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Flat ended projectile penetrating ultra-high strength concrete plate target
Theoretical and Applied Fracture Mechanics 51 (2009) 117–128
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Flat ended projectile penetrating ultra-high strength concrete plate target Y.S. Tai Department of Civil Engineering, ROC Military Academy, 1 Weiwu Rd., Fengshan 830, Taiwan, ROC
a r t i c l e
i n f o
Article history: Available online 9 April 2009 Keywords: Impact experiment Steel fiber reinforced concrete Numerical simulations
a b s t r a c t Reactive powder concrete (RPC), a composite that has been developed in recent years, is a special mixture that is cured to have a higher compressive strength than that of concrete (about 200 MPa). Adding a few steel fibers can markedly increase its mechanical properties, such as tensile and bending strength, impact resistance and toughness. Hence, RPC is highly promising for use in the containment structures of nuclear power plants and in the protection of military facilities. This study evaluates the resistance of ultra-high strength concrete targets by high-velocity impact experiments. Test variables include the impact velocity and the amount of steel fibers added. The experimental results reveal that RPC plates, because of their higher compressive strength, are more fragile than normal concrete (NC) plates. However, adding a small amount of steel fibers significantly improved the impact resistance of the target plates. Moreover, a numerical simulation based on the nonlinear finite element code LS-DYNA was performed. The results of the numerical simulation have a good agreement with the experimental data and can be used for further research. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The response of concrete to transient dynamic loading has been investigated extensively for both civil and military applications. For example, the containment structures of nuclear power plants are designed to survive the impact loading of an aircraft crash to avert the release of radioactive material. The protective structures of military facilities may be subjected to the dynamic loading that is caused by the impact of a missile or non-contact air explosion, for example. Accordingly, more thoroughly understanding the response and failure modes of concrete that is subjected to impact or explosive loading is vital for the effectiveness of protection provided by fortifications. Previously, since the unconfined compressive strength of normal concrete is typically less than 40 MPa, the impact resistance of a structure would be increased usually by increasing the reinforcement ratio or the thickness of the structural members. Since the reinforcement is too dense in structural members, the concrete is quite difficult to cast and insufficient strength is achieved. In civil engineering, new structures, including long-span bridges and high-rise buildings, are continuously constructed from engineering materials of increasing strength. Therefore, highstrength concrete (HSC), which is designed to have a strength under compression of over 41 MPa [1] is widely adopted. The compressive strength of concrete can be increased by increasing the strength of the cement paste and improving the interfacial zone, i.e. reducing the potential stress concentration between the aggreE-mail address: [email protected] 0167-8442/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2009.04.005
gate and the cement paste. Such an increase can be achieved by reducing the water to cement ratio, using fine pozzolanic materials and reducing the coarse aggregate size. Based on current knowledge, concrete with a 28 day ultra-high compressive strength of 150 MPa can be made easily. Reactive powder concrete (RPC), developed in [2], is a unique mixture that is cured to have an ultra-high compressive strength (about 200 MPa) – higher than that of normal concrete or highstrength concrete. The main improvements of RPC involve microstructural enhancement, including elimination of coarse aggregates; reduction of the water-to-cementitious material ratio, and lowering of the CaO–SiO2 ratio by introducing silica components. A compressive strength of between 200 and 800 MPa, and fracture energy of between 1200 and 40,000 J/m2 [2–4] are achieved. Incorporating steel fibers can markedly increase its tensile and bending strength, and its impact resistance. The tensile strength of normal concrete typically does not exceed 10% of the compressive strength, which is about 3–6 MPa. However, the tensile strength of RPC does not follow this proportional relationship. For a protective material, both tensile and compressive strength are important properties. In ballistics, they are important in resisting the cratering and break-up of a structure caused by projectile penetration [5]. Accordingly, RPC is expected to be used to protect military facilities and nuclear power plants. Reinforced concrete structures under impact load have been investigated since WW II and various test approaches have been developed. They include drop weight tests [7,8], pendulum-type tests, gas gun tests [9–12] and split Hopkinson pressure bar tests [13–15]. Furthermore, numerous empirical formulae have been
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developed and utilized to predict the effects of impact loading on concrete, including penetration depth, perforation limit and scabbing limit. Reviewed in [16] are the procedures that are involved in the analysis and design of concrete structures to resist missile impact, and described the processes of penetration and perforation into a concrete plate. The work in [17] analyzed data from medium to low-velocity impact (27–312 m/s) tests. The results are consistent with the empirical formula. In [18] examined the relationship between the compressive strength and the impact resistance of concrete, and the results reveal that the impact resistance increased with the compressive strength. Moreover, the type of reinforcement also affects impact resistance. In [19] adopted analytical solutions and experimental data to correct the results of the mathematical model and studied the resistance of a reinforced concrete structure to aircraft impact. In [20] and [21] adopted analytical and experimental approaches to provide semi-empirical formulae to evaluate the fracture behavior of containment structures following impact by an aircraft, a missile or explosive materials. The work in [8] applied an ogive-nosed projectile with various ballistic velocities to high-strength reinforced concrete targets with compressive strengths of 48 and 140 MPa to study changes in residual velocity after perforation. The results demonstrate that at low impact velocities, concrete targets with a compressive strength of 48 MPa were perforated, while similarly sized targets with strength of 140 MPa were not. However, for impact velocities of between 300 and 1100 m/s, the residual velocities of the projectiles after perforation exhibited no significant difference between normal and high-strength concrete targets, where the latter has triple the unconfined compressive strength of the former. Examined in [22] are the high-velocity projectile impact on slurry-infiltrated fiber concrete (SIFCON) and verified the effectiveness of fibers in reducing damage on the front and rear faces of concrete. Gravel was effective in increasing the penetration resistance of the specimens and the SIFCON layers, reducing the damage upon impact and retaining the damaged aggregate inside the target. Therefore, a composite of both gravel and fiber has been suggested to provide an optimum solution to the problem of reducing overall damage. Presented in [10] performed tests on high-strength concrete (HSC) under impact loading. The projectile penetration depth in HSC was less than that in regular strength concrete (RSC), indicating that a higher compressive strength increases resistance against dynamic punching, although it also increases target brittleness and crater diameter in the event of failure. Dancygier observed a reduced brittleness when steel fibers were incorporated into high-strength concrete. A comparison of the crater dimensions in fiber-reinforced and plain concrete specimens indicated that fibers tend to reduce the extent of cracking and thereby minimize the damaged area. It was observed in [5] that the depth of penetration by 0.9 kg projectiles in very high-strength concrete with a compressive strength of 180 MPa was about half of that in concrete with a compressive strength of 35 MPa, and around 30% less than that in concrete with a compressive strength of 104 MPa. They also found that incorporating steel fibers into the matrix does not markedly reduce penetration depth, but it does reduce visible damage. The studied high-performance steel fiber reinforced concrete (HPSFRC) with a compressive strength of 116 MPa under impact by a high-velocity projectile and compared their findings with those for targets made of reinforced high strength concrete (RHSC) with a compressive strength of 72 MPa. The test results revealed that under impacts by projectiles at high velocities, the RHSC targets exhibited smash failure, in which the target was broken thoroughly into many parts. The HPSFRC targets remained intact with some radial cracks on the front face [23]. Presented in [11] are the results of an experimental study of concrete with compressive strengths of 45–235 MPa. The results indicated that the penetration depth and crater diameter in target specimens declined as
the compressive strength of the concrete increased. The incorporation of steel fibers in concrete reduced the crater diameter and crack propagation, but had no effect on the penetration depth. Facilities for experimentally testing concrete under high-velocity impact loading are very expensive, and the experimental process is time-consuming. Therefore, these facts restrict experimental studies in this area. Lately, with advances in science and technology and increases in the effectiveness of numerical algorithms and computational speed, numerical predictions of structural responses to various loads are becoming increasingly useful, reducing the number of experiments required. Moreover, when analytical results are experimentally verified, numerical predictions can reduce experimental costs. The work in [24] applied LS-DYNA finite element analysis procedure to 60 mm thick fiber concrete plates to study the effect of projectiles with an initial velocity of 1500 m/s and damage during perforation. A lack of material parameters in the analysis is responsible for some discrepancies between simulated and experimental results. The finite element method was applied [25] to the structural dynamic response of reinforced concrete and its failure behavior under impact by projectiles with various velocities. Special military facilities such as radar stations and microwave platforms must be supported effectively to ensure preparedness for war. The impact resistance of these structures to provide proper protection is more important than for other buildings. The mode of failure depends on impact velocity, penetrator shape and target material [26]. This work studies the dynamic response and failure mode of normal concrete (NC) and RPC target plates impacted by flat-ended projectile at velocity ranging from 27.0 to 104.1 m/s. The test variables include the impact velocity of a projectile and the amount of steel fibers added. A finite element simulation of the impact situation has also been performed using an explicit finite element code, LS-DYNA [6]. The results of numerical simulations are discussed and compared with experimental results.
2. Experimental plans A series of experiments was performed for concrete plates with various compressive strengths and volumes of steel fibers to evaluate the resistance of concrete against impact. The following sections describe the materials used and the experimental procedures. 2.1. Materials 2.1.1. Cement ASTM Type II normal Portland cement was used in the concrete mixtures. This medium is sulfate-resisting cement with low calcium aluminates C3A content. 2.1.2. Aggregate Crushed gravel of continuous grades with a maximum particle size of 20 mm and a fineness modulus of 6.56 was used to produce NC plates. All of the aggregates were used under air-dried conditions with a total moisture content of under 0.25%. In NC mixtures, the fine aggregate was natural sand with a maximum particle size of 4.7 mm and a fineness modulus of 2.41. However, in ultra-highstrength concrete RPC, quartz sand with a maximum particle size of 0.6 mm was used. 2.1.3. Crushed quartz Crushed crystalline quartz powder is a critical component in heat-treated RPC concretes. The reactivity during heat treatment is maximal for an average particle size of between 5 and 25lm. An average particle size of 10 lm was used.
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2.1.4. Silica fume Dry non-compacted silica fume was adopted in most of the concrete mixtures. The silica fume had a silicon dioxide content of 90%, and a specific surface area of 18–20 m2/g. 2.1.5. Superplasticizers A retarding admixture was used in RPC mixes, and acrylic graft copolymer superplasticizers were adopted. 2.1.6. Steel fibers Waved steel fibers were made from cold drawn low-carbon steel. The fiber length was 12 mm and the diameter was 0.175 mm; therefore, the aspect ratio was 69. 2.2. Mixing proportions and casting of specimens Table 1 presents the mix proportions used in concrete a proportion is independent of volume. The concrete mixes were prepared using a Hobart-type laboratory mixer with a capacity of 0.15 m3. The cement, quartz fume, silica fume and silica sand were mixed first, and then water that contained the required amount of superplasticizer was added. The final mixing stage involved adding steel fibers. Fibers were added to concrete at 80, 160 and 400 kg per cubic meter of concrete, which densities are equivalent to 1.0%, 2.0% and 5.0% by volume of concrete. One-third of the superplasticizer was held back to be added during the final 3 min of the mixing period. The molds (with dimensions of 310 310 50 mm3) were oiled and placed on the vibration table at a low speed while the concrete was poured. After each mold had been properly filled, the vibration speed was increased to ensure good compaction. Following casting, the specimens were covered with a plastic membrane to prevent the evaporation of moisture and were stored in the laboratory at 25 °C for 24 h; they were then de-molded and placed in a thermostat-controlled water tank at 90 °C for curing for 96 h. Finally, specimens are removed and stored at room temperature until testing after 28 days. The quasi-static compressive tests were performed in a closed loop, servo-controlled MTS810 test machine with a capacity of 1000 kN, as presented in Fig. 1. Before testing, the ends of each specimen were made parallel by grinding. The stress–strain curves were plotted using a strain gauge with a gauge length of 30 mm, which was attached around the test specimen to monitor the axial deformations. In the experimental process, displacement was controlled and the loading rates were 0.05 mm/min. The flexure strength test was performed using a specimen with dimensions of 40 40 1600 mm. The impact experiments were performed about 60 days after the target plates were cast. 2.3. Impact experimental set-up Fig. 2 presents the set-up of the impact experiment, instrumentation and measurement methods used in the test. It is comprised of four parts; (1) compressed gas gun, (2) central control unit, (3) velocity measuring system and (4) transient data recorder. The compressed gas gun launches the projectile. The main components
Fig. 1. Quasi-static test machine.
of the gas gun are a 12 MPa pressure tank, a purpose-built ring section for compressed gas. A 2 m long smooth barrel with a caliber of 25 mm and a closed 80 80 80 cm3 impact chamber. The projectile is launched and hit the target plate when the pressure valve is triggered. Two pairs of interceptive grating sensors with LED light sources on the trajectory of the projectile are adopted to measure the velocity of impact just before the projectile strikes the target plate. The distance between the two pairs of grating sensors is 50 mm. When the projectile passes through two pairs of grating sensors, the light is interrupted and the voltage of the signal from the grating is increased and recorded by the digital transient data recorder. The impact velocity of the projectile is calculated by relating the time interval between the voltage changes to the distance between the sensors. The maximum attainable impact velocity of the projectile depends largely on its mass. In this study, flatended projectiles with a diameter of 25 mm, a length of 75 mm and a mass of 297 g were used. They were propelled by high compressed nitrogen at a pressure of about 80 bar to achieve impact velocities of 105 m/s. The variation of the impact velocity under different pressure is shown in Fig. 3. The projectiles were fabricated from SKH-51 tool steel. They were oil-hardened to a Rockwell C value of Rc = 60 to minimize plastic deformation during impact. The target was clamped to a square frame with an edge clamp distance of 40 mm, perpendicular to the longitudinal axis of the gas gun, as presented in Fig. 4. This arrangement was designed to provide fully clamped boundary conditions for the test plates. After each test, the impact chamber was opened for final inspection and to measure the target. Additionally, the projectile
Table 1 Mix proportions (kg/m3). Mix no.
w/c
Cement
Silica fume
Water
Coarse aggregate
Fine aggregate
Quartz sand
Crushed quartz
Steel fiber (%)
Superplasticizer
NC-F0 NC-F2 RPC-F0 RPC-F1 RPC-F2 RPC-F5
0.44 0.44 0.28 0.28 0.28 0.28
401 401 720 720 720 720
– – 216 216 216 216
178 178 204 204 204 204
1119 1119 – – – –
672 672 – – – –
– – 900 900 900 900
– – 252 252 252 252
– 2 – 1 2 5
– – 10.8 10.8 10.8 10.8
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Fig. 2. Scheme of the impact experiment set-up.
Fig. 5. Stress–strain curves for different concrete mixes. Fig. 3. Relation between the pressure and attainable impact velocity of the flatended steel projectile.
was examined visually no damage or plastic deformation was observed. 3. Experimental results and discussion 3.1. Quasi-static test results Figs. 5 and 6 present quasi-static mechanical test results for six concrete mixtures. Fig. 5 shows the stress–strain curves. According to Fig. 5, the compressive strength is 25.0, 25.2, 161.9, 175.3, 178.3
and 192.8 MPa for six concrete mixtures, respectively. It should be noted that RPC is about 6.4 stronger than NC. Additionally before the compressive strength is reached, the mechanical behavior of RPC exhibits linear-elastic behavior. However, after the stress has reached the peak value, rupture occurs immediately if no steel fibers have been added. Specimens with added steel fibers (RPC-F1, RPC-F2 and RPC-F5) exhibit an increased bridging effect associated with the toughness of the specimen, and an increase in toughness that is directly proportional to the volume fraction of steel fibers. The split tensile strengths of the normal concrete (NC-F0 and NC-F2) and reactive powder concrete (RPC-F0, RPC-F1, RPC-F2
Fig. 4. Scheme of the arrangement used for clamping the target plate to the steel frame (unit: mm).
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Fig. 6. Load–deflection curves for different concrete mixes.
and RPC-F5) specimens are shown in Table 2. For the specimen without any steel fiber, the split tensile strength is 7.3 MPa; a steel fiber volume fractions of 1.0% corresponds to a split tensile strength of 13.8 MPa; a volume fraction of 2.0% corresponds to a split strength of 21.9 MPa, and a volume fraction of 5.0% corresponds to a split strength of 31.6 MPa that is about 12 stronger than NC and 10 times stronger than NC-F2. Because the impact of projectile will induces a tensile waves reflected from the rear surface of the target plate. At the rear free surface, if the tension wave exceeds the tensile capacity of the concrete, then scabbing of the concrete is expected. Hence, the high-tensile characteristic of reactive powder concrete will be enhancing the impact resistance. Flexure load displacement plots for NC and RPC beam are shown in Fig. 6. Note that for RPC, the post crack toughness is also much great than normal concrete.
Fig. 7. Determination of the scabbing area of the target plate.
Table 2 Summary of impact test results. Test no.
NC-F0-1 NC-F0-2 NC-F0-3 NC-F2-1 NC-F2-2 NC-F2-3 RPC-F0-1 RPC-F0-2 RPC-F0-3 RPC-F1-1 RPC-F1-2 RPC-F1-3 RPC-F2-1 RPC-F2-2 RPC-F2-3 RPC-F5-1 RPC-F5-2 RPC-F5-3
Compressive strength (MPa)
Split tensile strength (MPa)
Flexural strength
25.0
2.6
10.6
25.2
3.1
13.3
161.9
7.3
22.0
175.3
13.8
27.2
178.3
21.9
35.8
192.8
31.6
72.8
PF: fully perforated; PC: projectile caught; PR: projectile rebounded. ND: no damaged; SD: slightly damaged; HD: heavily damaged. NA: unavailable (target ruptured or perforation).
Impact velocity (m/s)
Initial kinetic energy (J)
Damage Penetration depth (mm)
Scabbing area (mm2)
Final state of target
27.0 35.7 56.8 41.7 56.8 64.1 34.7 58.5 76.0 58.2 76.0 104.0 76.0 85.0 104.0 58.5 78.1 104.1
107.5 188.0 479.1 258.2 479.1 610.2 177.6 504.8 852.0 499.6 852.0 1595.4 852.0 1065.7 1595.4 504.8 899.7 1598.4
0.6 NA NA 5.3 NA NA NA NA NA 1.8 11.9 NA 3.4 4.7 5.5 1.4 2.9 4.7
10,354 11,223 16,300 SD 10,385 9010 23,520 28,865 NA 14,521 14,202 14,409 11,619 14,297 18,741 ND 816 8554
SDPR HDPF HDPF SDPR HDPF HDPF HDPC HDPF HDPF SDPR SDPC SDPC SDPR SDPR SDPR SDPR SDPR SDPR
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Fig. 8. Rear face damage patterns of the plates.
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Fig. 9. Comparison of the scabbing area.
3.2. Results of impact test The impact resistance performance of the NC and RPC plates containing various volume fractions of steel fibers are discussed. Photographs were taken after impact; the penetration depth, crater areas and final state of the projectile were measured as damage criteria. The penetration depth is measured to determine the actual displacement of the projectile into the target. An image analysis system and a reference measure are used to determine irregular crater areas, using dot per inch (dpi) values from the photographs. Fig. 7 presents the scabbing area of NC-F2-3. Table 2 summarizes the results of all tests. Fig. 8a–f present the damage on the rear faces of the target plates. Post-experimental works indicated that the failure of an NC-F0 plate under a low-velocity impact (27–56.8 m/s) was destructive (Fig. 8a). The target plates were broken up into numerous pieces. The conjectured cause of failure is that during the period of contact between the projectile and the plates, very high stresses are developed near the impact area, forming a shear-cone shaped fracture zone. The plate loses integrity and gains momentum, undergoing large displacements, which cause severe damage. Since adding steel fibers can substantially constrain crack propagation via the bridging effect. For the plates that contain 2% by volume of steel fibers (NC-F2) such as NC-F2-1, under impact by a projectile at a velocity about 41.7 m/s exhibits no perforation and the damage is slight. Target plates NC-F2-2 and NC-F2-3 under impact velocity about 56.8 and 64.1 m/s, respectively still maintained their integ-
Fig. 10. The concrete model.
rity after being perforated. (Fig. 8b). However, since the compression strength and the splitting strength of the concrete are relatively low, the target exhibits poor impact resistance. The compression strength of ultra-high strength concrete RPC is 6.4 higher than that of normal concrete. The results of the quasistatic mechanical test reveal that before the compressive strength is reached, the mechanical behavior is purely linear and elastic. When the compressive strength is reached, a specimen without
Fig. 11. Response of the concrete to uniaxial compression loading [29].
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Table 3 The material parameters for the concrete model. Density,q0 (kg/m3)
Shear modulus, G (MPa)
2600
22.8103 T 13.8
–
Strength constants A
B
N
C
fc0
Smax
0.79 e_ 1.0
1.35 – –
0.4 – –
0.007 – –
175.3 – –
3.5 – –
Damage constants D1
D2
efp
0.78
1.0
0.0168
Equation of state, EOS constants lcrush Pcrush (MPa)
K1 (GPa)
K2 (GPa)
K3 (GPa)
Plock (GPa)
llock
58.4
85.0
171.0
208
0.8
0.1
0.0017
any added steel fibers ruptures immediately. The corresponding fracture energy, defined as the area beneath the load–deflection curve, does not exceed 30 J [4]. Therefore, cracks are more likely to form and propagate in such targets because of the brittleness of the material, and because the targets collapsed as if smashed when subjected to different impact velocities (Fig. 8c). Adding steel fibers to RPC slightly increases the compression strength, but the bridging effect by which the fibers cross the path of the potential cracks, and the strong bond between fiber and concrete, improves resistance to fiber pullout during cracking, significantly constrains crack propagation, markedly increasing the toughness and fracture energy of the RPC [2,5]. Since toughness and fracture energy are important in determining impact resistance, depends on the volume of fiber added to the concrete. Therefore, the target plate damage declines as a volume of steel fibers is increased. The test data in Table 2 and Fig. 8d–f indicate that the size of the scabbing zone declines and becomes more localized as the volume of steel fibers mixed was increased from 1% to 5%. Fig. 9 compares the scabbing areas obtained in the tests. The severity of damage of RPC without added steel fibers under a low-velocity impact is evident. The scabbing area decreased by approximately 50% on addition of 1% steel fibers, and the failure mode changed from brittle to pseudo plastic. Furthermore, the scabbing area was clearly reduced when 5% steel fibers was added. 4. Numerical simulations of experiments Research on the impact loading of concrete plates requires considerable manpower, material and financial resources. Addition-
Fig. 12. Boundary conditions for analysis.
ally, measuring a large number of parameters during penetration, including the variation of the projectile’s velocity, the impact force and the failure process is difficult. Therefore, to study whether a numerical approach based on finite element simulation can describe the structural response is important. This work simulates the experiment (Specimen no: RPC-F1) described in Section 4 and based on LS-DYNA [27], which is a general-purpose finite element code for the analysis of large deformations, penetration and failure response dynamics of structures based on explicit time integration. 4.1. Concrete model Most concrete models are based on the phenomenological macroscopic behavior of concrete that is subjected to impact loading. The constitutive law uses the plastic flow rule in stress space to differentiate between hydrostatic and deviatory stresses. Different loading functions are used to describe the behavior of the two parts. The lower pressure zone is described in terms of the deviatoric stress. In the impact process, since a shock pressure induced in the material interior is as high as its maximum strength, the deviatoric stress has only a weak effect. The Hugoniot shock pressure and specific volume relationship – the equation of state (EOS) – is adopted to replace the stress–strain relationship. Furthermore, the material models incorporate the influence of strain rates and material damage. Many concrete models have been implemented in LS-DYNA, designed to elucidate the damage caused by, and other effects of, strain rate and cracks, to describe fully the dynamic
Fig. 13. Variation of the projectile velocity during penetration.
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responses of concrete in the impact procedure [24,27]. This work utilizes the ‘‘Johnson–Holmquist Concrete-JHC” model, based on
the work of Holmquist and co-workers [28,29], to forecast material dynamic behavior. The JHC concrete model is an elastic–viscoplastic model coupled with isotropic damage, where the response is separated into hydrostatic and deviatoric contributions. The deviatoric response is determined by equivalent strength model
r ¼ ½Að1 DÞ þ BPN ½1 þ C ln e_ 6 Smax
ð1Þ
in which r ¼ r is the normalized equivalent stress, where r denotes the actual equivalent stress, and fc0 is the quasi-static uniaxial compressive strength; P ¼ P=fc0 denotes the normalized pressure; e_ denotes the dimensionless strain rate, given by e_ ¼ e_ =e_ 0 ; e_ represents the actual strain rate; e_ 0 ¼ 1:0 s1 represents the reference strain rate; D is the damage parameter (0 6 D 6 1); C is the material coefficient relevant to strain rate, and A and B are material constants that are related to elastoplastic deformation. N and Smax are the pressure hardening exponent and the normalized maximum strength, respectively. The JHC model accumulated damage failure based on both equivalent plastic strain and plastic volumetric strain. The damage model is
D¼
=fc0
X Dep þ Dlp
ð2Þ
efp þ lfp
where Dep and Dlp represent the equivalent plastic strain increment and the plastic volumetric strain increment, respectively, during a cycle of integration, and efp þ lfp ¼ f ðPÞ is the plastic strain under pressure, given by
f ðPÞ ¼ efp þ lfp ¼ D1 ðP þ T ÞD2
ð3Þ
Fig. 14. The time history of the contact force in at the projectile–target interface.
where D1 and D2 represent damage constants; T ¼ T=fc0 is the normalized largest tensile strength, and T represents the maximum tensile stress. The material model has been described in detail in LS-DYNA [6] and [28]. These material parameters in the constitutive law, are calculated from the results of the quasi-static tests of specimen number RPC-F1 with an unconfined compressive strength of 175.3 MPa. First, the parameters that govern the strength of the concrete are required to characterize fully the material strength. The maximum tensile strength T = 13.8 MPa. Normalizing T to fc0 yields T* = 0.079. The strain rate constant C is determined by performing an SHPB test. However, in an earlier work the rate effects were found to be independent of initial strength. Accordingly, in this work, the constant C = 0.007 obtained in [28] is used. The cohesive strength is defined as the difference between the undamaged strength and the strength after complete fracture at a given pressure. Given the lack of test data at various pressures, the cohesive strength is assumed to be 0:75fc0 under quasi-static conditions. Normalization to e_ ¼ 1:0 yields A = 0.79. Smax represents the normalized maximum strength. According to Hanchak et al. test results, [9] the axial stress increases with pressure, and the relevant curves are almost parallel to each other for concretes with compressive strengths of 48 and 140 MPa (Fig. 10a). Hence, this work employs the extrapolation approach to estimate a normalized maximum strength of around Smax = 3.5. Then, the constants B and N are determined to provide an average relation. Fig. 10b displays the results. Fig. 11 plots the stress–strain results for a cylinder that is subjected to cyclic compression loading [30]. The stress–strain curve for quasi-static loading serves as a reasonable envelope for the peak values of stress in concrete under cyclic loading. An assumed failure surface can be defined from the quasi-static test results (Fig. 5), revealing total strength loss at an axial strain of approximately 0.02. The elastic strain is taken to be 0.0032; the equivalent plastic strain at fracture is efp ¼ 0:0168. The relationship between plastic strain and plastic volumetric strain in the uniaxial stress state is lfp ¼ ð1 þ 2vÞefp . Therefore, in Eq. (3) D1 is given by
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2ð1 þ vÞefp ðP þ T ÞD2
ð4Þ
where D2 = 1.0, T* = 0.079 and v ¼ 0:2, from which the constant D1 = 0.78 can be determined. Table 3 summarizes all of the material parameters used in the analysis in LS-DYNA. 4.2. Mesh and boundary conditions Fig. 4 shows the analytical configuration considered herein work. A concrete target plate is clamped between two steel frames
and the steel projectile is normally incident at the center of the plate. Based on the assumption that the clamp and impact are fully symmetric, only a quarter of the test arrangement was modeled, to reduce the size of the computational domain. Fig. 12 presents the boundary conditions for the numerical model. Symmetric boundary conditions are imposed on the center line of the plate and the clamped boundary conditions are imposed on the outer edge. The concrete specimen is modeled using 34,957 elements and the projectile is modeled using 780 elements. These elements are single-point integration elements with hourglass control. Additionally, the initial velocity of the projectile are 58.2, 76.0 or 104.0 m/s, measured experimentally.
Fig. 15. Impact processes and failure model (Case RPC-F1-3).
Fig. 16. Comparison of the experimental damage and numerical results.
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4.3. Contact algorithm and time integration Contact may be made across surfaces between the projectile and the target. In this study, separation and friction slide surface is adopted to model the impact event between the projectile and the target plate, and the effect of friction between projectile and target was neglected. This has been verified by using two different values of the assumed dynamic coefficient of friction namely 0 and 0.3 between the projectile and the target plate. No significant difference in the computational results was observed. The dynamic problems are treated using LS-DYNA by an explicit time integration scheme, with a sufficiently small time step for each increment. However, contact, material and non-linear geometry will causes the stable time step to be close to zero in the equation computation procedure. The whole computation time thus has infinite delays and produces divergent results. Accordingly, a time step scale factor of 0.6 is defined to ensure convergence.
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Fig. 15 presents the penetration of the projectile and the failure pattern of the case RPC-F1-3. At the moment of contact, flared shear cracks are form immediately in a region in the periphery of the projectile. Additionally, the compressive wave reflected from the rear face of the target changes to a tensile wave that interacts with the compressive wave and produces a rear crater (Fig. 15b). The clamp boundary conditions imposed on the outer edge result in visible tensile stresses at the boundary between the target and the vertical cracks (Fig. 15c). The velocity of the projectile falls rapidly when it makes contact with the target, falling to zero in about t = 125 ls; however, the cracks and the crater continue to extend because of inertia. A comparison of experiments and analysis for three cases are shown in Fig. 16; the plate is cut in half, and a cross section is shown as well as the iso-view of the projectile impact, and the damage pattern is similar to that obtained experimentally. It shows that the implemented JHC model is suitable to simulate the impact of projectile into RPC targets and the material parameters used in simulation are valid.
4.4. Failure criteria 5. Conclusions The impact of a projectile induces compressive shock waves on the front face of the target plate. The shock waves propagate through the thickness and reflect from the rear free surface as tensile waves. At the rear free surface, if the total pressure of the compression waves and the reflected tension waves exceeds the tensile capacity of the concrete, then scabbing of the concrete is expected. In the present study, uses tensile strain cutoff criteria in the numerical simulation, based on the assumption that when the strain in any concrete element reaches the split tensile strain. In addition, the impact and explosion cases under consideration, the maximum strain rate is generally on the order of 10–100 s1. For this magnitude of strain rate, the corresponding dynamic strength enhancement factor can reach 5.0 or above. Taking all these influences into account and in conjunction with trial parametric analysis, it is found that the dynamic tensile fracture strain should be around 0.02 for spallation with the mixture concrete material. Thus, the principal tensile strain reaching 0.02 is adopted as the primary criterion in the implementation of the erosion algorithm in the numerical simulation. 4.5. Numerical results and discussion The analysis was performed on a PC with P4 1.8 GHz processor and took about 5 h. Post processing was performed using LS-Prepost v.1.0. Figs. 13–16 plot the results of the analysis. Solutions are terminated after 500 ls. Fig. 13 plots the time history of the velocity when the projectile impacts the target plate, demonstrating the difference in the projectile when different impact velocities are applied to the targets. The velocity quickly fell when the time increased. Fig. 14a–c plots the time history of the contact force at the interface between the projectile and the target. The contact force is applying the penalty method in this analysis. In the process of analysis, the slave node is checked for penetration through master surface. When the slave node penetrated, a contact force is applied between the slave node and its contact point. However, the lateral inertia will causes original results exhibits some high frequency oscillation. Mainly are related to the familiar Pochhammer–Chree observed in SHPB experiments [31]. This can be filtered to 150 Hz using a Butterworth filter. During initial contact between the projectile and the target, the contact force similar a half-sine wave. For the case RPC-F1-1 (impact velocity of 58.2 m/ s), the peak contact force 116.5 kN at 108 ls suddenly rises (Fig. 14a). Then, declines as the speed of striking decreases, falling to zero in approximately t = 140 ls For cases RPC-F1-2 (Fig. 14b) and RPC-F1-3 (Fig. 14c), the peak contact force, of 133.2 and 153.3 kN, respectively.
This work studied the impact resistance of RPC and NC with various volume fractions of steel fibers under various impact velocities. The test results support the following conclusions. RPC is a special mixture that has been cured especially to have an ultra-high compressive strength. However, it is very fragile when no steel fiber is added. Accordingly, when the failure conditions are reached, the plates break into several pieces. Adding steel fibers increases the split tensile strength, flexure strength and reduces brittleness. 2% and 5% by volume of steel fibers yielded split tensile strengths of 21.9 and 31.6 MPa, around equal to the compressive strength of NC, improving impact resistance. The JHC material constitutive model was implemented using the finite element code LS-DYNA. The preliminary computations were reasonably consistent with experimental data, supporting the conclusion that the model fully described the dynamic effect on concrete and its cracking failure behavior at high pressures and high strain rates. Numerical simulations yielded details of the penetration process, and revealed the variation of the contact force at various impact velocity.
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[14] C.A. Ross, J.W. Tedesco, S.T. Kuennen, Effects of strain rate on concrete strength, ACI Mater. J. 92 (1) (1995) 37–47. [15] C.A. Ross, D.M. Jerome, J.W. Tedesco, M.L. Hughes, Moisture and strain rate effects on concrete strength, ACI Mater. J. 94 (1996) 293–300. [16] R.P. Kennedy, Review of procedures for the analysis and design of concrete structures to resist missile impact effects, Nucl. Eng. Des. 37 (2) (1976) 183–203. [17] C.E. Sliter, Assessment of empirical concrete impact formulas, ASCE J. Struct. Div. 106 (5) (1980) 1023–1045. [18] J.R. Clifton, L.I. Knab, Impact test of concrete, Cem. Concr. Res. 13 (4) (1983) 541–548. [19] K. Brandes, Assessment of the response of reinforced concrete structural members to aircraft crash impact loading, Nucl. Eng. Des. 110 (2) (1988) 177–183. [20] J. Eibl, G. Kobler, Impact research for containment design, Nucl. Eng. Des. 150 (2–3) (1994) 409–415. [21] A.M. Amde, A. Mirmiran, T.A. Walter, Local damage assessment of metal barriers under turbine missile impacts, J. Struct. Eng. 122 (1) (1996) 99–108. [22] W.F. Anderson, A.J. Watson, A.E. Kaminskyj, The resistance of SIFCON to high velocity impact, in: Proceedings of the Second International Conference on Structures Under Shock and Impact, Portsmouth, UK, 1992, pp. 89–98. [23] X. Luo, W. Sun, S.Y.N. Chan, Characteristics of high-performance steel fiberreinforced concrete subject to high velocity impact, Cem. Concr. Res. 30 (6) (2000) 907–914.
[24] L. Ågårdh, L. Laine, 3D FE-simulation of high-velocity fragment perforation of reinforced concrete slabs, Int. J. Impact Eng. 22 (9–10) (1999) 911–922. [25] Y.S. Tai, C.C. Tang, Numerical simulation: the dynamic behavior of reinforced concrete plates under normal impact, Theor. Appl. Fract. Mech. 45 (2) (2006) 117–127. [26] G.C. Sih, Initial damage states of hypervelocity impact of tungsten projectile on aluminum target, Int. J. Theor. Appl. Fract. Mech. 13 (3) (1990) 167–180. [27] L.J. Malvar, J.E. Crawford, J.W. Weswvich, D. Simons, A plasticity concrete material model for dyna3d, Int. J. Impact Eng. 19 (9–10) (1997) 847– 873. [28] T.J. Holmquist, G.R. Johnson, W.H. Cook, A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressures, in: Proceedings of the Fourteenth International Symposium on Ballistics, Quebec City, Canada, 1993, pp. 591–600. [29] G.R. Johnson, Computed radial stresses in a concrete target penetrated by a steel projectile, in: Proceedings of the Fifth International Conference on Structures Under Shock and Impact, Portsmouth, UK, 1998, pp. 793–806. [30] P. Karsan, J.O. Jirsa, Behavior of concrete under compressive loading, ASCE J. Struct. Div. 95 (ST12) (1969) 2543–2563. [31] S. Chocron, C.E. Anderson, D.J. Grosch, C.H. Popelar, Impact of the 7.62-mm APM2 projectile against the edge of a metallic target, Int. J. Impact Eng. 25 (2001) 423–437.
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Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec
Flat ended projectile penetrating ultra-high strength concrete plate target Y.S. Tai Department of Civil Engineering, ROC Military Academy, 1 Weiwu Rd., Fengshan 830, Taiwan, ROC
a r t i c l e
i n f o
Article history: Available online 9 April 2009 Keywords: Impact experiment Steel fiber reinforced concrete Numerical simulations
a b s t r a c t Reactive powder concrete (RPC), a composite that has been developed in recent years, is a special mixture that is cured to have a higher compressive strength than that of concrete (about 200 MPa). Adding a few steel fibers can markedly increase its mechanical properties, such as tensile and bending strength, impact resistance and toughness. Hence, RPC is highly promising for use in the containment structures of nuclear power plants and in the protection of military facilities. This study evaluates the resistance of ultra-high strength concrete targets by high-velocity impact experiments. Test variables include the impact velocity and the amount of steel fibers added. The experimental results reveal that RPC plates, because of their higher compressive strength, are more fragile than normal concrete (NC) plates. However, adding a small amount of steel fibers significantly improved the impact resistance of the target plates. Moreover, a numerical simulation based on the nonlinear finite element code LS-DYNA was performed. The results of the numerical simulation have a good agreement with the experimental data and can be used for further research. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The response of concrete to transient dynamic loading has been investigated extensively for both civil and military applications. For example, the containment structures of nuclear power plants are designed to survive the impact loading of an aircraft crash to avert the release of radioactive material. The protective structures of military facilities may be subjected to the dynamic loading that is caused by the impact of a missile or non-contact air explosion, for example. Accordingly, more thoroughly understanding the response and failure modes of concrete that is subjected to impact or explosive loading is vital for the effectiveness of protection provided by fortifications. Previously, since the unconfined compressive strength of normal concrete is typically less than 40 MPa, the impact resistance of a structure would be increased usually by increasing the reinforcement ratio or the thickness of the structural members. Since the reinforcement is too dense in structural members, the concrete is quite difficult to cast and insufficient strength is achieved. In civil engineering, new structures, including long-span bridges and high-rise buildings, are continuously constructed from engineering materials of increasing strength. Therefore, highstrength concrete (HSC), which is designed to have a strength under compression of over 41 MPa [1] is widely adopted. The compressive strength of concrete can be increased by increasing the strength of the cement paste and improving the interfacial zone, i.e. reducing the potential stress concentration between the aggreE-mail address: [email protected] 0167-8442/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2009.04.005
gate and the cement paste. Such an increase can be achieved by reducing the water to cement ratio, using fine pozzolanic materials and reducing the coarse aggregate size. Based on current knowledge, concrete with a 28 day ultra-high compressive strength of 150 MPa can be made easily. Reactive powder concrete (RPC), developed in [2], is a unique mixture that is cured to have an ultra-high compressive strength (about 200 MPa) – higher than that of normal concrete or highstrength concrete. The main improvements of RPC involve microstructural enhancement, including elimination of coarse aggregates; reduction of the water-to-cementitious material ratio, and lowering of the CaO–SiO2 ratio by introducing silica components. A compressive strength of between 200 and 800 MPa, and fracture energy of between 1200 and 40,000 J/m2 [2–4] are achieved. Incorporating steel fibers can markedly increase its tensile and bending strength, and its impact resistance. The tensile strength of normal concrete typically does not exceed 10% of the compressive strength, which is about 3–6 MPa. However, the tensile strength of RPC does not follow this proportional relationship. For a protective material, both tensile and compressive strength are important properties. In ballistics, they are important in resisting the cratering and break-up of a structure caused by projectile penetration [5]. Accordingly, RPC is expected to be used to protect military facilities and nuclear power plants. Reinforced concrete structures under impact load have been investigated since WW II and various test approaches have been developed. They include drop weight tests [7,8], pendulum-type tests, gas gun tests [9–12] and split Hopkinson pressure bar tests [13–15]. Furthermore, numerous empirical formulae have been
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developed and utilized to predict the effects of impact loading on concrete, including penetration depth, perforation limit and scabbing limit. Reviewed in [16] are the procedures that are involved in the analysis and design of concrete structures to resist missile impact, and described the processes of penetration and perforation into a concrete plate. The work in [17] analyzed data from medium to low-velocity impact (27–312 m/s) tests. The results are consistent with the empirical formula. In [18] examined the relationship between the compressive strength and the impact resistance of concrete, and the results reveal that the impact resistance increased with the compressive strength. Moreover, the type of reinforcement also affects impact resistance. In [19] adopted analytical solutions and experimental data to correct the results of the mathematical model and studied the resistance of a reinforced concrete structure to aircraft impact. In [20] and [21] adopted analytical and experimental approaches to provide semi-empirical formulae to evaluate the fracture behavior of containment structures following impact by an aircraft, a missile or explosive materials. The work in [8] applied an ogive-nosed projectile with various ballistic velocities to high-strength reinforced concrete targets with compressive strengths of 48 and 140 MPa to study changes in residual velocity after perforation. The results demonstrate that at low impact velocities, concrete targets with a compressive strength of 48 MPa were perforated, while similarly sized targets with strength of 140 MPa were not. However, for impact velocities of between 300 and 1100 m/s, the residual velocities of the projectiles after perforation exhibited no significant difference between normal and high-strength concrete targets, where the latter has triple the unconfined compressive strength of the former. Examined in [22] are the high-velocity projectile impact on slurry-infiltrated fiber concrete (SIFCON) and verified the effectiveness of fibers in reducing damage on the front and rear faces of concrete. Gravel was effective in increasing the penetration resistance of the specimens and the SIFCON layers, reducing the damage upon impact and retaining the damaged aggregate inside the target. Therefore, a composite of both gravel and fiber has been suggested to provide an optimum solution to the problem of reducing overall damage. Presented in [10] performed tests on high-strength concrete (HSC) under impact loading. The projectile penetration depth in HSC was less than that in regular strength concrete (RSC), indicating that a higher compressive strength increases resistance against dynamic punching, although it also increases target brittleness and crater diameter in the event of failure. Dancygier observed a reduced brittleness when steel fibers were incorporated into high-strength concrete. A comparison of the crater dimensions in fiber-reinforced and plain concrete specimens indicated that fibers tend to reduce the extent of cracking and thereby minimize the damaged area. It was observed in [5] that the depth of penetration by 0.9 kg projectiles in very high-strength concrete with a compressive strength of 180 MPa was about half of that in concrete with a compressive strength of 35 MPa, and around 30% less than that in concrete with a compressive strength of 104 MPa. They also found that incorporating steel fibers into the matrix does not markedly reduce penetration depth, but it does reduce visible damage. The studied high-performance steel fiber reinforced concrete (HPSFRC) with a compressive strength of 116 MPa under impact by a high-velocity projectile and compared their findings with those for targets made of reinforced high strength concrete (RHSC) with a compressive strength of 72 MPa. The test results revealed that under impacts by projectiles at high velocities, the RHSC targets exhibited smash failure, in which the target was broken thoroughly into many parts. The HPSFRC targets remained intact with some radial cracks on the front face [23]. Presented in [11] are the results of an experimental study of concrete with compressive strengths of 45–235 MPa. The results indicated that the penetration depth and crater diameter in target specimens declined as
the compressive strength of the concrete increased. The incorporation of steel fibers in concrete reduced the crater diameter and crack propagation, but had no effect on the penetration depth. Facilities for experimentally testing concrete under high-velocity impact loading are very expensive, and the experimental process is time-consuming. Therefore, these facts restrict experimental studies in this area. Lately, with advances in science and technology and increases in the effectiveness of numerical algorithms and computational speed, numerical predictions of structural responses to various loads are becoming increasingly useful, reducing the number of experiments required. Moreover, when analytical results are experimentally verified, numerical predictions can reduce experimental costs. The work in [24] applied LS-DYNA finite element analysis procedure to 60 mm thick fiber concrete plates to study the effect of projectiles with an initial velocity of 1500 m/s and damage during perforation. A lack of material parameters in the analysis is responsible for some discrepancies between simulated and experimental results. The finite element method was applied [25] to the structural dynamic response of reinforced concrete and its failure behavior under impact by projectiles with various velocities. Special military facilities such as radar stations and microwave platforms must be supported effectively to ensure preparedness for war. The impact resistance of these structures to provide proper protection is more important than for other buildings. The mode of failure depends on impact velocity, penetrator shape and target material [26]. This work studies the dynamic response and failure mode of normal concrete (NC) and RPC target plates impacted by flat-ended projectile at velocity ranging from 27.0 to 104.1 m/s. The test variables include the impact velocity of a projectile and the amount of steel fibers added. A finite element simulation of the impact situation has also been performed using an explicit finite element code, LS-DYNA [6]. The results of numerical simulations are discussed and compared with experimental results.
2. Experimental plans A series of experiments was performed for concrete plates with various compressive strengths and volumes of steel fibers to evaluate the resistance of concrete against impact. The following sections describe the materials used and the experimental procedures. 2.1. Materials 2.1.1. Cement ASTM Type II normal Portland cement was used in the concrete mixtures. This medium is sulfate-resisting cement with low calcium aluminates C3A content. 2.1.2. Aggregate Crushed gravel of continuous grades with a maximum particle size of 20 mm and a fineness modulus of 6.56 was used to produce NC plates. All of the aggregates were used under air-dried conditions with a total moisture content of under 0.25%. In NC mixtures, the fine aggregate was natural sand with a maximum particle size of 4.7 mm and a fineness modulus of 2.41. However, in ultra-highstrength concrete RPC, quartz sand with a maximum particle size of 0.6 mm was used. 2.1.3. Crushed quartz Crushed crystalline quartz powder is a critical component in heat-treated RPC concretes. The reactivity during heat treatment is maximal for an average particle size of between 5 and 25lm. An average particle size of 10 lm was used.
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2.1.4. Silica fume Dry non-compacted silica fume was adopted in most of the concrete mixtures. The silica fume had a silicon dioxide content of 90%, and a specific surface area of 18–20 m2/g. 2.1.5. Superplasticizers A retarding admixture was used in RPC mixes, and acrylic graft copolymer superplasticizers were adopted. 2.1.6. Steel fibers Waved steel fibers were made from cold drawn low-carbon steel. The fiber length was 12 mm and the diameter was 0.175 mm; therefore, the aspect ratio was 69. 2.2. Mixing proportions and casting of specimens Table 1 presents the mix proportions used in concrete a proportion is independent of volume. The concrete mixes were prepared using a Hobart-type laboratory mixer with a capacity of 0.15 m3. The cement, quartz fume, silica fume and silica sand were mixed first, and then water that contained the required amount of superplasticizer was added. The final mixing stage involved adding steel fibers. Fibers were added to concrete at 80, 160 and 400 kg per cubic meter of concrete, which densities are equivalent to 1.0%, 2.0% and 5.0% by volume of concrete. One-third of the superplasticizer was held back to be added during the final 3 min of the mixing period. The molds (with dimensions of 310 310 50 mm3) were oiled and placed on the vibration table at a low speed while the concrete was poured. After each mold had been properly filled, the vibration speed was increased to ensure good compaction. Following casting, the specimens were covered with a plastic membrane to prevent the evaporation of moisture and were stored in the laboratory at 25 °C for 24 h; they were then de-molded and placed in a thermostat-controlled water tank at 90 °C for curing for 96 h. Finally, specimens are removed and stored at room temperature until testing after 28 days. The quasi-static compressive tests were performed in a closed loop, servo-controlled MTS810 test machine with a capacity of 1000 kN, as presented in Fig. 1. Before testing, the ends of each specimen were made parallel by grinding. The stress–strain curves were plotted using a strain gauge with a gauge length of 30 mm, which was attached around the test specimen to monitor the axial deformations. In the experimental process, displacement was controlled and the loading rates were 0.05 mm/min. The flexure strength test was performed using a specimen with dimensions of 40 40 1600 mm. The impact experiments were performed about 60 days after the target plates were cast. 2.3. Impact experimental set-up Fig. 2 presents the set-up of the impact experiment, instrumentation and measurement methods used in the test. It is comprised of four parts; (1) compressed gas gun, (2) central control unit, (3) velocity measuring system and (4) transient data recorder. The compressed gas gun launches the projectile. The main components
Fig. 1. Quasi-static test machine.
of the gas gun are a 12 MPa pressure tank, a purpose-built ring section for compressed gas. A 2 m long smooth barrel with a caliber of 25 mm and a closed 80 80 80 cm3 impact chamber. The projectile is launched and hit the target plate when the pressure valve is triggered. Two pairs of interceptive grating sensors with LED light sources on the trajectory of the projectile are adopted to measure the velocity of impact just before the projectile strikes the target plate. The distance between the two pairs of grating sensors is 50 mm. When the projectile passes through two pairs of grating sensors, the light is interrupted and the voltage of the signal from the grating is increased and recorded by the digital transient data recorder. The impact velocity of the projectile is calculated by relating the time interval between the voltage changes to the distance between the sensors. The maximum attainable impact velocity of the projectile depends largely on its mass. In this study, flatended projectiles with a diameter of 25 mm, a length of 75 mm and a mass of 297 g were used. They were propelled by high compressed nitrogen at a pressure of about 80 bar to achieve impact velocities of 105 m/s. The variation of the impact velocity under different pressure is shown in Fig. 3. The projectiles were fabricated from SKH-51 tool steel. They were oil-hardened to a Rockwell C value of Rc = 60 to minimize plastic deformation during impact. The target was clamped to a square frame with an edge clamp distance of 40 mm, perpendicular to the longitudinal axis of the gas gun, as presented in Fig. 4. This arrangement was designed to provide fully clamped boundary conditions for the test plates. After each test, the impact chamber was opened for final inspection and to measure the target. Additionally, the projectile
Table 1 Mix proportions (kg/m3). Mix no.
w/c
Cement
Silica fume
Water
Coarse aggregate
Fine aggregate
Quartz sand
Crushed quartz
Steel fiber (%)
Superplasticizer
NC-F0 NC-F2 RPC-F0 RPC-F1 RPC-F2 RPC-F5
0.44 0.44 0.28 0.28 0.28 0.28
401 401 720 720 720 720
– – 216 216 216 216
178 178 204 204 204 204
1119 1119 – – – –
672 672 – – – –
– – 900 900 900 900
– – 252 252 252 252
– 2 – 1 2 5
– – 10.8 10.8 10.8 10.8
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Fig. 2. Scheme of the impact experiment set-up.
Fig. 5. Stress–strain curves for different concrete mixes. Fig. 3. Relation between the pressure and attainable impact velocity of the flatended steel projectile.
was examined visually no damage or plastic deformation was observed. 3. Experimental results and discussion 3.1. Quasi-static test results Figs. 5 and 6 present quasi-static mechanical test results for six concrete mixtures. Fig. 5 shows the stress–strain curves. According to Fig. 5, the compressive strength is 25.0, 25.2, 161.9, 175.3, 178.3
and 192.8 MPa for six concrete mixtures, respectively. It should be noted that RPC is about 6.4 stronger than NC. Additionally before the compressive strength is reached, the mechanical behavior of RPC exhibits linear-elastic behavior. However, after the stress has reached the peak value, rupture occurs immediately if no steel fibers have been added. Specimens with added steel fibers (RPC-F1, RPC-F2 and RPC-F5) exhibit an increased bridging effect associated with the toughness of the specimen, and an increase in toughness that is directly proportional to the volume fraction of steel fibers. The split tensile strengths of the normal concrete (NC-F0 and NC-F2) and reactive powder concrete (RPC-F0, RPC-F1, RPC-F2
Fig. 4. Scheme of the arrangement used for clamping the target plate to the steel frame (unit: mm).
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Fig. 6. Load–deflection curves for different concrete mixes.
and RPC-F5) specimens are shown in Table 2. For the specimen without any steel fiber, the split tensile strength is 7.3 MPa; a steel fiber volume fractions of 1.0% corresponds to a split tensile strength of 13.8 MPa; a volume fraction of 2.0% corresponds to a split strength of 21.9 MPa, and a volume fraction of 5.0% corresponds to a split strength of 31.6 MPa that is about 12 stronger than NC and 10 times stronger than NC-F2. Because the impact of projectile will induces a tensile waves reflected from the rear surface of the target plate. At the rear free surface, if the tension wave exceeds the tensile capacity of the concrete, then scabbing of the concrete is expected. Hence, the high-tensile characteristic of reactive powder concrete will be enhancing the impact resistance. Flexure load displacement plots for NC and RPC beam are shown in Fig. 6. Note that for RPC, the post crack toughness is also much great than normal concrete.
Fig. 7. Determination of the scabbing area of the target plate.
Table 2 Summary of impact test results. Test no.
NC-F0-1 NC-F0-2 NC-F0-3 NC-F2-1 NC-F2-2 NC-F2-3 RPC-F0-1 RPC-F0-2 RPC-F0-3 RPC-F1-1 RPC-F1-2 RPC-F1-3 RPC-F2-1 RPC-F2-2 RPC-F2-3 RPC-F5-1 RPC-F5-2 RPC-F5-3
Compressive strength (MPa)
Split tensile strength (MPa)
Flexural strength
25.0
2.6
10.6
25.2
3.1
13.3
161.9
7.3
22.0
175.3
13.8
27.2
178.3
21.9
35.8
192.8
31.6
72.8
PF: fully perforated; PC: projectile caught; PR: projectile rebounded. ND: no damaged; SD: slightly damaged; HD: heavily damaged. NA: unavailable (target ruptured or perforation).
Impact velocity (m/s)
Initial kinetic energy (J)
Damage Penetration depth (mm)
Scabbing area (mm2)
Final state of target
27.0 35.7 56.8 41.7 56.8 64.1 34.7 58.5 76.0 58.2 76.0 104.0 76.0 85.0 104.0 58.5 78.1 104.1
107.5 188.0 479.1 258.2 479.1 610.2 177.6 504.8 852.0 499.6 852.0 1595.4 852.0 1065.7 1595.4 504.8 899.7 1598.4
0.6 NA NA 5.3 NA NA NA NA NA 1.8 11.9 NA 3.4 4.7 5.5 1.4 2.9 4.7
10,354 11,223 16,300 SD 10,385 9010 23,520 28,865 NA 14,521 14,202 14,409 11,619 14,297 18,741 ND 816 8554
SDPR HDPF HDPF SDPR HDPF HDPF HDPC HDPF HDPF SDPR SDPC SDPC SDPR SDPR SDPR SDPR SDPR SDPR
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Fig. 8. Rear face damage patterns of the plates.
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Fig. 9. Comparison of the scabbing area.
3.2. Results of impact test The impact resistance performance of the NC and RPC plates containing various volume fractions of steel fibers are discussed. Photographs were taken after impact; the penetration depth, crater areas and final state of the projectile were measured as damage criteria. The penetration depth is measured to determine the actual displacement of the projectile into the target. An image analysis system and a reference measure are used to determine irregular crater areas, using dot per inch (dpi) values from the photographs. Fig. 7 presents the scabbing area of NC-F2-3. Table 2 summarizes the results of all tests. Fig. 8a–f present the damage on the rear faces of the target plates. Post-experimental works indicated that the failure of an NC-F0 plate under a low-velocity impact (27–56.8 m/s) was destructive (Fig. 8a). The target plates were broken up into numerous pieces. The conjectured cause of failure is that during the period of contact between the projectile and the plates, very high stresses are developed near the impact area, forming a shear-cone shaped fracture zone. The plate loses integrity and gains momentum, undergoing large displacements, which cause severe damage. Since adding steel fibers can substantially constrain crack propagation via the bridging effect. For the plates that contain 2% by volume of steel fibers (NC-F2) such as NC-F2-1, under impact by a projectile at a velocity about 41.7 m/s exhibits no perforation and the damage is slight. Target plates NC-F2-2 and NC-F2-3 under impact velocity about 56.8 and 64.1 m/s, respectively still maintained their integ-
Fig. 10. The concrete model.
rity after being perforated. (Fig. 8b). However, since the compression strength and the splitting strength of the concrete are relatively low, the target exhibits poor impact resistance. The compression strength of ultra-high strength concrete RPC is 6.4 higher than that of normal concrete. The results of the quasistatic mechanical test reveal that before the compressive strength is reached, the mechanical behavior is purely linear and elastic. When the compressive strength is reached, a specimen without
Fig. 11. Response of the concrete to uniaxial compression loading [29].
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Table 3 The material parameters for the concrete model. Density,q0 (kg/m3)
Shear modulus, G (MPa)
2600
22.8103 T 13.8
–
Strength constants A
B
N
C
fc0
Smax
0.79 e_ 1.0
1.35 – –
0.4 – –
0.007 – –
175.3 – –
3.5 – –
Damage constants D1
D2
efp
0.78
1.0
0.0168
Equation of state, EOS constants lcrush Pcrush (MPa)
K1 (GPa)
K2 (GPa)
K3 (GPa)
Plock (GPa)
llock
58.4
85.0
171.0
208
0.8
0.1
0.0017
any added steel fibers ruptures immediately. The corresponding fracture energy, defined as the area beneath the load–deflection curve, does not exceed 30 J [4]. Therefore, cracks are more likely to form and propagate in such targets because of the brittleness of the material, and because the targets collapsed as if smashed when subjected to different impact velocities (Fig. 8c). Adding steel fibers to RPC slightly increases the compression strength, but the bridging effect by which the fibers cross the path of the potential cracks, and the strong bond between fiber and concrete, improves resistance to fiber pullout during cracking, significantly constrains crack propagation, markedly increasing the toughness and fracture energy of the RPC [2,5]. Since toughness and fracture energy are important in determining impact resistance, depends on the volume of fiber added to the concrete. Therefore, the target plate damage declines as a volume of steel fibers is increased. The test data in Table 2 and Fig. 8d–f indicate that the size of the scabbing zone declines and becomes more localized as the volume of steel fibers mixed was increased from 1% to 5%. Fig. 9 compares the scabbing areas obtained in the tests. The severity of damage of RPC without added steel fibers under a low-velocity impact is evident. The scabbing area decreased by approximately 50% on addition of 1% steel fibers, and the failure mode changed from brittle to pseudo plastic. Furthermore, the scabbing area was clearly reduced when 5% steel fibers was added. 4. Numerical simulations of experiments Research on the impact loading of concrete plates requires considerable manpower, material and financial resources. Addition-
Fig. 12. Boundary conditions for analysis.
ally, measuring a large number of parameters during penetration, including the variation of the projectile’s velocity, the impact force and the failure process is difficult. Therefore, to study whether a numerical approach based on finite element simulation can describe the structural response is important. This work simulates the experiment (Specimen no: RPC-F1) described in Section 4 and based on LS-DYNA [27], which is a general-purpose finite element code for the analysis of large deformations, penetration and failure response dynamics of structures based on explicit time integration. 4.1. Concrete model Most concrete models are based on the phenomenological macroscopic behavior of concrete that is subjected to impact loading. The constitutive law uses the plastic flow rule in stress space to differentiate between hydrostatic and deviatory stresses. Different loading functions are used to describe the behavior of the two parts. The lower pressure zone is described in terms of the deviatoric stress. In the impact process, since a shock pressure induced in the material interior is as high as its maximum strength, the deviatoric stress has only a weak effect. The Hugoniot shock pressure and specific volume relationship – the equation of state (EOS) – is adopted to replace the stress–strain relationship. Furthermore, the material models incorporate the influence of strain rates and material damage. Many concrete models have been implemented in LS-DYNA, designed to elucidate the damage caused by, and other effects of, strain rate and cracks, to describe fully the dynamic
Fig. 13. Variation of the projectile velocity during penetration.
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responses of concrete in the impact procedure [24,27]. This work utilizes the ‘‘Johnson–Holmquist Concrete-JHC” model, based on
the work of Holmquist and co-workers [28,29], to forecast material dynamic behavior. The JHC concrete model is an elastic–viscoplastic model coupled with isotropic damage, where the response is separated into hydrostatic and deviatoric contributions. The deviatoric response is determined by equivalent strength model
r ¼ ½Að1 DÞ þ BPN ½1 þ C ln e_ 6 Smax
ð1Þ
in which r ¼ r is the normalized equivalent stress, where r denotes the actual equivalent stress, and fc0 is the quasi-static uniaxial compressive strength; P ¼ P=fc0 denotes the normalized pressure; e_ denotes the dimensionless strain rate, given by e_ ¼ e_ =e_ 0 ; e_ represents the actual strain rate; e_ 0 ¼ 1:0 s1 represents the reference strain rate; D is the damage parameter (0 6 D 6 1); C is the material coefficient relevant to strain rate, and A and B are material constants that are related to elastoplastic deformation. N and Smax are the pressure hardening exponent and the normalized maximum strength, respectively. The JHC model accumulated damage failure based on both equivalent plastic strain and plastic volumetric strain. The damage model is
D¼
=fc0
X Dep þ Dlp
ð2Þ
efp þ lfp
where Dep and Dlp represent the equivalent plastic strain increment and the plastic volumetric strain increment, respectively, during a cycle of integration, and efp þ lfp ¼ f ðPÞ is the plastic strain under pressure, given by
f ðPÞ ¼ efp þ lfp ¼ D1 ðP þ T ÞD2
ð3Þ
Fig. 14. The time history of the contact force in at the projectile–target interface.
where D1 and D2 represent damage constants; T ¼ T=fc0 is the normalized largest tensile strength, and T represents the maximum tensile stress. The material model has been described in detail in LS-DYNA [6] and [28]. These material parameters in the constitutive law, are calculated from the results of the quasi-static tests of specimen number RPC-F1 with an unconfined compressive strength of 175.3 MPa. First, the parameters that govern the strength of the concrete are required to characterize fully the material strength. The maximum tensile strength T = 13.8 MPa. Normalizing T to fc0 yields T* = 0.079. The strain rate constant C is determined by performing an SHPB test. However, in an earlier work the rate effects were found to be independent of initial strength. Accordingly, in this work, the constant C = 0.007 obtained in [28] is used. The cohesive strength is defined as the difference between the undamaged strength and the strength after complete fracture at a given pressure. Given the lack of test data at various pressures, the cohesive strength is assumed to be 0:75fc0 under quasi-static conditions. Normalization to e_ ¼ 1:0 yields A = 0.79. Smax represents the normalized maximum strength. According to Hanchak et al. test results, [9] the axial stress increases with pressure, and the relevant curves are almost parallel to each other for concretes with compressive strengths of 48 and 140 MPa (Fig. 10a). Hence, this work employs the extrapolation approach to estimate a normalized maximum strength of around Smax = 3.5. Then, the constants B and N are determined to provide an average relation. Fig. 10b displays the results. Fig. 11 plots the stress–strain results for a cylinder that is subjected to cyclic compression loading [30]. The stress–strain curve for quasi-static loading serves as a reasonable envelope for the peak values of stress in concrete under cyclic loading. An assumed failure surface can be defined from the quasi-static test results (Fig. 5), revealing total strength loss at an axial strain of approximately 0.02. The elastic strain is taken to be 0.0032; the equivalent plastic strain at fracture is efp ¼ 0:0168. The relationship between plastic strain and plastic volumetric strain in the uniaxial stress state is lfp ¼ ð1 þ 2vÞefp . Therefore, in Eq. (3) D1 is given by
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2ð1 þ vÞefp ðP þ T ÞD2
ð4Þ
where D2 = 1.0, T* = 0.079 and v ¼ 0:2, from which the constant D1 = 0.78 can be determined. Table 3 summarizes all of the material parameters used in the analysis in LS-DYNA. 4.2. Mesh and boundary conditions Fig. 4 shows the analytical configuration considered herein work. A concrete target plate is clamped between two steel frames
and the steel projectile is normally incident at the center of the plate. Based on the assumption that the clamp and impact are fully symmetric, only a quarter of the test arrangement was modeled, to reduce the size of the computational domain. Fig. 12 presents the boundary conditions for the numerical model. Symmetric boundary conditions are imposed on the center line of the plate and the clamped boundary conditions are imposed on the outer edge. The concrete specimen is modeled using 34,957 elements and the projectile is modeled using 780 elements. These elements are single-point integration elements with hourglass control. Additionally, the initial velocity of the projectile are 58.2, 76.0 or 104.0 m/s, measured experimentally.
Fig. 15. Impact processes and failure model (Case RPC-F1-3).
Fig. 16. Comparison of the experimental damage and numerical results.
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4.3. Contact algorithm and time integration Contact may be made across surfaces between the projectile and the target. In this study, separation and friction slide surface is adopted to model the impact event between the projectile and the target plate, and the effect of friction between projectile and target was neglected. This has been verified by using two different values of the assumed dynamic coefficient of friction namely 0 and 0.3 between the projectile and the target plate. No significant difference in the computational results was observed. The dynamic problems are treated using LS-DYNA by an explicit time integration scheme, with a sufficiently small time step for each increment. However, contact, material and non-linear geometry will causes the stable time step to be close to zero in the equation computation procedure. The whole computation time thus has infinite delays and produces divergent results. Accordingly, a time step scale factor of 0.6 is defined to ensure convergence.
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Fig. 15 presents the penetration of the projectile and the failure pattern of the case RPC-F1-3. At the moment of contact, flared shear cracks are form immediately in a region in the periphery of the projectile. Additionally, the compressive wave reflected from the rear face of the target changes to a tensile wave that interacts with the compressive wave and produces a rear crater (Fig. 15b). The clamp boundary conditions imposed on the outer edge result in visible tensile stresses at the boundary between the target and the vertical cracks (Fig. 15c). The velocity of the projectile falls rapidly when it makes contact with the target, falling to zero in about t = 125 ls; however, the cracks and the crater continue to extend because of inertia. A comparison of experiments and analysis for three cases are shown in Fig. 16; the plate is cut in half, and a cross section is shown as well as the iso-view of the projectile impact, and the damage pattern is similar to that obtained experimentally. It shows that the implemented JHC model is suitable to simulate the impact of projectile into RPC targets and the material parameters used in simulation are valid.
4.4. Failure criteria 5. Conclusions The impact of a projectile induces compressive shock waves on the front face of the target plate. The shock waves propagate through the thickness and reflect from the rear free surface as tensile waves. At the rear free surface, if the total pressure of the compression waves and the reflected tension waves exceeds the tensile capacity of the concrete, then scabbing of the concrete is expected. In the present study, uses tensile strain cutoff criteria in the numerical simulation, based on the assumption that when the strain in any concrete element reaches the split tensile strain. In addition, the impact and explosion cases under consideration, the maximum strain rate is generally on the order of 10–100 s1. For this magnitude of strain rate, the corresponding dynamic strength enhancement factor can reach 5.0 or above. Taking all these influences into account and in conjunction with trial parametric analysis, it is found that the dynamic tensile fracture strain should be around 0.02 for spallation with the mixture concrete material. Thus, the principal tensile strain reaching 0.02 is adopted as the primary criterion in the implementation of the erosion algorithm in the numerical simulation. 4.5. Numerical results and discussion The analysis was performed on a PC with P4 1.8 GHz processor and took about 5 h. Post processing was performed using LS-Prepost v.1.0. Figs. 13–16 plot the results of the analysis. Solutions are terminated after 500 ls. Fig. 13 plots the time history of the velocity when the projectile impacts the target plate, demonstrating the difference in the projectile when different impact velocities are applied to the targets. The velocity quickly fell when the time increased. Fig. 14a–c plots the time history of the contact force at the interface between the projectile and the target. The contact force is applying the penalty method in this analysis. In the process of analysis, the slave node is checked for penetration through master surface. When the slave node penetrated, a contact force is applied between the slave node and its contact point. However, the lateral inertia will causes original results exhibits some high frequency oscillation. Mainly are related to the familiar Pochhammer–Chree observed in SHPB experiments [31]. This can be filtered to 150 Hz using a Butterworth filter. During initial contact between the projectile and the target, the contact force similar a half-sine wave. For the case RPC-F1-1 (impact velocity of 58.2 m/ s), the peak contact force 116.5 kN at 108 ls suddenly rises (Fig. 14a). Then, declines as the speed of striking decreases, falling to zero in approximately t = 140 ls For cases RPC-F1-2 (Fig. 14b) and RPC-F1-3 (Fig. 14c), the peak contact force, of 133.2 and 153.3 kN, respectively.
This work studied the impact resistance of RPC and NC with various volume fractions of steel fibers under various impact velocities. The test results support the following conclusions. RPC is a special mixture that has been cured especially to have an ultra-high compressive strength. However, it is very fragile when no steel fiber is added. Accordingly, when the failure conditions are reached, the plates break into several pieces. Adding steel fibers increases the split tensile strength, flexure strength and reduces brittleness. 2% and 5% by volume of steel fibers yielded split tensile strengths of 21.9 and 31.6 MPa, around equal to the compressive strength of NC, improving impact resistance. The JHC material constitutive model was implemented using the finite element code LS-DYNA. The preliminary computations were reasonably consistent with experimental data, supporting the conclusion that the model fully described the dynamic effect on concrete and its cracking failure behavior at high pressures and high strain rates. Numerical simulations yielded details of the penetration process, and revealed the variation of the contact force at various impact velocity.
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