PMMA/CNT微发泡密度梯度吸能材料的优化设计研究

doi:10.19491/j.issn.1001-9278.2021.05.006

中国塑料 ›› 2021, Vol. 35 ›› Issue (5): 32-39.DOI: 10.19491/j.issn.1001-9278.2021.05.006

PMMA/CNT微发泡密度梯度吸能材料的优化设计研究

张轶竣¹^,², 张睿智², 郭成成², 沈强², 罗国强¹()

^1.武汉理工大学材料科学与工程学院，武汉 430070
^2.材料复合新技术国家重点实验室，武汉 430070

收稿日期:2020-12-30 出版日期:2021-05-26 发布日期:2021-05-24
基金资助:
国家自然科学基金(51932006);湖北省技术创新专项重大项目(2019AFA176)

Study on Optimal Design of PMMA/CNT Microcellular Density Gradient Materials for Energy Absorption

ZHANG Yijun¹^,², ZHANG Ruizhi², GUO Chengcheng², SHEN Qiang², LUO Guoqiang¹()

^1.School of Materials Science and Engineering，Wuhan University of Technology，Wuhan 430070，China
^2.State Key Laboratory of Advanced Technology for Materials Synthesis and Processing，Wuhan 430070，China

Received:2020-12-30 Online:2021-05-26 Published:2021-05-24
Contact: LUO Guoqiang E-mail:luoguoqiang1980@sina.com

摘要/Abstract

摘要：

基于聚甲基丙烯酸甲酯（PMMA）/碳纳米管（CNT）微孔发泡复合吸能材料，建立了一种等密度差密度梯度泡沫模型，通过在非线性唯象本构模型拟合得到的准静态压缩下的本构方程，计算了泡沫模型在不同载荷下的吸能效率分布特性及相应优劣势。系统研究了泡沫模型层间密度差、上下限密度差、泡沫层厚度梯度规律3种因素对梯度泡沫吸能效能的影响规律。结果表明，层间密度差为25 kg/m³与50 kg/m³的泡沫吸能效能较好；上下限密度差越小，吸能效率的峰值越高，在较低载荷的吸能效能会越差；单层密度接近于平均表观密度的泡沫层越厚，吸能效率峰值会越高。基于实验结果优化设计了一种吸能效率峰值达到0.326且吸能效能在<15 MPa载荷范围内相对于均质泡沫更有优势的梯度泡沫。这些结果对于密度梯度吸能材料的设计思路具有重要指导意义。

关键词: 梯度泡沫, 碳纳米管, 聚甲基丙烯酸甲酯, 复合材料, 微孔泡沫, 准静态压缩, 吸能性能

Abstract:

Compared to homogeneous foams， the density-graded foams have significant advantages such as lighter weight and better energy-absorption efficiency. To investigate the influence factors of the energy-absorption characteristics of density-graded foams and optimize their design， this paper focused on a microcellular energy-absorption foam based on poly（me-thyl methacrylate） and carbon nanotubes. A graded foam model was established with an equal interlayer density difference. Through the nonlinear phenomenological constitutive model fitting of a constitutive equation under the quasi-static compre-ssion， the distribution features and corresponding advantages and disadvantages of energy absorption efficiency of the foam model were calculated under different loads. The influence rules of interlayer density difference， upper and lower density differences and thickness graded rule of foam layer on the energy absorption efficiency of the foam model were studied. The results indicated that the foams with interlayer density differences of 25 kg/m³ and 50 kg/m³ exhibited a better energy absorption capability. With reducing the upper and lower density difference， the peak of energy absorption efficiency increased， but the energy absorption efficiency at lower loads decreased. The peak of energy absorption efficiency increased with an increase in the thickness of the foam layers， whose density was closer to the apparent density. Based on the experimental results， an optimal graded foam model was established， leading to a peak value of 0.326 for energy absorption efficiency as well as a better energy absorption capability than homogeneous foam within the loading range of 15 MPa. These results can provide an important guiding significance for the design of density gradient materials for energy absorption.

Key words: graded foam, carbon nanotube, poly（methyl methacrylate）, composite, microcellular foam, quasi-static compression, energy-absorption performance

中图分类号:

TQ325.7

张轶竣, 张睿智, 郭成成, 沈强, 罗国强. PMMA/CNT微发泡密度梯度吸能材料的优化设计研究[J]. 中国塑料, 2021, 35(5): 32-39.

ZHANG Yijun, ZHANG Ruizhi, GUO Chengcheng, SHEN Qiang, LUO Guoqiang. Study on Optimal Design of PMMA/CNT Microcellular Density Gradient Materials for Energy Absorption[J]. China Plastics, 2021, 35(5): 32-39.

图/表 11

图1 PMMA/CNT微孔泡沫材料在不同温度下发泡的微观结构

Fig.1 The microstructure of the PMMA/CNT nanocomposites foams foamed at different temperature

参数	表达式和值
A	$5.61 × 10 - 2 ρ ? - ? 7.840 ? 8$
B	12
C	$8.430 ? 8 × 10 - 6 ρ 2 + 2.873 × 10 - 3 ρ - 4.272 ? 9$
σ	50
β	50
γ	$- 10.837 × 10 - 6 ρ 2 + 2.194 × 10 - 3 ρ - 7.012 ? 8$

参数	表达式和值
A	$5.61 × 10 - 2 ρ ? - ? 7.840 ? 8$
B	12
C	$8.430 ? 8 × 10 - 6 ρ 2 + 2.873 × 10 - 3 ρ - 4.272 ? 9$
σ	50
β	50
γ	$- 10.837 × 10 - 6 ρ 2 + 2.194 × 10 - 3 ρ - 7.012 ? 8$

表1 本构方程中各参数的常数值或函数表达式

Tab.1 Mathematical expressions and values of the parameters

表1 本构方程中各参数的常数值或函数表达式

Tab.1 Mathematical expressions and values of the parameters

图2 标准等密度差梯度泡沫模型示意图

Fig.2 Schematic of the discretely standard graded foam

图3 标准梯度泡沫的应力?应变曲线及吸能效率曲线与均质泡沫对比

Fig.3 Comparison of stress?strain curves and energy absorption efficiency curves of standard graded foam with homogeneous foam

图4 各层间密度差泡沫应力?应变曲线及吸能效率曲线对比

Fig.4 Comparison of stress strain curves and energy absorption efficiency curves of different Δρ

图5 不同上下限密度差泡沫应力?应变曲线及吸能效率曲线对比

Fig.5 Comparison of stress strain curves and energy absorption efficiency curves of different density span

图6 哑铃形厚度梯度泡沫与纺锤形厚度梯度泡沫模型

Fig.6 The model map of Dumbbell form and Spindle form

单层密度/kg·m^-3	泡沫模型单层厚度/mm
单层密度/kg·m^-3	标准梯度	哑铃形	纺锤形
200	2.5	4	1
250	2.5	3	2
300	2.5	2	3
350	2.5	1	4
400	2.5	1	4
450	2.5	2	3
500	2.5	3	2
550	2.5	4	1

表2 哑铃形与纺锤形泡沫单层层厚参数

Tab.2 The layer thickness parameters of Dumbbell foam and Spindle foam

图7 密度呈哑铃形与纺锤形分布的梯度泡沫应力?应变曲线及吸能效率曲线对比

Fig.7 Comparison of stress strain curves and energy absorption efficiency curves of Dumbbell foam and Spindle foam

图8 优化梯度泡沫模型示意图

Fig.8 Schematic of the optimized graded foam model

图9 优化梯度泡沫模型吸能效率曲线

Fig.9 Energy absorption efficiency curves of the optimized graded foam model

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PMMA/CNT微发泡密度梯度吸能材料的优化设计研究

Study on Optimal Design of PMMA/CNT Microcellular Density Gradient Materials for Energy Absorption

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