- Email: [email protected]
Calculating fragment impact velocity from penetration data
International Journal of Impact Engineering 37 (2010) 530–536
Contents lists available at ScienceDirect
International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Calculating fragment impact velocity from penetration data Joseph B. Jordan a, Clay J. Naito b, * a b
Applied Research Associates, 104 Research Rd., Tyndall AFB, FL 32403, USA Department of Civil Engineering, Lehigh University, Bethlehem, PA 18015, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 August 2009 Received in revised form 27 October 2009 Accepted 2 November 2009 Available online 10 November 2009
Depth of penetration experiments were conducted with fragment simulating projectiles launched into CelotexÒ in order to develop an equation for the strike velocity as a function of the FSP mass and the depth of penetration into CelotexÒ recovery media. A powder gun launched FSPs, designed in accordance with STANAG-2920 [NATO STANAG-2920 Ballistic Test Method for Personal Armour Materials and Combat Clothing, 2nd ed., 1999.] weighing between 0.13 g and 53.78 g at striking velocities between 198 m/s and 1524 m/s. A multiple linear regression analysis was used to determine an empirical relationship for the strike velocity to the impact parameters of depth of penetration, fragment mass, and mean presented area. Sabot launched natural fragments weighing between 2.8 g and 15.8 g at striking velocities between 532 m/s and 1084 m/s were used to validate the equation. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: CelotexÒ Depth of penetration Experimental testing Fragment simulating projectiles Natural fragments
1. Introduction
Vs ¼ 17:90DOP 0:736 m0:255
When conducting fragmentation resistance tests of armor and protective structures it is important to understand the complete nature of any fragments completely perforating the materials under test. In order to assess the lethality of a fragment after interaction with a protective structure the mass and the residual velocity must be known. Obtaining the mass of these recovered fragments is a simple matter. Determining the velocity of multiple fragments coming off a mortar or rocket is routinely done in arena characterization tests. However, determining the velocity of the fragments after interaction with the armor or construction materials is much more difficult. One method that can be used is to calibrate the velocity as a function of depth of penetration into a recovery media and the fragment mass. Cellulosic fiberboard is commonly used as a recovery media. This material is available in adequate size at an economical cost making it ideal for fragment recovery. In the early 1960’s empirical equations for the determination of the impact velocity of fragments penetrating cellulosic fiberboard recovery media were developed [2]. The equation developed for compact cylindrical and spherical steel fragments impacting Maftex, a common fiberboard of the time, is presented in Eq. (1).
Where, Vs ¼ Strike velocity [m/s] DOP ¼ Depth of penetration [mm] m ¼ Fragment mass [g] Due to changes in the fiberboard industry Maftex is no longer commercially available. Cellulosic fiberboard is still commercially available and produced as CelotexÒ. When Eq. (1) is used to predict fragment simulating projectile (FSP) velocities under laboratory conditions based on mass and depth of penetration into CelotexÒ, a substantial error is observed. Table 1 compares experimental velocity from a baseline data set and the predicted velocity for FSPs weighing nominally 13.41 g into CelotexÒ. It should be noted that the baseline data presented was generated to provide a preliminary assessment of the accuracy of Eq. (1); the data is not used for the subsequent equation development because the actual mass of each FSP was not documented prior to testing. Fig. 1 shows depth of penetration versus strike velocity for the 11 shots in Table 1. As illustrated the accuracy of the historical model is poor (the average percent error is 19%). This error can be attributed to several factors such as; the recovery material used today, fragment geometry, and the accuracy of today’s instrumentation. A few years after Eq. (1) was developed; a study was conducted on the calculation of impact velocity from penetration data by Atkinson and Massengill [3]. The research found that in many cases the formulation provided unrealistically high velocity predictions. Finnegan et al. [4] determined fragment velocities into CelotexÒ
* Corresponding author. E-mail address: [email protected] (C.J. Naito). 0734-743X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2009.11.002
(1)
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536 Table 1 Baseline Ballistic test data comparison. Shot #
1 2 3 4 5 6 7 8 9 10 11
Table 2 Material properties of cellulose fiberboard panels.
Depth of penetration DOP (mm)
Measured strike velocity Vs (m/s)
Estimated velocity (Eq. (1)) Vs (m/s)
142.8 333.0 451.2 549.1 628.1 702.1 765.0 704.1 778.5 830.7 868.0
242.3 461.2 599.8 745.6 896.0 1054.2 1178.6 1046.9 1170.4 1328.6 1423.1
355.8 663.6 829.7 958.8 1058.5 1148.9 1223.8 1151.3 1239.6 1300.3 1343.1
St rike Velocit y [m/sec]
1200 1000 800 600 Predicted (Eq.1) Measured
200 0 200
400
600
800
Density (g/cm^3)
Tensile strength (kPa)
Maftex CelotexÒ SoundStop ASTM C208 sound deadening
0.24–0.27 [1] 0.28–0.29 [8] 0.16–0.50 [9]
1378–2068 [1] 1034a–4137b [8] 1034a–4137b [9]
a
1400
400
Material trade name
b
1600
0
531
1000
Depth of Penetration [mm] Fig. 1. Depth of Penetration versus Strike Velocity for 13.41 g FSPs into CelotexÒ.
using an equation that was proportional to the penetration depth divided by the fragment diameter. More recently de Bejar et al. [5] used semi-empirical equations to predict fragment velocities from depth of penetration into CelotexÒ. In order for the calculated data to match experimental data the formulation is scaled based on the weapon velocity to achieve a fit. The short coming of this method is the fact that the experimental data for a weapon is not always available prior to conducting testing. The objective of this investigation is to develop an equation for calculating fragment impact velocities as a function of mass and depth of penetration into CelotexÒ recovery media. 2. Recovery media The recovery media examined consists of a cellulosic fiber insulating board made up of wood or cane fibers felted together to create a homogeneous panel. In the original work [2] Maftex
Tensile strength parallel to the surface. Tensile strength perpendicular to the surface.
a common proprietary cellulosic fiber of the time, was used as the recovery media. This is a low density material which allows for the recovery of fragments without deformation to the fragments. Today Maftex originally manufactured by MacAndrews and Forbes Co. is no longer commercially available. CelotexÒ which is commercially available as a thermal and sound insulation is used. While Maftex and CelotexÒ are both cellulosic fiber insulating boards their material properties are similar but not identical, see Table 2. As illustrated, the density of CelotexÒ is marginally higher and the tensile strength has more variance. Cellulosic fiber insulating boards are manufactured in accordance with ASTM C208 [9]. The fiberboard used in this study is available in 1219 mm width by 1438 or 2743 mm length by 13 mm thickness. The thickness tolerance on the panels is 10% of the thickness (1.3 mm). Smith and Vormelker [6,7] characterized the compressive properties of CelotexÒ under static and impact conditions. It was found that CelotexÒ, like other fiberboards have a non-linear strength increase with strain under compressive loads. At small strains the stiffness is very low. As the fibers are compressed the stiffness exponentially increases. The increase typically occurs between a strain of 50% and 100%. Under impact conditions the strength gain follows a comparable curve with the exception that it initiates at a decreased strain level. The authors hypothesized that at a higher strain rates the interstitial air is unable to vent properly resulting in an earlier onset of strength gain. Due to the rate sensitivity of the material in compression the fiberboard is evaluated over a large range of impact velocities in this study. The data was collected in an environmentally controlled ballistic range. The temperature ranged from 21 to 23 C and the relative humidity was maintained between 50% and 55%. The fiberboard was stored at these conditions prior to testing. Research conducted on the sensitivity of the constitutive properties of CelotexÒ to variations in temperature, moisture and humidity found that the material is not significantly affected by normal variations in the environmental conditions [6]. Consequently the formulations developed in this research are applicable to field conditions.
Fig. 2. FSPs and RCC with four-piece Serrated Sabot (a) FSP, (b) RCC with Sabot partially open.
532
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
Table 3 Fragment simulating projectile characteristics. Nominal weight (g)
Shape
Radius (mm)
Length (mm)
Average presented area (mm2)
Form factor c ¼ A/m2/3
0.13 0.26 1.04 2.85 4.15 13.41 53.78
RCC RCC RCC FSP RCC FSP FSP
1.4 1.7 2.8 3.8 4.4 6.3 10.0
2.7 3.6 5.6 8.8 8.9 14.8 23.4
8.92 14.40 36.12 67.14 90.29 188.06 471.77 Average c ¼ 4.33
34.82 35.42 35.26 33.39 34.98 33.31 33.11
Fig. 3. Four-piece serrated Sabots with pusher plates used for launching fragments (b) Finger fragment, (b) Compact fragment.
3. Empirical relationships In this investigation the data was fitted to a multiple linear regression equation of the form
y ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3
(2)
Where: x1 ¼ fragment mass [grains] x2 ¼ depth of penetration [mm] x3 ¼ average presented area [mm2] y ¼ fragment velocity [m/s] Estimates of the coefficients b0, b1, b2, and b3 are obtained by applying the method of least squares and taking the sum of the squares of the residuals [10]. A goodness of fit for the data is determined by looking at the coefficient of determination R2. A R2 of 1.0 represents a perfect fit.
fragments with masses between 2.8 g and 15.8 g were launched from a 20 mm smooth bore powder gun using a four-piece sabot with a pusher plate as shown in Fig. 3. A scaled photograph of the natural fragments is shown in Fig. 4. Fragments four though ten shown in the photograph were classified as compact or chunky fragments. The remaining fragments were classified as finger fragments. A sabot stripper was placed 1.5 m downrange from the muzzle. Four infrared photoelectric velocity screens connected to two chronographs were used to determine the velocities, see Fig. 5. This allowed for two primary velocities V1 and V2, and two proof velocities to be recorded for each shot. The primary velocities were measured between screens 1 and 3 and screens 2 and 4. The proof
4. Experimental setup Two different fragment simulating projectile geometries were used during testing; blunt chiseled-nose FSP, and the right circular cylinder (RCC), Fig. 2. The FSPs and RCCs were manufactured in accordance with STANAG-2920 [1]. Three different masses of FSPs, 2.85 g, 13.41 g and 53.78 g, and 4 different masses of RCCs, 0.13 g, 0.26 g, 1.04 g and 4.15 g were used in the experimental testing. The characteristics of these fragment simulators are shown in Table 3. The geometry of each fragment, the average presented area, and the form factor is presented. All of the fragment simulated projectiles used in this study were compact fragments. Compact or chunky fragments are defined as fragments in which the ratio of the maximum presented area to the minimum presented area is not far from unity [2]. All FSPs were launched from rifled powder gun barrels, while all of the RCC’s were sabot launched from smooth bore powder gun barrels using four-piece serrated sabots with an integral pusher design. Additionally, natural fragments recovered from previous arena tests were used to validate the equation developed. These natural
Fig. 4. Natural fragments.
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
533
Fig. 5. Velocity measurement diagram.
Fig. 6. Typical condition of the Celotex at the end of the penetration event (a) Captured fragment, (b) Panel back side, (c) Indention on adjacent panel, (d) Measuring the indentation.
velocities were measured between screens 1 and 2, and screens 3 and 4. If the proof and primary velocities were off by more than 1% the data was considered unreliable and not used. The strike velocity Vs was determined with respect to the primary velocities in accordance with Eq. (3).
Vs ¼ V2 þ
698:5 ðV2 V1 Þ 609:6
(3)
5. DOP measurements In the original body of work [1] using Maftex recovery media it was stated that an effort should be made to measure each depth of penetration to the nearest half (6.35 mm) or quarter (3.18 mm)
Fig. 7. Sketch of DOP measurement.
534
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
Table 4 Ballistic test data.
Table 5 Fragment test data.
Shot #
V1 (m/s)
V2 (m/s)
Vs (m/s)
2-R-01 2-R-04 2-R-03 2-R-05 2-R-06
192.9 209.4 230.1 433.7 801.6
191.1 205.4 225.9 423.7 768.7
189.0 200.9 221.0 412.1 731.0
DOP (mm) 14.0 14.3 25.7 65.1 90.2
Mass (g) 0.13 0.13 0.13 0.14 0.13
4-R-07 4-R-08 4-R-06 4-R-05 4-R-04 4-R-03
220.4 237.7 350.8 504.4 734.9 978.7
217.6 234.1 342.9 492.6 719.9 969.9
214.5 229.9 333.8 478.9 702.8 959.7
26.3 28.6 40.5 78.6 116.5 154.8
0.25 0.27 0.26 0.27 0.25 0.25
16-R-13 16-R-12 16-R-11 16-R-10 16-R-09 16-R-08 16-R-07 16-R-06 16-R-05
232.0 342.6 346.9 563.3 791.9 951.6 1196.6 1220.7 1316.1
229.5 342.6 345.9 557.8 781.2 939.4 1181.7 1206.1 1296.9
226.7 342.6 344.9 551.5 769.0 925.4 1164.6 1189.3 1274.9
43.1 78.2 78.5 165.7 215.9 228.9 243.8 331.0 344.4
1.04 1.05 1.04 1.04 1.03 1.04 1.03 1.02 1.03
44-F-03 44-F-04 44-F-05 44-F-02 44-F-06 44-F-01 44-F-07 44-F-08 44-F-09 44-F-10 44-F-11
298.1 347.5 435.3 524.0 650.7 851.6 849.5 963.2 1103.7 1180.2 1732.2
298.1 347.5 429.8 519.4 645.9 841.9 842.2 953.4 1096.7 1172.9 1721.2
298.1 347.5 423.5 514.1 640.3 830.7 833.8 942.2 1088.6 1164.5 1708.6
118.4 135.1 182.9 243.8 269.6 398.9 358.9 357.2 445.4 471.0 547.5
2.85 2.84 2.85 2.85 2.85 2.84 2.86 2.84 2.85 2.86 2.85
64-R-09 64-R-08 64-R-07 64-R-01 64-R-02 64-R-03 64-R-04 64-R-05 64-R-06
349.3 655.6 832.7 1077.5 1222.9 1346.0 1486.8 1591.1 1628.8
348.4 653.5 828.4 1069.2 1212.8 1341.7 1471.9 1575.2 1672.7
347.3 651.0 823.6 1059.8 1201.3 1336.8 1454.8 1557.0 1661.2
132.6 310.3 384.4 466.3 538.9 565.3 571.5 586.0 604.0
4.18 4.18 4.17 4.15 4.14 4.19 4.15 4.15 4.16
207-F-22 207-F-11 207-F-01 207-F-21 207-F-02 207-F-03 207-F-20 207-F-19 207-F-23 207-F-04 207-F-05 207-F-18 207-F-06 207-F-17 207-F-07 207-F-08 207-F-16 207-F-09 207-F-15 207-F-12
274.9 344.1 431.3 440.7 482.2 498.7 705.0 703.2 703.8 767.2 902.8 1018.9 1069.5 1150.0 1205.8 1265.5 1273.1 1370.4 1369.8 1439.0
274.0 344.1 429.5 438.9 476.7 496.5 702.0 699.8 699.2 766.0 898.6 1014.7 1063.1 1143.6 1198.8 1261.3 1266.4 1361.2 1369.8 1430.7
273.0 344.1 427.4 436.8 470.4 494.1 698.5 696.0 701.5 764.6 893.7 1009.8 1055.8 1136.3 1190.7 1256.4 1258.8 1350.8 1369.8 1421.3
201.3 266.7 330.3 366.1 401.8 414.9 562.4 557.1 550.6 593.2 681.7 819.6 772.9 826.0 844.8 870.2 881.1 895.2 906.3 912.9
13.47 13.43 13.40 13.47 13.48 13.37 13.41 13.41 13.19 13.40 13.42 13.46 13.38 13.48 13.41 13.43 13.40 13.41 13.41 13.41
830-F-05 830-F-06 830-F-07 830-F-08 830-F-09 830-F-10 830-F-11
718.4 838.2 971.1 1052.2 1111.0 1152.4 1242.1
717.2 836.7 969.3 1050.0 1109.2 1151.2 1239.6
715.8 834.9 967.2 1047.6 1107.1 1149.8 1236.8
1054.7 1165.4 1162.6 1224.0 1296.9 1324.7 1352.2
53.91 53.71 53.75 53.80 53.76 53.86 53.76
sheet. How to determine the measurement was not addressed in the work, however determining the depth of penetration into a soft recovery media such as CelotexÒ can be ambiguous due to
Fragment Number
Type
Vs (m/s)
Mass (g)
DOP (mm)
1 2 3 4 5 7 8 9 10 11 12
Finger Finger Finger Compact Compact Compact Compact Compact Compact Finger Finger
531.8 641.3 690.8 765.8 963.5 526.2 1084.5 670.8 775.2 685.0 1068.5
15.84 14.13 12.64 6.23 6.47 2.95 4.43 5.14 6.76 9.53 12.17
238.8 387.0 310.1 246.4 249.4 127.7 271.6 221.9 271.8 464.2 349.5
the nature of the low strength material. During the penetration process the material becomes pulverized in the path of the projectile and begins to plug the panel in which the fragment is recovered as shown in Fig. 6 (a) and (b). The DOP measurement can also be influenced by the fragment recovery method used. Some research facilities prefer to collect the fragments while the CelotexÒ panels are in the vertical position, while others like to rotate the panels 90 into a horizontal position prior to collecting the fragments. Both methods give opportunity for the fragments to dislodge themselves or change depth during the recovery operation. In order to eliminate this uncertainty in the depth of penetration in this investigation, the DOP was measured to the depth of indentation (DOI) in the CelotexÒ as shown in Fig. 7. This allows for an accurate and repeatable method of measurement to be used during the collection of fragments without slowing or hindering the recovery operation. Prior to commencing the recovery operation the overall pack dimension is recorded. Individual panels of CelotexÒ are removed during the recovery operation until a fragment is found. The panels including the one in which the projectile or fragment is discovered are counted and removed from the recovery pack. The adjacent panel is investigated to determine the depth of the indentation (DOI). The indentation was measured using a depth gauge with base extension as shown in Fig. 6 (d). The accuracy of the gauge used in this study was 0.025 mm. The DOP is computed from the number of sheets removed plus the DOI as presented in Eq. (4).
DOP ¼ Number of sheets Sheet thickness þ DOI
(4)
6. Ballistic results and predictive equation development Experimental data for 69 impacts into CelotexÒ with the various FSPs and RCCs at striking velocities, Vs, between 189 and 1708 m/s are given in Table 4. Shots designated with ‘‘R’’ in the middle character are RCCs and while shots designated with ‘‘F’’ are FSPs. The mass, depth of penetration and mean presented area were used as variables for the empirical equation. The form of the equation is provided in Eq. (5). Using the least squares regression analysis previously discussed the Beta terms were computed and are presented in Eq. (6).
Vs ¼ b0 þ b1 m þ b2 DOP þ b3 A
(5)
Vs ¼ 462:5 þ 0:370m þ 1:95DOP 1:8A
(6)
2/3
By substituting A ¼ c$m as discussed in reference [2] into Eq. (6) the empirical relation in terms of mass and depth of penetration becomes:
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
535
Table 6 Goodness of fit using all fragments. Fragment
Actual Vs (m/s)
Eq (1) Vs (m/s)
Eq. (1) Error (%)
Eq. (7) Vs (m/s)
Eq. (7) Error number (%)
1 2 3 4 5 7 8 9 10 11 12
531.8 641.3 690.8 765.8 963.5 526.2 1084.5 670.8 775.2 685.0 1068.5
498.0 731.4 639.2 646.4 645.9 481.9 757.4 628.6 680.5 924.6 704.9
6.4 14.0 7.5 15.6 33.0 8.4 30.2 6.3 12.2 35.0 34.0 Average error 18.4
544.0 861.0 736.2 735.9 736.5 585.3 826.9 713.0 773.9 1093.4 821.4
2.3 34.3 6.6 3.9 23.6 11.2 23.8 6.3 0.2 59.6 23.1 Average error 17.7
Table 7 Goodness of fit using only compact fragments. Fragment
Actual Vs (m/s)
Eq. (1) Vs (m/s)
Eqn (1) Error (%)
Eqn (7) Vs (m/s)
Eq. (7) Error number (%)
3 4 5 7 8 9 10
690.8 765.8 963.5 526.2 1084.5 670.8 775.2
639.2 646.4 645.9 481.9 757.4 628.6 680.5
7.5 15.6 33.0 8.4 30.2 6.3 12.2 Average error 17.6
736.2 735.9 736.5 585.3 826.9 713.0 773.9
6.6 3.9 23.6 11.2 23.8 6.3 0.2 Average error 11.5
Vs ¼ 462:5 þ 0:370m þ 1:95DOP 61:79m0:667
(7)
The coefficient of determination (R2) equals 0.84 indicating that the regression equation is an adequate fit. 7. Equation validation The equation was validated using natural fragments recovered from arena tests. Both compact natural fragments and noncompact (finger) fragments were included for completeness. Table 5 shows the experimental data for 11 impacts into CelotexÒ with sabot launched natural fragments at striking velocities between 526.2 and 1084.5 m/s. Percent error between the observed value and the calculated value was used to determine the goodness of fit for the original Eqs. (1) and (7) developed in this investigation. Table 6 shows the percent error for all fragments, as well as, the average absolute error for Eqs. (1) and (7). The average absolute error for all the natural fragments launched is 18.4% and 17.7%, respectively for Eqs. (1) and (7). Since both equations were developed using only compact fragments, the percent error would be expected to be lower for compact natural fragments. Table 7 shows the percent error for each compact fragment and the average absolute error neglecting the non-compact (finger) fragments. While the average percent error for Eq. (1) improves slightly, the average percent error for Eq. (7) becomes an acceptable 11.5%. 8. Conclusions Depth of penetration experiments were conducted with fragment simulating projectiles impacting into CelotexÒ. The experimental data was used to develop an empirical equation for calculating fragment impact velocity from penetration data as a function of mass and depth of penetration into CelotexÒ recovery media. The equation was validated by sabot launching natural fragments recovered from arena tests into CelotexÒ. The
developed equation was shown to be a good fit when used to predict the velocity of compact natural fragments, and an acceptable fit for all natural fragments launched in this investigation. Because the equation was developed using a multiple linear regression analysis of a defined data set, the formulation should only be used with fragment masses weighing between 0.13 g and 53.78 g at striking velocities between 198 m/s and 1524 m/s. To properly estimate the impact velocity requires a precise measurement of depth of penetration into the recovery media. An accurate and rapid depth of penetration measurement technique is presented and recommended for field and laboratory applications. Acknowledgements The authors would like to thank the Air Force Research Laboratory (Robert Dinan, Program Manager) for funding this work under contract FA4819-07-D-0001. The experiments were performed at the Air Force Research Laboratory Ballistics Facility located at Tyndall AFB, FL. Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of the use thereof. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. References [1] NATO STANAG-2920 Ballistic Test Method for Personal Armour Materials and Combat Clothing, 2nd ed., NATO Standardization Agency, 1999. 32 p [2] The Johns Hopkins University, The calibration of a collection medium for the determination of particle velocity. Project Thor Tech. Report 50, 1962, Ballistics Research Laboratories, Aberdeen Proving Ground, MD. [3] Atkinson GW, Massengill EB. Calculating initial fragment velocity from penetration data. NAVWEPS Report 8280, Albuquerque, NM: US Naval Weapons Evaluation Facility; 1964. [4] Finnegan SA, Schulz JC, Heimdahl OER. Spatial fragment mass and velocity distributions for ordnance and ultra-ordnance speed impacts. Int J of Impact Eng 1990;10:159–70. [5] de Bejar LA, Davis JL, Simmons L. Standoff-mortar-induced fragment forces. Int J of Impact Eng 2008;35:1053–62.
536
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
[6] Smith AC, Vormelker PR. CelotexÒ Structural properties test. WSRCTR-2000–00444, Aiken SC: Westinghouse Savannah River Company; 2000. [7] Smith AC, Vormelker PR, Chapman G, Khan J, Miller KW, Khandkar MZH, Chapman G. Effect of orientation and strain rate on crush strength of cellulose fiberboard assemblies. WSRC-TR-2000–00508. Aiken SC: Westinghouse Savannah River Company 2000.
[8] Knight-Celotex, SoundstopÒ Sound Stopping Fiberboard, Section 09830, Submittal/Spec Sheet, www.soundstop.net. [9] ASTM Standard C208, 2008 Standard Specification for Cellulosic Fiber Insulating Board, ASTM International, West Conshohocken, PA, 2008, doi: 10.1520/ C0208-08A, www.astm.org. [10] Cheremisinoff N.P., Practical statistics for engineers and scientists, Lancaster Pennsylvania: Technomic Publishing Company Inc.; 1987.
Contents lists available at ScienceDirect
International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Calculating fragment impact velocity from penetration data Joseph B. Jordan a, Clay J. Naito b, * a b
Applied Research Associates, 104 Research Rd., Tyndall AFB, FL 32403, USA Department of Civil Engineering, Lehigh University, Bethlehem, PA 18015, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 August 2009 Received in revised form 27 October 2009 Accepted 2 November 2009 Available online 10 November 2009
Depth of penetration experiments were conducted with fragment simulating projectiles launched into CelotexÒ in order to develop an equation for the strike velocity as a function of the FSP mass and the depth of penetration into CelotexÒ recovery media. A powder gun launched FSPs, designed in accordance with STANAG-2920 [NATO STANAG-2920 Ballistic Test Method for Personal Armour Materials and Combat Clothing, 2nd ed., 1999.] weighing between 0.13 g and 53.78 g at striking velocities between 198 m/s and 1524 m/s. A multiple linear regression analysis was used to determine an empirical relationship for the strike velocity to the impact parameters of depth of penetration, fragment mass, and mean presented area. Sabot launched natural fragments weighing between 2.8 g and 15.8 g at striking velocities between 532 m/s and 1084 m/s were used to validate the equation. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: CelotexÒ Depth of penetration Experimental testing Fragment simulating projectiles Natural fragments
1. Introduction
Vs ¼ 17:90DOP 0:736 m0:255
When conducting fragmentation resistance tests of armor and protective structures it is important to understand the complete nature of any fragments completely perforating the materials under test. In order to assess the lethality of a fragment after interaction with a protective structure the mass and the residual velocity must be known. Obtaining the mass of these recovered fragments is a simple matter. Determining the velocity of multiple fragments coming off a mortar or rocket is routinely done in arena characterization tests. However, determining the velocity of the fragments after interaction with the armor or construction materials is much more difficult. One method that can be used is to calibrate the velocity as a function of depth of penetration into a recovery media and the fragment mass. Cellulosic fiberboard is commonly used as a recovery media. This material is available in adequate size at an economical cost making it ideal for fragment recovery. In the early 1960’s empirical equations for the determination of the impact velocity of fragments penetrating cellulosic fiberboard recovery media were developed [2]. The equation developed for compact cylindrical and spherical steel fragments impacting Maftex, a common fiberboard of the time, is presented in Eq. (1).
Where, Vs ¼ Strike velocity [m/s] DOP ¼ Depth of penetration [mm] m ¼ Fragment mass [g] Due to changes in the fiberboard industry Maftex is no longer commercially available. Cellulosic fiberboard is still commercially available and produced as CelotexÒ. When Eq. (1) is used to predict fragment simulating projectile (FSP) velocities under laboratory conditions based on mass and depth of penetration into CelotexÒ, a substantial error is observed. Table 1 compares experimental velocity from a baseline data set and the predicted velocity for FSPs weighing nominally 13.41 g into CelotexÒ. It should be noted that the baseline data presented was generated to provide a preliminary assessment of the accuracy of Eq. (1); the data is not used for the subsequent equation development because the actual mass of each FSP was not documented prior to testing. Fig. 1 shows depth of penetration versus strike velocity for the 11 shots in Table 1. As illustrated the accuracy of the historical model is poor (the average percent error is 19%). This error can be attributed to several factors such as; the recovery material used today, fragment geometry, and the accuracy of today’s instrumentation. A few years after Eq. (1) was developed; a study was conducted on the calculation of impact velocity from penetration data by Atkinson and Massengill [3]. The research found that in many cases the formulation provided unrealistically high velocity predictions. Finnegan et al. [4] determined fragment velocities into CelotexÒ
* Corresponding author. E-mail address: [email protected] (C.J. Naito). 0734-743X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2009.11.002
(1)
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536 Table 1 Baseline Ballistic test data comparison. Shot #
1 2 3 4 5 6 7 8 9 10 11
Table 2 Material properties of cellulose fiberboard panels.
Depth of penetration DOP (mm)
Measured strike velocity Vs (m/s)
Estimated velocity (Eq. (1)) Vs (m/s)
142.8 333.0 451.2 549.1 628.1 702.1 765.0 704.1 778.5 830.7 868.0
242.3 461.2 599.8 745.6 896.0 1054.2 1178.6 1046.9 1170.4 1328.6 1423.1
355.8 663.6 829.7 958.8 1058.5 1148.9 1223.8 1151.3 1239.6 1300.3 1343.1
St rike Velocit y [m/sec]
1200 1000 800 600 Predicted (Eq.1) Measured
200 0 200
400
600
800
Density (g/cm^3)
Tensile strength (kPa)
Maftex CelotexÒ SoundStop ASTM C208 sound deadening
0.24–0.27 [1] 0.28–0.29 [8] 0.16–0.50 [9]
1378–2068 [1] 1034a–4137b [8] 1034a–4137b [9]
a
1400
400
Material trade name
b
1600
0
531
1000
Depth of Penetration [mm] Fig. 1. Depth of Penetration versus Strike Velocity for 13.41 g FSPs into CelotexÒ.
using an equation that was proportional to the penetration depth divided by the fragment diameter. More recently de Bejar et al. [5] used semi-empirical equations to predict fragment velocities from depth of penetration into CelotexÒ. In order for the calculated data to match experimental data the formulation is scaled based on the weapon velocity to achieve a fit. The short coming of this method is the fact that the experimental data for a weapon is not always available prior to conducting testing. The objective of this investigation is to develop an equation for calculating fragment impact velocities as a function of mass and depth of penetration into CelotexÒ recovery media. 2. Recovery media The recovery media examined consists of a cellulosic fiber insulating board made up of wood or cane fibers felted together to create a homogeneous panel. In the original work [2] Maftex
Tensile strength parallel to the surface. Tensile strength perpendicular to the surface.
a common proprietary cellulosic fiber of the time, was used as the recovery media. This is a low density material which allows for the recovery of fragments without deformation to the fragments. Today Maftex originally manufactured by MacAndrews and Forbes Co. is no longer commercially available. CelotexÒ which is commercially available as a thermal and sound insulation is used. While Maftex and CelotexÒ are both cellulosic fiber insulating boards their material properties are similar but not identical, see Table 2. As illustrated, the density of CelotexÒ is marginally higher and the tensile strength has more variance. Cellulosic fiber insulating boards are manufactured in accordance with ASTM C208 [9]. The fiberboard used in this study is available in 1219 mm width by 1438 or 2743 mm length by 13 mm thickness. The thickness tolerance on the panels is 10% of the thickness (1.3 mm). Smith and Vormelker [6,7] characterized the compressive properties of CelotexÒ under static and impact conditions. It was found that CelotexÒ, like other fiberboards have a non-linear strength increase with strain under compressive loads. At small strains the stiffness is very low. As the fibers are compressed the stiffness exponentially increases. The increase typically occurs between a strain of 50% and 100%. Under impact conditions the strength gain follows a comparable curve with the exception that it initiates at a decreased strain level. The authors hypothesized that at a higher strain rates the interstitial air is unable to vent properly resulting in an earlier onset of strength gain. Due to the rate sensitivity of the material in compression the fiberboard is evaluated over a large range of impact velocities in this study. The data was collected in an environmentally controlled ballistic range. The temperature ranged from 21 to 23 C and the relative humidity was maintained between 50% and 55%. The fiberboard was stored at these conditions prior to testing. Research conducted on the sensitivity of the constitutive properties of CelotexÒ to variations in temperature, moisture and humidity found that the material is not significantly affected by normal variations in the environmental conditions [6]. Consequently the formulations developed in this research are applicable to field conditions.
Fig. 2. FSPs and RCC with four-piece Serrated Sabot (a) FSP, (b) RCC with Sabot partially open.
532
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
Table 3 Fragment simulating projectile characteristics. Nominal weight (g)
Shape
Radius (mm)
Length (mm)
Average presented area (mm2)
Form factor c ¼ A/m2/3
0.13 0.26 1.04 2.85 4.15 13.41 53.78
RCC RCC RCC FSP RCC FSP FSP
1.4 1.7 2.8 3.8 4.4 6.3 10.0
2.7 3.6 5.6 8.8 8.9 14.8 23.4
8.92 14.40 36.12 67.14 90.29 188.06 471.77 Average c ¼ 4.33
34.82 35.42 35.26 33.39 34.98 33.31 33.11
Fig. 3. Four-piece serrated Sabots with pusher plates used for launching fragments (b) Finger fragment, (b) Compact fragment.
3. Empirical relationships In this investigation the data was fitted to a multiple linear regression equation of the form
y ¼ b0 þ b1 x1 þ b2 x2 þ b3 x3
(2)
Where: x1 ¼ fragment mass [grains] x2 ¼ depth of penetration [mm] x3 ¼ average presented area [mm2] y ¼ fragment velocity [m/s] Estimates of the coefficients b0, b1, b2, and b3 are obtained by applying the method of least squares and taking the sum of the squares of the residuals [10]. A goodness of fit for the data is determined by looking at the coefficient of determination R2. A R2 of 1.0 represents a perfect fit.
fragments with masses between 2.8 g and 15.8 g were launched from a 20 mm smooth bore powder gun using a four-piece sabot with a pusher plate as shown in Fig. 3. A scaled photograph of the natural fragments is shown in Fig. 4. Fragments four though ten shown in the photograph were classified as compact or chunky fragments. The remaining fragments were classified as finger fragments. A sabot stripper was placed 1.5 m downrange from the muzzle. Four infrared photoelectric velocity screens connected to two chronographs were used to determine the velocities, see Fig. 5. This allowed for two primary velocities V1 and V2, and two proof velocities to be recorded for each shot. The primary velocities were measured between screens 1 and 3 and screens 2 and 4. The proof
4. Experimental setup Two different fragment simulating projectile geometries were used during testing; blunt chiseled-nose FSP, and the right circular cylinder (RCC), Fig. 2. The FSPs and RCCs were manufactured in accordance with STANAG-2920 [1]. Three different masses of FSPs, 2.85 g, 13.41 g and 53.78 g, and 4 different masses of RCCs, 0.13 g, 0.26 g, 1.04 g and 4.15 g were used in the experimental testing. The characteristics of these fragment simulators are shown in Table 3. The geometry of each fragment, the average presented area, and the form factor is presented. All of the fragment simulated projectiles used in this study were compact fragments. Compact or chunky fragments are defined as fragments in which the ratio of the maximum presented area to the minimum presented area is not far from unity [2]. All FSPs were launched from rifled powder gun barrels, while all of the RCC’s were sabot launched from smooth bore powder gun barrels using four-piece serrated sabots with an integral pusher design. Additionally, natural fragments recovered from previous arena tests were used to validate the equation developed. These natural
Fig. 4. Natural fragments.
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
533
Fig. 5. Velocity measurement diagram.
Fig. 6. Typical condition of the Celotex at the end of the penetration event (a) Captured fragment, (b) Panel back side, (c) Indention on adjacent panel, (d) Measuring the indentation.
velocities were measured between screens 1 and 2, and screens 3 and 4. If the proof and primary velocities were off by more than 1% the data was considered unreliable and not used. The strike velocity Vs was determined with respect to the primary velocities in accordance with Eq. (3).
Vs ¼ V2 þ
698:5 ðV2 V1 Þ 609:6
(3)
5. DOP measurements In the original body of work [1] using Maftex recovery media it was stated that an effort should be made to measure each depth of penetration to the nearest half (6.35 mm) or quarter (3.18 mm)
Fig. 7. Sketch of DOP measurement.
534
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
Table 4 Ballistic test data.
Table 5 Fragment test data.
Shot #
V1 (m/s)
V2 (m/s)
Vs (m/s)
2-R-01 2-R-04 2-R-03 2-R-05 2-R-06
192.9 209.4 230.1 433.7 801.6
191.1 205.4 225.9 423.7 768.7
189.0 200.9 221.0 412.1 731.0
DOP (mm) 14.0 14.3 25.7 65.1 90.2
Mass (g) 0.13 0.13 0.13 0.14 0.13
4-R-07 4-R-08 4-R-06 4-R-05 4-R-04 4-R-03
220.4 237.7 350.8 504.4 734.9 978.7
217.6 234.1 342.9 492.6 719.9 969.9
214.5 229.9 333.8 478.9 702.8 959.7
26.3 28.6 40.5 78.6 116.5 154.8
0.25 0.27 0.26 0.27 0.25 0.25
16-R-13 16-R-12 16-R-11 16-R-10 16-R-09 16-R-08 16-R-07 16-R-06 16-R-05
232.0 342.6 346.9 563.3 791.9 951.6 1196.6 1220.7 1316.1
229.5 342.6 345.9 557.8 781.2 939.4 1181.7 1206.1 1296.9
226.7 342.6 344.9 551.5 769.0 925.4 1164.6 1189.3 1274.9
43.1 78.2 78.5 165.7 215.9 228.9 243.8 331.0 344.4
1.04 1.05 1.04 1.04 1.03 1.04 1.03 1.02 1.03
44-F-03 44-F-04 44-F-05 44-F-02 44-F-06 44-F-01 44-F-07 44-F-08 44-F-09 44-F-10 44-F-11
298.1 347.5 435.3 524.0 650.7 851.6 849.5 963.2 1103.7 1180.2 1732.2
298.1 347.5 429.8 519.4 645.9 841.9 842.2 953.4 1096.7 1172.9 1721.2
298.1 347.5 423.5 514.1 640.3 830.7 833.8 942.2 1088.6 1164.5 1708.6
118.4 135.1 182.9 243.8 269.6 398.9 358.9 357.2 445.4 471.0 547.5
2.85 2.84 2.85 2.85 2.85 2.84 2.86 2.84 2.85 2.86 2.85
64-R-09 64-R-08 64-R-07 64-R-01 64-R-02 64-R-03 64-R-04 64-R-05 64-R-06
349.3 655.6 832.7 1077.5 1222.9 1346.0 1486.8 1591.1 1628.8
348.4 653.5 828.4 1069.2 1212.8 1341.7 1471.9 1575.2 1672.7
347.3 651.0 823.6 1059.8 1201.3 1336.8 1454.8 1557.0 1661.2
132.6 310.3 384.4 466.3 538.9 565.3 571.5 586.0 604.0
4.18 4.18 4.17 4.15 4.14 4.19 4.15 4.15 4.16
207-F-22 207-F-11 207-F-01 207-F-21 207-F-02 207-F-03 207-F-20 207-F-19 207-F-23 207-F-04 207-F-05 207-F-18 207-F-06 207-F-17 207-F-07 207-F-08 207-F-16 207-F-09 207-F-15 207-F-12
274.9 344.1 431.3 440.7 482.2 498.7 705.0 703.2 703.8 767.2 902.8 1018.9 1069.5 1150.0 1205.8 1265.5 1273.1 1370.4 1369.8 1439.0
274.0 344.1 429.5 438.9 476.7 496.5 702.0 699.8 699.2 766.0 898.6 1014.7 1063.1 1143.6 1198.8 1261.3 1266.4 1361.2 1369.8 1430.7
273.0 344.1 427.4 436.8 470.4 494.1 698.5 696.0 701.5 764.6 893.7 1009.8 1055.8 1136.3 1190.7 1256.4 1258.8 1350.8 1369.8 1421.3
201.3 266.7 330.3 366.1 401.8 414.9 562.4 557.1 550.6 593.2 681.7 819.6 772.9 826.0 844.8 870.2 881.1 895.2 906.3 912.9
13.47 13.43 13.40 13.47 13.48 13.37 13.41 13.41 13.19 13.40 13.42 13.46 13.38 13.48 13.41 13.43 13.40 13.41 13.41 13.41
830-F-05 830-F-06 830-F-07 830-F-08 830-F-09 830-F-10 830-F-11
718.4 838.2 971.1 1052.2 1111.0 1152.4 1242.1
717.2 836.7 969.3 1050.0 1109.2 1151.2 1239.6
715.8 834.9 967.2 1047.6 1107.1 1149.8 1236.8
1054.7 1165.4 1162.6 1224.0 1296.9 1324.7 1352.2
53.91 53.71 53.75 53.80 53.76 53.86 53.76
sheet. How to determine the measurement was not addressed in the work, however determining the depth of penetration into a soft recovery media such as CelotexÒ can be ambiguous due to
Fragment Number
Type
Vs (m/s)
Mass (g)
DOP (mm)
1 2 3 4 5 7 8 9 10 11 12
Finger Finger Finger Compact Compact Compact Compact Compact Compact Finger Finger
531.8 641.3 690.8 765.8 963.5 526.2 1084.5 670.8 775.2 685.0 1068.5
15.84 14.13 12.64 6.23 6.47 2.95 4.43 5.14 6.76 9.53 12.17
238.8 387.0 310.1 246.4 249.4 127.7 271.6 221.9 271.8 464.2 349.5
the nature of the low strength material. During the penetration process the material becomes pulverized in the path of the projectile and begins to plug the panel in which the fragment is recovered as shown in Fig. 6 (a) and (b). The DOP measurement can also be influenced by the fragment recovery method used. Some research facilities prefer to collect the fragments while the CelotexÒ panels are in the vertical position, while others like to rotate the panels 90 into a horizontal position prior to collecting the fragments. Both methods give opportunity for the fragments to dislodge themselves or change depth during the recovery operation. In order to eliminate this uncertainty in the depth of penetration in this investigation, the DOP was measured to the depth of indentation (DOI) in the CelotexÒ as shown in Fig. 7. This allows for an accurate and repeatable method of measurement to be used during the collection of fragments without slowing or hindering the recovery operation. Prior to commencing the recovery operation the overall pack dimension is recorded. Individual panels of CelotexÒ are removed during the recovery operation until a fragment is found. The panels including the one in which the projectile or fragment is discovered are counted and removed from the recovery pack. The adjacent panel is investigated to determine the depth of the indentation (DOI). The indentation was measured using a depth gauge with base extension as shown in Fig. 6 (d). The accuracy of the gauge used in this study was 0.025 mm. The DOP is computed from the number of sheets removed plus the DOI as presented in Eq. (4).
DOP ¼ Number of sheets Sheet thickness þ DOI
(4)
6. Ballistic results and predictive equation development Experimental data for 69 impacts into CelotexÒ with the various FSPs and RCCs at striking velocities, Vs, between 189 and 1708 m/s are given in Table 4. Shots designated with ‘‘R’’ in the middle character are RCCs and while shots designated with ‘‘F’’ are FSPs. The mass, depth of penetration and mean presented area were used as variables for the empirical equation. The form of the equation is provided in Eq. (5). Using the least squares regression analysis previously discussed the Beta terms were computed and are presented in Eq. (6).
Vs ¼ b0 þ b1 m þ b2 DOP þ b3 A
(5)
Vs ¼ 462:5 þ 0:370m þ 1:95DOP 1:8A
(6)
2/3
By substituting A ¼ c$m as discussed in reference [2] into Eq. (6) the empirical relation in terms of mass and depth of penetration becomes:
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
535
Table 6 Goodness of fit using all fragments. Fragment
Actual Vs (m/s)
Eq (1) Vs (m/s)
Eq. (1) Error (%)
Eq. (7) Vs (m/s)
Eq. (7) Error number (%)
1 2 3 4 5 7 8 9 10 11 12
531.8 641.3 690.8 765.8 963.5 526.2 1084.5 670.8 775.2 685.0 1068.5
498.0 731.4 639.2 646.4 645.9 481.9 757.4 628.6 680.5 924.6 704.9
6.4 14.0 7.5 15.6 33.0 8.4 30.2 6.3 12.2 35.0 34.0 Average error 18.4
544.0 861.0 736.2 735.9 736.5 585.3 826.9 713.0 773.9 1093.4 821.4
2.3 34.3 6.6 3.9 23.6 11.2 23.8 6.3 0.2 59.6 23.1 Average error 17.7
Table 7 Goodness of fit using only compact fragments. Fragment
Actual Vs (m/s)
Eq. (1) Vs (m/s)
Eqn (1) Error (%)
Eqn (7) Vs (m/s)
Eq. (7) Error number (%)
3 4 5 7 8 9 10
690.8 765.8 963.5 526.2 1084.5 670.8 775.2
639.2 646.4 645.9 481.9 757.4 628.6 680.5
7.5 15.6 33.0 8.4 30.2 6.3 12.2 Average error 17.6
736.2 735.9 736.5 585.3 826.9 713.0 773.9
6.6 3.9 23.6 11.2 23.8 6.3 0.2 Average error 11.5
Vs ¼ 462:5 þ 0:370m þ 1:95DOP 61:79m0:667
(7)
The coefficient of determination (R2) equals 0.84 indicating that the regression equation is an adequate fit. 7. Equation validation The equation was validated using natural fragments recovered from arena tests. Both compact natural fragments and noncompact (finger) fragments were included for completeness. Table 5 shows the experimental data for 11 impacts into CelotexÒ with sabot launched natural fragments at striking velocities between 526.2 and 1084.5 m/s. Percent error between the observed value and the calculated value was used to determine the goodness of fit for the original Eqs. (1) and (7) developed in this investigation. Table 6 shows the percent error for all fragments, as well as, the average absolute error for Eqs. (1) and (7). The average absolute error for all the natural fragments launched is 18.4% and 17.7%, respectively for Eqs. (1) and (7). Since both equations were developed using only compact fragments, the percent error would be expected to be lower for compact natural fragments. Table 7 shows the percent error for each compact fragment and the average absolute error neglecting the non-compact (finger) fragments. While the average percent error for Eq. (1) improves slightly, the average percent error for Eq. (7) becomes an acceptable 11.5%. 8. Conclusions Depth of penetration experiments were conducted with fragment simulating projectiles impacting into CelotexÒ. The experimental data was used to develop an empirical equation for calculating fragment impact velocity from penetration data as a function of mass and depth of penetration into CelotexÒ recovery media. The equation was validated by sabot launching natural fragments recovered from arena tests into CelotexÒ. The
developed equation was shown to be a good fit when used to predict the velocity of compact natural fragments, and an acceptable fit for all natural fragments launched in this investigation. Because the equation was developed using a multiple linear regression analysis of a defined data set, the formulation should only be used with fragment masses weighing between 0.13 g and 53.78 g at striking velocities between 198 m/s and 1524 m/s. To properly estimate the impact velocity requires a precise measurement of depth of penetration into the recovery media. An accurate and rapid depth of penetration measurement technique is presented and recommended for field and laboratory applications. Acknowledgements The authors would like to thank the Air Force Research Laboratory (Robert Dinan, Program Manager) for funding this work under contract FA4819-07-D-0001. The experiments were performed at the Air Force Research Laboratory Ballistics Facility located at Tyndall AFB, FL. Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of the use thereof. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. References [1] NATO STANAG-2920 Ballistic Test Method for Personal Armour Materials and Combat Clothing, 2nd ed., NATO Standardization Agency, 1999. 32 p [2] The Johns Hopkins University, The calibration of a collection medium for the determination of particle velocity. Project Thor Tech. Report 50, 1962, Ballistics Research Laboratories, Aberdeen Proving Ground, MD. [3] Atkinson GW, Massengill EB. Calculating initial fragment velocity from penetration data. NAVWEPS Report 8280, Albuquerque, NM: US Naval Weapons Evaluation Facility; 1964. [4] Finnegan SA, Schulz JC, Heimdahl OER. Spatial fragment mass and velocity distributions for ordnance and ultra-ordnance speed impacts. Int J of Impact Eng 1990;10:159–70. [5] de Bejar LA, Davis JL, Simmons L. Standoff-mortar-induced fragment forces. Int J of Impact Eng 2008;35:1053–62.
536
J.B. Jordan, C.J. Naito / International Journal of Impact Engineering 37 (2010) 530–536
[6] Smith AC, Vormelker PR. CelotexÒ Structural properties test. WSRCTR-2000–00444, Aiken SC: Westinghouse Savannah River Company; 2000. [7] Smith AC, Vormelker PR, Chapman G, Khan J, Miller KW, Khandkar MZH, Chapman G. Effect of orientation and strain rate on crush strength of cellulose fiberboard assemblies. WSRC-TR-2000–00508. Aiken SC: Westinghouse Savannah River Company 2000.
[8] Knight-Celotex, SoundstopÒ Sound Stopping Fiberboard, Section 09830, Submittal/Spec Sheet, www.soundstop.net. [9] ASTM Standard C208, 2008 Standard Specification for Cellulosic Fiber Insulating Board, ASTM International, West Conshohocken, PA, 2008, doi: 10.1520/ C0208-08A, www.astm.org. [10] Cheremisinoff N.P., Practical statistics for engineers and scientists, Lancaster Pennsylvania: Technomic Publishing Company Inc.; 1987.