Page 101 - 《爆炸与冲击》2025年第9期

100
10
10
0.1
0.1 s 100 5−5 0 s 5−5 0
5−5 0 5−5 0 5− 50 5− 50
5− 50 5− 50 0 0− 5 0 0− 5
0 0− 5 0 0− 5
0.01 0.1 0.01 0.1
第 45 卷 崔 鹏，等： 动荷载下硅砂的破碎特性及吸能效应试验研究 第 9 期
(a) 162.73−166.50 s −1 (b) 220.33−227.53 s −1
100

10

lgP(d) 1

0.1 Pre-impact Post-impact
2.5−5.0 mm 2.5−5.0 mm
1.25−2.50 mm 1.25−2.50 mm
0.60−1.25 mm 0.60−1.25 mm
0.01 0.1 1
lg(d i /d max )
(c) 314.65−325.52 s −1
图 21 分形维数演化模式
Fig. 21 Fractal dimension evolution model

2
 −0.15σ max +1.63 2.5 mm≤d＜5.0 mm， R = 0.65
2
γ = −0.17σ max +2.01 1.25 mm≤d＜2.50 mm， R = 0.95 (11)
 2
−0.2σ max +2.30 0.60 mm≤d＜1.25 mm， R = 0.99

1.8
162.73−166.50 s −1 1.6 2.5−5.0 mm
1.6 220.33−227.53 s −1 1.25−2.50 mm
1.4 314.65−325.52 s −1 1.4 0.60−1.25 mm
Fractal dimension 1.0 Fractal dimension 1.2
1.2
0.8
0.6
0.4 1.0
0.2 0.8
0.15 0.20 0.25 0.30 0.35 0.40 0.45
0 1 2 3 4
Effective diameter/mm Relative breakage

图 22 不同应变率下有效粒径与分形维数的关系 图 23 不同粒径下相对破碎率与分形维数的关系
Fig. 22 Relationship between effective particle size and fractal Fig. 23 Relationship between relative breakage and fractal
dimension at different strain rates dimension under different particle sizes

2.0

1.8
1.6
Fractal dimension 1.2
1.4

1.0
0.8
1.25−2.50 mm
0.6 2.5−5.0 mm
0.60−1.25 mm
0.4
2 3 4 5 6 7
Peak stress/MPa
图 24 分形维数与峰值应力的关系
Fig. 24 Relationship between fractal dimension and peak stress

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