Handout 1 - Clemson University

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p(t)= p, -P~(t / T-)(1-t T-j)e 4 t T Equation 3.1-7 In this formula the time is measured from the start of the negative phase ta+T+. As previously mentioned, in its passage through the air, the blast front increases not only the pressure but also the density, the temperature and it accelerates the air particles to produce a particle velocity u in the direction of the travel. J. Dewey (1964) has proposed an empirical equation to fit time histories of particle velocity for blast waves generated by TNT explosions. This equation involves four parameters [33]: u(t) = u,(1- pt)e~ + a ln(1+ pit) Equation 3.1-8 where u,: peak particle velocity immediately behind shock front a and P: parameters to be determined through experimental fitting The ideal blast wave of Figure 3.1-1 exhibits only one shock, the primary shock. However, for any finite explosion source, the ideal blast wave can also exhibit numerous repeated shocks of small amplitude at time instances after ta. Theses shocks are created by the successive implosion of rarefaction waves from the contact surface between explosion products and air. Secondary and tertiary shocks of this nature, also called "pete" and "repete", have been observed and can be seen in the following Figure 3.1-2. These waves have little effect on the characteristics of the positive phase of the blast wave with the exception of the positive duration T+, except if a secondary wave happens to arrive just before the initial decay reaches ambient pressure. On the other hand, repeated shocks can strongly affect the negative phase, abruptly terminating it or sharply reducing the negative impulse I or amplitude P, [32].
SECONDARY SHOCKS TERTIARY SHOCK Figure 3.1-2: Recorded pressure time histories of actual blast waves [32] Quite often, the characteristics of air blast waves are more complicated and more difficult to analyze than the features previously mentioned. If the blast source is of low specific energy content, as such relatively a low-pressure mass of expanding gas, then the finite pressure pulse generated in the surrounding air may progress some distance before "shocking up" [32]. If the blast source is a cased explosive charge, recorded time histories of pressure may have large amounts of disturbances and pressure fluctuations superimposed on the primary pressure variation of the blast wave. These disturbances are the ballistic shocks generated by fragments of the casing moving at supersonic speed through the air. The fragment velocity decay rate is slower than that of the blast front, therefore they outrun the shock front for some time and produce disturbances before the blast wave arrival. However, the long in run the blast front catches up with the fragments are which decelerated due to drag forces [32]. This effect is illustrated in the following 3.1-3. Figure
Page 1: Development of a Helmet Liner for P
Page 4 and 5: control samples. The peak transmitt
Page 7 and 8: List of Contents 1 In trod u ction
Page 9 and 10: List of Figures Figure 2.1-1: Survi
Page 11 and 12: Figure 7.2-1: Air pressure values i
Page 13: Figure B-20: Integrated absolute pr
Page 17 and 18: 1 Introduction This first introduct
Page 19 and 20: protection against blast waves is l
Page 21: experimental apparatus, procedure a
Page 24 and 25: Tertiary: Results form individuals
Page 26 and 27: Skull CONTRE COUP COUP Figure 2.1-2
Page 28 and 29: membranes is the pressure integrate
Page 30 and 31: idging veins and other features was
Page 32 and 33: droplets were shown to mitigate the
Page 34 and 35: ought to the ignition temperature o
Page 36 and 37: To describe completely the characte
Page 40 and 41: R -30 ft R -38 ft L MILLISECOND TIM
Page 42 and 43: By applying the equations of mass,
Page 44 and 45: T 2 e 2 =[+ 2y (M2 _1 2+(y-1)M1 T,
Page 46 and 47: 5.5 4.5 4 35 3 I I -I I J I _L1 1 L
Page 48 and 49: Explosive Mass Specific energy TNT
Page 50 and 51: where y: ratio of specific heat for
Page 52 and 53: PS a 808 1+ 4.5) Z 2Z 1+ - 1+ 2Z Z3
Page 54 and 55: 3.4.2 Fluid-Structure Interaction t
Page 56 and 57: ps = p, = tipA Us Equation 3.4-11 7
Page 58 and 59: 3.5 Constitutive Model of Materials
Page 60 and 61: 3.5.2 Mie Grineisen Equation of Sta
Page 62 and 63: The VN 600 is a closed cell foam ba
Page 64 and 65: 3. Densification. This causes the s
Page 66 and 67: 1. A linear elastic region for smal
Page 68 and 69: A pressure load cell, used to measu
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Page 72 and 73: X 10 50 mmlmin experimental 500 mm/
Page 74 and 75: Typical values of the Poisson's rat
Page 76 and 77: The only parameter that has not bee
Page 78 and 79: compression tests the value of oco/
Page 80 and 81: 4.3 Filler Materials The filler mat
Page 82 and 83: 4.4 Plexiglas PMMA Plexiglas PMMA s
Page 85 and 86: 5 Experimental Blast Mitigation Stu
Page 87 and 88: Figure 5.1-2: Experimental apparatu
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5.2 Test Samples Blast tests were c
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imaging that reveal localized chang
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5.4 Incoming Blast Wave Parameters
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5.5 Results The experimental evalua
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of air in all the three materials.
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the benchmark case with a 45% and 3
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The final category of examined mate
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Pree-Pieict 5.19 0.57 1.13 0.02 Sol
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configuration that was selected for
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16 " Free - Field 5.19 0.57 1.13 0.
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6 Numerical Simulation of Material
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Figure 6.1-2: Single cavity configu
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Figure 6.1-4: Surface element regio
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The dilatational wave speed is give
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Air at Pal= atm and Ta = 200C ambie
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0.325 MPa approximately, while the
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[x1 E6] 0.35- 0.30- 0.254 0.20 0.15
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The calculated profiles J (Figure a
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elements have experienced; the use
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0.05 0 -0.05 -0.1 005 - -Gas F -.15
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espectively. Comparison with the pr
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[x1.E6] 0.25 0.20 0.15 0.10 0.05 0.
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[xl.E3] 60 -44 -20. 0press -~1 A444
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6.3 Conclusions This chapter was de
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7 Numerical Simulation of Material
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The Eulerian-Lagrangian contact for
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scenarios respectively, adequate fo
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The density jump across the shock w
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IxI.E]] D.10 DOS 8 -OD [x1.E3J Time
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wave is 1 MPa. This trend is mainta
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compliance with theory in regard to
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element is equal to or greater than
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Time [s] Figure 7.3-2: Reflected wa
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numerical viscosity in order to ass
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Figure 7.4-2: Regions of constraine
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Figure 7.4-4: 3D view of Eulerian d
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,P% 91 Figure 7.4-6: Boundary condi
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Mesh and Material Assignment The Pl
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Hugoniot shock model in combination
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500000 400000 300000 200000 100000
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The following Table 7.5-1 contains
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The transmitted pressure parameters
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viscosity may have smoothened out e
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ms respectively after the incoming
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3000 25M 15M- 10-0 20040 -0.1 -0.0
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Figure 7.5-10 shows vertical the di
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section of the air behind the solid
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8 Final Conclusions The objective o
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scaling rules were employed in orde
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demonstrates a smoother spatial dis
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spherical incoming wave. Furthermor
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A. Appendix A - Scaling of Mechanic
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Hydrostatic - Strain Pressure Cures
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e due to the fact that for small st
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B. Appendix B - Impulse Loading The
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[x1.E6] 0.40 0.30 L 0.20 0.10 0.00
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[x1.E6] 0.40 0.35 0.30 0.25 0.20 0.
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[xl E3] 20. 10. 0. -10. -20. 0.0 Lo
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[x1.E3] 30. 20. 10. 0. -10. -20. -3
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- I I I I -0.15 -0.1 -0.05 0 0.05 0
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C.1 - 005- .05 0- I I I I 0 15 -01
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References 1. C. Wilson, Improvised
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28. S. Zhuang, G. Ravichandran, et
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56. http://www.3d-cam.com/materials
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Handout 1 - Clemson University

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