Strain Rate Effect of GFRP-Reinforced Circular Steel Tube under Low-Velocity Impact
-
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。
-
关键词:
- 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. -
表 1 试件设计尺寸
Table 1. Design size of tested specimens
Specimen D×t/(mm×mm) [θ/(°)]n tc/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 A/MPa B/MPa n m Tm/K Tr/K 272.28 899.7 0.94 0.1515 1795 293 D1 D2 D3 D4 D5 –43.408 44.608 0.016 0.0145 –0.046 Failure modes Initial failure criterions Damage evolution laws Fiber tensile failure Ft1=(σ1Xt)2+(σ4S12)2+(σ6S13)2⩾1 Dt1=εft1εft1−εit1(1−εit1ε1) Fiber compression failure Fc1=(σ1Xc)2⩾1 Dc1=εfc1εfc1−εic1(1−εic1ε1) Resin tensile failure Ft2=(σ2Yt)2+(σ4S12)2+(σ5S23)2⩾1 Dt2=εft2εft2−εit2(1−εit2ε2) Resin compression failure Fc2=(τnt(θ)SA23+μntσn(θ))2+(τnl(θ)S12+μnlσn(θ))2 Dc2=γfrγfr−γir(1−γirγr) Stretch in-layer delamination Ft3=(σ3Zt)2+(σ6S13)2+(σ5S23)2 Dt3=εft3εft3−εit3(1−εit3ε3) Compression in-layer delamination Fc3=(σ3Zc)2+(σ6S13)2+(σ5S23)2 Dc3=εfc3εfc3−εic3(1−εic3ε3) Modulus/GPa Poisson’s ratio Strength/MPa Fracture energy/(N·mm) E1=41.29; E2=E3=4.21; ν12=ν13=0.31; Xt =884.5; Xc =837.17; Yt=Zt=37.38; Γt1=28.25; Γc1=80.1; G12=G13=3.16; G23=3.0 ν23=0.42 Yc =Zc=145; S12=S13=44.765; S23=50.88 Γt2=Γt3=0.36; Γc2=Γc3=7.24 Elastic properties/GPa Strength/MPa Fracture toughness/(N·mm−1) B-K parameter Knn =4210; Ktt=3160; Kll=3160 Tn =37.380; Tt=44.765; Tl=44.765 Gn =0.36; Gt=1.33; Gl=1.33 η=2.6 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 α β γ Parameter α β γ E11/GPa 41.29 1.139 0.276 Xt/MPa 837.17 7.721 0.886 E22/GPa 4.21 0.437 0.262 Yt/MPa 37.38 13.088 0.131 G12/GPa 3.16 –0.941 0.054 Yc/MPa 145 0.11 1.278 Xt/MPa 881.5 7.721 0.886 S/MPa 44.756 15.656 0.086 表 8 仿真试件设计
Table 8. Design of simulated specimens
Specimen D/mm t/mm [θ/(°)]n tc/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 -
[1] 岳清瑞, 杨勇新. 纤维增强复合材料加固结构耐久性研究综述 [J]. 建筑结构学报, 2009, 30(6): 8–15.YUE Q R, YANG Y X. Introduction to durability of concrete strengthened with fiber reinforced polymers [J]. Journal of Building Structures, 2009, 30(6): 8–15. [2] ZHI X D, WU Q J, WANG C. Experimental and numerical study of GFRP-reinforced steel tube under axial impact loads [J]. International Journal of Impact Engineering, 2018, 122: 23–37. doi: 10.1016/j.ijimpeng.2018.07.018 [3] BATUWITAGE C, FAWZIA S, THAMBIRATNAM D, et al. Impact behaviour of carbon fibre reinforced polymer (CFRP) strengthened square hollow steel tubes: a numerical simulation [J]. Thin-Walled Structures, 2018, 131: 245–257. doi: 10.1016/j.tws.2018.06.033 [4] ALAM M I, FAWZIA S. Numerical studies on CFRP strengthened steel columns under transverse impact [J]. Composite Structures, 2015, 120: 428–441. doi: 10.1016/j.compstruct.2014.10.022 [5] 李洋, 王俊, 刘伟庆. 纤维复合材料-钢组合柱侧向冲击试验和有限元仿真分析 [J]. 钢结构, 2017, 32(2): 21–26.LI Y, WANG J, LIU W Q. Experimental study and FE simulation of the anti-impact performance of GFRP-steel column subjected to transverse impact [J]. Steel Construction, 2017, 32(2): 21–26. [6] KADHIM M M A, WU Z J, LEE S C. Loading rate effects on CFRP strengthened steel square hollow sections under lateral impact [J]. Engineering Structures, 2018, 171: 874–882. doi: 10.1016/j.engstruct.2018.04.066 [7] KADHIM M M A, WU Z J, LEE S C. Experimental study of CFRP strengthened steel columns subject to lateral impact loads [J]. Composite Structures, 2018, 185: 94–104. doi: 10.1016/j.compstruct.2017.10.089 [8] JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large Strains, high strain rates and high temperatures [C]//Proceedings of the Seventh International Symposium on Ballistics. The Hague, Netherlands, 1983: 1–7. [9] ZERILLI F J, ARMSTRONG R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations [J]. Journal of Applied Physics, 1987, 61(5): 1816–1825. doi: 10.1063/1.338024 [10] LIN L, FAN F, ZHI X D. Dynamic constitutive relation and fracture model of Q235A steel [J]. Applied Mechanics and Materials, 2013, 274: 463–466. doi: 10.4028/www.scientific.net/AMM.274 [11] ZHANG D N, SHANGGUAN Q Q, XIE C J, et al. A modified Johnson-Cook model of dynamic tensile behaviors for 7075-T6 aluminum alloy [J]. Journal of Alloys and Compounds, 2015, 619: 186–194. doi: 10.1016/j.jallcom.2014.09.002 [12] TAN J Q, ZHAN M, LIU S, et al. A modified Johnson-Cook model for tensile flow behaviors of 7050-T7451 aluminum alloy at high strain rates [J]. Materials Science and Engineering:A, 2015, 631: 214–219. doi: 10.1016/j.msea.2015.02.010 [13] HASHIN Z. Failure criterion for unidirectional fiber composite [J]. Journal of Applied Mechanics, 1980, 47: 329–334. doi: 10.1115/1.3153664 [14] PUCK A, SCHURMANN H. Failure analysis of FRP laminates by means of physically based phenomenological models [J]. Composites Science and Technology, 2001, 62: 1633–1662. [15] SINGH H, NAMALA K K, MAHAJAN P. A damage evolution study of E-glass/epoxy composite under low velocity impact [J]. Composites Part B: Engineering, 2015, 76: 235–248. doi: 10.1016/j.compositesb.2015.02.016 [16] LIAO B B, LIU P F. Finite element analysis of dynamic progressive failure of plastic composite laminates under low velocity impact [J]. Composite Structures, 2017, 159: 567–578. doi: 10.1016/j.compstruct.2016.09.099 [17] Dassault Systèmes Simulia Corp. ABAQUS 6.11 user’s manual [Z]. Providence, RI: Dassault Systèmes Simulia Corp, 2011. [18] SHOKRIEH M M, KARAMNEJAD A. Investigation of strain rate effects on the dynamic response of a glass/epoxy composite plate under blast loading by using the finite difference method [J]. Mechanics of Composite Materials, 2014, 50(3): 295–310. doi: 10.1007/s11029-014-9415-1 -