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An investigation on mass loss of ogival projectiles penetrating concrete targets
International Journal of Impact Engineering 38 (2011) 770e778
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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
An investigation on mass loss of ogival projectiles penetrating concrete targets ZhongCheng Mu*, Wei Zhang Hypervelocity Impact Research Center, Harbin Institute of Technology, P.O. BOX 3020, Science Park, No. 2, Yikuang Street, Nangang District, Harbin 150080, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2011 Received in revised form 7 April 2011 Accepted 10 April 2011 Available online 19 April 2011
Mass loss of an ogival projectile during its normal penetration in concrete target was investigated in this paper. Experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating into concrete targets were conducted in the striking velocity range of 500e1500 m/s. Discussions revealed that projectile mass loss derives mainly from the nose part for both short-rod and long-rod projectiles during the penetration process. Furthermore, an engineering model was proposed to determine upper limit of rigid penetration regime as the maximum value of the striking velocity, which was based on the feature of projectile mass loss in the hydrodynamic transition between rigid penetration regime and semihydrodynamic penetration regime. Good agreements are obtained between engineering predictions and experimental results. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Mass loss Ogival projectile Concrete targets Upper limit
1. Introduction In terms of the striking velocity there are roughly three penetration regimes [1]. The first is the rigid penetration regime, in which a projectile suffers from slight deformation or mass loss that can be neglected. In this regime it is generally assumed that penetration efficiency increases proportionally with the striking velocity, which has been an undisputed conclusion based on numerous penetration experiments and classical empirical equations. The second regime could be defined based on the valid application range of the AlekseevskiieTate model, proposed independently by Alekseevskii [2] and Tate [3], where strength parameters of projectiles and targets are considered by modifying Bernouli equation. As in the first regime, penetration efficiency increases with the striking velocity, but it is nonlinear. Chen and Li [1] defined this regime as the semi-hydrodynamic penetration regime. The last is the hydrodynamics penetration regime, where the striking velocity in this regime is usually greater than 3.0 km/s. The highlighted characteristic is that strengths of projectiles and targets are negligible, thus the penetration process can be characterized as a fluidefluid interaction, which is governed by the law of steady-state fluid dynamics. Penetration in this regime is considered as the hydrodynamic so that only material densities are of primary importance. For metal materials, lots of investigations consisting of penetration experiments, numerical simulations and theoretical analyses have
* Corresponding author. Tel.: þ86 451 86417976 19; fax: þ86 451 86402055. E-mail address: [email protected] (Z. Mu). 0734-743X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2011.04.002
been done on these three regimes, and many successful conclusions have been drawn. However this situation is different in the penetration field of concrete materials, lots of previous studies and investigations concentrated mainly on the first penetration regime, typical reviews can be found in Kennedy [4], Backmann and Goldsmith [5], Zukas et al. [6], Brown [7], Williams [8], Corbett et al. [9], Goldsmith [10] and Li et al. [11]. Yet, when the research focus transfers from the sub-ordnance velocity to the high-speed velocity, it is not reasonable to ignore projectile deformation and projectile mass loss, which would decrease penetration efficiency and prompt to the occurrence of trajectory instabilities such as trajectory deviation. And in the past few years projectile mass loss has already gained interests among the international research communities, it is very necessary and beneficial to investigate the projectile mass loss during the penetration process of concrete materials. Many physical processes may occur along with the penetration process, including erosion of projectile surface accompanied by high temperature and possible phase transformation, transportation of the melted material onto the shank, injection of the melted material into the target medium and chemical reactions on the surface like fast oxidation, projectile structural failure including mainly compressive, tensile, severe bending and shear failures, etc. [12]. These processes are possible sources contributing to projectile mass loss, but it is pretty difficult to obtain some detailed observations or some characteristic parameters experimentally, though much effort has been put into understanding the penetration process. Klepaczko [12] conducted some work on the theoretical and experimental investigation of dynamic friction for the surface between projectile and target, which mainly involved in evolution of the friction
ZhongCheng Mu, W. Zhang / International Journal of Impact Engineering 38 (2011) 770e778
Nomenclature
v V
average crater diameter Cd C, K empirical constant E kinetic energy unconfined compressive strength of concrete target fc L/D ratio of the shank length to the projectile diameter m projectile mass m0.5, V0.5 mass and volume of the hemispherical projectile Dm projectile mass loss Mohr’s hardness scale of coarse aggregate Ma P penetration depth hardness of projectile material Rc
DV a g rt j
coefficient and dynamic plasticity of asperities. Some theoretical studies were also carried out on the melt and erosion due to high temperature and high pressure, especially when the striking velocity was in the order of 103 m/s. A comprehensive study of the mechanisms that are involved in the penetration process is very significant for understanding the projectile mass loss. Some investigations have been done as to some aspects of projectile mass loss in the recent years. Both quantitative and qualitative observations of such projectile mass loss have been documented by Forrestal et al. [13] and Frew et al. [14]. Furthermore, Silling and Forrestal [15] found that there existed a linear relation between projectile mass loss and the initial kinetic energy of projectiles and constructed an abrasion algorithm for projectile mass loss. Jones et al. [16,17] also reported some evaluation of projectile mass loss based on the dynamic friction, an expression for work was used in conjunction with thermodynamic consideration. Klepaczko and Hughes [18] defined the universal parameters of the rate of wear and the rate sensitivity of wear, and constructed an effective method for analyzing the rate of mass abrasion. Chen et al. [19] analyzed effect factors on projectile mass loss and constructed a general engineering model on mass abrasion of kinetic energy penetrators. It is noted that previous investigations of projectile mass loss mainly focus on long-rod projectiles. A systematic study on projectile mass loss, both theoretically and experimentally, including different material properties, different nose shapes and different L/D ratios, is very beneficial in the design of advanced kinetic energy penetrators. In the present paper, firstly experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating normally concrete targets were conducted with the striking velocity range of 500e1500 m/s, and results were discussed in detail. Furthermore, combining the collected data of Forrestal et al. [13] and Frew et al. [14] with results of the present penetration experiments, the hydrodynamic transition between rigid penetration regime and
771
velocity volume volume loss maximum size of coarse aggregate rate of projectile mass loss density of concrete target CRH (caliber-radius-head) for ogival nose
Subscripts c upper limit of rigid penetration regime i initial value r residual value s, n shank and nose of projectiles
semi-hydrodynamic penetration regime was investigated. And an engineering model on upper limit of rigid penetration regime was presented in light of some features of projectile mass loss in hydrodynamic transition regime. 2. Experimental setup and program 2.1. Experimental setup A two-stage light gas gun as the accelerate facility was used to perform this series of penetration experiments. The gun mainly consists of a pressurized chamber, a 57 mm caliber pump tube, a 12.7 mm diameter and 3 m long launch tube, an impact chamber and a sabot trap plate. The striking velocity was controlled by pressured gas (pressure and kinds of gas: hydrogen/nitrogen) and selection of the diaphragm thickness. A laser light barrier measurement system placed at the hatch of experimental chamber was employed to trigger the timing device and to get the striking velocity. One laser-curtain of the laser light barrier measurement system was used to trigger the digital high-speed camera system, which aimed to capture the penetration events. From the captured impact images projectile motion was obtained, and the striking velocity could be further validated. Each specimen was placed in a containment jig and aligned such that the projectile could hit the target center. In this series of penetration experiments projectile shank diameter was centerless ground to fit snugly into the bore of a 12.7 mm launch tube, so sabots or obturators were not necessary. Fig. 1 shows the sketch of the experimental system. 2.2. Targets and projectiles Projectiles with a diameter of 12.6 mm, a shank length of 34 mm and a nose shape of 2 CRH (caliber-radius-head) were manufactured by 38CrSi steel and heat treated to a hardness of Rc 42, as
Fig. 1. Sketch of the experimental system.
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shown in Fig. 2a. All concrete specimens (Fig. 2b) in this series of penetration experiments were conducted in a small concrete mixer. For each mix, a brick of 360 360 400 mm3 used for penetration experiments and 3 cubes of 100 100 100 mm3 used for unconfined compressive experiments were cast under the room temperature. After 24 h these specimens were demoulded, maintained in standard curing room for 28 days. Finally concrete targets with a nominal unconfined compressive strength of 51 MPa, and density of 2440 kg/m3 were obtained.
Table 1 Experimental results for short-rod projectiles with CRH 2. Test no.
mi (g) vi (m/s) mr (g) g
Cd(mm) P (mm) jr
Test10-10 Test10-01 Test10-02 Test10-14 Test10-04 Test10-05 Test10-12 Test10-08
26.6 26.5 26.7 26.7 26.6 26.7 26.4 26.6
140 151 160 165 189 210 251 299
621 715 859 913 1112 1191 1291 1449
26.4 26.0 25.7 25.7 24.6 24.1 23.5 19.4
0.751 1.89 3.75 3.75 7.52 9.74 11.0 27
75 92 120 132 140 144 140 162
gn
1.87 0.748 1.67 1.954 1.38 3.85 1.25 4.77 0.91 7.46 0.67 9.73 0.5 12.0 e e
3. Experimental results and discussion 3.1. Results description In this series of penetration experiments, available hits depended on whether the projectile impacted the maximum coarse aggregate, which could contribute to the deviation of penetration trajectory. Available hits are listed in Table 1. The striking velocity was in the range from 500 m/s to 1500 m/s. The damage of concrete targets caused by the impact was defined by average crater diameter and penetration depth. The final crater diameter was gained by measuring the average of the four axes in the impact face (Fig. 3a). Penetration depth was measured by rigid bores. The damage of projectiles was shown by mass loss, variation of nose shape and micro-observation of post-test projectiles. In Fig. 4 observations of post-test projectiles indicated that when the striking velocity was
below 1291 m/s, the geometries of post-test projectiles still kept the ogival shape with the change of CRH. In order to gain accurate CRH of post-test projectiles, we adopted the digital microscope to measure the radius of the post-test nose contour, as shown in Fig. 3b. The final radius of the post-test nose was the average of four contour arcs. During the penetration process, materials including projectile and target ahead of the projectile nose are subjected to very high compressive stress, which could be the main reason of mass loss for projectiles and crack propagation for targets. Generally, for thick concrete targets, penetration mainly includes two stages: initial crater and hole enlargement in Fig. 5. At the initial crater, pictures captured by high-speed camera show that a dense debris cloud can be seen ejecting from the impact face in Fig. 6. As the projectile penetrating further into the target, the penetration enters the hole enlargement stage, a tunnel is formed in the target center. The kinetic energy of the projectile is mainly consumed in this stage of hole enlargement. Thus penetration depth mainly includes two parts, as shown in Fig. 5. 3.2. Discussions on experimental results Based on penetration experimental results, mass loss of posttest projectiles versus corresponding initial kinetic energy is plotted in Fig. 7. A nearly linear relation between projectile mass
Fig. 2. Projectile and concrete target in the experiment.
Fig. 3. Measurement of the crater diameter for post-test targets and CRH for post-test projectiles.
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773
Fig. 4. Photographs of post-test projectiles.
loss and the initial kinetic energy is found for the striking velocity up to about 1191 m/s. This relation is given by
g ¼
Dm mi
¼
1 2 Cv þ K 2 i
(1)
where Dm ¼ mi mr, C and K are empirical constants. The conclusion is analogous to the results of Silling and Forrestal [15]. However a threshold striking velocity is found from the relation, which is due to the emergence of constant K. When the striking velocity is below this threshold velocity, the penetration process could be seen as the ideal rigid penetration. The reason contributing to the difference could be explained in terms of projectile material properties, materials with the properties of high wear resistance and high melting heat will have a very slight mass loss for low-speed penetration so that the projectile could behave approximately ideal rigid. Klepaczko and Hughes [18], Silling and Forrestal [15] and Chen et al. [19] had a consistent conclusion: when the projectile is longrod projectile (L/D > 5), mass loss mostly occurs in the projectile nose. But mass loss of short-rod projectile (L/D < 5) is not still clear. Generally, projectile mass loss includes two parts: shank mass loss and nose mass loss, as following.
Dm ¼ Dms þ Dmn
(2)
Herein it is assumed that projectile density is invariable during the penetration process, then the rate of projectile mass loss can be read
g ¼
Dm mi
¼
DV Vi
¼
DVs þ DVn Vi
Fig. 5. Definition of penetration depth.
(3)
For the ogival projectile, nose volume is given as following.
"sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ffi 1 1 1 1 1 1 þ j 4j 3j 12j2 # 1 1 1 cos 1 1 2j 2j
Vn ¼ p D3 j3
(4)
The rate of mass loss on the nose part can be given by
gn ¼
DVn
(5)
Vi
Therefore based on CRH measurements of post-test projectiles, mass loss on the nose part from Eq. (5) has an agreement with that of the whole projectile from experimental results, as shown in Table 1. Thus it could be declared that mass loss of short-rod projectiles mainly occurs in the projectile nose as long-rod projectiles. Thus Eq. (3) can be read
g¼
Dm mi
¼
Dmn mi
¼
DVn Vi
(6)
Here an interesting phenomenon is found from Table 1. Test1008 demonstrates that when the striking velocity is out of the instable regime, both penetration depth and projectile mass loss again obtain the rising trend (the instable regime will be discussed in the next section). From the observation of post-test projectiles, it was noted that the nose shape changed from the hemisphericallike shape to the cone-like shape, as given in Fig. 8. This indicates that the increasing penetration efficiency due to the change of nose shape outweighs the deceasing penetration efficiency caused by projectile mass loss. This phenomenon could be attributed to the adiabatic shear phenomenon which causes the projectile to selfsharpen during the penetration process, micro-cracks in Fig. 9c further enhance to some degree this standpoint, detailed work will be addressed in future work. Many physical mechanics may contribute to projectile mass loss during the penetration process, mainly including high sliding friction, melting due to high pressure and high temperature, phase transformation, and structural failure, etc. To explore possible factors resulting in projectile mass loss, optical microphotographical observations of post-test projectiles were carried out by scanning electron microscope (SEM). Post-test projectiles with corresponding to three different stages of striking velocity at vi ¼ 715, 1112, 1449 m/s, respectively were sectioned along the axis direction by wire-electrode cutting and polished. Fig. 9 represents the micrographs. It is found that no micro-cracks appear in the projectile when the striking velocity is 715 m/s, whereas both other two events have the micro-crack appearance. This indicates that the sources causing projectile mass loss have a difference at different striking velocity range. And the total length of projectiles have a very slight variation at vi ¼ 621 m/s and 715 m/s, thus it could be declared that mass loss is mostly caused by the sliding friction when the striking velocity is below 715 m/s. Above 715 m/s,
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Fig. 7. Relation between projectile mass loss and the initial kinetic energy.
the change of total length is obvious, at the tip of the projectile nose there are obvious blunting and melt phenomenon, this indicates that material melt due to high temperature is one of mass loss sources at this velocity range, meanwhile micro-cracks of optical micrographs in Fig. 9b and c lead us to think that there exists another source contributing to projectile mass loss together in this striking velocity range. 4. Upper limit of the rigid penetration 4.1. Hydrodynamic transition regime An interesting phenomenon was found in Forrestal and Piekutowski [20] and Piekutowski et al. [21], penetration depth undergoes a dramatic decrease when the striking velocity approaches to a point. Chen and Li [1] indicated the point should be responsible for the transition point between the first penetration regime (rigid penetration) and the second penetration regime (semi-hydrodynamic penetration). However the phenomenon is only gained based on metal targets, for concrete material it is not still clear. Therefore for concrete material, in order to gain the feature of the transition between rigid penetration regime and semihydrodynamic penetration regime, six cases on concrete penetration experiments are listed and plotted in Table 2 and Fig. 10, where Cases 1 and 2 are reported by Forrestal et al. [13], Cases 3e5 by Frew et al. [14] and Case 6 is from the present experiment. Furthermore, based on CRH evaluations of post-projectiles of Cases 1e5 in Chen et al. [19] and the investigation of Case 6 in Section 3, CRH
Fig. 6. Debris cloud pictures of typical penetration experiment.
Fig. 8. Profile of post-test projectile at vi ¼ 1449 m/s.
ZhongCheng Mu, W. Zhang / International Journal of Impact Engineering 38 (2011) 770e778
775
Fig. 9. Typical optical micrograph of the brink of the section plane for post-test projectiles.
variations of post-projectiles on Cases 1e6 with the striking velocity are plotted in Fig. 11. Results show that the variation trends of penetration depth with the striking velocity are in close agreement with that of projectile mass loss in Fig. 10. In Cases 1 and 2, penetration depth increases proportionally with the striking velocity within a certain range of striking velocity. According to the feature of rigid penetration regime, this striking velocity range could be seen as the rigid penetration regime. And when the striking velocity exceeds this striking velocity range, both penetration depth and projectile mass loss begin simultaneously entering an instable regime, where both penetration depth and projectile mass loss have a very slight variation with the striking velocity, as shown in the rectangle of Fig. 10. And combining with the investigation of nose shapes of post-projectiles in Fig. 11, it is found that once entering this zone, the nose shape is eroded to a hemispherical-like shape, and the hemispherical shape is nearly maintained in this zone, which explains the slight variation of this zone, especially on projectile mass loss. For Cases 3e5, there no exists an instable regime, it is reasonable to take account of the explanation of Cases 1 and 2. The maximum striking velocity in penetration experiments of Cases 3e5 are within the range of rigid penetration regime, which are not enough for the phenomenon of “hemispherical-like shape”. For Case 6, at the point of the maximum striking velocity of the penetration experiments, the feature is similar with that of the instable regime, penetration depth has a slight decease, and the nose shape could be evaluated approximately as the hemisphericallike shape. Thus this indicates that the maximum striking velocity in Case 6 has entered the instable regime. Discussions above reveal that this instable regime is responsible for the transition between rigid penetration regime and Table 2 Experimental conditions of six penetration events for ogival projectiles penetrating concrete targets.
Targets fc (MPa) rt (kg/m3) a (mm) Aggregate material Ma Projectiles Material Rc m (g) mn/m (%) D (mm) L/D CRH g0.5 (%)
Case 1 Case 2 Case 3
Case 4
Case 5
Case 6
62.8 2300 9.5 Quartz
51 2300 9.5 Quartz
58.4 2320 9.5 Limestone
58.4 2320 9.5 Limestone
58.4 2320 9.5 Limestone
51 2440 10 Limestone
7.0
7.0
3.0
3.0
3.0
3.0
4340 steel 45 478 9.8 20.3 8.3 3 6.2
4340 steel 45 1600 9.9 30.5 8.3 3 6.2
4340 steel 45 478 9.8 20.3 8.3 3 6.2
4340 steel 45 1620 9.8 30.5 8.3 3 6.2
AmerMet100 38CrSi 53 478 9.8 20.3 8.3 3 6.2
42 26.6 21.4 12.6 2.7 2 12
semi-hydrodynamic penetration regime. Herein we call the instable regime as hydrodynamic transition regime. Thus together with Chen and Li [1], it could be drawn that penetration depth undergoes a dramatic decrease and a slight instable variation with the increase of striking velocity for metal targets and concrete targets respectively in hydrodynamic transition regime. And it is noted that motivations driving the hydrodynamic transition could be summarized in terms of projectile mass loss. For metal targets, the motivation driving the hydrodynamic transition is that projectile happens to the deformation without mass loss: in the penetration process, due to the compressive or tensile or bend failure, the projectile deviates from the target centerline (Forrestal and Piekutowski [20], Piekutowski et al. [21]), or the projectile nose happens to the deformation analogous with the deformation of Taylor Test (Rosenberg and Dekel [22]). On the other hand, for concrete targets, the motivation is that the projectile happens to the erosion with mass loss (Forrestal et al. [13], the present experiments in this study): projectile nose shape has a variation, but the geometries of post-test projectiles still keep the prototypical shape. Thus we could say that the feature and the mechanics in hydrodynamic transition regime are different for different property materials.
4.2. Engineering model of upper limit of rigid penetration regime Based on the investigation of projectile mass loss when penetrating concrete targets normally, it is indicated that the initial point where the nose shape is eroded to a hemispherical-like shape could be considered as the transition point between rigid penetration regime and hydrodynamic transition regime. This leads us to think that upper limit of the rigid penetration regime could be gained by this feature. Aim to gain upper limit of the rigid penetration regime in terms of the feature of hydrodynamic transition regime, as in the work of Section 3, the relation of Cases 1e5 between projectile mass loss and the initial kinetic energy are fit linearly in Fig. 12. Table 3 documents the fit data of Cases 1e6. Comparisons between Fig. 10 and Fig. 12 indicate that the variation trends between projectile mass loss and the initial kinetic energy keep simultaneous with that of the rate of mass loss and the striking velocity, so upper limit of the linear relation between projectile mass loss and the initial kinetic energy could be considered as upper limit of rigid penetration regime. Thus mass loss at the upper limit of the linear relation can be given by
Dm ¼ mi m0:5
(7)
where m0.5 is the projectile mass with CRH 0.5 nose shape. According to the conclusion from Section 3, whatever the projectile is long rod or short rod, projectile mass loss is mainly
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Fig. 10. Penetration data from Sandia experiments and the present experiments.
concentrated on the nose part. By Eqs. (6) and (7), the critical gc could be given by
gc ¼
Dm mi
¼
Vi V0:5 Vi
(8)
together with the Eq. (1), the upper limit on the initial kinetic energy reads
Ec ¼
1 ½mð1 KÞ m0:5 C
(9)
Further upper limit of the linear relation as the maximum striking velocity yields
v2c ¼
2 ðg KÞ C 0:5
(10)
Thus for ogival projectiles, upper limit of rigid penetration regime as the maximum striking velocity could be evaluated by Eq. (10). Since the hydrodynamic transition is a range, it is pretty difficult to gain the exact transition point between rigid penetration regime and hydrodynamic transition regime experimentally, but the scope of
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777
Table 4 Upper limit of rigid penetration regime theoretically and experimentally for six penetration events.
Theoretical value (m/s) Experimental value (m/s)
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
958
996
1371
1381
1277
1279
>926 & 985
>900& 1009
>1162
>1176
>1165
>1191 & 1291
significantly affects the upper limit by the comparison between Case 1 and Case 3, it is reasonable to explain the difference between two events based on the hardness of coarse aggregate. Similarly, events of Case 3 and Case 5 indicate that projectile strength is an important factor for the upper limit. In the present investigation we found that projectile strength has a decreasing trend to the upper limit, a like phenomenon has been gained in our another work [23], although targets investigated are metal materials. This implies to some degree that enhancing the projectile hardness is not always the first option in terms of improving the penetration efficiency, which is a very important practical problem in engineering applications. As shown in Table 3, Case 3 and Case 4 is in like manner, comparison between them indicates that the effect of projectile diameter to the upper limit could be ignored, which is very meaningful for the lab-scale research. The upper limit of Case 2 is larger than that of Case 1. Together with the conclusion of Case 3 and Case 4, we could obtain a clear understanding for the effect of compressive strength of the target: the upper limit has a decreasing trend with the compressive strength raise.
Fig. 11. CRH variations with the striking velocity.
5. Conclusion remarks
Fig. 12. The linear fit between projectile mass loss and initial kinetic energy for six penetration events.
the transition point could be evaluated approximately. Table 4 shows comparisons of the upper limit between the predictions from Eq. (10) and experimental results. Clearly, engineering predictions of Cases 1e6 on the upper limit are all within the scope of experimental evaluations, this indicates fully that the engineering model is reasonable. 4.3. Dominant factors on upper limit of rigid penetration regime According to the analyses above, several dominant factors regarding events of the penetration process can be investigated in terms of the upper limit. Firstly the hardness of coarse aggregate
Table 3 Linear fit data for six penetration events. Constants
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
C K
0.135 0
0.125 0
0.066 0
0.065 0
0.076 0
0.187 0.033
In this work, based on the review of previous Sandia experiments and the analyses on the present experiments, mass loss of ogival projectiles penetrating concrete targets normally was examined. For short-rod projectiles, two conclusions are same to that of long-rod projectiles. One is that analytical results in the present experiments show that projectile mass loss increases linearly with the initial kinetic energy until the striking velocity approaches to upper limit of the linear relation. The other is that examinations of post-test projectiles indicate that mass loss of short-rod projectiles mainly occur also on the projectile nose. Meanwhile by comparisons of optical micrographs of post-test projectiles at different striking velocity range, it is gained that roles of the sources contributing to projectile mass loss are different at the different striking velocity range, there are primary and secondary differentiations on the sources, detailed work will be addressed in future work. On the other hand, the hydrodynamic transition between rigid penetration regime and semi-hydrodynamic penetration regime is investigated. The feature of projectile mass loss in the hydrodynamic transition enables us to construct an engineering model to predict upper limit of the rigid penetration regime. Good agreements are obtained between engineering predictions and experimental results. The engineering model is determined with no physical basis, upper limit of the rigid penetration regime can be evaluated approximately by only two hits of penetration experiments, the simple form can obtain the popular in engineering application. Furthermore, dominant factors which include coarse aggregate hardness, projectile material hardness, projectile diameter and compressive strength of targets are discussed on the effect to upper limit of the rigid penetration regime.
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Acknowledgements The authors would like to thank Prof. QingMing Li of Aerospace and Civil Engineering, the University of Manchester for his careful reading and comments of the manuscript. References [1] Chen XW, Li QM. Transition from non-deformable projectile penetration to semi-hydrodynamic penetration. ASCE J Eng Mech 2004;130:123e7. [2] Alekseevskii VP. Penetration of a rod into a target at high velocity. Combust Explos Shock Waves 1966;2(2):63e6. [3] Tate A. A theory for the deceleration of long rods after impact. J Mech Phys Solids 1967;15(6):387e99. [4] Kennedy RP. A review of procedures for the analysis and design of concrete structures to resist missile impact effects. Nucl Eng Des 1976;37(2):183e203. [5] Backmann ME, Goldsmith W. The mechanics of penetration of projectiles into targets. Int J Eng Sci 1978;16:1e99. [6] Zukas JA, Nicholas T, Swift HF, Greszczuk LB, Curran DR. Impact dynamics. New York: Wiley; 1982. [7] Brown SJ. Energy release protection for pressurized systems. Part II: review of studies into impact terminal ballistics. Appl Mech Rev 1986;39:177e201. [8] Williams MS. Modelling of local impact effects on plain and reinforced concrete. ACI Struct J 1994;91(2):178e87. [9] Corbett GG, Reid SR, Johnson W. Impact loading of plates and shells by freeflying projectiles: a review. Int J Impact Eng 1996;18(2):141e230. [10] Goldsmith W. Review: non-ideal projectile impact on targets. Int J Impact Eng 1999;22(2e3):95e395. [11] Li QM, Reid SR, Wen HM, Telford AR. Local impact effects of hard missiles on concrete targets. Int J Impact Eng 2005;32(1e4):224e84.
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An investigation on mass loss of ogival projectiles penetrating concrete targets ZhongCheng Mu*, Wei Zhang Hypervelocity Impact Research Center, Harbin Institute of Technology, P.O. BOX 3020, Science Park, No. 2, Yikuang Street, Nangang District, Harbin 150080, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 January 2011 Received in revised form 7 April 2011 Accepted 10 April 2011 Available online 19 April 2011
Mass loss of an ogival projectile during its normal penetration in concrete target was investigated in this paper. Experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating into concrete targets were conducted in the striking velocity range of 500e1500 m/s. Discussions revealed that projectile mass loss derives mainly from the nose part for both short-rod and long-rod projectiles during the penetration process. Furthermore, an engineering model was proposed to determine upper limit of rigid penetration regime as the maximum value of the striking velocity, which was based on the feature of projectile mass loss in the hydrodynamic transition between rigid penetration regime and semihydrodynamic penetration regime. Good agreements are obtained between engineering predictions and experimental results. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Mass loss Ogival projectile Concrete targets Upper limit
1. Introduction In terms of the striking velocity there are roughly three penetration regimes [1]. The first is the rigid penetration regime, in which a projectile suffers from slight deformation or mass loss that can be neglected. In this regime it is generally assumed that penetration efficiency increases proportionally with the striking velocity, which has been an undisputed conclusion based on numerous penetration experiments and classical empirical equations. The second regime could be defined based on the valid application range of the AlekseevskiieTate model, proposed independently by Alekseevskii [2] and Tate [3], where strength parameters of projectiles and targets are considered by modifying Bernouli equation. As in the first regime, penetration efficiency increases with the striking velocity, but it is nonlinear. Chen and Li [1] defined this regime as the semi-hydrodynamic penetration regime. The last is the hydrodynamics penetration regime, where the striking velocity in this regime is usually greater than 3.0 km/s. The highlighted characteristic is that strengths of projectiles and targets are negligible, thus the penetration process can be characterized as a fluidefluid interaction, which is governed by the law of steady-state fluid dynamics. Penetration in this regime is considered as the hydrodynamic so that only material densities are of primary importance. For metal materials, lots of investigations consisting of penetration experiments, numerical simulations and theoretical analyses have
* Corresponding author. Tel.: þ86 451 86417976 19; fax: þ86 451 86402055. E-mail address: [email protected] (Z. Mu). 0734-743X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2011.04.002
been done on these three regimes, and many successful conclusions have been drawn. However this situation is different in the penetration field of concrete materials, lots of previous studies and investigations concentrated mainly on the first penetration regime, typical reviews can be found in Kennedy [4], Backmann and Goldsmith [5], Zukas et al. [6], Brown [7], Williams [8], Corbett et al. [9], Goldsmith [10] and Li et al. [11]. Yet, when the research focus transfers from the sub-ordnance velocity to the high-speed velocity, it is not reasonable to ignore projectile deformation and projectile mass loss, which would decrease penetration efficiency and prompt to the occurrence of trajectory instabilities such as trajectory deviation. And in the past few years projectile mass loss has already gained interests among the international research communities, it is very necessary and beneficial to investigate the projectile mass loss during the penetration process of concrete materials. Many physical processes may occur along with the penetration process, including erosion of projectile surface accompanied by high temperature and possible phase transformation, transportation of the melted material onto the shank, injection of the melted material into the target medium and chemical reactions on the surface like fast oxidation, projectile structural failure including mainly compressive, tensile, severe bending and shear failures, etc. [12]. These processes are possible sources contributing to projectile mass loss, but it is pretty difficult to obtain some detailed observations or some characteristic parameters experimentally, though much effort has been put into understanding the penetration process. Klepaczko [12] conducted some work on the theoretical and experimental investigation of dynamic friction for the surface between projectile and target, which mainly involved in evolution of the friction
ZhongCheng Mu, W. Zhang / International Journal of Impact Engineering 38 (2011) 770e778
Nomenclature
v V
average crater diameter Cd C, K empirical constant E kinetic energy unconfined compressive strength of concrete target fc L/D ratio of the shank length to the projectile diameter m projectile mass m0.5, V0.5 mass and volume of the hemispherical projectile Dm projectile mass loss Mohr’s hardness scale of coarse aggregate Ma P penetration depth hardness of projectile material Rc
DV a g rt j
coefficient and dynamic plasticity of asperities. Some theoretical studies were also carried out on the melt and erosion due to high temperature and high pressure, especially when the striking velocity was in the order of 103 m/s. A comprehensive study of the mechanisms that are involved in the penetration process is very significant for understanding the projectile mass loss. Some investigations have been done as to some aspects of projectile mass loss in the recent years. Both quantitative and qualitative observations of such projectile mass loss have been documented by Forrestal et al. [13] and Frew et al. [14]. Furthermore, Silling and Forrestal [15] found that there existed a linear relation between projectile mass loss and the initial kinetic energy of projectiles and constructed an abrasion algorithm for projectile mass loss. Jones et al. [16,17] also reported some evaluation of projectile mass loss based on the dynamic friction, an expression for work was used in conjunction with thermodynamic consideration. Klepaczko and Hughes [18] defined the universal parameters of the rate of wear and the rate sensitivity of wear, and constructed an effective method for analyzing the rate of mass abrasion. Chen et al. [19] analyzed effect factors on projectile mass loss and constructed a general engineering model on mass abrasion of kinetic energy penetrators. It is noted that previous investigations of projectile mass loss mainly focus on long-rod projectiles. A systematic study on projectile mass loss, both theoretically and experimentally, including different material properties, different nose shapes and different L/D ratios, is very beneficial in the design of advanced kinetic energy penetrators. In the present paper, firstly experiments of 38CrSi short-rod projectiles with ogival nose shape penetrating normally concrete targets were conducted with the striking velocity range of 500e1500 m/s, and results were discussed in detail. Furthermore, combining the collected data of Forrestal et al. [13] and Frew et al. [14] with results of the present penetration experiments, the hydrodynamic transition between rigid penetration regime and
771
velocity volume volume loss maximum size of coarse aggregate rate of projectile mass loss density of concrete target CRH (caliber-radius-head) for ogival nose
Subscripts c upper limit of rigid penetration regime i initial value r residual value s, n shank and nose of projectiles
semi-hydrodynamic penetration regime was investigated. And an engineering model on upper limit of rigid penetration regime was presented in light of some features of projectile mass loss in hydrodynamic transition regime. 2. Experimental setup and program 2.1. Experimental setup A two-stage light gas gun as the accelerate facility was used to perform this series of penetration experiments. The gun mainly consists of a pressurized chamber, a 57 mm caliber pump tube, a 12.7 mm diameter and 3 m long launch tube, an impact chamber and a sabot trap plate. The striking velocity was controlled by pressured gas (pressure and kinds of gas: hydrogen/nitrogen) and selection of the diaphragm thickness. A laser light barrier measurement system placed at the hatch of experimental chamber was employed to trigger the timing device and to get the striking velocity. One laser-curtain of the laser light barrier measurement system was used to trigger the digital high-speed camera system, which aimed to capture the penetration events. From the captured impact images projectile motion was obtained, and the striking velocity could be further validated. Each specimen was placed in a containment jig and aligned such that the projectile could hit the target center. In this series of penetration experiments projectile shank diameter was centerless ground to fit snugly into the bore of a 12.7 mm launch tube, so sabots or obturators were not necessary. Fig. 1 shows the sketch of the experimental system. 2.2. Targets and projectiles Projectiles with a diameter of 12.6 mm, a shank length of 34 mm and a nose shape of 2 CRH (caliber-radius-head) were manufactured by 38CrSi steel and heat treated to a hardness of Rc 42, as
Fig. 1. Sketch of the experimental system.
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shown in Fig. 2a. All concrete specimens (Fig. 2b) in this series of penetration experiments were conducted in a small concrete mixer. For each mix, a brick of 360 360 400 mm3 used for penetration experiments and 3 cubes of 100 100 100 mm3 used for unconfined compressive experiments were cast under the room temperature. After 24 h these specimens were demoulded, maintained in standard curing room for 28 days. Finally concrete targets with a nominal unconfined compressive strength of 51 MPa, and density of 2440 kg/m3 were obtained.
Table 1 Experimental results for short-rod projectiles with CRH 2. Test no.
mi (g) vi (m/s) mr (g) g
Cd(mm) P (mm) jr
Test10-10 Test10-01 Test10-02 Test10-14 Test10-04 Test10-05 Test10-12 Test10-08
26.6 26.5 26.7 26.7 26.6 26.7 26.4 26.6
140 151 160 165 189 210 251 299
621 715 859 913 1112 1191 1291 1449
26.4 26.0 25.7 25.7 24.6 24.1 23.5 19.4
0.751 1.89 3.75 3.75 7.52 9.74 11.0 27
75 92 120 132 140 144 140 162
gn
1.87 0.748 1.67 1.954 1.38 3.85 1.25 4.77 0.91 7.46 0.67 9.73 0.5 12.0 e e
3. Experimental results and discussion 3.1. Results description In this series of penetration experiments, available hits depended on whether the projectile impacted the maximum coarse aggregate, which could contribute to the deviation of penetration trajectory. Available hits are listed in Table 1. The striking velocity was in the range from 500 m/s to 1500 m/s. The damage of concrete targets caused by the impact was defined by average crater diameter and penetration depth. The final crater diameter was gained by measuring the average of the four axes in the impact face (Fig. 3a). Penetration depth was measured by rigid bores. The damage of projectiles was shown by mass loss, variation of nose shape and micro-observation of post-test projectiles. In Fig. 4 observations of post-test projectiles indicated that when the striking velocity was
below 1291 m/s, the geometries of post-test projectiles still kept the ogival shape with the change of CRH. In order to gain accurate CRH of post-test projectiles, we adopted the digital microscope to measure the radius of the post-test nose contour, as shown in Fig. 3b. The final radius of the post-test nose was the average of four contour arcs. During the penetration process, materials including projectile and target ahead of the projectile nose are subjected to very high compressive stress, which could be the main reason of mass loss for projectiles and crack propagation for targets. Generally, for thick concrete targets, penetration mainly includes two stages: initial crater and hole enlargement in Fig. 5. At the initial crater, pictures captured by high-speed camera show that a dense debris cloud can be seen ejecting from the impact face in Fig. 6. As the projectile penetrating further into the target, the penetration enters the hole enlargement stage, a tunnel is formed in the target center. The kinetic energy of the projectile is mainly consumed in this stage of hole enlargement. Thus penetration depth mainly includes two parts, as shown in Fig. 5. 3.2. Discussions on experimental results Based on penetration experimental results, mass loss of posttest projectiles versus corresponding initial kinetic energy is plotted in Fig. 7. A nearly linear relation between projectile mass
Fig. 2. Projectile and concrete target in the experiment.
Fig. 3. Measurement of the crater diameter for post-test targets and CRH for post-test projectiles.
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773
Fig. 4. Photographs of post-test projectiles.
loss and the initial kinetic energy is found for the striking velocity up to about 1191 m/s. This relation is given by
g ¼
Dm mi
¼
1 2 Cv þ K 2 i
(1)
where Dm ¼ mi mr, C and K are empirical constants. The conclusion is analogous to the results of Silling and Forrestal [15]. However a threshold striking velocity is found from the relation, which is due to the emergence of constant K. When the striking velocity is below this threshold velocity, the penetration process could be seen as the ideal rigid penetration. The reason contributing to the difference could be explained in terms of projectile material properties, materials with the properties of high wear resistance and high melting heat will have a very slight mass loss for low-speed penetration so that the projectile could behave approximately ideal rigid. Klepaczko and Hughes [18], Silling and Forrestal [15] and Chen et al. [19] had a consistent conclusion: when the projectile is longrod projectile (L/D > 5), mass loss mostly occurs in the projectile nose. But mass loss of short-rod projectile (L/D < 5) is not still clear. Generally, projectile mass loss includes two parts: shank mass loss and nose mass loss, as following.
Dm ¼ Dms þ Dmn
(2)
Herein it is assumed that projectile density is invariable during the penetration process, then the rate of projectile mass loss can be read
g ¼
Dm mi
¼
DV Vi
¼
DVs þ DVn Vi
Fig. 5. Definition of penetration depth.
(3)
For the ogival projectile, nose volume is given as following.
"sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ffi 1 1 1 1 1 1 þ j 4j 3j 12j2 # 1 1 1 cos 1 1 2j 2j
Vn ¼ p D3 j3
(4)
The rate of mass loss on the nose part can be given by
gn ¼
DVn
(5)
Vi
Therefore based on CRH measurements of post-test projectiles, mass loss on the nose part from Eq. (5) has an agreement with that of the whole projectile from experimental results, as shown in Table 1. Thus it could be declared that mass loss of short-rod projectiles mainly occurs in the projectile nose as long-rod projectiles. Thus Eq. (3) can be read
g¼
Dm mi
¼
Dmn mi
¼
DVn Vi
(6)
Here an interesting phenomenon is found from Table 1. Test1008 demonstrates that when the striking velocity is out of the instable regime, both penetration depth and projectile mass loss again obtain the rising trend (the instable regime will be discussed in the next section). From the observation of post-test projectiles, it was noted that the nose shape changed from the hemisphericallike shape to the cone-like shape, as given in Fig. 8. This indicates that the increasing penetration efficiency due to the change of nose shape outweighs the deceasing penetration efficiency caused by projectile mass loss. This phenomenon could be attributed to the adiabatic shear phenomenon which causes the projectile to selfsharpen during the penetration process, micro-cracks in Fig. 9c further enhance to some degree this standpoint, detailed work will be addressed in future work. Many physical mechanics may contribute to projectile mass loss during the penetration process, mainly including high sliding friction, melting due to high pressure and high temperature, phase transformation, and structural failure, etc. To explore possible factors resulting in projectile mass loss, optical microphotographical observations of post-test projectiles were carried out by scanning electron microscope (SEM). Post-test projectiles with corresponding to three different stages of striking velocity at vi ¼ 715, 1112, 1449 m/s, respectively were sectioned along the axis direction by wire-electrode cutting and polished. Fig. 9 represents the micrographs. It is found that no micro-cracks appear in the projectile when the striking velocity is 715 m/s, whereas both other two events have the micro-crack appearance. This indicates that the sources causing projectile mass loss have a difference at different striking velocity range. And the total length of projectiles have a very slight variation at vi ¼ 621 m/s and 715 m/s, thus it could be declared that mass loss is mostly caused by the sliding friction when the striking velocity is below 715 m/s. Above 715 m/s,
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Fig. 7. Relation between projectile mass loss and the initial kinetic energy.
the change of total length is obvious, at the tip of the projectile nose there are obvious blunting and melt phenomenon, this indicates that material melt due to high temperature is one of mass loss sources at this velocity range, meanwhile micro-cracks of optical micrographs in Fig. 9b and c lead us to think that there exists another source contributing to projectile mass loss together in this striking velocity range. 4. Upper limit of the rigid penetration 4.1. Hydrodynamic transition regime An interesting phenomenon was found in Forrestal and Piekutowski [20] and Piekutowski et al. [21], penetration depth undergoes a dramatic decrease when the striking velocity approaches to a point. Chen and Li [1] indicated the point should be responsible for the transition point between the first penetration regime (rigid penetration) and the second penetration regime (semi-hydrodynamic penetration). However the phenomenon is only gained based on metal targets, for concrete material it is not still clear. Therefore for concrete material, in order to gain the feature of the transition between rigid penetration regime and semihydrodynamic penetration regime, six cases on concrete penetration experiments are listed and plotted in Table 2 and Fig. 10, where Cases 1 and 2 are reported by Forrestal et al. [13], Cases 3e5 by Frew et al. [14] and Case 6 is from the present experiment. Furthermore, based on CRH evaluations of post-projectiles of Cases 1e5 in Chen et al. [19] and the investigation of Case 6 in Section 3, CRH
Fig. 6. Debris cloud pictures of typical penetration experiment.
Fig. 8. Profile of post-test projectile at vi ¼ 1449 m/s.
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Fig. 9. Typical optical micrograph of the brink of the section plane for post-test projectiles.
variations of post-projectiles on Cases 1e6 with the striking velocity are plotted in Fig. 11. Results show that the variation trends of penetration depth with the striking velocity are in close agreement with that of projectile mass loss in Fig. 10. In Cases 1 and 2, penetration depth increases proportionally with the striking velocity within a certain range of striking velocity. According to the feature of rigid penetration regime, this striking velocity range could be seen as the rigid penetration regime. And when the striking velocity exceeds this striking velocity range, both penetration depth and projectile mass loss begin simultaneously entering an instable regime, where both penetration depth and projectile mass loss have a very slight variation with the striking velocity, as shown in the rectangle of Fig. 10. And combining with the investigation of nose shapes of post-projectiles in Fig. 11, it is found that once entering this zone, the nose shape is eroded to a hemispherical-like shape, and the hemispherical shape is nearly maintained in this zone, which explains the slight variation of this zone, especially on projectile mass loss. For Cases 3e5, there no exists an instable regime, it is reasonable to take account of the explanation of Cases 1 and 2. The maximum striking velocity in penetration experiments of Cases 3e5 are within the range of rigid penetration regime, which are not enough for the phenomenon of “hemispherical-like shape”. For Case 6, at the point of the maximum striking velocity of the penetration experiments, the feature is similar with that of the instable regime, penetration depth has a slight decease, and the nose shape could be evaluated approximately as the hemisphericallike shape. Thus this indicates that the maximum striking velocity in Case 6 has entered the instable regime. Discussions above reveal that this instable regime is responsible for the transition between rigid penetration regime and Table 2 Experimental conditions of six penetration events for ogival projectiles penetrating concrete targets.
Targets fc (MPa) rt (kg/m3) a (mm) Aggregate material Ma Projectiles Material Rc m (g) mn/m (%) D (mm) L/D CRH g0.5 (%)
Case 1 Case 2 Case 3
Case 4
Case 5
Case 6
62.8 2300 9.5 Quartz
51 2300 9.5 Quartz
58.4 2320 9.5 Limestone
58.4 2320 9.5 Limestone
58.4 2320 9.5 Limestone
51 2440 10 Limestone
7.0
7.0
3.0
3.0
3.0
3.0
4340 steel 45 478 9.8 20.3 8.3 3 6.2
4340 steel 45 1600 9.9 30.5 8.3 3 6.2
4340 steel 45 478 9.8 20.3 8.3 3 6.2
4340 steel 45 1620 9.8 30.5 8.3 3 6.2
AmerMet100 38CrSi 53 478 9.8 20.3 8.3 3 6.2
42 26.6 21.4 12.6 2.7 2 12
semi-hydrodynamic penetration regime. Herein we call the instable regime as hydrodynamic transition regime. Thus together with Chen and Li [1], it could be drawn that penetration depth undergoes a dramatic decrease and a slight instable variation with the increase of striking velocity for metal targets and concrete targets respectively in hydrodynamic transition regime. And it is noted that motivations driving the hydrodynamic transition could be summarized in terms of projectile mass loss. For metal targets, the motivation driving the hydrodynamic transition is that projectile happens to the deformation without mass loss: in the penetration process, due to the compressive or tensile or bend failure, the projectile deviates from the target centerline (Forrestal and Piekutowski [20], Piekutowski et al. [21]), or the projectile nose happens to the deformation analogous with the deformation of Taylor Test (Rosenberg and Dekel [22]). On the other hand, for concrete targets, the motivation is that the projectile happens to the erosion with mass loss (Forrestal et al. [13], the present experiments in this study): projectile nose shape has a variation, but the geometries of post-test projectiles still keep the prototypical shape. Thus we could say that the feature and the mechanics in hydrodynamic transition regime are different for different property materials.
4.2. Engineering model of upper limit of rigid penetration regime Based on the investigation of projectile mass loss when penetrating concrete targets normally, it is indicated that the initial point where the nose shape is eroded to a hemispherical-like shape could be considered as the transition point between rigid penetration regime and hydrodynamic transition regime. This leads us to think that upper limit of the rigid penetration regime could be gained by this feature. Aim to gain upper limit of the rigid penetration regime in terms of the feature of hydrodynamic transition regime, as in the work of Section 3, the relation of Cases 1e5 between projectile mass loss and the initial kinetic energy are fit linearly in Fig. 12. Table 3 documents the fit data of Cases 1e6. Comparisons between Fig. 10 and Fig. 12 indicate that the variation trends between projectile mass loss and the initial kinetic energy keep simultaneous with that of the rate of mass loss and the striking velocity, so upper limit of the linear relation between projectile mass loss and the initial kinetic energy could be considered as upper limit of rigid penetration regime. Thus mass loss at the upper limit of the linear relation can be given by
Dm ¼ mi m0:5
(7)
where m0.5 is the projectile mass with CRH 0.5 nose shape. According to the conclusion from Section 3, whatever the projectile is long rod or short rod, projectile mass loss is mainly
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Fig. 10. Penetration data from Sandia experiments and the present experiments.
concentrated on the nose part. By Eqs. (6) and (7), the critical gc could be given by
gc ¼
Dm mi
¼
Vi V0:5 Vi
(8)
together with the Eq. (1), the upper limit on the initial kinetic energy reads
Ec ¼
1 ½mð1 KÞ m0:5 C
(9)
Further upper limit of the linear relation as the maximum striking velocity yields
v2c ¼
2 ðg KÞ C 0:5
(10)
Thus for ogival projectiles, upper limit of rigid penetration regime as the maximum striking velocity could be evaluated by Eq. (10). Since the hydrodynamic transition is a range, it is pretty difficult to gain the exact transition point between rigid penetration regime and hydrodynamic transition regime experimentally, but the scope of
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Table 4 Upper limit of rigid penetration regime theoretically and experimentally for six penetration events.
Theoretical value (m/s) Experimental value (m/s)
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
958
996
1371
1381
1277
1279
>926 & 985
>900& 1009
>1162
>1176
>1165
>1191 & 1291
significantly affects the upper limit by the comparison between Case 1 and Case 3, it is reasonable to explain the difference between two events based on the hardness of coarse aggregate. Similarly, events of Case 3 and Case 5 indicate that projectile strength is an important factor for the upper limit. In the present investigation we found that projectile strength has a decreasing trend to the upper limit, a like phenomenon has been gained in our another work [23], although targets investigated are metal materials. This implies to some degree that enhancing the projectile hardness is not always the first option in terms of improving the penetration efficiency, which is a very important practical problem in engineering applications. As shown in Table 3, Case 3 and Case 4 is in like manner, comparison between them indicates that the effect of projectile diameter to the upper limit could be ignored, which is very meaningful for the lab-scale research. The upper limit of Case 2 is larger than that of Case 1. Together with the conclusion of Case 3 and Case 4, we could obtain a clear understanding for the effect of compressive strength of the target: the upper limit has a decreasing trend with the compressive strength raise.
Fig. 11. CRH variations with the striking velocity.
5. Conclusion remarks
Fig. 12. The linear fit between projectile mass loss and initial kinetic energy for six penetration events.
the transition point could be evaluated approximately. Table 4 shows comparisons of the upper limit between the predictions from Eq. (10) and experimental results. Clearly, engineering predictions of Cases 1e6 on the upper limit are all within the scope of experimental evaluations, this indicates fully that the engineering model is reasonable. 4.3. Dominant factors on upper limit of rigid penetration regime According to the analyses above, several dominant factors regarding events of the penetration process can be investigated in terms of the upper limit. Firstly the hardness of coarse aggregate
Table 3 Linear fit data for six penetration events. Constants
Case 1
Case 2
Case 3
Case 4
Case 5
Case 6
C K
0.135 0
0.125 0
0.066 0
0.065 0
0.076 0
0.187 0.033
In this work, based on the review of previous Sandia experiments and the analyses on the present experiments, mass loss of ogival projectiles penetrating concrete targets normally was examined. For short-rod projectiles, two conclusions are same to that of long-rod projectiles. One is that analytical results in the present experiments show that projectile mass loss increases linearly with the initial kinetic energy until the striking velocity approaches to upper limit of the linear relation. The other is that examinations of post-test projectiles indicate that mass loss of short-rod projectiles mainly occur also on the projectile nose. Meanwhile by comparisons of optical micrographs of post-test projectiles at different striking velocity range, it is gained that roles of the sources contributing to projectile mass loss are different at the different striking velocity range, there are primary and secondary differentiations on the sources, detailed work will be addressed in future work. On the other hand, the hydrodynamic transition between rigid penetration regime and semi-hydrodynamic penetration regime is investigated. The feature of projectile mass loss in the hydrodynamic transition enables us to construct an engineering model to predict upper limit of the rigid penetration regime. Good agreements are obtained between engineering predictions and experimental results. The engineering model is determined with no physical basis, upper limit of the rigid penetration regime can be evaluated approximately by only two hits of penetration experiments, the simple form can obtain the popular in engineering application. Furthermore, dominant factors which include coarse aggregate hardness, projectile material hardness, projectile diameter and compressive strength of targets are discussed on the effect to upper limit of the rigid penetration regime.
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