剪切增稠液浸渍凯夫拉织物的动态本构模型

叶义晨; 文鹤鸣

doi:10.11858/gywlxb.20240968

剪切增稠液浸渍凯夫拉织物的动态本构模型

doi: 10.11858/gywlxb.20240968

叶义晨,
文鹤鸣^*, ,

中国科学技术大学中国科学院材料力学行为和设计重点实验室, 安徽合肥　230026

详细信息

作者简介:
叶义晨（2000－），男，硕士研究生，主要从事冲击动力学研究. E-mail：ysa@mail.ustc.edu.cn

通讯作者:
文鹤鸣（1965－），男，博士，教授，主要从事冲击动力学研究. E-mail：hmwen@ustc.edu.cn

中图分类号: O347.3; O521.2
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- 文章访问数: 516
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出版历程
- 收稿日期: 2024-12-30
- 修回日期: 2025-03-12
- 录用日期: 2025-05-26
- 网络出版日期: 2025-03-17
- 刊出日期: 2025-07-07

A Dynamic Constitutive Model for Shear Thickening Fluid Impregnated Kevlar Fabric

YE Yichen,
WEN Heming^{*
, ,}

CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, Anhui, China

摘要

摘要: 剪切增稠液（shear thickening fluid, STF）浸渍凯夫拉（Kevlar）织物是一种新型复合材料，相比纯Kevlar织物，具有更好的抗冲击性能，研究其动态本构模型具有重要的理论意义和应用价值。首先，通过引入动态增强因子（应变率效应）和残余强度因子，结合STF的流变特性和纱线拔出实验结果，发展了STF浸渍Kevlar织物的连续介质损伤力学本构模型；然后，利用提出的本构模型，开展了不同冲击速度下STF浸渍Kevlar织物侵彻的数值模拟；最后，将模拟结果与文献中的相关实验结果进行对比分析。结果表明：所建立的本构模型能够预测STF浸渍Kevlar织物在冲击载荷作用下的力学响应和破坏形貌，并且能够描述STF浸渍后Kevlar织物抗冲击性能的增强效应。
- 剪切增稠液 /
- Kevlar织物 /
- 连续介质损伤力学本构模型 /
- 流变特性 /
- 纱线间摩擦
Abstract: Shear thickening fluid (STF) impregnated Kevlar fabric is a new type of composite materials which has better impact resistance as compared with neat Kevlar fabric. On the basis of previous work, a dynamic constitutive model for STF impregnated Kevlar fabric is firstly developed by introducing dynamic increase factor (strain rate effect) and residual strength factor in combination with the rheological properties of STF and yarn pull out test results. Numerical simulations of STF impregnated Kevlar fabric at different impact velocities are then conducted using the proposed constitutive model. Finally, the numerical results are compared with the relevant experimental data. It is shown that the present constitutive model can predict well the impact response of STF impregnated Kevlar fabrics in terms of residual velocity, load-displacement curve and damage morphology, lending support to the accuracy and usefulness of the dynamic constitutive model for STF impregnated Kevlar fabric.
- shear thickening fluid /
- Kevlar fabric /
- continuum damage mechanical constitutive model /
- rheological properties /
- inter-yarn friction

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图 1 典型STF流变特性示意图

Figure 1. Schematic diagram of the typical rheological properties of STF

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图 2 损伤演化示意图

Figure 2. Schematic diagram of damage evolution

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图 3 STF浸渍Kevlar织物的DIF曲线^[23–25]

Figure 3. DIF curves of STF impregnated Kevlar fabric^[23–25]

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图 4 动态本构模型的数值算法流程图

Figure 4. Flowchart of numerical algorithms for the dynamic constitutive model

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图 5 弹道冲击实验^[26]有限元模型

Figure 5. Finite element model of ballistic impact tests^[26]

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图 6 弹道冲击实验中STF流变特性的拟合曲线与实验数据^[26]的对比

Figure 6. Comparison of fitting curves with the rheological properties of STF used in ballistic impact experiments^[26]

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图 7 弹道冲击实验中模拟的残余速度与实验结果^[26]的对比

Figure 7. Comparison of the numerically predicted residual velocities with the ballistic impact experimental results^[26]

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图 8 弹道冲击实验^[26]与数值模拟得到的破坏形貌的对比

Figure 8. Comparison of the damage morphology of ballistic impact experiments^[26] with that obtained from the numerical simulations

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图 9 不同损伤模式的损伤云图

Figure 9. Numerically predicted damage nephograms of different modes

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图 10 低速冲击实验^[35]的有限元模型

Figure 10. Finite element model of low velocity impact experiments^[35]

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图 11 低速冲击实验中STF流变特性的拟合曲线与实验数据^[35]的对比

Figure 11. Comparison of fitting curve with the experimentally obtained rheological properties of STF used in low velocity impact experiments^[35]

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图 12 数值模拟得到的载荷-位移、能量吸收-位移曲线与低速冲击实验结果^[35]的对比

Figure 12. Comparison of the load and energy absorption-displacement curves obtained from numerical simulations with the low velocity impact experimental results^[35]

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图 13 数值模拟得到的破坏形貌与低速冲击实验结果^[35]的对比

Figure 13. Comparison of the damage morphology obtained from the numerical simulations with that observed in the low velocity impact experiments^[35]

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图 14 准静态穿刺实验^[36]的有限元模型

Figure 14. Finite element model of quasi-static puncture experiments^[36]

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图 15 准静态穿刺实验中STF流变特性的拟合曲线与实验数据^[36]的对比

Figure 15. Comparisons of fitting curve with the experimentally obtained rheological properties of STF used in quasi-static puncture experiments^[36]

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图 16 数值模拟得到的载荷-位移曲线、能量吸收-位移曲线与准静态穿刺实验结果^[36]的对比

Figure 16. Comparison of the load and energy absorption-displacement curves obtained from numerical simulations with quasi-static puncture experimental results^[36]

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图 17 数值模拟得到的破坏形貌与准静态穿刺实验结果^[36]的对比

Figure 17. Comparison of the damage morphology obtained from the numerical simulations with that observed in quasi-static puncture experiments^[36]

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表 1 不同损伤模式下的等效位移和等效应力^[14–15]

Table 1. Equivalent displacement and equivalent stress for different damage modes^[14–15]

Damage mode	${\delta _{j,{\rm{eq}}}}$	${\sigma _{j,{\rm{eq}}}}$
Tensile/shear damage in X-direction	${L_{\rm{c}}}\sqrt {{{\left\langle {{\varepsilon _{11}}} \right\rangle }^2}+{{{{\gamma _{12}^2}} }}+{{ {{\gamma _{31}^2}} }}} $	${L_{\rm{c}}}\left( {{E_{11}}{{\left\langle {{\varepsilon _{11}}} \right\rangle }^2}+{G_{12}}{{{{\gamma _{12}^2}} }}+{G_{31}}{{{{\gamma _{31}^2}} }}} \right)/{\delta _{\rm{1,eq}}}$
Tensile/shear damage in Y-direction	${L_{\rm{c}}}\sqrt {{{\left\langle {{\varepsilon _{22}}} \right\rangle }^2}+{{ {{\gamma _{12}^2}} }}+{{ {{\gamma _{23}^2}} }}} $	${L_{\rm{c}}}\left( {{E_{22}}{{\left\langle {{\varepsilon _{22}}} \right\rangle }^2}+{G_{12}}{{ {{\gamma _{12}^2}} }}+{G_{23}}{{{{\gamma _{23}^2}}}}} \right)/{\delta _{\rm{2,eq}}}$
Compression damage in X-direction	${L_{\rm{c}}}\sqrt {{{\left\langle {{{\varepsilon }_{11}'}} \right\rangle }^2}} $	${L_{\rm{c}}}\left( {{E_{11}}{{\left\langle {{{\varepsilon}_{11} '}} \right\rangle }^2}} \right)/{\delta _{\rm{3,eq}}}$
Compression damage in Y-direction	${L_{\rm{c}}}\sqrt {{{\left\langle {{{\varepsilon }_{22}'}} \right\rangle }^2}} $	${L_{\rm{c}}}\left( {{E_{22}}{{\left\langle {{{\varepsilon }_{22}'}} \right\rangle }^2}} \right)/{\delta _{\rm{4,eq}}}$
Transverse compression damage	${L_{\rm{c}}}\sqrt {{{\left\langle {{{\varepsilon }_{33}'}} \right\rangle }^2}} $	${L_{\rm{c}}}\left( {{E_{33}}{{\left\langle {{{\varepsilon }_{33}'}} \right\rangle }^2}} \right)/{\delta _{\rm{5,eq}}}$
In-plane shear damage	${L_{\rm{c}}}\sqrt {{{{{\gamma _{12}^2}} }}} $	${L_{\rm{c}}}\left( {{G_{12}}{{ {{\gamma _{12}^2}} }}} \right)/{\delta _{\rm{6,eq}}}$
Transverse tensile/shear damage	${L_{\rm{c}}}\sqrt {{{\left\langle {{\varepsilon _{33}}} \right\rangle }^2}+{{{{\gamma _{23}^2}} }}+{{{{\gamma _{31}^2}} }}} $	${L_{\rm{c}}}\left( {{E_{33}}{{\left\langle {{\varepsilon _{33}}} \right\rangle }^2}+{G_{23}}{{ {{\gamma _{23}^2}} }}+{G_{31}}{{ {{\gamma _{31}^2}} }}} \right)/{\delta _{\rm{7,eq}}}$

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表 2 数值模拟中STF浸渍Kevlar织物的材料参数^{[23, 28–34]}

Table 2. Material parameters of STF impregnated Kevlar fabric in the numerical simulations^{[23, 28–34]}

E₁₁/GPa	E₂₂/GPa	E₃₃/GPa	G₁₂/GPa	G₂₃/GPa	G₃₁/GPa	${\nu _{12}}$	${\nu _{23}}$	${\nu _{31}}$
70	70	7	16.4	1.8	1.8	0.33	0.40	0.40

X_t/MPa	Y_t/MPa	Z_t/MPa	X_c/MPa	Y_c/MPa	Z_c/MPa	S₁₂/MPa	S₂₃/MPa	S₃₁/MPa
2 758	2 758	24	580	580	60	180	180	180

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表 3 弹道冲击实验中STF流变特性的拟合参数^[26]

Table 3. Parameters for fitting the rheological properties of STF used in ballistic impact experiments^[26]

w/%	${\eta _0}/({\rm{Pa}} \cdot{\rm{ s}})$	${\eta _{\rm{c}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\eta _{\rm{max}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\dot \gamma _{\rm{c}}}$/s⁻¹	${\dot \gamma _{\rm{max}}}$/s⁻¹	K_Ⅰ	K_Ⅱ	K_Ⅲ	n_Ⅰ	n_Ⅱ	n_Ⅲ
15	38.775	0.972	50.624	78.952	238.946	−1 000	−0.001 7	0.003 6	0.46	1.0	1.4
35	1 078.201	14.663	9 540.340	9.603	16.151	−1 000	−0.006 5	0.040 0	0.71	1.1	1.0

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表 4 弹道冲击实验中数值模拟的材料参数^[26]

Table 4. Material parameters for the numerical simulations of ballistic impact experiments^[26]

w/%	$ {\rho _{\rm{areal}}} $/(kg·m⁻²)	$ {f_{\rm{rs0}}} $	$ k $	$ \xi $
15	0.523	0.4	0.272	0.444
35	0.722	0.4	0.957	0.321

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表 5 低速冲击实验中STF流变特性的拟合参数^[35]

Table 5. Parameters for fitting the rheological properties of STF used in low velocity impact experiments^[35]

${\eta _0}/({\rm{Pa}} \cdot{\rm{ s}})$	${\eta _{\rm{c}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\eta _{\rm{max}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\dot \gamma _{\rm{c}}}$/s⁻¹	${\dot \gamma _{\rm{max}}}$/s⁻¹	K_Ⅰ	K_Ⅱ	K_Ⅲ	n_Ⅰ	n_Ⅱ	n_Ⅲ
20.677	5.26	362	54.5	164.725	−5	−0.02	0.005	0.7	1.2	2.0

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表 6 低速冲击实验中数值模拟的材料参数^[35–36]

Table 6. Material parameters for the numerical simulations of low velocity impact experiments^[35–36]

$ {\rho _{\rm{{areal}}}} $/(kg·m⁻²)	$ {f_{\rm{rs0}}} $	$ k $	$ \xi $
0.3032	0.16	0.814	0.796

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表 7 准静态穿刺实验中STF流变特性的拟合参数^[36]

Table 7. Parameters for fitting the rheological properties of STF used in quasi-static puncture experiments^[36]

${\eta _0}/({\rm{Pa}} \cdot {\rm{s}})$	${\eta _{\rm{c}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\eta _{\rm{max}}}/({\rm{Pa}} \cdot{\rm{ s}})$	${\dot \gamma _{\rm{c}}}$/s⁻¹	${\dot \gamma _{\rm{max}}}$/s⁻¹	K_Ⅰ	K_Ⅱ	K_Ⅲ	n_Ⅰ	n_Ⅱ	n_Ⅲ
2845	852	7449	58.808	570.207	−20000	−0.006	0.0012	0.47	1.7	1.4

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表 8 准静态穿刺实验中数值模拟的材料参数^[36]

Table 8. Material parameters for the numerical simulations of quasi-static puncture experiments^[36]

$ {\rho_{\rm{{areal}}}}$/(kg·m⁻²)	$ {f_{\rm{{rs0}}}} $	$ k $	$ \xi $
0.5443	0.1	0.814	0.741

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