Quasi-static mechanical properties and constitutive model of fly ash cenosphere/aluminum syntactic foam
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摘要: 为研究粉煤灰空心球/Al(Fly ash cenosphere/aluminum syntactic foam，FAC/Al)复合泡沫材料静力性能，采用万能试验机对铝基复合泡沫材料进行了准静态轴向压缩性能试验，考察了不同空心球平均粒径(分别为150、200和300 μm)对铝基复合泡沫材料变形失效模式及力学性能的影响，并获取了具有不同空心球粒径的复合材料在准静态下的应力-应变曲线，在此基础上分析了空心球粒径大小对复合材料能量吸收性能的影响。试验结果表明，在准静态荷载作用下，随着空心球粒径的增大，复合材料的压缩屈服强度、吸能能力及理想吸能效率有着明显的降低。此外，在获得的应力-应变曲线基础上，采用最小二乘法拟合得到了铝基复合泡沫在准静态荷载作用下的本构方程，并对其进行了验证，结果表明该方程具有较好的拟合度。Abstract: In order to study the quasi-static performance of fly ash cenosphere/aluminum (FAC/Al) syntactic foam, quasi-static compression performance tests were conducted on the FAC/Al specimens by using a universal testing machine. The effects of different average particle sizes on the deformation and failure modes and mechanical performance of the aluminum matrix composite foam material specimens were investigated, and the stress-strain curves of the material specimens with different particle sizes under quasi-static load were obtained. And based on the stress-strain curves, the effects of particle sizes on the energy absorption performance of the material were analyzed. And the test results show that the compressive yield strength and energy absorption capacity and the ideal absorption efficiency of the material decrease with the increase of the particle sizes. In addition, by using the least square method to fit based on the stress-strain curves, the constitutive equation of FAC/Al under quasi-static load was given and verified, and the results show that the equation has a good fitting.
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图 1 粉煤灰空心球(FAC)/Al基复合泡沫的设计思路[23]
Figure 1. Design for fly ash cenosphere (FAC)/aluminum syntactic foam
图 6 试验前后FAC/Al复合泡沫的金相显微图像
Figure 6. Metallographic microscopic images of FAC/Al composite foams ((a) Before test; (b) After test)
图 7 P-R001-L15-200 FAC/Al复合泡沫试件在应变率10−3s−1下的应力-应变曲线 (a) 和变形过程 (b)
Figure 7. Stress-strain curve (a) and deformation process (b) of FAC/Al syntactic foam specimen P-R001-L15-200 under the strain rate of 10−3s−1
图 8 15 mm高FAC/Al复合泡沫试件在应变率10−2 s−1下的应力-应变曲线
Figure 8. Stress-strain curves of the FAC/Al syntactic foam specimens with height of 15 mm under the strain rate of 10−2 s−1
图 10 5 mm高FAC/Al复合泡沫试件在应变率10−2 s−1下的应力-应变曲线
Figure 10. Stress-strain curves of the FAC/Al syntactic foam specimens with height of 5 mm under the strain rate of 10−2 s−1
图 11 不同应变率下15 mm高、200 μm粒径FAC/Al复合泡沫试件的应力-应变曲线
Figure 11. Stress-strain curves of the FAC/Al syntactic foam specimens with 200 μm cenosphere in height of 15 mm under different strain rates
图 12 15 mm高、不同FAC粒径的FAC/Al复合泡沫试件平均弹性模量与应变率的关系
Figure 12. Relationship between the average elastic modulus and strain rate of the FAC/Al syntactic foam specimens with different cenospheres in height of 15 mm
图 13 15 mm高、不同FAV粒径FAC/Al复合泡沫吸能能力-应变曲线
Figure 13. Energy absorption ability-strain curves of the FAC/Al syntactic foam specimens with different cenospheres in height of 15 mm
图 14 15 mm高、不同FAC粒径FAC/Al复合泡沫吸能效率-应力曲线
Figure 14. Energy absorption efficiency-stress curves of the FAC/AL specimens with different cenospheres in height of 15 mm
图 15 15 mm高、不同FAC粒径FAC/Al复合泡沫理想吸能效率-应力曲线
Figure 15. Ideal energy absorption efficiency-stress curves of the FAC/Al syntactic foam specimens with different cenospheres in height of 15 mm
图 9 15 mm FAC/Al复合泡沫试件在应变率10−1 s−1下的应力-应变曲线
Figure 9. Stress-strain curves of the FAC/Al syntactic foam specimens with height of 15 mm under the strain rate of 10−1 s−1
图 16 FAC/Al复合泡沫试件P-R001-L15-200和P-R01-L15-200的试验与拟合曲线对比
Figure 16. Test curve and fitting curve of the FAC/Al syntactic foam specimen P-R001-L15-200 and P-R01-L15-200
图 17 FAC/Al复合泡沫密度影响函数
$G(\rho )$ 与密度的关系Figure 17. Relationship between G(ρ) and density of FAC/Al syntactic foam
图 18 FAC/Al复合泡沫试件P-R01-L15-300和P-R1-L15-150的试验曲线与拟合曲线对比
Figure 18. Test and fitting curves of the FAC/Al syntactic foam specimen P-R01-L15-300 and P-R1-L15-150
表 1 FAC/Al复合泡沫试件几何参数及加载应变率
Table 1. Geometric parameters and loading strain rates of FAC/Al syntactic foam specimens
Group Foam Length/mm Cenosphere particle size/μm Strain rate/s−1 Diameter/mm Group1 P-R001-L15-150 15 150 0.001 10 P-R001-L15-200 15 200 0.001 10 P-R001-L15-300 15 300 0.001 10 Group2 P-R01-L15-150 15 150 0.01 10 P-R01-L15-200 15 200 0.01 10 P-R01-L15-300 15 300 0.01 10 Group3 P-R1-L15-150 15 150 0.1 10 P-R1-L15-200 15 200 0.1 10 P-R1-L15-300 15 300 0.1 10 Group4 P-R01-L5-150 5 150 0.01 10 P-R01-L5-200 5 200 0.01 10 P-R01-L5-300 5 300 0.01 10 Notes: P—Compression; R001, R01 and R1—Strain rate are 0.001, 0.01 and 0.1, respectively; L15 and L5—Length are 15 and 5 mm, respectively; 150, 200 and 300—Cenosphere particle size. 
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表 2 FAC/Al复合泡沫应变相关形状函数的拟合参数Ai
Table 2. Fitting parameters of strain dependent shape function Ai of FAC/Al syntactic foam specimens
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 2 199.66 −21 182.08 −265 269.12 6.70×106 −5.71×107 2.62×108 −7.13×108 1.15×109 −1.02×109 3.83×108
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