Handout 1 - Clemson University

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where y: ratio of specific heat for air R = CR (Y) t2E1/5 Equation 3.3-4 p, ) E p, = C () - -- Equation 3.3-5 CR0') and C, (y): constants depending only on the properties of the medium R: distance between source of explosion and wave front t: time from explosion E: energy released during explosion Sachs (1944) proposed a more general blast scaling model in an attempt to account for the effects of altitude or other changes on ambient conditions on air blast waves. Sach's scaling law states that dimensionless groups can be formed that involve pressure, time, impulse and certain parameters for the ambient air and that these groups are unique functions of a dimensionless distance parameter. Specifically, the following groups are stated to be unique functions of (R = Rp)'' 3 /F") [7, 32] P - p - I -a O t -a Op O / P = -, = El" 3 P 3 ' El' Kinney and Graham [36] have proposed another scaling rule based on the previous scaling rules of Hopkinson and Sachs. Two explosions can be expected to give identical blast waves at distances which are proportional to the cube root of the respected energy release. That is, to produce a given blast at twice the distance requires eight times the explosive energy release. However, the nature of the medium also must be considered. The density of the atmosphere may be taken as a measure of the mass of air through
which the explosive blast has propagated. Therefore, the atmospheric transmission factors for distance fd and time ft are introduced as: fd 1/3 C 1/3 where p: atmospheric density .r)1/3 .3 112 T 1/3 1/6 Equation 3.3-6 pt-e- T P (T PO T" P T po: density of a reference atmosphere P: atmospheric pressure (absolute) Po: pressure for the reference atmosphere (absolute) T: atmospheric temperature To: temperature at a reference atmosphere Using the atmospheric transmission factor for distance the scaled distance is measured by: A similar formula with Equation 3.3-1 The peak overpressure is then calculated by: Equation 3.3-7 P P, = overpressure _ratio x atmospheric _ pressure = - P P where the overpressure ratio is given as a function of the empirical formula [36]: Z= fd -R w 1'3 Equation 3.3-8 scaled distance by an
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 38 and 39: p(t)= p, -P~(t / T-)(1-t T-j)e 4 t
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 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
Page 70 and 71: 49.2 2 1.076 64.8 3 1.243 74.5 4 1.
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
Page 89 and 90: 5.2 Test Samples Blast tests were c
Page 91 and 92: imaging that reveal localized chang
Page 93 and 94: 5.4 Incoming Blast Wave Parameters
Page 95 and 96: 5.5 Results The experimental evalua
Page 97 and 98: of air in all the three materials.
Page 99 and 100: 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
Page 213 and 214:
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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