Energy Dissipation Analyses on LightWeight Foam Concrete under Impact Loads

Yuan Pu, Ma Qinyong, Zhang Haidong

MOE Research Center of Mine Underground Engineering, Anhui University of Science and Technology, Huainan, Anhui 232001, China e-mail: [email protected]

ABSTRACT A modified aluminium split Hopkinson pressure bar apparatus with diameter of 37 mm was developed to conduct the impact uniaxial compression tests for light-weight foam concrete. Light-weight foam concrete specimens whose density was 220 kg/m3 were processed into a cylinder with a length to diameter ratio of 0.45. Then the mechanism of energy dissipation for light-weight foam concrete under impact loads was investigated by analysing the incident wave energy, reflected wave energy, transmitted wave energy and energy absorption rate of lightweight foam concrete in impact uniaxial compression tests. The results show that the energy absorption rate of light-weight foam concrete decreases in a negative power relation with the incident wave energy increasing. The reflected wave energy is very close to incident wave energy, and the transmitted wave energy passing through the light-weight foam concrete is almost zero. All this illustrates that the mechanism of energy dissipation for light-weight foam concrete is not absorbing the wave energy on it, but reflecting them. When light-weight foam concrete is used in compound structure as a protective layer or interlayer, light-weight foam concrete can reduce vibration effectively and act a perfect energy dissipation effect. Thus the anti-impact property of structure is improved.

KEYWORDS: foam concrete; split Hopkinson pressure bar; energy dissipation; energy

absorption rate

INTRODUCTION With more attention paid to the safety and protection of structures, researches on porous materials, such as aluminum foam, polyurethane foam, foam concrete, have become more and more widely for its good buffering, vibration damping and energy absorption characteristics. It is essential to predict the high strain rate response of structures under impact loads which based on the best understanding of dynamic properties. Early researches mainly focus on the statics properties and microstructure of porous materials (Ridha & Shim, 2008; Just & Middendorf, 2009; Kunhanandan &Ramamurthy, 2007 and Wang, 2013). But researches on statics properties cannot explain the mechanism for energy absorption or buffering for low strain rate. Then, some - 8667 -

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researchers begin to conduct test under impact loads to investigating its dynamic properties (Song et al. 2007; Song et al. 2006; Flores & Li, 2011 and Tan et al. 2005). Split Hopkinson pressure bar apparatus (Kolsky, 1949) is a widely used apparatus in investigating dynamic properties of materials at high strain rate. The dynamic responses of underground tunnels with or without foam concrete foam concrete backfill layer are simulated by software ANSYS/LS-DYNA (Tang et al. 2006), the results shows that the stress value peak in tunnel with foam concrete backfill layer reduced by 95% compared with tunnel without foam concrete backfill layer. Aluminum split Hopkinson pressure bar apparatus is developed to study dynamic compression properties of foam concretes in four densities, 450, 600, 750 and 900 kg/m3 and the dynamic flow stress and dynamic Young’s modulus increases gradually with the density increasing (Liu & Li, 2010). Compound protective structure under with foam concrete under blasting loads is investigated (Wang et al. 2006), and the result shows that foam concrete has a great effect on energy absorption and reflection. Energy absorbing characteristics of compound protective structure under explosion is studied by model tests and compound protective structure is made by concrete with a foam concrete interlayer (Zhang 2010). Compound protective structure works on sacrificing the outer concrete layer and foam concrete interlayer to protect the inner layer concrete structure. Combining with the researches at home or abroad, foam concrete whose density is lower than 300 kg/m3 is taking as research object, impact uniaxial compression tests are developed to investigate the energy dissipation in light-weight foam concrete under various impact loads by modified aluminum split Hopkinson pressure bar apparatus with a diameter of 37mm.

TEST METHODS Light-weight Foam Concrete Light-weight foam concrete is made of Portland cement, fly ash and silica fume. Foaming agent is mixed at the stage of slurry agitation to produce uniformly distributed air voids. After curing and hardening, light-weight foam concrete in a porous structure is obtained. Light-weight foam concrete has a similar exterior with aluminum foams, but it is easily curing and does not need autoclaved curing. The main raw materials for foam concrete are Portland cement and fly ash. So its price is low and it is environmental friendly. Air voids in foam concrete are distributed uniformly and the thickness between air voids is very thin. As the diameter of air voids is much bigger than the thickness between air voids, the light-weight foam concrete get a big porosity, low density, and low impedance. Figure 1 shows a specimen of light-weight foam concrete whose density is 220 kg/m3. As can be seen from Figure 1, light-weight foam concrete has a closed-cell structure with an average cell size of 2 mm. Air voids in light-weight foam concrete are almost in sphere shape and are distributed uniformly. The thickness between air voids is very thin, and the diameter of air voids is much bigger than the thickness between air voids. True density of light-weight foam concrete is tested by pycnometer and it is 2 330 kg/m3. Through apparent density and true density tests, the porosity of light-weight foam concrete is obtained, and the value is more than 90%.

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Figure 1: Light-weight foam concrete By the research of Pankow et al. (2009), the inertial effect and friction effect in impact uniaxial compression test is the least when the length to radius ratio is 0.875 + 0.540εend, where εend is the final strain value of specimen. So light-weight foam concrete is processed into a cylinder with size of φ37 mm×16.5 mm. The flat should be within 0.02 mm and the deviation perpendicular to bar axis should be within 0.25 degree.

Modified Split Hopkinson Pressure Bar Apparatus Aluminum split Hopkinson pressure bar apparatus with diameter of 37 mm made by University of science and technology of China is adopted to develop impact uniaxial compression tests for light-weight foam concrete. The length of striker bar is 0.60 m. In order to avoiding the overlap of incident wave and reflected wave, the length of input bar should be more than twice of striker bar length. And the length of output bar should insure transmitted wave without disturbed. So the length of input bar and output bar are both 2.00 m. Striker bar, input bar, output bar are all made of aluminum alloy. The density of bars is 2700 kg/m3, the Young’s modulus is 70 GPa, and the longitudinal wave velocity is 5090 m/s. CS-1D dynamic strain indicator is used to collect and amplify the electrical signals measured by strain gauges. And Wheatstone bridge is used to connect the strain gauges and CS-1D dynamic strain indicator. TST 3406 dynamic testing analyzer is adopted to store these electronic signals for post data processing. As low density and small longitudinal wave velocity, the wave impedance of light-weight foam concrete is quite small and the wave impedance ratio between foam concrete and pressure bar is only 3/100. For very small wave impedance ratio, if impact uniaxial compression tests are developed by conventional aluminum split Hopkinson pressure bar, the ring time in incident pulse is very short, only 30 μs, which is not suitable for low impedance materials and the common foil type resistance strain gauge mounted on output bar cannot collect effective transmitted signals. So conventional aluminum split Hopkinson pressure bar should be modified to overcome its limitations. For short rising time in incident pulse, pulse shaping technique is adopted to extend the rising time and reduce the rising slope (Frew et al. 2005; Dai et al. 2010; Yuan et al. 2014). A slow rising incident wave is preferred to minimize the effect of dispersion, achieve dynamic stress

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equilibrium and ensure homogeneous deformation of specimen in impact uniaxial compression test. Grease is adopted as pulse shaper in impact compression tests. The rising time is extended to 150 μs and the incident pulse length is also extended from 300 μs to 400 μs. For weak transmitted pulse, it can be handled from two aspects, reducing wave impedance of output bar or changing measuring devices. In previous researches about impact tests for soft materials, viscoelastic pressure bar (Zhao et al. 1997) made of low impedance materials like PMMA or Nylon is suggested, but low impedance pressure bar always demonstrates a viscoelastic behavior. Hollow output bar (Chen et al. 1999) is also applied to improve the transmitted signals, but the ends of output bar should get special processed and it only improve the amplitude of transmitted wave by less than an order of magnitude. Higher sensitivity measurements can also be effective in collecting weak transmitted signals with a good signal to noise ratio. An X-cut quartz piezoelectric transducer (Chen et al. 2000) and semiconductor stain gauge (Liu et al. 1998) are developed to capture the transmitted force or transmitted strain directly. X-cut quartz is more sensitive in detecting forces than foil type resistance strain gauges. But the X-cut quartz piezoelectric transducer should be embedded in the middle of aluminum output bar. Semiconductor stain gauge with sensitive coefficient of 110 is also developed to capture the surface strain of output bar. It can be easily mounted on output bar and it gets a higher signal to noise ratio.

0.24

Voltage /V

0.18 0.12 0.06 0.00 -0.06 -0.12 -0.18 -0.24

0

100

200

300

400

500

Time /µs

600

700

800

900

Figure 2: Waves in impact uniaxial compression test In this paper, two methods, pulse shaping technique and semiconductor strain gauge technique, are both applied to modify conventional aluminum split Hopkinson pressure bar apparatus. Incident wave, reflected wave and transmitted wave measured in impact tests are shown in figure 2. Incident wave in figure 2 gets a very slow rise and a long rising time. Transmitted wave measured by semiconductor strain gauges is clear with a high signal to noise ratio. According to the theory of one dimensional stress wave propagation, dynamic characteristics of light-weight foam concrete, dynamic stress-strain curve , strain rate, dynamic flow stress, can be concluded by the electric signals obtained from strain gauges mounted on input bar and output bar.

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ENERGY DISSIPATION ANALYSES The involved energies in impact uniaxial compression test by modified split Hopkinson pressure bar apparatus are incident pulse energy WI, reflected pulse energy WR, transmitted pulse energy WT and absorbing energy of specimen WS (Song & Chen, 2006; Yuan & Ma, 2013). The calculation for above mentioned energies is shown as follows

Wi =

AC σ (t )i2 dt = EAC ∫ ε (t )i2 dt ∫ E

(i=I,R,T)

(1)

where σi(t) is the time resolved axial stress, εi(t) is time resolved axial strain, A is the crosssection area of pressure bar, C is the longitudinal wave velocity of bar material and E is the Young’s modulus of bar material. Subscript I, R, and T stand for incident wave, reflected wave and transmitted wave respectively. Since Vaseline is applied on both ends of specimens, energy loss caused by friction between the contact of specimen and pressure bar can be neglected during energy analyses. So the absorbing energy of light-weight foam concrete in impact compression test can be calculated as follows WS=WI－WR－WT

(2)

Substitution of equation (1) to equation (2) with the assumptions of stress uniformity gives

WS = 2 EAC ∫ ε (t ) R ε (t )T dt

(3)

In order to investigate the absorbing energy ability of light-weight foam concrete, a dimensionless quantity energy absorption rate (EAR) is introduce and determined by the equation EAR=WS/WI

(4)

Impact uniaxial compression tests for light-weight foam concrete are developed by modified aluminum split Hopkinson pressure bar apparatus in various velocities of striker. Figure 3 shows a time resolved energies involved in impact compression test when striker velocity is 5.90 m/s. And table 1 is energy statistics in impact uniaxial compression tests. Seen from figure 3, the time resolved energy for incident wave increases with the time growing at the initial phase. When reaching a certain value, it keeps constants. And the reflected wave energy shows a similar performance. The difference between incident wave energy and reflected wave energy is transmitted wave energy and energy absorbed by light-weight foam concrete. The transmitted energy and energy absorbed by light-weight foam concrete is much small. The reflected wave energy is slight less than incident wave energy. Thus, during the impact compression test, only few energy passes the light-weight foam concrete and reaches the output bar, most of the incident energy is reflected by light-weight foam concrete to input bar. Taking striker velocity v as horizontal coordinate, incident wave energy WI as vertical coordinate, data in table 1 is drawn as scatter diagram shown in figure 4. Incident wave energy WI increases with the striker velocity v squared growing. There is almost a linear relation between incident wave energy WI and striker velocity v squared. So quadratic function only containing striker velocity v squared is developed in fitting analysis and the function is given WI =0.626 v2

R2=0.99

Taking incident wave energy WI as horizontal coordinate, reflected wave energy WR as vertical coordinate, data in table 1 is drawn as scatter diagram shown in figure 5. Reflected wave

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energy WR increases with the incident wave energy WI growing. There is an approximate linear relation between incident wave energy WI and reflected wave energy WR. Thus linear function without intercept is adopted in fitting analysis and the function is given R2=0.99

WR =0.991 WI 20

Energy /J

16 12

WI WR WT WS

8 4 0 0

50

100

150

200

Time /µs

250

300

350

400

Figure 3: Curve of energy versus time Table 1: Energy statistics of impact uniaxial compression tests Number

v/(m·s-1)

WI/J

WR/J

WS/J

EAR/%

1

4.77

12.100

11.821

0.276

2.28

2

5.63

18.131

17.847

0.283

1.56

3

5.90

18.848

18.539

0.308

1.64

4

7.64

32.941

32.577

0.363

1.10

5

7.64

38.414

38.100

0.312

0.81

6

8.71

45.829

45.331

0.496

1.08

7

9.08

54.674

54.179

0.493

0.90

8

11.11

78.884

78.373

0.510

0.65

Taking incident wave energy WI as horizontal coordinate, energy absorption rate EAR of light-weight foam concrete as vertical coordinate, data in table 1 is drawn as scatter diagram shown in figure 6. Energy absorption rate EAR decreases with the incident wave energy WI increasing in a negative power relation approach. It decreases fast at the initial phase, then keep constants when reducing to a certain value. Power function is adopted in fitting analysis and the function is given EAR =11.563 WI － 0.67

R2=0.94

Taking striker velocity v as horizontal coordinate, energy absorption rate EAR of light-weight foam concrete as vertical coordinate, data in table 1 is drawn as scatter diagram shown in figure 7. Energy absorption rate EAR decreases with the striker velocity v increasing in a negative power relation approach. It decreases quickly at the initial phase, then keep constants after reducing to a certain value Power function is adopted in fitting analysis and the function is given

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90

90

75

75

60

60

WR /J

WI /J

WI =22.617 v－1.49

45

45

30

30

15

15

0

4

5

6

7

8

-1

v /m·s

9

10

11

0

12

0

Figure 4: Curve of WI vs ν

15

30

45

WI /J

60

75

90

Figure 5: Curve of WR vs WI 2.5

2.0

2.0

EAR /%

2.5

EAR /%

1.5

1.5

1.0

1.0

0.5 0.0

R2=0.91

0.5 0

15

30

45

WI /J

60

75

Figure 6: Curve of EAR vs WI

90

0.0 4

5

6

7

8 9 v /m·s-1

10

11

12

Figure 7: Curve of EAR vs ν

CONCLUSIONS By the impact uniaxial compression tests for light-weight foam concrete with density of 220 kg/m3 under various striker velocities, energies in impact compression tests is developed to investigate the energy dissipation in foam concrete, conclusions are obtained as follows. 1. There is almost a linear relation between incident wave energy WI and striker velocity v squared. And reflected wave energy WR is in same order of magnitude with incident wave energy WI and their values are almost the same. 2. Energy absorption rate EAR of light-weight foam concrete decreases with incident wave energy WI growing. And there is almost a negative power relation between Energy absorption rate EAR and incident wave energy WI. There is also a similar relation between Energy absorption rate EAR and striker velocity v. 3. During impact compression test, energy passing light-weight foam concrete and transmitted wave energy is very small and can be neglected compared with incident wave energy. Thus the mechanism of energy dissipation for light-weight foam concrete is not absorbing the wave energy on it, but reflecting them. When light-weight foam concrete is used in compound structure as a protective layer or interlayer, light-weight foam concrete can reduce vibration

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effectively and act a perfect energy dissipation effect, then the anti-impact property of structure is improved.

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