- Email: [email protected]
Projectile penetration of reinforced concrete blocks: Test and analysis
Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
Contents lists available at SciVerse ScienceDirect
Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec
Projectile penetration of reinforced concrete blocks: Test and analysis I.M. Kamal ⇑, E.M. Eltehewy ⇑ Civil Engineering Department, Military Technical College, Cairo, Egypt, 32 Street No. 9, El-Mokatam, Cairo, Egypt
a r t i c l e
i n f o
Article history: Available online 28 June 2012 Keywords: Concrete Blocks Ferrocement Penetration 3D-simulation AUTODYN 3D
a b s t r a c t Concrete blocks are usually used to provide protection against incidental dynamic loadings such as the impact of a steel projectile. This paper presents results of an experimental test and numerical investigation of reinforced concrete blocks’ penetration resistance. Investigation test was conducted experimentally using a steel blunt-nose projectile with a diameter of 23 mm and a mass of 175 g with striking velocity about 980 m/s hitting concrete blocks reinforced by different number of layers of woven wire steel mesh (Ferrocement). Nonlinear three-dimensional numerical simulation of the investigation test was carried out using AUTODYN which is probably the most extensively code dealing with penetration problems. A comparison was conducted between the results of the numerical model and the experimental test measurements and show relatively good agreement. The main findings show that the penetration depth and the damage in the front and rear face of target specimens exhibit an overall reduction with using wire meshes as a reinforcement. On the other hand, the results showed that increasing the reinforcement ratio has slight influence on the perforation resistance and face damaged area. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is widely used as construction material for military and civilian applications because of its relatively high effect and economic, it is often used as protection layer in fortified structures for missile impact. Since the attach will be an unexpected extreme load, it results in both local and overall dynamic response of the block. Different from plain concrete in which mainly the strength dominates its ability of resisting penetration, reinforced concrete may be influenced by both the concrete strength and the amount of reinforcement. The penetration/perforation process of reinforced concrete includes initial cratering, tunneling and rear cratering, the same as that of plain concrete. Plenty of studies were conducted on behavior of reinforced concrete targets subjected to missile impact. Studies mostly focus on how to prevent excessive local damage and collapse of the block. These include using different types of block materials, different arrangement of reinforcement of reinforced concrete block, providing a steel plate, etc. From the previous studies, the main factors affecting the penetration resistance of concrete are the compressive strength, the tensile strength and the strain rate [1–6]. The depth of penetration
⇑ Corresponding authors. E-mail address: [email protected] (I.M. Kamal). 0167-8442/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tafmec.2012.06.005
is mainly determined by the compressive strength and the strain rate dependent. Response of concrete in compression and the strain rate in tension were of great importance when studying spalling and scabbing of projectile impacts. So projectiles penetration/perforation of reinforced concrete targets, used to improve the tensile strength and strain rate, have been receiving remarkable attention recently [7–9]. One of the most important ways to enhance the concrete properties is the Ferrocement which, improves the resistance of the concrete slabs to fragmentation, and increases the ability of the slabs to withstand impact loads [10–13]. This paper employs the explicit dynamic finite element code 3D-AUTODYN to analyze the behavior of reinforced concrete blocks during projectile penetration. [14–17]. 2. Test program Comparative penetration tests were conducted experimentally on various square plain concrete and Ferrocement specimens. The projectile used in this study was blunt-nose steel penetrator 23 mm diameter and 64 mm length as shown in Fig. 1. The material properties of the penetrator were 475HB for Brinell hardness, 1726 MPa yield Strength, 1900 MPa ultimate strength, and 7% for strain at fracture. The impact velocity was measured and reported for every shot with electro-optical velocity measurement device and it was about 980 m/s.
32
I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
Fig. 1. Dimensions in millimeters for 23 mm API missile.
mesh. The impact velocity was measured and reported for every shot.
2.1. Materials Two main materials are used in this study. First, concrete blocks with mix proportions for one cubed meter by weight were 350 kg Portland cement, 700 kg sand, and 1400 kg dolomite with 19 mm maximum aggregate size. The adopted water/cement ratio by weight was 0.5. Mechanical properties of used concrete were 2350 kg/m3 for mass density, 35 MPa compressive strength, 3.1 MPa tensile strength, and 29 GPa for modulus of elasticity. Second, 500 500 mm galvanized woven wire mesh of 50 mm square opening and 2.0 mm diameter was used to reinforce the concrete blocks. The mechanical properties of steel with alloy No. 1006 used in this study which, obtained from material data sheet were 7850 kg/m3 for mass density, 250 MPa yield Strength, 360 MPa ultimate strength, and 210 GPa for modulus of elasticity. 2.2. Specimens Four target specimens with dimensions of 550 550 mm were constructed. One specimen was unreinforced (plain) concrete considered as a control specimen, and three reinforced concrete specimens reinforced by different number of woven wire steel mesh (Ferrocement) layers. Unit block thickness was 200 mm with reinforcement mesh from front side and rear side. Each specimen consists from two unit blocks to form 400 mm total thickness. Dimensions and details of used wire mesh and specimens are presented in Fig. 2 and Table 1.
3. Finite element analysis models Three dimensional simulation for the penetration and perforation of reinforced concrete target were performed depending on the set of the test data. The finite element models were built for the four specimens SC2, SW1-1, SW1-2 and SW2-3 which were presented in Table 1. 3.1. Description of the mesh Lagrange processor has been used in AUTODYN for the analyses. In this paper two classes of target blocks were considered. Unreinforced (plain) concrete, and reinforced concrete (Ferrocement), projectile and the concrete target are modeled as Lagrangian meshes in all models, while the reinforcing steel bars (meshes) were described as beam elements in Ferrocement models. All parts were symmetric on X = 0 planes to reduce the size of the computational domain. The geometry of the projectile, concrete target and steel mesh will be described below.
2.3. Penetration resistance test
3.1.1. Projectile mesh The geometry of the projectile part, as shown in Fig. 4, was defined using a structural Lagrangian mesh, and was divided to 13 nodes in the I-direction, 7 nodes in the J-direction and 26 nodes in the K-direction. The IJK-index corresponds to the Cartesian coordinate system.
The blocks were mounted on a stationary stiff steel frame in front of the gun as far as 50 m, where the surface (550 550 mm) was normal to the missile path and the thickness (200 mm) was parallel to path of missile. These specimens were supported by the steel frame along their perimeter to prevent movement in both directions. Then they were fired by the projectile 23 mm, as shown in Fig. 3, with care take that penetrator does not strike the wire
3.1.2. Plain concrete mesh For model SC2 of plain concrete material (Conc.35 MPa) were defined using a structural Lagrangian mesh, everyone was divided to 46 nodes in the I-direction, 91 nodes in the J-direction and 41 nodes in the K-direction. Zoning technique was used to densify the meshes in critical regions. Fig. 5 shows the geometry and meshing of model SC2.
Fig. 2. The dimensions and details of wire mesh and specimens.
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 1 Specimens details. NO
Name
Thick-ness (cm)
Description
No of meshes
No of blocks
Front face
Rear face
1
SC2
40
2slabs 20 cm control slab
–
–
2
SW1-1
40
2slabs 20 cm slab with 2 layer
1 layer
1 layer
3
SW1-2
40
2slabs 20 cm slab with 4layer
2 layer
2 layer
4
SW2-3
40
2slabs 20 cm slab with 6 layer
3 layers
3 layers
Table 2 Results of penetration tests. NO
Name
Velocity (m/s)
Penetration depth (cm)
Dim. of damage (front face) d1(cm)
1 2 3 4
SC 2 SW1-1 SW1-2 SW2-3
976 994 996 978
40 29 28.7 28
Full 35 32 28
d2(cm) 39 33 30
Dim. of damage (rear face) Df (cm)
D1(cm)
d2(cm)
Df (cm)
37 32.5 29
Full Non Non Non
Non Non Non
Non Non Non
Fig. 3. Penetration resistance test rig.
3.1.3. Ferrocement mesh The Ferrocement models SW3-2, SW1-2, and SW1-1 contains concrete material (Conc. 35 MPa) and steel mesh layers of (STEEL 1006) beside projectile part. Concrete elements were defined using a structured Lagrangian mesh; everyone was divided to 44 nodes in the I-direction, 75 nodes in the J-direction and 31 nodes in the K-direction, Steel layer was defined using 1197 beam element for each layer; zoning technique was used to refine the mesh in the critical regions as shown in Fig. 6. Nodes of steel layer are attached to the concrete nodes one to one at the intersections preventing the two materials from sliding. 3.2. Material modeling The governing equations are the conservation of mass, momentum and energy. To complete the description of the continuum, additional relations describing the material behavior are needed (besides the load and boundary conditions): it is the material model which has typically four basic types of information must be specified for each material: (1) Equation of state: pressure as function of density and internal energy.
Fig. 4. Geometry and meshing of the projectile part.
(2) Strength model: strength model, which defines the yield surface. (3) Failure model: failure model prescribing when the material no longer has strength (4) Erosion model: erosion criteria. When a material is eroded it is transformed from solid element to a free mass node (Lagrange only). According to Ref. [6], [15,16] and many other researches, RHT material model, this is a modular strength model for brittle materials developed by Riedel [15] is particularly useful for modeling the dynamic loading of concrete. That is because the model computes the following phenomena associated with brittle materials:
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 3 Results of finite element models.
Fig. 5. Geometry and Meshing of the Model SC2.
Pressure hardening, Strain hardening, Strain rate hardening, Third invariant dependence for compressive and tensile meridians, damage effects (strain softening),volumetric compaction (using the P-alpha equation of state), crack-softening. The main material parameter for concrete was chosen from the AUTODYN material library (concrete 35 MPa) and modified according to the values investigated experimentally as reported in Table 3. The material model used for represent steel mesh material was Johnson Cook strength model [17]. The main material parameter for steel was chosen from the AUTODYN material library (STEEL 1006) and modified according to the values obtained from material data sheet and listed in Table 4. The main material parameter for steel used in projectile was chosen from the AUTODYN material library (STEEL 4340) and modified according to the values obtained from material data sheet as mentioned previously. The erosion model used was geometric strain. 3.3. Model interaction and boundary conditions For the projectile – concrete interaction, the impact slide surface was between two Lagrange subgrides, so the interaction between these subgrides should be specified as Lagrange/Lagrange interaction. The interaction was achieved using the gap interaction logic. In the gap interaction logic, each surface segment is surrounded
Velocity (m/s)
Penetration depth (cm)
Front face damage (crater diameter cm)
Rear face damage (crater diameter cm)
SC2
980
40
20 < D < 55
55
2
SW11
980
28.6
About 20 cm
Fine cracks
3
SW12
980
28.2
About 20 cm
Fine cracks
4
SW23
980
27.4
About 20 cm
Fine cracks
NO
Name
1
Model disruption
by a contact detection zone. The radius of this contact detection zone is called the gap size. The initial condition for projectile part in all model was 980 m/s in Z direction and the boundary conditions in all model for all target parts were constant velocity in Y direction Vy = 0 and for target were constant velocity in Z direction Vz = 0. 4. Results and model verification 4.1. Test results The response of the specimens was determined and recorded in terms of the measured penetration depth and front and rear damaged areas. These have been chosen as faluir indecator parameters because, rear face damage is considered to be related to penetration process and because the performance of structural elements that have to resist impact is commonly classified by their ability to resist penetration and prevent rear face scabbing and total perforation. The equivalent diameter of the damaged area (Deq) calculated from the following equation [3]:
Deq ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 d2
ð1Þ
where d1 and d2 are the maximum and minimum values of measured damage diameter respectively as shown in figures from Figs. 7–9. Test results of penetration depth and damage for front and rear faces were measured and recorded in Table 2.
Fig. 6. Geometry, meshing and joining of the model SW1-2 and SW1-1.
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 4 Comparison between the results of finite element models and experimental tests. No.
Sample
Model description
Penetration depth (cm) Test
FE Model
Compatibility
Test
FE Model
1
SC2
40
40
100%
Full/full
55/55
2
SW2-3
28
27.4
98%
29/Fine crack
More than 20/F.C
3
SW1-2
28.7
28.2
98%
32.5/Fine crack
More than 20/F.C
4
SW1-1
29
28.6
99%
35.5/Fine crack
More than 20/F.C
and rear face; however the results do not have the same excellent compatibility percentages as in the penetration depth case.
4.2. Numerical simulation results Four finite element models were performed in this paper. As in the experimental tests, the responses of the concrete blocks were determined in terms of penetration depth, front and rear damaged areas. The finite element models results are presented in Table 3 and Fig. 10. 4.3. Finite element model verification Table 4 and figures from Figs. 7–9 present a comparison between the results of the finite element simulation models and experimental tests introduced in Section 2 of this study, this comparison were in terms of penetration depth, front and rear damaged areas. From the previous comparison, it is clear that the results determined by the finite element models were quite compatible with those obtained by experimental tests measurements. This comparison showed an excellent compatibility percentage for penetration depth as presented in Table 4. Also, there is a good compatibility between finite element models and experimental test measurements results in shape and diameter of damage for both front
FE Model Front Damage
Dim. of damage front/rear face
Test Front Damage
4.4. Discussion 4.4.1. Effect of using ferrocement on penetration depth: Penetration depth is the most important factor in determining the enhancement of penetration resistance of concrete. Fig. 11 illustrates the penetration depth time history for plain concrete specimen (SC2) and Ferrocement specimens with different number of mesh layers (SW1-1, SW1-2, and SW2-3). From previous results in Table 2 Figs. 10 and 11, it is noticed that, using Ferrocement in the specimens leads to reduction in the penetration depth. The reduction percentage compare with plain concrete specimen (SC2) was between 27.5% for Ferrocement specimen with one steel layer in each face (SW1-1) and 30% for Ferrocement specimen with three steel layers in each face (SW23). Also, it is clear that increasing the number of steel layers in Ferrocement specimen has a slight effect on penetration depth reduction, since increasing the number of steel layers from one layer to three layers in each face of the specimen enhanced the penetration resistance only by 3%.
FE Model Rear Damage
Test Rear Damage
Fig. 7. Front and rear damage of SC2 sample.
FE Model Front Damage
Test Front Damage
FE Model Rear Damage
Fig. 8. Front and rear damage of SW1-1 sample.
Test Rear Damage
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
FE Model Front Damage
Test Front Damage
FE Model Rear Damage
Test Rear Damage
Fig. 9. Front and rear damage of SW2-3 sample.
(a) SC2 FE Model
(b) SW1-1 FE Model
(c) SW1-2 FE Model
(d) SW2-3 FE Model
Fig. 10. Penetration depth in centimeter for different FE models.
4.4.2. Effect of using ferrocement on damage in front/rear face Spalling or damage in front face of target was affected mainly by tensile strength and strain of concrete of which enhanced by using Ferrocement. Fig. 12 shows a comparison for the strain–time history for a point at 10 cm from the axis of penetration on the front face between plain concrete specimen (SC2) and one steel layer specimen (SW1). Fig. 13 presents the strain–time history for the same point on the front face for the Ferrocement specimens with different numbers of steel layers. In comparison with plain concrete specimen (SC2), using the Ferrocement in specimens (SW1-1), (SW1-2), and (SW2-3) reduced the damage in front face between 47.5% and 53.5% because of the decreasing in the strain, the maximum strain was 0.0138 for plain
concrete specimen (SC2) and reduced to 0.0044 for in case of Ferrocement specimen (SW1-1) as presented in Fig. 12. Increasing the number of steel layers decreased the damage in front face compare with the plain concrete model by 47.5% when using one layer in (SW1-1) model and by 53.5% for two layers in (SW1-2) model. Also, the main reason was the reduction in the strain as presented in Fig. 13. Scabbing or damage in rear face is the second mode of failure after perforation; it is mainly affected by the tensile strength of concrete, which enhanced by using Ferrocement. Fig. 14 shows the strain–time history for the same point at 10 cm from the axis of penetration on the rear face for all models. From this figure, it is clear that increasing the number of steel layers decreased the strain, which reduced the damage in rear face.
Fig. 11. Penetration depth time history for different FE models.
Fig. 12. Enhancement in strain in block front face with using ferrocement.
I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
37
reducing the front and rear face damage. On the other hand, increasing number of layers of wire mesh in Ferrocement blocks has slight influence on the depth of penetration, but it has a remarkable effect on front/rear face damage. The results demonstrated that the optimum and economic number of layers was one layer of wire steel mesh in each concrete block face. The proposed finite element model can be used efficiently in characterizing the behavior of concrete blocks under the effect of projectile impact. The reliability of this model performance is demonstrated by a comparison between finite element models results and experimental test ones. It exhibited qualitatively correct behavior compared with the experimental test investigation results with more accuracy for penetration depth than front/rear face damage. References
Fig. 13. Enhancement in strain in block front face by increasing number of steel layers.
Fig. 14. Enhancement in strain in block rear face by increasing number of steel layers.
5. Conclusions The test investigation and its numerical simulation of the Ferrocement blocks penetration resistance showed that using Ferrocement enhances the penetration resistance of concrete blocks and
[1] M. Vladimir, C. Vardis, Analysis of the penetration resistance of concrete, J. Eng. Mech. 3 (1998) 328–337. [2] M.H. Zhang, V.P.W. Shim, G. Lu, C.W. Chew, Resistance of high-strength concrete to projectile impact, Int. J. Impact Eng. 31 (2005) 825–841. [3] N. Avraham, David Z. Yankelevsky, Chanoch jaegermann ‘‘response of high performance concrete plates to impact of non-deforming projectiles, Int. J. Impact Eng. 34 (2007) 1768–1779. [4] V.K. Luk, M.J. Forrestal, Penetration into semi-finite reinforced concrete targets with spherical and ogival nose projectiles, Int. J. Impact Eng. (1987) 6291– 6301. [5] P.S. Song, J.C. Wu, S. Hwang, B.C. Sheu, Assessment of statistical variations in impact resistance of high-strength concrete and high-strength steel fiberreinforced concrete, Cem. Concr. Res. 35 (2005) 393–399. [6] D. Cargile, N.D. Neeley, Very-high-strength concretes for use in blast- and penetration-resistant structures, AMPTIAC Quart 6 (2003) 61–67. [7] J. Leppänen, Concrete subjected to projectile and fragment impacts modelling of crack softening and strain rate dependency in tension, Int. J. Impact Eng. 32 (2006) 1828–1841. [8] X.W. Chen, X.L. Li, F.L. Huang, H.J. Wu, Y.Z. Chen, Normal perforation of reinforced concrete target by rigid projectile, Int. J. Impact Eng. 35 (2008) 1119–1129. [9] Q.M. Li, S.R. Reid, H.M. Wen, A.R. Telford, Local impact effects of hard missiles on concrete targets, Int. J. Impact Eng. 32 (2005) 224–284. [10] R.P. Kennedy, A review of procedures for the analysis and design of concrete structures to resist missile impact effects, Nucl. Eng. Des 37 (1976) 183–203. [11] S. Hori, Experimental study on local damage and behavior of ferrocement panels subjected to missile impact, Master thesis, Department of Built Environment, Tokyo Institute of Technology, March 2003, 135p. [12] A.W. Hago, K.S. Al-Jabri, A.S. Alnuaimi, H. Al-Moqbali, M.A. Al-Kubaisy, Ultimate and service behavior of Ferrocement roof slab panels, Construct. Build. Mater. 19 (2005) 31–37. [13] Abdullah K. Takiguchi, K. Nishimura, S. Hori, Behaviour of ferrocement subjected to missile impact, in: Proceedings of the 17th International Conference on Structural Mechanics in Reactor Technology (SMIRT 17)Prague, Czech Republic, August 17–22 (2003) pp. 1–6. [14] AUTODYN explicit software for non-linear dynamics, AUTODYN Electronic Document Library, MultiVersions, Century Dynamics Inc., 2005. [15] T.L. Teng, Y.A. Chu, F.A. Chang, H.S. Chin, Numerical analysis of oblique impact on reinforced concrete, Cem. Concr. Compos. 27 (2005) 481–492. [16] C.Y. Tham, Reinforced concrete perforation and penetration simulation using AUTODYN-3D, Finite Elem. Anal. Des. 41 (2005) 1401–1410. [17] C.Y. Tham, Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile, Finite Elem. Anal. Des 42 (2006) 1258–1268.
Contents lists available at SciVerse ScienceDirect
Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec
Projectile penetration of reinforced concrete blocks: Test and analysis I.M. Kamal ⇑, E.M. Eltehewy ⇑ Civil Engineering Department, Military Technical College, Cairo, Egypt, 32 Street No. 9, El-Mokatam, Cairo, Egypt
a r t i c l e
i n f o
Article history: Available online 28 June 2012 Keywords: Concrete Blocks Ferrocement Penetration 3D-simulation AUTODYN 3D
a b s t r a c t Concrete blocks are usually used to provide protection against incidental dynamic loadings such as the impact of a steel projectile. This paper presents results of an experimental test and numerical investigation of reinforced concrete blocks’ penetration resistance. Investigation test was conducted experimentally using a steel blunt-nose projectile with a diameter of 23 mm and a mass of 175 g with striking velocity about 980 m/s hitting concrete blocks reinforced by different number of layers of woven wire steel mesh (Ferrocement). Nonlinear three-dimensional numerical simulation of the investigation test was carried out using AUTODYN which is probably the most extensively code dealing with penetration problems. A comparison was conducted between the results of the numerical model and the experimental test measurements and show relatively good agreement. The main findings show that the penetration depth and the damage in the front and rear face of target specimens exhibit an overall reduction with using wire meshes as a reinforcement. On the other hand, the results showed that increasing the reinforcement ratio has slight influence on the perforation resistance and face damaged area. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is widely used as construction material for military and civilian applications because of its relatively high effect and economic, it is often used as protection layer in fortified structures for missile impact. Since the attach will be an unexpected extreme load, it results in both local and overall dynamic response of the block. Different from plain concrete in which mainly the strength dominates its ability of resisting penetration, reinforced concrete may be influenced by both the concrete strength and the amount of reinforcement. The penetration/perforation process of reinforced concrete includes initial cratering, tunneling and rear cratering, the same as that of plain concrete. Plenty of studies were conducted on behavior of reinforced concrete targets subjected to missile impact. Studies mostly focus on how to prevent excessive local damage and collapse of the block. These include using different types of block materials, different arrangement of reinforcement of reinforced concrete block, providing a steel plate, etc. From the previous studies, the main factors affecting the penetration resistance of concrete are the compressive strength, the tensile strength and the strain rate [1–6]. The depth of penetration
⇑ Corresponding authors. E-mail address: [email protected] (I.M. Kamal). 0167-8442/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tafmec.2012.06.005
is mainly determined by the compressive strength and the strain rate dependent. Response of concrete in compression and the strain rate in tension were of great importance when studying spalling and scabbing of projectile impacts. So projectiles penetration/perforation of reinforced concrete targets, used to improve the tensile strength and strain rate, have been receiving remarkable attention recently [7–9]. One of the most important ways to enhance the concrete properties is the Ferrocement which, improves the resistance of the concrete slabs to fragmentation, and increases the ability of the slabs to withstand impact loads [10–13]. This paper employs the explicit dynamic finite element code 3D-AUTODYN to analyze the behavior of reinforced concrete blocks during projectile penetration. [14–17]. 2. Test program Comparative penetration tests were conducted experimentally on various square plain concrete and Ferrocement specimens. The projectile used in this study was blunt-nose steel penetrator 23 mm diameter and 64 mm length as shown in Fig. 1. The material properties of the penetrator were 475HB for Brinell hardness, 1726 MPa yield Strength, 1900 MPa ultimate strength, and 7% for strain at fracture. The impact velocity was measured and reported for every shot with electro-optical velocity measurement device and it was about 980 m/s.
32
I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
Fig. 1. Dimensions in millimeters for 23 mm API missile.
mesh. The impact velocity was measured and reported for every shot.
2.1. Materials Two main materials are used in this study. First, concrete blocks with mix proportions for one cubed meter by weight were 350 kg Portland cement, 700 kg sand, and 1400 kg dolomite with 19 mm maximum aggregate size. The adopted water/cement ratio by weight was 0.5. Mechanical properties of used concrete were 2350 kg/m3 for mass density, 35 MPa compressive strength, 3.1 MPa tensile strength, and 29 GPa for modulus of elasticity. Second, 500 500 mm galvanized woven wire mesh of 50 mm square opening and 2.0 mm diameter was used to reinforce the concrete blocks. The mechanical properties of steel with alloy No. 1006 used in this study which, obtained from material data sheet were 7850 kg/m3 for mass density, 250 MPa yield Strength, 360 MPa ultimate strength, and 210 GPa for modulus of elasticity. 2.2. Specimens Four target specimens with dimensions of 550 550 mm were constructed. One specimen was unreinforced (plain) concrete considered as a control specimen, and three reinforced concrete specimens reinforced by different number of woven wire steel mesh (Ferrocement) layers. Unit block thickness was 200 mm with reinforcement mesh from front side and rear side. Each specimen consists from two unit blocks to form 400 mm total thickness. Dimensions and details of used wire mesh and specimens are presented in Fig. 2 and Table 1.
3. Finite element analysis models Three dimensional simulation for the penetration and perforation of reinforced concrete target were performed depending on the set of the test data. The finite element models were built for the four specimens SC2, SW1-1, SW1-2 and SW2-3 which were presented in Table 1. 3.1. Description of the mesh Lagrange processor has been used in AUTODYN for the analyses. In this paper two classes of target blocks were considered. Unreinforced (plain) concrete, and reinforced concrete (Ferrocement), projectile and the concrete target are modeled as Lagrangian meshes in all models, while the reinforcing steel bars (meshes) were described as beam elements in Ferrocement models. All parts were symmetric on X = 0 planes to reduce the size of the computational domain. The geometry of the projectile, concrete target and steel mesh will be described below.
2.3. Penetration resistance test
3.1.1. Projectile mesh The geometry of the projectile part, as shown in Fig. 4, was defined using a structural Lagrangian mesh, and was divided to 13 nodes in the I-direction, 7 nodes in the J-direction and 26 nodes in the K-direction. The IJK-index corresponds to the Cartesian coordinate system.
The blocks were mounted on a stationary stiff steel frame in front of the gun as far as 50 m, where the surface (550 550 mm) was normal to the missile path and the thickness (200 mm) was parallel to path of missile. These specimens were supported by the steel frame along their perimeter to prevent movement in both directions. Then they were fired by the projectile 23 mm, as shown in Fig. 3, with care take that penetrator does not strike the wire
3.1.2. Plain concrete mesh For model SC2 of plain concrete material (Conc.35 MPa) were defined using a structural Lagrangian mesh, everyone was divided to 46 nodes in the I-direction, 91 nodes in the J-direction and 41 nodes in the K-direction. Zoning technique was used to densify the meshes in critical regions. Fig. 5 shows the geometry and meshing of model SC2.
Fig. 2. The dimensions and details of wire mesh and specimens.
33
I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 1 Specimens details. NO
Name
Thick-ness (cm)
Description
No of meshes
No of blocks
Front face
Rear face
1
SC2
40
2slabs 20 cm control slab
–
–
2
SW1-1
40
2slabs 20 cm slab with 2 layer
1 layer
1 layer
3
SW1-2
40
2slabs 20 cm slab with 4layer
2 layer
2 layer
4
SW2-3
40
2slabs 20 cm slab with 6 layer
3 layers
3 layers
Table 2 Results of penetration tests. NO
Name
Velocity (m/s)
Penetration depth (cm)
Dim. of damage (front face) d1(cm)
1 2 3 4
SC 2 SW1-1 SW1-2 SW2-3
976 994 996 978
40 29 28.7 28
Full 35 32 28
d2(cm) 39 33 30
Dim. of damage (rear face) Df (cm)
D1(cm)
d2(cm)
Df (cm)
37 32.5 29
Full Non Non Non
Non Non Non
Non Non Non
Fig. 3. Penetration resistance test rig.
3.1.3. Ferrocement mesh The Ferrocement models SW3-2, SW1-2, and SW1-1 contains concrete material (Conc. 35 MPa) and steel mesh layers of (STEEL 1006) beside projectile part. Concrete elements were defined using a structured Lagrangian mesh; everyone was divided to 44 nodes in the I-direction, 75 nodes in the J-direction and 31 nodes in the K-direction, Steel layer was defined using 1197 beam element for each layer; zoning technique was used to refine the mesh in the critical regions as shown in Fig. 6. Nodes of steel layer are attached to the concrete nodes one to one at the intersections preventing the two materials from sliding. 3.2. Material modeling The governing equations are the conservation of mass, momentum and energy. To complete the description of the continuum, additional relations describing the material behavior are needed (besides the load and boundary conditions): it is the material model which has typically four basic types of information must be specified for each material: (1) Equation of state: pressure as function of density and internal energy.
Fig. 4. Geometry and meshing of the projectile part.
(2) Strength model: strength model, which defines the yield surface. (3) Failure model: failure model prescribing when the material no longer has strength (4) Erosion model: erosion criteria. When a material is eroded it is transformed from solid element to a free mass node (Lagrange only). According to Ref. [6], [15,16] and many other researches, RHT material model, this is a modular strength model for brittle materials developed by Riedel [15] is particularly useful for modeling the dynamic loading of concrete. That is because the model computes the following phenomena associated with brittle materials:
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 3 Results of finite element models.
Fig. 5. Geometry and Meshing of the Model SC2.
Pressure hardening, Strain hardening, Strain rate hardening, Third invariant dependence for compressive and tensile meridians, damage effects (strain softening),volumetric compaction (using the P-alpha equation of state), crack-softening. The main material parameter for concrete was chosen from the AUTODYN material library (concrete 35 MPa) and modified according to the values investigated experimentally as reported in Table 3. The material model used for represent steel mesh material was Johnson Cook strength model [17]. The main material parameter for steel was chosen from the AUTODYN material library (STEEL 1006) and modified according to the values obtained from material data sheet and listed in Table 4. The main material parameter for steel used in projectile was chosen from the AUTODYN material library (STEEL 4340) and modified according to the values obtained from material data sheet as mentioned previously. The erosion model used was geometric strain. 3.3. Model interaction and boundary conditions For the projectile – concrete interaction, the impact slide surface was between two Lagrange subgrides, so the interaction between these subgrides should be specified as Lagrange/Lagrange interaction. The interaction was achieved using the gap interaction logic. In the gap interaction logic, each surface segment is surrounded
Velocity (m/s)
Penetration depth (cm)
Front face damage (crater diameter cm)
Rear face damage (crater diameter cm)
SC2
980
40
20 < D < 55
55
2
SW11
980
28.6
About 20 cm
Fine cracks
3
SW12
980
28.2
About 20 cm
Fine cracks
4
SW23
980
27.4
About 20 cm
Fine cracks
NO
Name
1
Model disruption
by a contact detection zone. The radius of this contact detection zone is called the gap size. The initial condition for projectile part in all model was 980 m/s in Z direction and the boundary conditions in all model for all target parts were constant velocity in Y direction Vy = 0 and for target were constant velocity in Z direction Vz = 0. 4. Results and model verification 4.1. Test results The response of the specimens was determined and recorded in terms of the measured penetration depth and front and rear damaged areas. These have been chosen as faluir indecator parameters because, rear face damage is considered to be related to penetration process and because the performance of structural elements that have to resist impact is commonly classified by their ability to resist penetration and prevent rear face scabbing and total perforation. The equivalent diameter of the damaged area (Deq) calculated from the following equation [3]:
Deq ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d1 d2
ð1Þ
where d1 and d2 are the maximum and minimum values of measured damage diameter respectively as shown in figures from Figs. 7–9. Test results of penetration depth and damage for front and rear faces were measured and recorded in Table 2.
Fig. 6. Geometry, meshing and joining of the model SW1-2 and SW1-1.
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37 Table 4 Comparison between the results of finite element models and experimental tests. No.
Sample
Model description
Penetration depth (cm) Test
FE Model
Compatibility
Test
FE Model
1
SC2
40
40
100%
Full/full
55/55
2
SW2-3
28
27.4
98%
29/Fine crack
More than 20/F.C
3
SW1-2
28.7
28.2
98%
32.5/Fine crack
More than 20/F.C
4
SW1-1
29
28.6
99%
35.5/Fine crack
More than 20/F.C
and rear face; however the results do not have the same excellent compatibility percentages as in the penetration depth case.
4.2. Numerical simulation results Four finite element models were performed in this paper. As in the experimental tests, the responses of the concrete blocks were determined in terms of penetration depth, front and rear damaged areas. The finite element models results are presented in Table 3 and Fig. 10. 4.3. Finite element model verification Table 4 and figures from Figs. 7–9 present a comparison between the results of the finite element simulation models and experimental tests introduced in Section 2 of this study, this comparison were in terms of penetration depth, front and rear damaged areas. From the previous comparison, it is clear that the results determined by the finite element models were quite compatible with those obtained by experimental tests measurements. This comparison showed an excellent compatibility percentage for penetration depth as presented in Table 4. Also, there is a good compatibility between finite element models and experimental test measurements results in shape and diameter of damage for both front
FE Model Front Damage
Dim. of damage front/rear face
Test Front Damage
4.4. Discussion 4.4.1. Effect of using ferrocement on penetration depth: Penetration depth is the most important factor in determining the enhancement of penetration resistance of concrete. Fig. 11 illustrates the penetration depth time history for plain concrete specimen (SC2) and Ferrocement specimens with different number of mesh layers (SW1-1, SW1-2, and SW2-3). From previous results in Table 2 Figs. 10 and 11, it is noticed that, using Ferrocement in the specimens leads to reduction in the penetration depth. The reduction percentage compare with plain concrete specimen (SC2) was between 27.5% for Ferrocement specimen with one steel layer in each face (SW1-1) and 30% for Ferrocement specimen with three steel layers in each face (SW23). Also, it is clear that increasing the number of steel layers in Ferrocement specimen has a slight effect on penetration depth reduction, since increasing the number of steel layers from one layer to three layers in each face of the specimen enhanced the penetration resistance only by 3%.
FE Model Rear Damage
Test Rear Damage
Fig. 7. Front and rear damage of SC2 sample.
FE Model Front Damage
Test Front Damage
FE Model Rear Damage
Fig. 8. Front and rear damage of SW1-1 sample.
Test Rear Damage
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I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
FE Model Front Damage
Test Front Damage
FE Model Rear Damage
Test Rear Damage
Fig. 9. Front and rear damage of SW2-3 sample.
(a) SC2 FE Model
(b) SW1-1 FE Model
(c) SW1-2 FE Model
(d) SW2-3 FE Model
Fig. 10. Penetration depth in centimeter for different FE models.
4.4.2. Effect of using ferrocement on damage in front/rear face Spalling or damage in front face of target was affected mainly by tensile strength and strain of concrete of which enhanced by using Ferrocement. Fig. 12 shows a comparison for the strain–time history for a point at 10 cm from the axis of penetration on the front face between plain concrete specimen (SC2) and one steel layer specimen (SW1). Fig. 13 presents the strain–time history for the same point on the front face for the Ferrocement specimens with different numbers of steel layers. In comparison with plain concrete specimen (SC2), using the Ferrocement in specimens (SW1-1), (SW1-2), and (SW2-3) reduced the damage in front face between 47.5% and 53.5% because of the decreasing in the strain, the maximum strain was 0.0138 for plain
concrete specimen (SC2) and reduced to 0.0044 for in case of Ferrocement specimen (SW1-1) as presented in Fig. 12. Increasing the number of steel layers decreased the damage in front face compare with the plain concrete model by 47.5% when using one layer in (SW1-1) model and by 53.5% for two layers in (SW1-2) model. Also, the main reason was the reduction in the strain as presented in Fig. 13. Scabbing or damage in rear face is the second mode of failure after perforation; it is mainly affected by the tensile strength of concrete, which enhanced by using Ferrocement. Fig. 14 shows the strain–time history for the same point at 10 cm from the axis of penetration on the rear face for all models. From this figure, it is clear that increasing the number of steel layers decreased the strain, which reduced the damage in rear face.
Fig. 11. Penetration depth time history for different FE models.
Fig. 12. Enhancement in strain in block front face with using ferrocement.
I.M. Kamal, E.M. Eltehewy / Theoretical and Applied Fracture Mechanics 60 (2012) 31–37
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reducing the front and rear face damage. On the other hand, increasing number of layers of wire mesh in Ferrocement blocks has slight influence on the depth of penetration, but it has a remarkable effect on front/rear face damage. The results demonstrated that the optimum and economic number of layers was one layer of wire steel mesh in each concrete block face. The proposed finite element model can be used efficiently in characterizing the behavior of concrete blocks under the effect of projectile impact. The reliability of this model performance is demonstrated by a comparison between finite element models results and experimental test ones. It exhibited qualitatively correct behavior compared with the experimental test investigation results with more accuracy for penetration depth than front/rear face damage. References
Fig. 13. Enhancement in strain in block front face by increasing number of steel layers.
Fig. 14. Enhancement in strain in block rear face by increasing number of steel layers.
5. Conclusions The test investigation and its numerical simulation of the Ferrocement blocks penetration resistance showed that using Ferrocement enhances the penetration resistance of concrete blocks and
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