一种新形式的钢纤维混凝土冲击动态本构关系及材料参数的确定

叶中豹; 李永池; 赵凯; 黄瑞源; 孙晓旺; 张永亮

doi:10.11883/bzycj-2016-0252

摘要: 采用∅75 mm大口径SHPB系统进行了钢纤维体积率为0%、0.75%、1.5%三种混凝土材料动态性能实验，得出了不同钢纤维含量、不同应变率下的材料应力-应变关系曲线，实验结果表明：随着纤维含量及应变率的增加，钢纤维混凝土材料的峰值应变、峰值应力都随之提高，并在峰值应力之后出现应力的应变软化现象。以此实验结果为基础，提出了一种依赖于应变和应变率相关函数的新型非线性黏塑性动态本构关系，并通过对实验曲线的三步逐次最小二乘优选模拟，得到了相应的材料参数。结果表明，该本构关系对实验数据的模拟效果较好。

关键词:

Abstract: In the present study we carried out the dynamic compression experiments of steel fiber reinforced concrete with the fiber volume ratios of 0%, 0.75% and 1.5% using the ∅75 mm large-diameter split Hopkinson pressure bar experimental system to obtain the stress-strain curves at different strain rates. The experimental results show that with the increase of the fiber content and the strain rate, both the peak strain and the peak stress of the steel reinforced concrete rise higher, and the strain softening is observed after the peak stress. Based on the assumption that there are two independent factors controlling the dynamic behavior of the steel fiber reinforced concrete, one related to the strain to indicate the nonlinear stress-strain behavior and the other related to the strain rate to express the strain rate effect, a new type of the dynamic nonlinear visco-plastic constitutive equation was proposed. The details concerning how to get the equation and the material parameters were discussed thoroughly. The experiment curves were fitted using the least squares optimization numerical simulations. Good agreement between the numerical simulations and the experiment curves was achieved, thereby concluding that the new constitutive relation proposed is perfect for steel fiber reinforced concrete.

Key words:

steel fiber reinforced concrete (SFRC) /
SHPB /
strain rate effect /
dynamic constitutive relation

图 1 应力应变曲线

Figure 1. Stress-strain curve

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图 2 实验拟合曲线

Figure 2. Experimental and fitting curves

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图 3 不同条件下的实验和拟合曲线

Figure 3. Experimental and fitting curves under different conditions

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表 1 钢纤维混凝土原料配比

Table 1. Mix proportion of the steel fiber concrete

试件	φ/%	各组分的体积质量/(kg·m^-3)
试件	φ/%	水泥	细骨料	粗骨料	减水剂	水	钢纤维
A	0	440	834	1 018	6.6	158	0
B	0.75	440	834	997	6.6	158	59
C	1.5	440	834	978	6.6	158	117

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表 2 式(2)拟合参数

Table 2. Fitting parameters in Eq.(2)

φ/%	a₁/GPa	a₂/TPa	a₃/TPa	a₄/TPa
0	22.9	-2.28	76.5	-828

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表 3 拟合结果

Table 3. Fitting results

φ/%	${\dot \varepsilon }$ /s^-1	$k\left( {\dot \varepsilon } \right)$
0	45.42	1.00
0	62.51	1.18
0	86.12	1.60
0.75	38.24	1.28
0.75	82.21	1.56
0.75	120.13	1.99
1.5	75.68	1.14
1.5	130.08	1.70
1.5	149.13	2.25

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表 4 式(4)拟合参数

Table 4. Fitting parameters in Eq. (4)

φ/%	c₀	c₁	c₂
0	1.0	0.21	1.14
0.75	1.3	0.10	0.64
1.5	3.4	-7.00	5.10

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