Ultra-high performance fibre-reinforced concrete under impact of an AP projectile: Parameter identification and numerical modelling using the DFHcoh-KST coupled model

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Highlights

  • Ballistic impact of AP projectile against UHPFRC target is numerically simulated.

  • The DFHcoh-KST damage-plasticity coupled model is used for UHPFRC.

  • Model parameters are calibrated with spalling and highly-confined QOC tests.

  • The yield strength, tensile strength and friction are seen to be key-parameters.

  • The crack bridging of fibres needs to be taken into account to predict the damage pattern.

Abstract

This paper proposes an experimental identification of the parameters of a coupled plasticity-damage model to be used for numerically simulate the mechanical behaviour of an Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC) under impact. In the DFHcoh-KST model, a parabolic relation describes the pressure dependency of yield stresses (in the sense of Von Mises plasticity), and an anisotropic damage model (accounting for strain rate effect and crack bridging of fibre) is used to describe the tensile failure of concrete. This model is implemented in the Finite Element (FE) code Abaqus to simulate the ballistic impact of an AP (Armour-Piercing) projectile. The model parameters are identified under different loading conditions based on quasi-oedometric compression tests, bending tests and spalling tests. Tunnelling and erosion criterion are used in the numerical simulation to overcome the strong element distortions in the FE simulation in the tunnel region. The influence of friction at the projectile-target interface is also discussed. This study shows that yield strength and tensile damage are fundamental to predict the penetration depth of an almost rigid projectile into a UHPFRC target and that the crack bridging of fibre needs to be taken into account to correctly predict the final damage pattern. In contrast, the modelling of the UHPFRC material compaction is found to be negligible due to its low porosity. Finally, numerical results are compared to classical post-mortem observation and a 3D X-ray Computed Tomography (X-ray CT) reconstruction.

Introduction

Ultra-High Performance Concrete (UHPC) is a cementitious material having a compressive strength between 150 MPa and 250 MPa. In the commercial form, it usually contains short steel fibres to achieve ductile behaviour in bending and, if possible, overcome the use of any classical active and passive reinforcements ([1], [2], [3]). The concrete used in this study, labelled Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC), was designed to add to the high compressive strength high-energy absorption capacity that makes it ideal for protective solutions against ballistic and explosion threats [4], [5], [6].

For the past 20 years, projectile impact experiments have been carried out on UHPFRC targets to confirm the ability of such material. For a given velocity, the penetration depth of the projectile into the target was found to be less than the values measured experimentally for conventional concrete [7]. Using steel fibres reduces the damage of the impacted elements and increases the safety of the personnel [8]. This type of concrete was subjected to edge-on impact experiments, which shows that despite the intense multiple cracking process induced in the target due to the impact loading, it retained an excellent cohesion resistance [9]. Many empirical formulas have been proposed in the past by curve-fitting test data to predict the penetration depth of a projectile in a thick target. However, they are applicable strictly within the limits of the tests from which the data were acquired. A complementary approach is to develop numerical models to better predict the penetration resistance of concrete targets [10,11]. The modelling approach should take into account the main local mechanisms activated during penetration to be accurate such as pore collapse, shear deformation, mode I dynamic fracturing and multiple cracking [12].

When a rigid penetrator hits a concrete target, high-pressure compressive stresses develop in the vicinity of the projectile [12], [13], [14]. Moreover, the radial displacement that follows the compressive wave generates hoop tensile stresses in the target and produces the initiation and propagation of numerous cracks [15]. A plasticity model describing the yield strength and irreversible compaction as function of the applied pressure such as the KST (Krieg-Swenson-Taylor) model [16,17] or a viscoplastic model describing the loss of yield strength with the increment of equivalent plastic strain [18] may be used to account for the pressure sensitivity of concrete behaviour. However, in such plasticity model the tensile response remains roughly described. On the other hand, a continuum model based on an isotropic damage description may be used to account for the loss of stiffness and mode I fracturing under tensile dynamic loading as in [19], for conventional concrete, and in [20], for UHPFRC. Finally, a coupled plasticity-damage model seems to provide the most efficient tools in order to simulate the penetration process and induced damage mechanisms in concrete targets under impact of rigid projectile [12].

An anisotropic damage model, denoted DFH (Denoual-Forquin-Hild), was proposed in [21,22] and coupled with the KST plasticity model. The model is based on a micromechanical description of crack inceptions from critical defects, their propagation, and the obscuration of critical defects due to cracks previously triggered. This model has already been used to simulate UHPC during edge-on impact tests [9,22]. In addition, a cohesion law was proposed and introduced in DFH damage model to account for the post-peak dynamic tensile response of concrete (DFHcoh model) [25]. The DFHcoh-KST model was successfully used to numerically simulate the penetration of ogive-nosed steel penetrator within plain concrete targets with a thickness of 300 mm or 800 mm [12]. In particular, this numerical work has highlighted the strong influence of free water content in concrete through its confined behaviour and tensile strength and the influence of friction at the target-projectile interface. It may be noted that discrete approaches may also be followed [23,24].

The parametric identification of the DFHcoh-KST model is not an easy task; the appropriate experimental data have to be chosen based on their particular loading conditions. This work has been already done for conventional concrete by considering quasi-oedometric compression tests (KST parameters) along with bending tests and spalling tests (DFHcoh parameters) in [12].

In this work, numerical simulations of a ballistic impact are performed using the coupled DFHcoh-KST model [25]. The model with cohesion strength has been considered to take into account for the softening behaviour provided by fibres in the damaged zone due to bridging phenomena that counter the opening of cracks. The mechanical behaviour of a UHPFRC called Ductal® [26], and the model parameters are identified under different loading conditions employing quasi-oedometric compression tests, bending tests and spalling tests. Tunnelling and erosion methods are used to overcome the enormous element distortions of the FE simulations. The tunnelling method consists in meshing a tunnel of small diameter compared to the projectile diameter along the expected projectile path. Consequently, the projectile enlarges the tunnel during the penetration process. The second method, known as the erosion method, consists in eliminating each finite-element reaching a certain criterion defined as the equivalent plastic strain reaching a maximum value. The influence of both methods is studied in the present paper. Moreover, the influence of the friction at the projectile-target interface is also discussed. The sensitivities to yield strength, material compaction, strain rate effect and tensile damage are pointed out to evaluate the real influence of the UHPFRC behaviour on its ballistic performance. Numerical predictions provided by the Finite-Element (FE) code Abaqus are compared to experimental results based on classical post-mortem observation and 3D X-ray Computed Tomography (X-ray CT) reconstruction.

Section snippets

Concrete main properties

A commercial UHPFRC called Ductal®, belonging to the family of Reactive Powder Concrete, has been used in this study. Ductal® is the first marketed UHPC, which was launched in the late 90s [26]. This material presents water to cement ratio of 0.21. In the concrete formulation, the maximum aggregate size is about 0.6 mm. Its composition includes fine sand, crushed grains of quartz, and silica fumes to reduce the porosity of the cementitious matrix (total water porosity ≈ 5-6 %). The steel fibres

Ballistic impact test

A ballistic impact test has been performed upon a 60 mm-thick Ductal® slab with a pointed bullet, reference FB5 (calibre 5.56 × 45 mm), of 4.0 g launched at an impact speed of 950 ±10 m/s. The projectile specifications (shape, morphology, mass, diameter, materials, etc.) are defined in the DIN EN 1522 European Standard [29]. It is composed of a hard steel penetrator and a soft lead core, both encapsulated in a full copper alloy casing. This bullet is 5.7 mm in diameter and 23 mm in length. The

DFHcoh-KST coupled model

Under high confining pressures, concrete materials usually adopt a “ductile” and “compactable” behaviour. In the present work, the KST (Krieg–Swenson–Taylor) model was used to describe the confined behaviour of UHPFRC. It includes an equation of state linking the volumetric strain εv to the hydrostatic pressure P which is a piecewise linear curve entered point by point:P(εv)={Kiεvifεvεv1Pi1εvεviϵvi1εvi+Piεvεvi1ϵviεvi1ifεvi1>εv>εviKf(εvεvn)+Pnifεvεvnwhere Ki and Kf are respectively

Numerical simulation of impact

Numerical simulations of the ballistic test were conducted with the finite element (FE) code Abaqus–Explicit. The DFHcoh-KST coupled model used for UHPFRC is implemented as a VUMAT user-defined subroutine.

The constitutive behaviour of the steel penetrator is considered as elastic-perfectly plastic, whereas the lead core is considered elastic (the lead was recovered almost non-deformed after the experiment). The jacket of the bullet was not included in the numerical model (if the copper casing

µC-tomography analysis

The target (60 × 60 × 95 mm3) was scanned using the X-ray CT scanner in 3SR Laboratory. In the device set-up, the source-detector distance is fixed to 767 mm. The X-ray source generates a polychromatic cone-beam that is detected by a flat panel detector with 1536 × 1920 pixels, each measuring 0.127 × 0.127 mm. Radiographs at several angles are needed to obtain a 3D image. To this end, the sample is placed on a rotation stage, allowing rotation around a vertical axis (Fig. 15). The X-ray source

Damage pattern analysis

The numerically predicted damage pattern is compared to the experimental result. Fig. 17 shows a comparison between numerical and experimental damage patterns on the two orthogonal cross-sections of the target at the end of the projectile penetration phenomena. A good correlation is obtained between the experimental test and the numerical damage pattern predicted in this study. Experimental and numerical crater dimensions due to scabbing and spalling phenomena on both front and rear faces of

Conclusions

In this work, quasi-static and dynamic mechanical tests were conducted on Ductal® concrete with and without fibres to identify the mechanical behaviour of UHPFRC respect to static and dynamic tensile loading and under static highly-confined compression. The parameters of DFHcoh-KST anisotropic-plasticity damage coupled model were calibrated based on quasi-oedometric compression tests, quasi-static bending tests, and dynamic spalling tests. 3D numerical simulations of the ballistic test were

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work has been performed in the framework of the Brittle's CODEX chair supported by the UGA (Univ. Grenoble Alpes) Foundation and sponsored by the LafargeHolcim company. This sponsor is gratefully acknowledged by the authors.

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