Accepted Manuscript Title: Development of an experimental set-up for dynamic force measurements during impact and perforation, coupling to numerical simulations Author: W.Z. Zhong, I.A. Mbarek, A. Rusinek, R. Bernier, T. Jankowiak, G. Sutter PII: DOI: Reference:
S0734-743X(16)30011-2 http://dx.doi.org/doi: 10.1016/j.ijimpeng.2016.01.006 IE 2638
To appear in:
International Journal of Impact Engineering
Received date: Revised date: Accepted date:
15-4-2015 5-11-2015 15-1-2016
Please cite this article as: W.Z. Zhong, I.A. Mbarek, A. Rusinek, R. Bernier, T. Jankowiak, G. Sutter, Development of an experimental set-up for dynamic force measurements during impact and perforation, coupling to numerical simulations, International Journal of Impact Engineering (2016), http://dx.doi.org/doi: 10.1016/j.ijimpeng.2016.01.006. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Development of an Experimental Set-up for Dynamic Force Measurements
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during Impact and Perforation, coupling to Numerical Simulations
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W.Z. Zhong1, I.A. Mbarek2, A. Rusinek2, R. Bernier2, T. Jankowiak3, G. Sutter4
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1 Route d’Ars Laquenexy, 57078 Metz, France
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Institute of Systems Engineering, China Academy of Engineering Physics, 621999, Mianyang, China
National Engineering School of Metz (ENIM), Laboratory of Mechanics, Biomechanics, Polymers and Structures,
Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznań, Poland
LEM3, UMR 7239, Lorraine University, Ile du Saulcy 57045 Metz Cedex 1, France
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Corresponding author : A. Rusinek
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E-mail:
[email protected]
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Telephone: +33 387346930
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Highlights A specific device has been developed to define more quantities during perforation tests. Actually thanks to the new set-up, it is possible to define:
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The initial impact velocity V0 The residual velocity VR The ballistic limit is reached VB The global resistance force history F(t) as well as the resistance force evolution as function of the initial impact velocity F(V0)
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The failure pattern depending on the projectile shape.
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Abstract: Quasi-static tension and dynamic compression experiments on S235JR mild steel were
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performed using a screw-driven machine and a split Hopkinson pressure bar (SHPB) device. A
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wide range of strain rates from 10-4 to 2500 s-1 has been covered during experiments. The
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Johnson-Cook constitutive relation was adopted to describe the material visco-plastic behaviour.
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Ballistic impact experiments on S235JR plates with conical-nose shaped projectile were carried
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out using pneumatic gas gun having different impact velocities varying from 49 to 181 m/s. A new
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experimental set-up allowing resistance force measurement during impact and perforation was
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developed. Different impact velocities and thicknesses were evaluated during ballistic experiments.
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All the projectiles are 12.8 mm in diameter and 28g in weight. The ballistic impact device is
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equipped with laser sensors for velocities measurements and piezoelectric sensors for dynamic
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force measurement. Based on numerical and experimental investigations, the ballistic properties
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and failure modes of the material have been studied. The finite element code ABAQUS/Explicit
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was used to simulate the perforation process but also to have a better understanding of the
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measurement. A good agreement between experiments and numerical results has been observed in
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terms of ballistic curves, failure patterns, resistance force as well as the energy balance.
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Keywords: ballistic impact, sheet steel, resistance force, dynamic failure, numerical simulation.
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1 Introduction
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Ballistic behaviour of thin metal plates is paid close attention in military and civil protection
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field recently [1,2,3]. The ballistic impact problems were mainly focused on military interest. The
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perforation and penetration of thin plate structures have become more interesting in transport and
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aerospace fields. For instance, the automobile manufacturing industry, the ship hull manufacturing,
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aviation and spacecraft designing [4,5,6].The ballistic properties are strongly related to the
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material behaviour under dynamic loading and to the interaction between the projectile and the
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thin steel target during perforation process. Thus, in order to improve ballistic curves prediction,
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many dynamic constitutive relations have been improved and modified by several researchers
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[7-13]. For instance, Johnson and Cook [7] proposed a dynamic constitutive relation based on a
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phenomenological approach. The model has been frequently used in impact and perforation
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problems analysis thanks to its simplicity, namely its five parameters to describe the
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thermo-viscoplastic behaviour of the material. Verleysen[8] investigated effect of strain rate on the
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forming behaviour of sheet metals and describe the materials’ stress-strain curves using
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Johnson-Cook model. Ericeand Gálvez [9] presented a coupled elastoplastic-damage constitutive
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model to simulate failure behaviour of inconel plates. Rusinek and Rodríguez-Martínez [10]
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provided two extensions of the Rusinek-Klepaczko constitutive relation in order to define the
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behaviour of Aluminium alloys at wide ranges of strain rate and temperature. Dey [11] and Børvik
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[12] studied the influence of a modified Johnson-Cook constitutive relation using numerical
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simulations of the perforation of steel plates. The thermoelastic-thermoviscoplastic constitutive
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models used in the simulation of the penetration and perforation process are discussed by Kane
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[13] and Voyiadjis [14].
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In ballistic impact experiments, the projectile nose shape and itsdiameter, the impact conditions ,
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the projectile velocity, the thickness of the target and the boundary conditions are very important
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parameters which are mainly taken into account to analyze the resistance of the target against
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impact and perforation as well as the fracture behaviour [15,16,17]. Chen and Li [18] studied the
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oblique perforation of thick metallic plates with rigid projectiles having different nose shapes.
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Kpenyigba [19] and Rusinek [20] studied the influence of the projectile nose shape (conical, blunt
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and hemispherical nose-shaped projectiles) and its diameter on the ballistic properties and the
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failure modes of thin steel targets. Many advanced optical measuring facilities and
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precise instruments are usually used to measure the initial and residual velocities of the projectile
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and to better analyze the target failure mechanisms [21,22,23]. Grytten and Fagerholt [20]
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developed a new optical system using structured light for full-field continuous measurements of
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the out-of-plane deformation during perforation experiments. To analyze the mechanical
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behaviour of tempered bainitic steel, microstructural and fractographical examinations were
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carried out on small samples taken from the perforated region by Atapek and Karagoz [21]. Some
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multi-layered plates were also considered to investigate about the resistance of the targets against
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perforation as well as the energy absorbed by the target during the perforation process. Dey and
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Teng [24] studied the resistance against ballistic perforation of double-layered steel plates
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impacted by blunt and ogival nose-shaped projectiles. Flores-Johnson and Saleh [25] investigated
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about the ballistic performance of monolithic, double-and triple-layered metallic plates. It was
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found that monolithic plates have a better ballistic performance than that of multi-layered plates.
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The finite element method with explicit time integration procedure is an effective technique to
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predict the ballistic response of a target impacted by a projectile [26,27]. It is an economic and
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convenient approach which is commonly used to well analyze the impact process and to improve
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the researches about perforation issues. Numerical simulations are also an effective supplement for
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theoretical and experimental investigations which were carried out to analyze the dynamic
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behavior of impacted structures [28,29,30,31]. Recently, finite element analysis has been used by
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many researchers to simulate perforation problems. Rodríguez-Martínez and Arias [32,33] carried
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out a numerical study on the perforation of thin steel plates impacted by projectiles having
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different nose shapes. The predictedballistic limit and the failure time were in agreement with
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experimental results. Swaddiwudhipong and Islamb [34] adopted coupled SPH-FEM to simulate
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the high velocity perforation of steel and Aluminum plates. Rosenberg and Dekel [35] simulated
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numerically the perforation of ductile plates by sharp-nosed rigid projectiles, and distinguished
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between dishing and hole enlargement processes which are the main perforation mechanisms for
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thin and thick plates, respectively. Deb and Raguraman [36] described the impact behavior of
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jacketed projectiles on steel armour plates and pointed that the proper choice of the contact
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algorithm, the element size as well as the strain rate-dependent material properties is very
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important to predict precisely the residual velocity of the projectile.
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Although more and more researches are focused on the ballistic impact field, several
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publications are discussing the high strength material penetration problems at high impact
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velocities. Less attention is paid to the measurement of the global force induced by the projectile
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on the target during impact and perforation. Several relatively low strength materials, such as low
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carbon steel and Aluminum alloys etc, are widely applied in automobiles manufacturing industry
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and in aeronautic industry. For instance, non-alloyed structural steel S235JRhas a low strength but
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a good ductility thanks to which, the S235JR is widely applied in engineering structures
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nowadays.
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This paper presents quasi-static and dynamic experimental analysis of the mechanical properties
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of the S235JR mild steel. The mechanical behavior of the target is described by the Johnson-Cook
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constitutive model. Ballistic impact experiments on S235JR plates subjected to perforation with a
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conical nose-shaped projectile are carried out using a pneumatic gas gun. The target thicknesses
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are 1.5 and 2.0 mm and the impact velocities are varying from 49 m/s to 181 m/s. The
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experimental protocol allows us to measure the initial and residual velocities as well as the
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resistance forces of the target. The energy absorbed by the S235JR plates at a wide range of
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impact velocities is discussed. Moreover, a model of a S235JR target with a conical nose-shaped
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projectile is established using the finite element code ABAQUS/Explicit and allow to simulate the
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perforation process. The predicted values in terms of residual velocities and resistanceforces are
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compared to experimental results and a good agreement is found between the numerical and the
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experimental investigations.
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2 S235JR steel mechanical properties
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2.1 Quasi-static tension experiment
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Quasi-static uniaxial tension tests of S235JR steel were performed using a conventional
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screw-driven machine. The dimensions of the flat dumbbell-shaped specimen are shown in Fig.
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1-a. The thickness is 1.5 mm with an active length of 40 mm. All tests were conducted at room
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temperature, 293 K, for a constant loading velocity.
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During the tests, an inclined fracture plane occurs along the thickness of the specimens and a
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necking zone is found along the oblique direction as Fig. 1-b. It shows that shear fracture and
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necking are the main failure modes for S235JR steel subjected to quasi-static tension. The load
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and deformation displacement are recorded during the tests for an imposed velocity. All true
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stress-strain curves are well consistent and the mean tension strain-stress curve, for 10-4 s-1 strain
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rate, is presented in Fig. 2. It shows that the average yield strength of the S235JR steel is close to
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252 MPa.
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2.2 Dynamic compression experiment
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The aforementioned tension tests characterize theS235JR mechanical behavior under
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quasi-static loading. In order to evaluate the strain rate influence on the material properties, split
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Hopkinson pressure bar (SHPB) experiments under compression loading are performed to
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evaluate S235JR steel dynamic properties. The experimental setup and the specimen dimensions
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are shown in Fig.3. The diameter of the bar is 18 mm and the length of the striker is 300 mm
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allowing to reach large deformation. The diameter and the thickness of the compression specimen
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are 8 mm and 3 mm, respectively. The specimen deformation after compression is shown in Fig.
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3-b. The cylinder specimen is compressed into a thinner cylinder with a larger diameter, without
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macroscopic fracture on the surfaces.
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Two strain rates of 1450 1/s and 2100 1/s are considered in the present SHPB experiments to
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determine the S235JR dynamic properties. For all considered cases, four experiments at least were
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performed to confirm the reproducibility of the tests. The compression and tension behavior of the
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material is assumed to be identical, and the Johnson-Cook model is used to describe the S235JR
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mechanical properties. Based on the recorded strain waves on the incident and the transmitted bars,
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the corresponding stress-strain curves for the S235JR steel are presented in Fig. 4. It can be
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concluded that the S235JR steel mechanical properties are strain rate dependent. The dynamic
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yield stresses are 550 MPa and 568 MPa at strain rates of 1450 1/s and 2100 1/s respectively,
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which are much greater than the quasi-static value 252MPa. So only a constitutive model
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including strain rate effect can effectively describe the mechanical behavior of S235JR steel sheets
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subjected to impact and perforation.
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3 Constitutive model description of S235JR
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3.1 John-Cook constitutive model
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The Johnson–Cook (JC) model is an empirical formula based on a phenomenological approach
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and which was proposed by Johnson and Cook in 1983 [7]. It is commonly used to describe the
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thermo-viscoplastic behavior of metallic materials. The influence of strain rate and temperature
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are taken into account in this model as shown, Eq.1.
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A B
n p
p 1 C ln 0
1
T T0 Tm T0
m
(1)
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where A is the yield stress, B is a constant of the material, n is the hardening coefficient, C is the
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strain rate sensitivity, m is the temperature coefficient, 0 is the reference strain rate and p is the
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plastic strain rate. T is the current temperature, T 0 is a reference temperature and T m is a
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reference melt temperature.
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3.2 Constitutive model parameters of S235JR
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Since this work is more focused on the analyze of the resistance force measurement under
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dynamic perforation using different experimental set-ups, a simplified Johnson-Cook constitutive
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model is used to describe the S235JR steel properties, without temperature sensitivity. The
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numerical part including the simplified constitutive relation allows to describe properly the
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experimental observations as the force increase and the ballistic curves. The numerical part
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including the simplified constitutive relation can effectively describe the same trends. Under
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isothermal conditions, the constants used to describe the material mechanical behaviour are taking
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into account hardening and strain rate sensitivity. According to the quasi-static and dynamic
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experimental results, four constants are used to describe the material mechanical behaviour of the
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S235JR steel.
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The quasi-static test strain rate is taken as the reference strain rate and then 0 is equal to 0.0001 1/s.
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The parameter A is the yield stress at a reference strain rate, and it is taken equal to 252 MPa. The
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hardening modulus parameter B is 520 MPa. The hardening parameter is 0.638 and the strain rate
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sensitivity parameter is 0.046. Experiments results have been compared to the analytical results
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for different strain rates. Fig.5 shows a good agreement between experiments and JC model for
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different strain rate loadings.
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4 Perforation experiment of S235JRplate with conical-nose projectile
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4.1 Experimental set up description
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The ballistic experiments were carried out using a pneumatic gas gun device. The experimental
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layout diagram and the overall view are shown in Fig.6-a and Fig.6-b respectively. The whole
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experimental device consists of a pneumatic gas gun, two laser measuring velocity sensors, the
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target, the target holder and the projectile catcher box. The projectile initial velocity V0 can be
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adjusted by changing the initial pneumatic gas pressure. The diameter of the gun barrel is 13 mm
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and roughly equal to the diameter of the projectile. During normal impact tests, no sabot is
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required to guide the projectile inside the barrel allowing a complete perforation of the plate only
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by the projectile.
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The device is instrumented with two velocity sensors: the first one is to measure the initial
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impact velocity V0, Fig. 6-c ,and the second one is used to measure the velocity of the projectile
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after perforation allowing to define the residual velocity Vr, Fig. 6-d. During the impact and
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perforation of S235JR targets, there was no plug ejection. Consequently, the residual velocity laser
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sensor measures only the accurate velocity of the projectile after perforation. Even if there was a
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plug ejection, the residual velocity sensor can define not only the plug velocity but also the
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residual velocity of the projectile. Knowing the projectile length, it is possible to distinguish
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between the velocity signals due to the projectile displacement from those due to the plug
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displacement. The residual velocity is mainly affected by the projectile initial impact velocity and
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its shape, the mechanical properties and the thickness of the target. The boundary conditions used
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during this work affect only the force measurements and not the residual velocity. In fact, the force
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measurements are linked to the target behavior as well as the set-up response but the residual
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velocity is strongly linked to the projectile itself and to the target behavior, coupled to the failure
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criteria. Consequently, the use of the three boundary conditions on the target will not affect the
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residual velocity measurements.
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For each sensor, the distance between two lasers is 5 cm. When the projectile crosses the first
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laser, a time counter is triggered-namely t1. Likewise, the second time counter t2 is triggered when
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the projectile reaches the second laser beam. The difference between the two time counters define
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the time interval Δt=t2-t1.Thanks to the time interval and the distance Δx between the two lasers,
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the initial impact velocity and the residual velocity may be defined. During the impact and
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perforation of S235JR targets, there was no plug ejection. Consequently, the residual velocity laser
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sensor measures only the accurate velocity of the projectile after perforation. Moreover, four
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piezoelectric sensors are fixed on the target fixation device in order to measure on time the
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resistance force, Fig. 6-e and Fig.7.
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The force sensors measure the resistance force induced by the projectile on the target during
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impact and perforation. Thus, the global instantaneous force can be estimated for each initial
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impact velocityV0. The four piezoelectric sensors are fixed between the support plate and the
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target holder. The 9011A Kistler sensors are used to measure uniaxial quasi-static and dynamic
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forces along the impact direction, shown in Fig.6-e. The natural frequency of each sensor is 65
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kHz. Every sensor is able to measure a wide range of resistance forces from 0 to 15kN with an
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acceptable force gap of +5kN. The four piezoelectric sensors can measure a maximum force
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between 60 and 80kN.
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The fixation device is designed to be rigid and resistant to bending effect during impact and
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perforation. It weighs about 40 Kg. The material used to machine this device is armor steel having
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a yield stress equal to 850 MPa. Using this original set-up, it is possible to measure an additional
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mechanical property, the force on time F(t). This quantity is mainly related to the material
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behavior and to the whole structure response, as it will be discussed in the next part.
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4.2 Projectile and target description
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The shape and the dimensions of the projectile used during perforation are shown in Fig. 8-a.A
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conical nose-shaped projectile requires less energy than a hemispherical one to perforate the target.
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In order to obtain a larger force sensitivity of the material tested on the set-up, a conical
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nose-shaped projectile is considered during perforation. In order to measure the impact forces with
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the new set-up, it is more appropriate to use a conical projectile since the 4 sensors can measure a
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maximum force value of 80 kN. The diameter of the projectile is 12.8 mm, the body length is 25
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mm and the half angle of the conical nose is 36°. The mass of the projectile is assumed constant
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and equal to 28 g in order to keep the same kinetic energy for a fixed initial impact velocity. The
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material used to machine the projectiles is a Maraging steel with a heat treatment to increase their
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hardness, until 640 HV, and to reach a yield stress of almost 2GPa. Thus, the projectile can be
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considered as rigid during impact and perforation testing.
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The dimensions of the target used during perforation experiments are shown in Fig. 8-b.The
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S235JR sheet steel plate is a square of 130 × 130 mm2. The active part is 100 × 100 mm2 with two
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different thicknesses, 1.5 mm and 2.0mm, to analyze the ballistic properties of S235JR plates
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using the new and original device developed for impact and perforation tests.
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4.3 Perforation experiments of S235JR plate
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Perforation experiments were performed using the conical-nose projectile for both target
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thickness1.5 mm and 2.0 mm, mentioned previously. A wide range of initial impact velocities was
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considered for a typical definition of the ballistic curves of the steel sheet targets, from 49 m/s to
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181 m/s. The failure mode of the target can be described using three damage phases: no
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perforation, critical perforation and complete perforation. Those three typical failure phases
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observed during experiments are shown in Fig. 9. The "no perforation" phase means that the
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projectile lacks the sufficient kinetic energy required to go through the target and it bounces off,
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Fig. 9-a. "Critical perforation" phase displays that the projectile has enough kinetic energy to
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perforate the target, but not enough to reach the complete perforation of the sheet steel, Fig.
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9-b.For this case, the projectile stayed in that position: totally stuck in the sheet steel plate which
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means that the initial impact velocity is very close to the ballistic limit of the target. The third
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phase "complete perforation" means that the projectile has an excess of kinetic energy: It can
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perforate easily the target and go through it with a certain residual velocity, Fig.9-c.
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A series of impact test experiments have been performed with S235JR steel plates with two
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thicknesses and at different initial impact velocities. The ballistic curves for the 1.5 and 2 mm
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steel targets are shown in Fig. 10. For the thicknesses 1.5 mm and 2.0 mm, the ballistic limits are
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approximately 117 m/s and 145 m/s, respectively. The ballistic curves can be fitted using the
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relation proposed by Recht et al. [37], shown in Eq. 2.
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(2)
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where VB is the ballistic limit and α is a fitting parameter which depends on the projectile shape
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[19].The fitting equation of the ballistic curves of 1.5 and 2.0 mm are obtained in the equations
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below. Based on Eq. 2, the fitting parameters of the ballistic curve of a 1.5 mm target are defined
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in Eq. 3.
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V r 1 .5 V 0
2 . 173
117
2 . 173
1 2 . 173
(3)
The fitting equation of the ballistic curve of a 2.0 mm target is as well mentioned as follow, Eq.
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4.
Vr2 V0
293
2
145
2
1 2
(4)
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The failure modes of each target are also shown in Fig. 10. The results show that using a conical
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projectile, a failure mode by petalling occurs inducing a radial necking due to piercing. When the
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projectile perforates the target, an average of four petals is formed and the plastic strain is
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localized at the ends of the petals. As discussed by Kpenyigba et al. [19], the number of petals
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formed after impact is strongly linked to the projectile nose shape. For this angle and for the tested
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range of impact velocities, there is no transition in the target failure mode. The bend angle of the
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petals’ root is over 70 degree which behaves as ductile.
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The energy dissipations in the target at different impact velocities can be computed using the
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initial impact and residual velocities. The relation between the projectile initial impact velocity
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and the target energy dissipation is shown in Fig. 11. For 1.5 and 2.0 mm targets, the mean values
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of the energy dissipation are calculated and are about 173.4 J and 290.2 J, respectively in the
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performed range of impact velocities. During the ballistic impact tests, the highest impact velocity
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performed with a 28g conical projectile is about181 m/s. As the target mechanical behavior is
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strain rate dependent, higher impact velocities can induce a variation in the energy dissipation of
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the target during perforation process. Knowing the impact velocity V0 and the residual velocity VR,
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the experimental energy absorbed by the plate during perforation, Wexperiments, is calculated using,
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Eq. 5:
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(5) Where
is the mass of the projectile.
The results in terms of the energy absorbed by the plate for two thicknesses 1.5 and 2.0 mm are
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reported in Fig. 11. It shows that the initial impact velocity does not affect the target energy
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dissipation in the performed impact velocity range. The target failure mode is the same “complete
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perforation with petalling “and the energy dissipation is quasi-constant for both 1.5 and 2 mm
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targets thicknesses, in the performed impact velocities. The energy dissipation in the S235JR steel
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sheets is strongly linked to the thickness of the target. As shown in Fig.11, the average energy
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dissipation ratio W1.5mm/ W2mm is equal to 59.7% which is far from 75% the target thicknesses
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ratio. This shows that no relation exists between the thickness and the energy absorption of the
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target during impact and perforation.
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During the perforation process of steel sheet targets, one part of the kinetic energy of the
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projectile is absorbed by the global target deformation, elastic and plastic deformation, and by
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crack propagation. The global energy absorbed by the target during perforation is considered as
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the sum of the five following energies as proposed by Nazeer et al. [16], Eq. 6.
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(6)
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where Mp is the mass of the projectile, V0 is the initial impact velocity, We is the elastic bending
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energy of the plate, Wfp is the plastic bending energy , Wep is the plastic stretching energy of the
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plate, Wfr is the bending energy of the petals and Wr is the crack propagation energy. The
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temperature effects are neglected during thin targets perforation process. During ballistic impact,
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the energy lost by friction can be assumed as minor comparing to the total energy balance [19].
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The full expressions of the energies mentioned in Eq.6are detailed in [16].
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Based on this description not mentioned in this paper, it has been found that the total energy
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absorbed by the target increases with the number of petals and cracks formed in the target during
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perforation. It is noticed that the elastic bending energy of the target is very low compared to the
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other quantities: it represents less than 0.05 % of the total energy absorbed by the target during
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ballistic impact. Thus, the energy lost by elastic deformation can be considered as minor in the
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total energy balance for both 1.5 and 2.0mm targets. The major part in the energy balance and
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which represents more than 70% of the total absorbed energy is converted into plastic stretching
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of the target.
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The energy balance and the ballistic curves mentioned previously are calculated thanks to the
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initial impact and residual velocities. The main goal of this study is focused on the development of
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the experimental set-up used to measure the resistance force of the target during impact and
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perforation. The resistance forces measured by the piezoelectric sensors at different initial impact
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velocities and with several boundary conditions will be discussed in the following section.
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4.4 Influence of boundary conditions on the force measurement
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Actually, the force measured by the sensors is including the contact force between the target and
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the projectile and the force due to the inertial effects. The force due to the inertial effects is always
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the same with one imposed set-up, only the contact force changes from one material to another. In
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fact, the target behavior does not change from one boundary condition to another. Only the whole
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structure response changes when the boundary conditions are changed. In order to investigate the
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effects of boundary conditions on the resistance force measurement during ballistic impact
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experiments, three different configurations have been adopted to estimate the force are shown in
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Fig.12.The different set-ups bring varied boundary conditions which affect the resistance force
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measurements. The boundary conditions with rubber slides and glued specimen are not commonly
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used in ballistic applications, they were only used to show the influence on the force
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measurements。Fig.12-a shows that the target is totally embedded with a 5.3 Kg steel frame. In the
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Fig.12-b, the plate is not directly embedded with the steel frame. Instead, it is fixed between the
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target holder and the rubber slides. Several rubber layers are used with a thickness varying from 6
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to 15 mm. As for the third configuration shown in Fig.12-c, the target is fixed on the target holder
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using only a double face adhesive tape. In order to investigate the influence of the target-fixing
364
method on the dynamic response of the force measuring sensors, the same conical projectile is
365
used to test a wide range of impact velocity ranging from 49 to 181 m/s.
366
Fig. 13 shows the resistance force evolution as function of the time for two different impact
367
velocities - lower and higher than the ballistic limit - and using three different set-ups, Fig. 12. It is
368
noticed that all the curves has a polynomial trend which is in agreement with the results stated by
369
Jankowiak et al.[3] based on a numerical work.
370 371
The global resistance force as function of the initial impact velocity and the boundary
372
conditions are shown in Fig. 14. Those points stand for the maximum value of the measured forces
373
for each impact velocity. For the three considered set ups, three experiments at least have been
374
performed to confirm the reproducibility and the repeatability of the tests. An average of the three
375
tests in terms of resistance force is reported in Fig.14. Using the configurations previously
376
mentioned, it is observed that layering rubber slides decreases the global resistance force against
377
perforation. Thus, when the equivalent thickness of the layered rubber slides increases, the
378
measured resistance force decreases. For example using12 mm rubber slides, the resistance force
379
decreases of 50% compared to the measured force, case a) steel frame set-up.This means that by
Page 17 of 38
18
380
layering the rubber slides between the 5.3 kg steel frame and the target, the frame is clearly
381
dumped and it is assumed that the inertial effects are reduced thanks to the rubber. As for the
382
double faced adhesive tape set up, the resistance forces are medium compared to the results of all
383
the other set up. Its value is smaller than the force measured with the steel frame target-fixing set
384
up shown in Fig. 13-a, and higher than that measured using the rubber slides, Fig. 13-b. When the
385
target is fixed with the adhesive tape, the inertial effects due to the vibration of the fixing device
386
mass are reduced.
387 388
In order to well define the constitutive relation parameters, several numerical simulations,
389
taking into account the material behavior and the failure criteria level, have been performed.
390
Based on the previous experimental results, it is observed that the force includes not only the
391
resistance force of the target but also the structural answer of the set-up. However, it is possible to
392
catch how the inertial behavior is acting. If a softer material is used, the force will decrease and if
393
the ballistic curve is lower, the force decrease will be faster. In addition to have a better
394
understanding of the set-up, a numerical model has been built to estimate, the residual velocity
395
and the impact force.
396
5 Numerical simulation of S235JR plate perforation process
397
Thanks to the numerical study, the ballistic curves and the resistance force curves can be
398
predicted. Eventually, the numerical results will be compared to the experiments in order to
399
validate the models, failure criteria and constitutive relation, used in the impact and perforation
400
simulations.
401
5.1 Numerical model description
Page 18 of 38
19
402
A simplified3D numerical model used to simulate the perforation process of S235JRsheet steel
403
plate with conical-nose projectile using finite element code ABAQUS/Explicit, is shown in
404
Fig.16.Four cylinders placed in the target distal face stand for the four piezoelectric sensors and
405
are used to record the history of the four resistance forces,as illustrated in Fig.16-b. The cylinders
406
are5 mm length and 5 mm in diameter. The global force history is the sum of the four elementary
407
resistance forces measured by every sensor.The whole numerical model is built with over 360000
408
nodes and 320000 hexahedral C3D8R finite elements. The central zone of the target is built with
409
fine-meshed elements and an average size of each element is equal to 0.18 mm, Fig.15-c. This
410
mesh allows to avoid the effect of mesh dependency of the results. The S235JR platehas an active
411
part of 100×100 mm² as during the experiments. The specimen is fixed along the perimeter of the
412
target holder and embedded with the steel frame.
413
To define the contact between the projectile and the plate, a penalty formulation with contact
414
pair is assumed. Moreover, a contact restriction is defined to keep the interaction between the
415
outer surface of the projectile and the interior/exterior nodes of the plate during the simulation of
416
the perforation process, mainly when failure takes place. Based on the numerical results, the
417
residual velocity of the projectile, the resistance forces and the target failure mode are analyzed
418
and compared to the experiments.
419 420
A power lawhardening model σ=Kεpn has been used to describe the mechanical behavior of the
421
projectile, with K=2250 MPa and n=0.0871. The Johnson-Cook constitutive relation is defined to
422
describe the visco-plastic behavior of the target under isothermal conditions.
423
To have a complete validation of the numerical model, the resistance force curves and the
Page 19 of 38
20
424
ballistic curves are reported in the following section and compared to the experimental results
425
obtained with the “Steel frame without rubber” set-up, Fig. 12-a.
426 427
5.2 Numerical results of the S235JR plate
428
A wide range of impact velocity ranging from 49 m/s to 181 m/s has been tested during the
429
numerical simulations. Basically, the accurate value of failure strain used to simulate the
430
perforation process of thin mild steel sheets impacted by conical projectiles is about 1.2 [18].Thus,
431
in order to analyse the influence of the failure strain level on the numerical results, all simulations
432
has been run with different failure criteria levels. The resistance force of the target against
433
perforation at different impact velocities is shown in Fig.16. It shows that for initial impact
434
velocity lower than the ballistic limit, the resistance force value is the highest and it reaches 43kN
435
for 101 m/s. It is noticed that the shape of the resistance force as function of the time for 72 m/s
436
and 101 m/s is different from that obtained with initial impact velocities higher than the ballistic
437
limit, 150 and 181 m/s. As shown in Fig.16, the projectile impacts the target and bounces off for
438
72 and 101 m/s. When the projectile perforates completely the target with a non-null residual
439
velocity the total resistance force decreases abruptly and the curve has a different shape, in the
440
“complete perforation” case. This is due to the perforation process after the ballistic limit mainly
441
when the failure of the steel sheet takes places.
442 443 444
By analyzing the results after impact or perforation, it is found that the failure modes observed
445
experimentally are in agreement with the numerical results. As shown in Fig.17, two failure modes
Page 20 of 38
21
446
are observed: piercing of the target for an impact velocity of 50 m/s and a main failure mode by
447
petalling inducing radial necking for impact velocities exceeding 70 m/s. According to
448
experiments, the average number of primary petals is four as discussed in details in [19].
449 450
In this present paper, three set-ups were studied during experiments. It is clear that the boundary
451
conditions of the target influence the resistance force measurements only and not the residual
452
velocities measurements. The global resistance forces of the target are measured with the same
453
impact velocities used during experiments. Fig. 18 shows a comparison between experiments and
454
numerical results in terms of global resistance force. For 1.5 mm target thickness, it is observed
455
that the global force increases with impact velocity for the "no perforation" cases, and decreases
456
gradually when the initial impact velocity is higher than the ballistic limit, as shown in Fig. 18.In
457
other terms, for the performed impact velocities, the force increases continually until the impact
458
velocity reaches the critical value for which there is a transition in the failure mode from simple
459
piercing to complete petalling. For this critical impact velocity 101 m/s for 1.5 mm thickness
460
targets, the global effort is the maximum for all the three experiment set-up as well as the
461
numerical results. This is acceptable because this velocity matches the maximal impact velocity
462
that did not give a full perforation so the projectile tries vainly to exceed the target and this
463
explains the fact that the kinetic energy of the projectile is totally absorbed by the target. When the
464
impact velocity matches the ballistic limit, the global effort starts to decrease continually. It is
465
visible that when the ballistic limit is reached a failure mode by complete petalling occurs and the
466
projectile exceeds easily the target. So the target does not absorb the total kinetic energy of the
467
projectile but only a part of it and the remaining part is the residual kinetic energy of the projectile
Page 21 of 38
22
468
and this explains the decrease of the measured force value. Moreover, for each impact
469
velocity-force curve, two trends can be distinguished, for V0≤ 101 m/s and When V0 exceeds 101
470
m/s.
471 472 473
Thus, based on the maximum resistance force curve as function of the initial impact velocity, it is possible to estimate if the initial impact velocity is lower or higher than the ballistic limit.
474
It is noticed that the failure strain value used to define the failure criteria during ballistic impact
475
simulations has an influence on the obtained results in terms of resistance force. It is clear that the
476
use of adequate failure criteria which takes into account the effects of hardening and strain rate
477
sensitivity and thermal softening gives more accurate resistance force measurements.
478
Using the same initial impact velocities as experiments, the numerical results are discussed and
479
compared to the experimental perforation results in terms of ballistic curves. Fig.19 shows both
480
experimental and numerical ballistic curves for targets thickness 1.5 mm. The comparison in terms
481
of ballistic limit shows that the difference between experimental and numerical results, with 1.3
482
and 1.5 failure strain levels. Subsequently the simulation on 2.0 mm target gains the similar results.
483
A good agreement between the two approaches is observed. Based on the energy dissipation
484
during perforation process mentioned previously in Fig.11 and the numerical simulation results, it
485
can be concluded that energy dissipation is mainly dependent on the target thickness and not on
486
the initial impact velocity.
487
To conclude, the choice of thermo-viscoplastic failure criteria may give more accurate results in
488
terms of resistance forces. In this paper, the dynamic response of the target has been studied only
489
under isothermal conditions. The thermal softening effect on the force measurements and the
Page 22 of 38
23
490
ballistic curves can be studied in the future.
491 492 493
6 Conclusions
494
In the present work, the mechanical behaviour of S235JR steel was examined under dynamic
495
and quasi-static loadings. A simplified Johnson-Cook constitutive model of the material is given
496
by quasi-static tension and dynamic compression experiments under isothermal conditions. The
497
mechanical behaviour of the S235JRplate subjected to the impact of a conical-nose projectile is
498
analyzed using ballistic impact experiments and numerical investigations. The perforation tests
499
were performed at a wide range of impact velocities, and with two target thicknesses 1.5 and 2.0
500
mm. The simplified Johnson-Cook constitutive relation has been used to describe the S235JR steel
501
mechanical behaviour in the impact and perforation simulations.
502
Based on the full study conducted by experiments and numerical simulations, the following
503
conclusions can be drawn:
504
The mechanical properties of the S235JR steel are strain-rate dependent. The simplified
505
Johnson-Cook constitutive relation used under isothermal conditions can effectively describe
506
the material mechanical behavior under high strain rate loading.
507
Ballistic curves of 1.5 and 2 mm targets and the energy absorbed by the plates show that the
508
initial impact velocity of the projectile does not affect the total energy absorbed by the target
509
during the perforation process.
510 511
The resistance force level is strongly linked to the boundary conditions of the target itself, to the whole structure response and to the material used for the plate.
Page 23 of 38
24
512
513 514
The resistance force has a maximum value for initial impact velocities which are close to the ballistic limit. This was observed in both experimental and numerical analyses.
Based on experiments and simulations, it is observed that the key point to define properly all
515
the process of perforation is not only the constitutive relation description but also the failure
516
model and the damage description used in FE codes. In this experimental study coupled to
517
numerical simulations, it is observed that using as failure description a critical failure strain
518
level is not enough to cover all measured quantities.
519
The next step consists then on choosing failure criteria which allows to find a good agreement
520
between numerical and experimental investigations in terms of ballistic curves and failure
521
patterns and resistance force evolution, all together.
522
The other problem which will be future analyzed is the impact force of the projectile and
523
which cannot be measured directly using presented methodology in laboratory tests. It can be
524
measured in simulations based on the deceleration and the mass of the projectile. The impact
525
force can be estimated also using the initial and residual velocities and failure time which was
526
proposed by Jankowiak et al.[3]. This methodology can be extended also for laboratory test
527
using High Speed Camera with precise description of the failure time.
528
The set-up developed to measure the dynamic force using experiments will allow us to define
529
the boundary conditions effect on the structural answer including the material behaviour and the
530
set-up used to fix the plate. However, the material behaviour effect may be analyzed by
531
comparing different materials response. The test allows to validate the used constitutive relation
532
mainly by comparing the force on time measured during experiments and that obtained with
533
numerical simulations.
Page 24 of 38
25
534 535
Acknowledgement
536
The authors gratefully acknowledge the funding given by Industeel of Arcelor Mittal in France
537
– The Creusot, the National Natural Science Foundation of China under the contract No.11302211,
538
11390361, 11472257. This work is supported by the National Centre for Research and
539
Development UOD-DEM-1-203/001.
540 541 40mm 25mm
40mm
542
25mm
15mm
R=50mm 160mm
R=50mm
40mm
543 544
545 546
547 548
Page 25 of 38
26
500
True stress /MPa
400 300 200
Sample-1 Sample-2 Sample-3 average curve
100 0 0.00
0.05
0.10
0.15
0.20
0.25
True strain /(-)
549 550 551
Compression
rubber
incident bar specimen transmitted bar striker
Φ8mm×3mm
Flat
Initial state
552 553
(a) SHPB device.
Final state
(b) Specimen typical deformation.
554 555
900
750
750
600
600
450
Dynamic compression experiment Average strain rate: 1450 s Sample-1 Sample-2 Sample-3 Average curve
300 150 0 0.00
556 557 558
Ture stress /MPa
Ture stress /MPa
900
0.03
0.06
0.09
-1
450
Dynamic compression experiment Average strain rate: 2100 s Sample-1 Sample-2 Sample-3 Average curve
300 150
0.12
Ture strain /(-)
(a) strain rate 1450 s-1
0.15
0 0.00
0.05
0.10
-1
0.15
0.20
Ture strain /(-)
(b) strain rate 2100 s-1
Fig.4 Dynamic compression stress-strain curves at different loading rates.
Page 26 of 38
27
559
1000 Quasi-static compression & Johnson-cook model -1
JC (0.0001 s )
Quasi-static experiment
True stress, (MPa)
800
Dynamic compression & Johnson-cook model -1
JC (1450 s )
-1
JC (2100 s )
Dynamic experiment (1450 s ) Dynamic experiment (2100 s )
-1 -1
600 400 200 0 0.00
0.03
0.06
0.09
0.12
0.15
0.18
True strain, (-)
560 561 562
Force sensor Target
Pneumatic gas gun Projectile
V0
Target holder
Initial impact velocity, V0
Force sensor
Catcher VR
Residual velocity, VR
563 564
(a) Measurement layout diagram of the target perforation process.
Target holder
Gun barrel Manometer Pneumatic gas gun
Target holder Target
V0 measurement
565 566
(b) Pneumatic gas set-up
(c) Initial velocity sensor measurement, V0
Page 27 of 38
28
567 568
(d) Residual velocity measurement, Vr
(e) Force sensors.
569 570
571 572 573 36°
Active part Embedded part Projectile
130mm
Target dimensions 130mm×130mm×1.5/2.0mm Active part dimensions 100mm×100mm×1.5/2.0mm
25mm
574
12.8mm
575
(a) Projectile.
100mm
(b) Target.
Page 28 of 38
29
576 577
578 579
V0=88 m/s (a) No perforation.
VB=117 m/s (b) Critical perforation.
V0=150 m/s (c) Complete perforation.
580 581
582 583 584
Page 29 of 38
30
585 586 587 588 Sheet steel
Sensor 1, 2
Sheet steel
Projectile
Projectile
Steel frame Mass: 5300g
Steel frame Mass: 5300g
Slides of rubber
Sensor 3, 4
Sensor 1, 2
Sensor 3, 4
589 590
(a) Target fixed with steel frame
(b) Target fixed with rubber
Sensor 1, 2
Projectile
Steel sheet (Glued by double faced adhesive tape)
Sensor 3, 4
591 592 593
(c) Target fixed with double faced adhesive tape
Page 30 of 38
31
594 595 50 S t e e l f r a m e ,1 0 1 m / s S t e e l f r a m e ,1 5 0 m / s
R e s is ta n c e fo r c e , F (k N )
40
30 S235JR 1 .5 m m th ic k n e s s 1 2 .8 m m -2 8 g p r o je c t il e 20
S te e l fra m e
10
0 0
0 .0 0 0 1
0 .0 0 0 2
0 .0 0 0 3
0 .0 0 0 4
0 .0 0 0 5
T im e , (s )
596 597
(a) Steel frame set-up 35 6 m m R u b b e r , 1 0 1 m /s 6 m m R u b b e r , 1 5 0 m /s
R e s is ta n c e fo rc e , F (k N )
30
25
20
15 S235JR 1 .5 m m th ic k n e s s 10
1 2 .8 m m -2 8 g p r o je c t il e 6 m m R u b b e r s l id e s
5
0 0
598 599
0 .0 0 0 1
0 .0 0 0 2
0 .0 0 0 3
0 .0 0 0 4
0 .0 0 0 5
T im e , (s )
(b) Rubber slides set-up
Page 31 of 38
32
40 G l u e d s p e c im e n , 1 0 1 m / s
35
G l u e d s p e c im e n , 1 5 0 m / s
R e s is ta n c e fo r c e , F (k N )
30 S235JR 25
1 .5 m m th ic k n e s s 1 2 .8 m m -2 8 g p r o je c t il e G l u e d s p e c im e n
20
15
10
5
0 0
0 .0 0 0 1
0 .0 0 0 2
0 .0 0 0 3
0 .0 0 0 4
0 .0 0 0 5
0 .0 0 0 6
T im e , (s )
600 601
(c) Glued specimen set-up
602 603
50 Petalling
Maximum resistance force, F (kN)
45 No rubber
Complete perforation
40 35
Glued specimen
30
6 mm rubber
25 20 12 mm rubber
15
15 mm rubber
10 5 0 0
604
20
40
60
80
100
120
140
160
180
Initial impact velocity, V0 (m/s)
605 606
Page 32 of 38
33
Sensor2 Sensor 1 Target Projectile Target holder
Sensor3
Sensor4
607 608
609
(a) Impact face
(b) Distal face
(c) Target mesh
Fig. 15 Numerical model used during simulations and mesh density distribution of the plate.
610
50000 Material : Mild steel S235
45000 40000
Resistane force, F (N)
101 m/s
Thickness : 1.5 mm
Failure strain : 1.5
35000
123 m/s
72 m/s
30000 25000 150 m/s
20000 15000 10000 5000
50 m/s
181 m/s
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Loading time, t (ms)
611 612
Fig.16 Resistance force curve at different impact velocity, target thickness 1.5mm
613
614
a)
b)
c)
d)
e)
615
Fig. 17 Experimental failure observed during experiments for different initial impact velocities;
616
a- 50 m/s, b- 72 m/s, c- 101 m/s, d- 123 m/s, e- 150 m/s, f- 181 m/s
f)
617
Page 33 of 38
34
45 Experiments
40
Maximum resistane force, F (kN)
Average value
35 30
Numerical results failure strain : 1.5
25 20 15
Numerical results
10
failure strain : 1.3
5
Material : Mild steel S235 Tickness : 1.5 mm
0 0
20
40
60
80
100
120
140
160
180
200
Initial impact velocity, V0 (m/s)
618 619
Fig.18 Total force comparison between experimental and numerical results
620
for two different failure strain level
621
200 Material : Mild steel S235
180
Numerical results
Thickness : 1.5 mm
Residual velocity, VR (m/s)
160
Failure strain : 1.3
140 120 100 80 60 40
V0
=
VR
Numerical results Failure strain : 1.5
20 0 0
40
60
80
100
120
140
160
180
200
Initial impact velocity, Vo (m/s)
622 623
20
Fig. 19 Residual velocity comparison between experiments and numerical simulation
624 625
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