GFRP增强圆钢管在低速冲击荷载作用下的应变率效应

武启剑; 支旭东

doi:10.11858/gywlxb.20180653

GFRP增强圆钢管在低速冲击荷载作用下的应变率效应

doi: 10.11858/gywlxb.20180653

武启剑^{1, 2,},
支旭东^{1, 2,*, ,}

1.
哈尔滨工业大学结构工程灾变与控制教育部重点实验室，黑龙江哈尔滨　150090
2.
哈尔滨工业大学土木工程防灾减灾工信部重点实验室，黑龙江哈尔滨　150090

基金项目: 国家自然科学基金(51478144)

详细信息

作者简介:
武启剑（1991－），男，博士研究生，主要从事从事大跨空间结构研究. E-mail：951064631@qq.com

通讯作者:
支旭东（1977－），男，博士，教授，主要从事大跨空间结构研究. E-mail：zhixudong@hit.edu.cn

中图分类号: O383.3; TU398.9
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出版历程
- 收稿日期: 2018-10-16
- 修回日期: 2018-11-06

Strain Rate Effect of GFRP-Reinforced Circular Steel Tube under Low-Velocity Impact

WU Qijian^{1, 2
,},
ZHI Xudong^{1, 2,*
, ,}

1.
Key Laboratory of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
2.
Key Laboratory of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China

摘要

摘要: 讨论了玻璃纤维/环氧树脂复合材料（Glass Fiber Reinforced Plastic，GFRP）增强Q235圆钢管在低速冲击荷载作用下的应变率效应。通过轴压试验和轴向低速冲击试验获得了试件在准静态和低速冲击状态下的力学响应（轴向荷载及轴向位移），为后续仿真工作提供了依据。编写了可以考虑初始失效、损伤演化及应变率效应的GFRP材料子程序（VUMAT），并基于ABAQUS对构件的轴压及轴向冲击过程进行了仿真再现。通过仿真将不考虑应变率效应、只考虑钢管应变率效应、只考虑GFRP应变率效应、考虑钢管及GFRP应变率效应4种情况下的结果进行了对比分析。
- 应变率效应 /
- 钢管 /
- 玻璃纤维/环氧树脂复合材料 /
- 低速冲击试验 /
- 有限元模拟
Abstract: This paper discussed the strain rate effect of glass fiber/epoxy resin composite (GFRP)-reinforced Q235 circular steel tube under low-velocity impact load. Firstly, the responses (axial load and displacement) of GFRP-reinforced steel tube under quasi-static and low-velocity impact load were obtained through axial compression tests and low-velocity impact tests respectively, which provided gist for the subsequent simulation. Secondly, a VUMAT subroutine considered initial failure modes, damage evolution and strain rate effect of GFRP was introduced; then the axial compression and low-velocity impact processes were simulated. Finally, the results under 4 situations (ignoring strain rate effect, considering the strain rate effect of steel tube, considering the strain rate effect of GFRP and considering the strain rate effect of both steel tube and GFRP) was compared using simulation.
- strain rate effect /
- steel tube /
- glass fiber/epoxy resin composite /
- low-velocity impact test /
- finite element simulation

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图 1 试件符号说明及实物图

Figure 1. Symbol description and pictures of specimen

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图 2 轴压试验系统

Figure 2. Compression test system

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图 3 落锤试验系统

Figure 3. Drop hammer test system

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图 4 D-58-1.5-30-3.0的重复试验结果

Figure 4. Repeated test results of D-58-1.5-30-3.0

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图 5 轴压试验及低速冲击试验结果对比

Figure 5. Comparison of test results between compression test and low-velocity impact test

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图 6 GFRP增强圆钢管有限元模型

Figure 6. Finite element model of GFRP reinforced circular steel tube

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图 7 落锤有限元模型

Figure 7. Finite element model of drop hammer

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图 8 钢管材性试验结果^[2]

Figure 8. Material test result for steel tube^[2]

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图 9 VUMAT子程序算法

Figure 9. Computational algorithm of the VUMAT subroutine

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图 10 仿真与试验试件损伤模式对比

Figure 10. Comparison between simulation and measured damage modes

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图 11 仿真及试验荷载-位移曲线对比

Figure 11. Compared load-displacement curves between simulation and low-velocity impact test

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图 12 D-58-2.0-90-4.5在不同情况下的仿真结果

Figure 12. Simulated results of D-58-2.0-90-4.5 with different situations

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图 14 仿真结果对比

Figure 14. Comparison of simulated result

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图 13 试件A-1～A-5的仿真结果

Figure 13. Simulated results of A-1–A-5

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表 1 试件设计尺寸

Table 1. Design size of tested specimens

Specimen	D×t/(mm×mm)	[$\theta$/(°)]_n	t_c/mm	L/mm	Type of test	v/(m·s⁻¹)	Maximum strain rate/s⁻¹
S-58-1.5-30	58.0×1.5	[30/–30]₃	2.0	100.0	Compression
S-58-2.0-90	58.0×2.0	[90]₆	2.0	100.0	Compression
D-58-1.5-30-3.0	58.0×1.5	[30/–30]₃	2.0	100.0	Impact	3.0	9.5
D-58-1.5-30-4.5	58.0×1.5	[90]₆	2.0	100.0	Impact	4.5	21.1
D-58-2.0-90-4.5	58.0×2.0	[90]₆	2.0	100.0	Impact	4.5	21.1

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表 2 Johnson-Cook模型参数^[2]

Table 2. Parameters of the Johnson-Cook model^[2]

A/MPa	B/MPa	n	m	T_m/K	T_r/K
272.28	899.7	0.94	0.1515	1795	293

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表 3 Johnson-Cook断裂准则参数^[2]

Table 3. Parameters of the Johnson-Cook fracture criterion^[2]

D₁	D₂	D₃	D₄	D₅
–43.408	44.608	0.016	0.0145	–0.046

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表 4 初始失效准则及损伤演化法则^[2]

Table 4. Initial failure criterions and damage evolution laws^[2]

Failure modes	Initial failure criterions	Damage evolution laws
Fiber tensile failure	$F_1^{\rm t} = {\left( {\dfrac{{\sigma {}_1}}{{{X_{\rm t}}}}} \right)^2} + {\left( {\dfrac{{\sigma {}_4}}{{{S_{12}}}}} \right)^2} + {\left( {\dfrac{{\sigma {}_6}}{{{S_{13}}}}} \right)^2} \geqslant 1{\rm{ }}$	$D_1^{\rm t} = \dfrac{{\varepsilon _1^{\rm {ft}}}}{{\varepsilon _1^{\rm {ft}} - \varepsilon _1^{\rm {it}}}}\left( {1 - \dfrac{{\varepsilon _1^{\rm {it}}}}{{{\varepsilon _1}}}} \right)$
Fiber compression failure	$F_1^{\rm c} = {\left( {\dfrac{{\sigma {}_1}}{{{X\rm_c}}}} \right)^2} \geqslant 1$	$D_1^{\rm c} = \dfrac{{\varepsilon _1^{\rm{fc}}}}{{\varepsilon _1^{\rm{fc}} - \varepsilon _1^{\rm{ic}}}}\left( {1 - \dfrac{{\varepsilon _1^{\rm{ic}}}}{{{\varepsilon _1}}}} \right)$
Resin tensile failure	$F_2^{\rm t} = {\left( {\dfrac{{\sigma {}_2}}{{{Y_{\rm t}}}}} \right)^2} + {\left( {\dfrac{{\sigma {}_4}}{{{S_{12}}}}} \right)^2} + {\left( {\dfrac{{\sigma {}_5}}{{{S_{23}}}}} \right)^2} \geqslant 1{\rm{ }}$	$D_2^{\rm t} = \dfrac{{\varepsilon _2^{\rm{ft}}}}{{\varepsilon _2^{\rm {ft}} - \varepsilon _2^{\rm{it}}}}\left({1 - \dfrac{{\varepsilon _2^{\rm{it}}}}{{{\varepsilon _2}}}} \right)$
Resin compression failure	$F_2^{\rm c} = {\left( {\dfrac{{{\tau _{nt}}\left( \theta \right)}}{{S_{23}^{\rm A} + {\mu _{nt}}{\sigma _n}\left( \theta \right)}}} \right)^2} + {\left( {\dfrac{{{\tau _{nl}}\left( \theta \right)}}{{{S_{12}} + {\mu _{nl}}{\sigma _n}\left( \theta \right)}}} \right)^2}$	$D_2^{\rm c} = \dfrac{{\gamma_{\rm r}^{\rm f}}}{{\gamma _{\rm r}^{\rm f} - \gamma _{\rm r}^{\rm i}}}\left( {1 - \dfrac{{\gamma _{\rm r}^{\rm i}}}{{{\gamma _r}}}} \right)$
Stretch in-layer delamination	$F_3^{\rm t} = {\left( {\dfrac{{{\sigma _3}}}{{{Z_{\rm t}}}}} \right)^2} + {\left( {\dfrac{{{\sigma _6}}}{{{S_{13}}}}} \right)^2} + {\left( {\dfrac{{{\sigma _5}}}{{{S_{23}}}}} \right)^2}$	$D_3^{\rm t} = \dfrac{{\varepsilon _3^{\rm ft}}}{{\varepsilon _3^{\rm ft} - \varepsilon _3^{\rm it}}}\left( {1 - \dfrac{{\varepsilon _3^{\rm it}}}{{{\varepsilon _3}}}} \right)$
Compression in-layer delamination	$F_3^{\rm c} = {\left( {\dfrac{{{\sigma _3}}}{{{Z_{\rm c}}}}} \right)^2} + {\left( {\dfrac{{{\sigma _6}}}{{{S_{13}}}}} \right)^2} + {\left( {\dfrac{{{\sigma _5}}}{{{S_{23}}}}} \right)^2}$	$D_3^{\rm c} = \dfrac{{\varepsilon _3^{\rm fc}}}{{\varepsilon _3^{\rm fc} - \varepsilon _3^{\rm ic}}}\left( {1 - \dfrac{{\varepsilon _3^{\rm ic}}}{{{\varepsilon _3}}}} \right)$

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表 5 GFRP单向板材料性能^[2]

Table 5. Material properties of GFRP unidirectional laminate^[2]

Modulus/GPa	Poisson’s ratio	Strength/MPa	Fracture energy/(N·mm)
E₁=41.29; E₂=E₃=4.21;	${\nu}$₁₂=${\nu}$₁₃=0.31;	X_t=884.5; X_c=837.17; Y_t=Z_t=37.38;	${\varGamma _1^{\rm t} = 28.25}$; ${\varGamma _1^{\rm c} = 80.1}$;
G₁₂=G₁₃=3.16; G₂₃=3.0	${\nu}$₂₃=0.42	Y_c=Z_c=145; S₁₂=S₁₃=44.765; S₂₃=50.88	${\varGamma _2^{\rm t} = \varGamma _3^{\rm t}= 0.36}$; ${\varGamma_2^{\rm c} = \varGamma_3^{\rm c}=7.24}$

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表 6 界面性能参数^[2]

Table 6. Parameters of cohesive behavior^[2]

Elastic properties/GPa	Strength/MPa	Fracture toughness/(N·mm⁻¹)	B-K parameter
K_nn=4210; K_tt=3160; K_ll=3160	T_n=37.380; T_t=44.765; T_l=44.765	G_n=0.36; G_t=1.33; G_l=1.33	$\eta$=2.6

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表 7 GFRP应变率效应模型所需参数

Table 7. Parameters for the model considering the strain rate effect of GFRP

Parameter	${\alpha}$	${\;\beta }$	${\gamma}$	Parameter	${\alpha}$	${\;\beta }$	${\gamma}$
E₁₁/GPa	41.29	1.139	0.276	X_t/MPa	837.17	7.721	0.886
E₂₂/GPa	4.21	0.437	0.262	Y_t/MPa	37.38	13.088	0.131
G₁₂/GPa	3.16	–0.941	0.054	Y_c/MPa	145	0.11	1.278
X_t/MPa	881.5	7.721	0.886	S/MPa	44.756	15.656	0.086

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表 8 仿真试件设计

Table 8. Design of simulated specimens

Specimen	D/mm	t/mm	[$\theta$/(°)]_n	t_c/mm	L/mm	Displacement/mm	Loading speed/(m·s⁻¹)
A-1	58.0	2.0	[90]₆	2.0	100	20.0	Quasi-static
A-2	58.0	2.0	[90]₆	2.0	100	20.0	2.0
A-3	58.0	2.0	[90]₆	2.0	100	20.0	4.0
A-4	58.0	2.0	[90]₆	2.0	100	20.0	6.0
A-5	58.0	2.0	[90]₆	2.0	100	20.0	8.0
B-1	58.0	2.0	[90]₆	3.0	100	20.0	Quasi-static
B-2	58.0	2.0	[90]₆	3.0	100	20.0	2.0
B-3	58.0	2.0	[90]₆	3.0	100	20.0	4.0
B-4	58.0	2.0	[90]₆	3.0	100	20.0	6.0
B-5	58.0	2.0	[90]₆	3.0	100	20.0	8.0
C-1	58.0	3.0	[90]₆	2.0	100	20.0	Quasi-static
C-2	58.0	3.0	[90]₆	2.0	100	20.0	2.0
C-3	58.0	3.0	[90]₆	2.0	100	20.0	4.0
C-4	58.0	3.0	[90]₆	2.0	100	20.0	6.0
C-5	58.0	3.0	[90]₆	2.0	100	20.0	8.0

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