Numerical simulation of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) under high velocity impact of deformable projectile

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1 Numerical simulation of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) under high velocity imact of deformable rojectile R. Yu, Deartment of the Built Environment, Eindhoven University of Technology, Eindhoven 5600 MB, the Netherlands P. Siesz, Deartment of the Built Environment, Eindhoven University of Technology, Eindhoven 5600 MB, the Netherlands H.J.H. Brouwers, Deartment of the Built Environment, Eindhoven University of Technology, Eindhoven 5600 MB, the Netherlands ABSTRACT This aer resents the numerical simulation of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) under high velocity imact of deformable rojectile. The 3D finite element models for the target and deformable rojectile are built in LS-DYNA. The Johnson Holmquist Concrete model is utilized to simulate the reaction of UHPFRC late under the imact. The rojectile is a small-mass flat-nose rojectile with a diameter of 15 mm and a length of 50 mm, which is meshed with 8-node hexahedron solid elements, with the mesh size of about 3 mm. The target is an UHPFRC late with a dimension of mm, and it is meshed with 8-node hexahedron solid elements. The imact seed of the rojectile is 1000 m/s. During the imact rocess, the variation of the velocity, acceleration, energy of the rojectile and the UHPFRC late are evaluated. The simulation results show that, comared to the normal concrete, the UHPFRC can effective reduce the crater and scabbing dimensions on the concrete late. However, to avoid the erforation of the high seed rojectile, the thickness of the UHPFRC late should be rudently considered. Keywords: Numerical simulation, Ultra-High Performance Fibre Reinforced Concrete (UHPFRC), high velocity imact, deformable rojectile, LS-DYNA INTRODUCTION Ultra-high erformance fibre reinforced concrete (UHPFRC) is the outcome of a demand that began in the 1930s to find means of imroving the mechanical strength of concrete. The so-called ultra-high erformance concretes (UHPC) result in high comressive strength values of 150 N/mm 2 and more [1]. To overcome their brittle failure mechanism and to imrove the ost-critical behavior, fibres (esecially steel fibres) are added to the concrete mix [2]. The alication of steel fibres gives UHPFRC much greater ductility comare to reinforced normal strength or normal weight concretes (Figure 1), which means the UHPFRC can absorb more energy comared to the normal concrete [3]. Hence, it can be redicted that UHPFRC is one of the otential candidates for roducing imact resistant concrete. However, in the testing of imact resistance caacity of concrete, all the methods and aaratus cost a lot of resources and labours, which cause that the modeling of concrete under imact loading becomes more and more oular[4-6]. As commonly known, concrete has very comlicated nonlinear behavior, which is difficult to be fully described for general stress conditions by a simle constitutive model. When concrete is subjected to extreme loads such as high velocity imact of missiles and fragments, the modeling of concrete can be further comlicated due to rate effects, overloading and large deformations [7]. With the advancement in the comuting ower, it is now ossible to erform numerical simulation for the resonse of concrete structures subjected to severe shock and imact loads, including the modeling of the loading sources if necessary. A number of commercial hydrocodes such as ABAQUS [8], AUTODYN [9] and LS-DYNA [10] are available for the general simulation of structural nonlinear dynamic resonses. Esecially the LS- DYNA, which erform erfect in simulating the hysical rojectile imact with different loading rates, is utilized frequently in recent years. For instance, Agardh [11] resented the simulations using LS-DYNA for the rojectile erforation of a 60 mm thick fibre-reinforced concrete slab with a velocity of 1500 m/s. The material model used was Tye 78 Soil/Concrete with erosion. The results were in fairly good agreement 1

2 with test results, but more studies are necessary to assess the sensitivity of certain material arameters. Teng [12] emloyed hydrodynamic finite element code LS-DYNA to study the dynamic resonse of steel fibre reinforced concrete (SFRC) subject to imact loading. The elastic-lastic hydrodynamic material model was emloyed to model the non-linear softening behavior of SFRC. The results show that the roosed methodology is useful and efficient can be further develoed for designing the rotection of military structures, nuclear ower lants and other facilities against high-velocity rojectiles. Beu [13] described the evaluation of the local damage of concrete lates by the imact of high-velocity rigid rojectiles. Imact tests for concrete lates have been conducted by using the system to examine failure modes of the local damage of concrete lates. The damage or failure behavior has been discussed on the basis of the failure rocess catured by a high seed video camera and the strain histories obtained by strain gauges on the concrete late. Numerical simulations have been also carried out in order to exlain the mechanism of the local damage observed in the exeriment. Li [14] investigated several widely used material models for lain concrete under dynamic loading, esecially the Concrete Damage model and the Elastic-Plastic Hydrodynamic model to determine an aroriate material model for engineered cementitious comosite (ECC) materials under dynamic loading. A material model which is aroriate to simulate the dynamic behavior of ECC materials is established based on the Concrete Damage model. The roosed material model is validated via numerical simulation of the imact rocess of a hybrid-fibre ECC slab struck by a high-velocity rojectile. Nevertheless, it can be noticed that the numerical simulation of UHPFRC under high velocity imact of deformable rojectile can seldom be found. This should be attributed to that the UHPFRC is still a tye of advanced concrete, and most investigations on its characteristics are focus on the quasi-static testing. Hence, the objective of this study is to simulate the rocess of UHPFRC under high velocity imact of deformable rojectile. The variation of velocity, acceleration and energy of the concrete late and the rojectile are also analysed. Figure 1. Mechanical roerties of conventional concrete and UHPFC under comressive load (left) and tensile load (right) [3] Johnson-Holmsquist Concrete model METHODOLOGY To fully describe the concrete s dynamic effect within the imact rocedure, several concrete models have been imlemented in LS-DYNA [10]. In this aer, the Johnson-Holmsquist Concrete model is chosen to describe the reaction of UHPFRC late under the high velocity imact. The equivalent strength of material is exressed as a function of the ressure, strain rate and damage: [ ( ) + N A 1 D BP ] 1 + C = σ ln ε ' where P* denotes the normalized ressure, shown as P = P f ; P denotes resure; f ' denotes the quasistatic uniaxial comressive strength; ε denotes the dimensionless strain rate, given by ε = ε ε 0 ; 2 / c c / ε

3 reresents the actual strain rate; 0 damage arameter. Additionally A, B, N, and C denote the material arameters. ε reresents the reference strain rate; D ( 0 D 1 ) denotes the The model accumulates damage both from equivalent lastic strain and lastic volumetric strain, and is exressed as: D = ε + µ ε + µ f f Here, ε and µ reresent the equivalent lastic strain increment and lastic volumetric strain f f increment, resectively, during one cycle integral comutation. ( ε + µ ) reresents the lastic strain to fracture under a constant ressure, which can be exressed as follows: ε f + µ f = D 1 D ( P + T ) 2 ' where D 1 and D 2 reresent damage constants, and T = T / f c reresents the maximum tensile stress). is the normalized largest tensile strength (T Figure 2. The relationshi between hydrostatic ressure and material volumetric strain [15] The equation of state (EOS) of this model describes the relationshi between hydrostatic ressure and volume. The loading and unloading rocess of concrete can be divided into three resonse regions (Figure 2). The first zone is the linear elastic zone, where the material is elastic state. The elastic bulk modulus is given by k = P crush / µ, where P crush crush and µ crush reresent the ressure and volumetric strain arising in a uniaxial comression test. Within the elastic zone, the loading and unloading equation of state is given by: P = Kµ where µ = ρ / ρ 0 1, ρ denotes the current density, and ρ 0 denotes the reference density. The second zone arises at P crush < P < P lock, where the material is in the lastic transition state. In this area, the concrete interior voids gradually reduce in size as the ressure and lastic volumetric strain increase. The unloading curve is solved by the difference from the adjacent regions. 3

4 The third area defines the relationshi for fully dense material. The concrete has no air voids. The relationshi between ressure and the volumetric strain is given by: µ + K 2 µ K 3 µ P = K + where K 1, K 2, K 3 are constants and µ µ lock µ = ( µ lock is the locking volumetric strain). 1 + µ Numerical simulation of erforation of concrete slabs lock In this study, the erforation of concrete late under deformable rojectile imact is analysed. The 3D finite element models for the target and deformable rojectile are built in LS-DYNA (as shown in Figure 3). The rojectile is a small-mass flat-nose rojectile with a diameter of 15 mm and a length of 50 mm, which is meshed with 8-node hexahedron solid elements, with the mesh size of about 3 mm. The target is a square concrete late with a dimension of mm, and it is meshed with 8-node hexahedron solid elements. The angle between the rojectile imact direction and the normal direction of the late is 10. The velocity of the deformable rojectile is 1000 m/s. The material model for UHPFRC late and rojectile are Johnson-Holmsquist Concrete model and Johnson-Cook model, resectively. The material arameters for the UHPFRC are shown in Table 1. Density (kg/m 3 ) Shear modulus (MPa) Table 1. Material arameters of UHPFRC Strength constants A B N C (MPa) (MPa) S max Damage constants D1 D2 f f ( ε + µ ) EOS constant P crush (MPa) μ crush K 1 (GPa) K 2 (GPa) K 3 (GPa) P lock (MPa) μ lock ' f c f t ε (s -1 ) 10 Figure 3. 3D finite element models for the target and deformable rojectile (after meshing) 4

5 Imact rocess simulation EXPERIMENTAL RESULTS AND DISCUSSION The stress distribution of the UHPFRC late and the deformable rojectile during the imact rocess are shown in Figure 4 and 5. It can be seen that the deformable rojectile is still embedded in the UHPFRC late at 20 μs, and the stress around the rojectile head and the crater are larger than the other lace. Moreover, due to the influence of steel fibre and the good combination between fibres and concrete matrix, the rear face of the UHPFRC late obviously deform during the imact rocess (Figure 4a), which can effectively absorb the imact energy and reduce the velocity of the rojectile. However, due to the relatively small thickness (30 mm) of the concrete late and the high velocity (1000 m/s) of the rojectile, the UHPFRC is erforated by the deformable rojectile. During the erforation rocess, the deformation of the rojectile head can also be noticed. This simulation results are similar as that illustrated in [12], in which the elastic-lastic hydrodynamic material model is emloyed to model the non-linear softening behavior of steel fibre reinforced concrete (SFRC). Nevertheless, it can be found that the crater and scabbing dimensions of the UHPFRC late are smaller than that of SFRC. This should be attributed to the large steel fibre amount and the erfect combination between fibres and concrete matrix of UHPFRC. a) t = 20 μs b) t = 40 μs c) t = 60 μs 5

6 d) t = 80 μs Figure 4. Stress distribution of the UHPFRC late and rojectile during the imact rocess a) Front face of the target at 20 μs b) Rear face of the target at 20 μs c) Front face of the target at 40 μs d) Rear face of the target at 40 μs e) Front face of the target at 60 μs f) Rear face of the target at 60 μs 6

7 g) Front face of the target at 80 μs h) Rear face of the target at 80 μs Figure 5. Stress distribution on the front and rear face of the target at different time Velocity and acceleration analysis To evaluate the velocity and acceleration of the rojectile and concrete late during the imact rocess, some oints on the models are chosen ramdomly, as shown in Figure 6. The variation of resultant velocity and acceleration of these oints with time are illustrated in Figure 7 to 10. As can be seen that the original velocity of the rojectile is 1000m/s, which reduce to around 930 m/s after the erforation (Figure 7). From Figure 8, it can be noticed that the acceleration of the rojectile obviously flucturate at the beginning of the imact (before 20 μs). Then, after the UHPFRC is erfoated, the acceleration of the rojectile is close to zero. Moreover, Figure 9 show the resultant velocity of the chosen oints on the concrete target during the imact. It is obvious that the residule velocity of the oint (31167) is much higher than the other two oints, which means this concrete art (reresented by the oint 31167) is seerated with the concrete matrix by the external imact, and the final velocity of the seerated concrete art is around 440 m/s. Additionally, the effect of the imact on the oints (31062 and 31258) is not significant, which can be found in Figure 9 and 10. Hence, this further demostrate that the UHPFRC can significantly reduce the crater and scabbing dimension on the concrete late. However, to definitely avoid the erforation of the high seed rojectile, the thickness of the UHPFRC late should be rudently considered. Figure 6. Chosen oints of the concrete target and rojectile Figure 7. Resultant velocity of the chosen oints on the rojectile (velocity unit: 10 km/s) 7

8 Figure 8. Resultant acceleration of the chosen oints on the rojectile (acceleration unit: cm/μs 2 ) Figure 9. Resultant velocity of the chosen oints on the concrete target (velocity unit: 10 km/s) Figure 10. Resultant acceleration of the chosen oints on the concrete target (acceleration unit: cm/μs 2 ) Energy analysis The variation of the kinetic energy of the rojectile and the total energy with time are shown in Figure 11 and 12. Note that the kinetic energy of the rojectile clearly decrease when the imat haens. This should be attributed to the energy absorbtion caacity of the UHPFRC late. After 40 μs, the kinetic energy of the rojectile is almost constant, which imly that the rojectile has already assed through the UHPFRC late after 40 μs. Furthermore, from the results of the total energy, it can be found that the final total energy is a 8

9 little bit larger than that of kinetic energy of the rojectile. This should be owned to the kinetic energy of the salling concrete art (as shown in Fig 4 and 9). Figure 11. Kinetic energy of the rojectile (energy unit: 10 5 J) Figure 12. Total energy of the concrete late and the rojectile (energy unit: 10 5 J) CONCLUSIONS This aer resents the numerical simulation of the Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) under high velocity imact of deformable rojectile. The Johnson Holmquist Concrete model (imlemented in LS-DYNA) is utilized to simulate the reaction of UHPFRC late. The 3D finite element models for the target and deformable rojectile are built in LS-DYNA. From the results addressed in this aer the following conclusions are drawn: - Johnson Holmquist Concrete model can be successfully utilized to simulate the rocess of UHPFRC under high velocity imact of deformable rojectile. - Comared to the normal concrete or normal steel fibre reinforced concrete, UHPFRC can effectively reduce the crater and scabbing dimensions on the concrete late. - To definitely avoid the erforation of the high seed rojectile, the thickness of the UHPFRC is quite imortant and should be rudently considered. ACKNOWLEDGEMENTS The authors wish to exress their gratitude to the following sonsors of the Building Materials research grou at TU Eindhoven: Rijkswaterstaat Centre for Infrastructure, Graniet-Imort Benelux, Kijlstra Betonmortel, Struyk Verwo, Attero, Enci, Provincie Overijssel, Rijkswaterstaat Directie Zeeland, A&G Maasvlakte, BTE, Alvon Bouwsystemen, V.d. Bosch Beton, Selor, Twee R Recycling, GMB, Schenk 9

10 Concrete Consultancy, Geochem Research, Icoal, BN International, APP All Remove, Consensor, Eltomation, Knauf Gis, Hess ACC Systems, Kronos and Joma (in chronological order of joining). REFERENCES [1] Bache, H. H., Densified cement/ultra-fine article based materials. In: Second International Conference on Suerlasticizers in Concrete, Ottawa, Canada, 1991, June. [2] Richard P., Cheyrezy M., Comosition of reactive owder concretes, Cement and Concrete Research, 1995, 25 (7): [3] Wu C., Oehlers D.J., Rebentrost M., Leach J., Whittaker A.S., Blast testing of ultra-high erformance fibre and FRP-retrofitted concrete slabs. Engineering Structures, 2009, 31(9): [4] Xu Z., Hao H., Li H.N., Mesoscale modeling of fibre reinforced concrete material under comressive imact loading. Construction and Building Materials, 26: [5] Xu Z., Hao H., Li H.N., Mesoscale modeling of dynamic tensile behavior of fibre reinforced concrete with siral fibres. Cement and Concrete Research, 42: [6] Kim S.M., Abu Al-Rub R.K., Meso-scale comutational of the lastic-damage resonse of cementitious comosites. Cement and Concrete Research, 41: [7] Tu Z., Lu Y., Evaluation of tyical concrete material models used in hydrocodes for high dynamic resonse simulations. International Journal of Imact Engineering, 2009, 36: [8] ABAQUS User s manual, Inc. [9] AUTODYN v4.2 user manual, Century Dynamics, Inc. [10] LS-DYNA keyword user s manual, version 970, Livermore Software Technology Cororation, Aril. [11] Agardh L., Laine L., 3D FE-simulation of high-velocity fragment erforation of reinforced concrete slabs. International Journal of Imact Engineering, 1999, 22: [12] Teng T.L., Chu Y.A., Chang F.A., Shen B.C., Cheng D.S., Develoment and validation of numerical model of steel fibre reinforced concrete for high-velocity imact. Comutational Materials Science, 2008, 42: [13] Beu M., Miwa K., Itoh M., Katayama M., Ohno T., Damage evaluation of concrete lates by highvelocity imact. International Journal of Imact Engineering, 2008, 35: [14] Li J., Zhang Y.X., Evaluation of constitutive models of hybrid-fibre engineered cementitious comosites under dynamic loadings. Construction and Building Materials, 2012, 30: [15] Holmquist T.J., Johnson G.R., Cook W.H., A comutational constitutive model for concrete subjected to large strains, high stain rates, and high ressures. In: The 14 th international symosium on ballistics, Quebec 1993,