日期: 2024-01-24
- 录用日期: 2024-02-02
- 网络出版日期: 2024-03-19

Prediction of elastic properties of short fiber reinforced composites based on machine learning

1.
State key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2.
School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China
3.
Beijing Institute of Mechanical and Electrical Engineering, Beijing 100074, China

摘要

摘要: 短纤维增强复合材料弹性力学性能受其内部结构和基础材料性能影响显著，参数化分析这些影响需要极高的实验或数值分析成本。针对这一问题，本文将基于周期性代表性体积单元(RVE)的数值均匀化方法与人工神经网络(ANN)进行结合，分别构建了空间随机分布、层内随机分布和定向排列三种形式的短纤维增强复合材料力学性能预测代理模型。每个代理模型均可以快速实现不同参数组合(纤维长度、长径比、体积分数以及纤维和基体材料属性)下复合材料的等效弹性性能预测，拟合优度R²均在0.98以上，计算所用时间与常规模拟计算相比可忽略不计，大大节省了实验和计算成本，为短纤维增强复合材料的设计定制创造了重要条件。
- 短纤维复合材料 /
- RVE /
- 参数化计算 /
- 代理模型 /
- 弹性性能预测
Abstract: The elastic and mechanical properties of short fiber reinforced composites are significantly affected by their internal structure and the properties of the underlying materials, and the parametric analysis of these effects requires extremely high experimental or numerical analysis costs. In order to solve this problem, this paper combines the numerical homogenization method based on periodic representative volume units (RVE) and artificial neural network (ANN) to construct three forms of mechanical property prediction surrogate models of short fiber reinforced composites: spatial random distribution, intralayer random distribution and aligned distribution, respectively. Each surrogate model can quickly predict the equivalent elastic properties of composites under different parameter combinations (fiber length, aspect ratio, volume fraction, and fiber and matrix material properties), and the goodness of fit R² is above 0.98, the calculation time is negligible compared to conventional simulation calculations, which greatly saves experimental and computational costs and creates important conditions for the design and customization of short fiber-reinforced composites.
- short fiber composites /
- RVE /
- parametric calculation /
- proxy model /
- elastic performance prediction

HTML全文

图 1 基于RSA算法的周期性RVE生成流程图

Figure 1. Flow chart of the periodic RVE generation based on RSA algorithm

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图 2 长径比为15、体积分数为10%的空间随机分布纤维增强复合材料的RVE

Figure 2. RVE of composites reinforced by spatially randomly distributed fibers with aspect ratio of 15 and volume fraction of 10%

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图 3 基于纤维边界几何近似的体素网格生成算法流程图

Figure 3. Flow chart of voxel mesh generation algorithm based on fiber boundary geometry approximation

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图 4 不同单元尺寸下单根纤维体素网格和RVE体素网格

Figure 4. Voxel mesh of a single fiber with different element sizes and voxel mesh of the RVE.

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图 5 六种加载方式：(a) E₁₁；(b) E₂₂；(c) E₃₃；(d) G₁₂；(e) G₁₃；(f) G₂₃(箭头表示位移载荷施加方向，红色虚线表示变形后的形状)

Figure 5. Six loading methods: (a) E₁₁; (b) E₂₂; (c) E₃₃; (d) G₁₂; (e) G₁₃; (f) G₂₃ (Arrows indicate the direction in which the displacement load is applied, the red dotted line indicates the deformed shape)

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图 6 T300短碳纤维(Csf)/Mg复合材料等效弹性性能随单元尺寸减小的变化：(a)弹性模量；(b)泊松比

Figure 6. Variation of effective material properties of T300 short fiber (Csf)/Mg composite regarding the decrease of the element size: (a) Elastic Modulus; (b) Poisson’s ratio

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图 7 长径比为10、体积分数为10%的层内随机分布Csf/Mg复合材料的RVE

Figure 7. RVE of Csf/Mg composites reinforced by in-layer randomly distributed fibers with aspect ratios of 15 and volume fraction of 10%

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图 8 长径比为40、体积分数为30%的定向分布Csf/Mg复合材料的RVE

Figure 8. RVE of Csf/Mg composites reinforced by aligned distributed fibers with aspect ratios of 40 and volume fraction of 30%

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图 9 有限元分析与代理模型相结合的全局框架示意图

Figure 9. Global framework diagram of finite element analysis combined with surrogate model

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图 10 三层人工神经网络结构(ANN)

Figure 10. Three layer artificial neural network structure(ANN)

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图 11 Csf/Mg复合材料弹性力学性能预测的拟合回归图：(a) 纤维在空间随机分布；(b) 纤维在层内随机分布；(c) 纤维定向分布

Figure 11. Fitting regression diagram for prediction of elastic mechanical properties of Csf/Mg composites: (a) The fibers are randomly distributed in space; (b) The fibers are randomly distributed in layer; (c) The fibers are aligned in Z direction

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图 12 随机纤维生成的不均匀性：(a) 位置不均匀；(b) 取向不均匀

Figure 12. Nonuniformity in random fiber generation: (a) Uneven position; (b) Uneven orientation

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表 1 数值均匀化、Digimat和拉伸试验^[20]得到的Csf/Mg复合材料等效弹性性能比较

Table 1. Comparison of effective elastic properties of Csf/Mg composite obtained from the numerical homogenization, Digimat and tensile experiment^[20]

Properties	Numerical homogenization	Digimat	Tensile experiment	Error_N-T	Error_D-T
E/GPa	49.42	52.98	50.45	2.0%	5.0%
G/GPa	18.12	19.44	19.02	4.7%	2.2%
ν	0.3430	0.3384	0.3425	0.1%	1.2%

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表 2 计算结果与Liu^[10]的工作和Digimat的比较

Table 2. Comparison of the computational results with Liu’s^[10] work and Digimat

Properties	Random distribution in layer			Aligned distribution
Properties	Present work	Liu’s work	Digimat	Present work	Liu’s work	Digimat
E₁₁/GPa	2.8648	2.8176	2.7382	3.0210	3.4347	2.9302
E₂₂/GPa	2.6166	2.7453	2.5915	3.1762	3.4951	2.9302
E₃₃/GPa	2.1908	2.1695	2.0903	17.933	19.712	20.540
G₁₂/GPa	1.0134	1.0467	0.99472	1.0272	1.1591	0.98722
G₁₃/GPa	0.74077	0.74028	0.71036	1.1158	1.3543	1.0744
G₂₃/GPa	0.73648	0.73819	0.70854	1.2524	1.3049	1.0744
ν₁₂	0.34793	0.33629	0.34558	0.4407	0.42266	0.48406
ν₂₁	0.31873	0.32766	0.32706	0.4634	0.43010	0.48406
ν₁₃	0.33177	0.34107	0.34547	0.053278	0.055075	0.045703
ν₃₁	0.25533	0.26263	0.26372	0.31627	0.31608	0.32037
ν₂₃	0.34807	0.34568	0.35505	0.054968	0.054838	0.045703
ν₃₂	0.29293	0.27318	0.28638	0.31035	0.30928	0.32037

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表 3 选定变量及其取值范围

Table 3. Input variables and their value ranges

	l_f/mm	a_f	V_f/%	E_f/GPa	ν_f	E_m/GPa	ν_m
Random distribution in space	1-5	5-15	5-10	70-230	0.20-0.35	0.1-6	0.30-0.45
Random distribution in layer	1-5	10-15	5-10	70-230	0.20-0.35	0.1-6	0.30-0.45
Aligned distribution	1-10	20-40	20-30	70-230	0.20-0.35	0.1-6	0.30-0.45
Notes: l_f—Length of fiber; a_f—Aspect ratio of fiber; V_f—Volume fraction of fiber; E_f—Young’s modulus of fiber; ν_f—Poisson’s ratio of fiber; E_m—Young’s modulus of matrix; ν_m—Poisson’s ratio of matrix.

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