Influence of projectile shape on dynamic behavior of steel sheet subjected to impact and perforation

Authors thank Ministry of Science and Higher Education of Poland for financial support under Grants: R00 0097 12. Authors thank also M. Tavian technician in electronics from ENIM for his contribution on the development of the residual velocity measurement sensors.The paper describes a work focused on the process of perforation of steel sheet.Experimental,analytical and numerical investigations have been carried out to analyze in details the perforation process.Based on these approaches,the ballistic properties of the material and the failure modes depending on the projectile nose shape(conical,blunt or hemispherical) have been studied.Different failure modes have been observed,including petaling, plug ejection and circumference necking.The special study about the number of petals has been done for different nose angles using conical shape projectiles.The complete energy balance is also reported and the absorbed energy by the steel sheet has been obtained by measuring initial and residual projectile velocities.A wide range of impact velocities from 35to180m/s has been covered during the tests.All the projectiles are 13mm in diameter and the plates are1mm thick.Moreover,the mass ratio(projectile mass/steel sheet mass) and the ratio between the span of the steel sheet and the diameter of the projectile are constant, equal to 0.38 and 3.85, respectively

Finite element simulation of steel ring fragmentation under radial expansion

24 pages, 25 figures.This paper presents a numerical analysis of the expansion of a mild steel ring with of 50 mm diameter, 1 mm thickness and a cross section of 1 mm2. A hardening relation which takes into account strain, strain rate and temperature is proposed to define precisely the thermoviscoplastic behaviour of the material considered in the study. As a second step, an algorithm to integrate the thermoviscoplastic constitutive equations, including the hardening law, is implemented in the commercial finite element code ABAQUS/Explicit via a user subroutine. Finally, this tool is used to simulate the problem of a ring expanding radially in a broad range of strain rates, covering both low and high initial velocities (from 1 to 370 m/s). The aim is to analyse the effect of loading velocity on the number of fragments resulting from the multiple failure of the ring and also the influence of the hardening behaviour of the material on the number of fragments and on the failure mode of the ring, considering different values of the plastic strain hardening exponent n0. A simple failure criterion was used, based on a critical value of the equivalent strain which depends on the hardening exponent. The numerical predictions, in perfect agreement with the experimental observations, are compared with several analytical or numerical models used to solve the same problem in other materials such as aluminium, steel or copper.Publicad

Constitutive Models for Dynamic Strain Aging in Metals: Strain Rate and Temperature Dependences on the Flow Stress

A new constitutive model for Q235B structural steel is proposed, incorporating the effect of dynamic strain aging. Dynamic strain aging hugely affects the microstructural behavior of metallic compounds, in turn leading to significant alterations in their macroscopic mechanical response. Therefore, a constitutive model must incorporate the effect of dynamic strain aging to accurately predict thermo-mechanical deformation processes. The proposed model assumes the overall response of the material as a combination of three contributions: athermal, thermally activated, and dynamic strain aging stress components. The dynamic strain aging is approached by two alternative mathematical expressions: (i) model I: rate-independent model; (ii) model II: rate-dependent model. The proposed model is finally used to study the mechanical response of Q235B steel for a wide range of loading conditions, from quasi-static loading ( ε˙=0.001 s−1 and ε˙=0.02 s−1 ) to dynamic loading ( ε˙=800 s−1 and ε˙=7000 s−1 ), and across a broad range of temperatures ( 93 K−1173 K ). The results from this work highlight the importance of considering strain-rate dependences (model II) to provide reliable predictions under dynamic loading scenarios. In this regard, rate-independent approaches (model I) are rather limited to quasi-static loading

Analysis of inertia and scale effects on dynamic neck formation during tension of sheet steel

14 pages, 17 figures.It is well known that a specimen for impact testing must be optimized in terms of its dimensions. The main reason is to reduce strain gradients due to the effects of elastic–plastic wave propagation. On the other hand, when a split Hopkinson bar in tension is applied, the net displacement of the specimen ends is very limited, usually from 2.0 to 3.0 mm. Thus, to reach a maximum strain of 0.5 the specimen length must be reduced in dimensions from 4.0 to 6.0 mm. Consequently, small diameters or lateral dimensions and lengths must be applied to assure one-dimensional deformation. Such small lengths substantially perturb the determination of real material behavior. So the main motivation of this study was to perform a systematic analysis, numerical and analytical, to find differences in the behavior of short and long specimens loaded in impact tension. The finite element code ABAQUS/Explicit has been used to simulate several specimen lengths from 10 to 40 mm submitted to impact velocities ranging from 10 to 100 m/s.Publicad

Numerical simulations of impact behaviour of thin steel plates subjected to cylindrical, conical and hemispherical non-deformable projectiles

In this paper, a numerical study of normal perforation of thin steel plates impacted by different projectile shapes is reported. The numerical simulations of this problem have been performed using a finite element code, ABAQUS-Explicit with a fixed and an adaptive mesh for the plate. To define the thermoviscoplastic behaviour of the material constituting the plate, the Johnson-Cook model has been used. This homogeneous behaviour has been coupled with the Johnson-Cook fracture criterion to predict completely the perforation process. Three kinds of projectile shape (blunt, conical and hemispherical) have been simulated with a large range of impact velocities from 190 to 600 m/s. The analysis considers the influence of adiabatic shear bands, plastic work and the gradient of temperature generated in the plate. The numerical results predict correctly the behaviour projectile-plate in agreement with experimental data published by other authors.Publicad

A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper

In this paper a physical-based constitutive relation for defining the thermo-viscoplastic behaviour of FCC metals with dependence on strain on thermal activation processes is presented. The model, based on previous considerations reported by Rusinek and Klepaczko [Rusinek A, Klepaczko JR. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plasticity 2001;17:87-115], is founded on physical aspects of the material behaviour. The proposed constitutive relation is applied to define the behaviour of oxygen-free high conductivity (OFHC) copper using the experimental data reported in Nemat-Nasser and Li [Nemat-Nasser S, Li Y. Flow stress of FCC polycrystals with application to OFHC copper. Acta Mater 1998;46:565-77]. The description of the material behaviour provided by the model gets satisfactory agreement with the experiments. The analytical predictions of this constitutive description are compared with those obtained from the models due to Voyiadjis and Almasri [Voyiadjis GZ, Almasri AH. A physically based constitutive model for fcc metals with applications to dynamic hardness. Mech Mater 2008;40:549-63], and Nemat-Nasser and Li. This comparison reveals that the original formulation proposed in this paper is a suitable alternative to other physically based relations for modeling OFHC copper.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (ProjectCCG08UC3M/MAT4464) and to the Ministerio de Ciencia e Innovación de España (ProjectDPI/200806408)Publicad

Thermo-viscoplastic behaviour of 2024-T3 aluminium sheets subjected to low velocity perforation at different temperatures

This paper deals with the mechanical behaviour of the aluminium alloy 2024-T3. This alloy has particular relevance since it is widely used in the aeronautical industry for building aircraft structures. The deformation behaviour of this material has been characterised in tension under wide ranges of strain rate and temperature. Among the aluminium alloys, the AA 2024-T3 highlights due to its high flow stress and strain hardening. Moreover, the material temperature sensitivity has been found dependent on plastic strain. The Modified Rusinek-Klepaczko constitutive description [Rusinek A, Rodriguez-Martinez JA, Arias A. A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper. Int. J. Mech. Sci. 52 (2010) 120-135], which takes into account such dependence of the temperature sensitivity on plastic strain, has been applied for modelling the thermo-viscoplastic response of the material. Satisfactory agreement between experiments and analytical predictions provided by the Modified Rusinek-Klepaczko model has been found. In order to study the material behaviour under impact loading, low velocity perforation tests on AA 2024-T3 sheets have been performed at different initial temperatures using a drop weight tower. Plastic instabilities formation and progression are identified as the cause behind the target collapse for all the impact tests conducted. The results from these perforation tests are compared with those reported in [Rodriguez-Martinez JA, Pesci R, Rusinek A, Arias A, Zaera R, Pedroche DA. Thermo-mechanical behaviour of TRIP 1000 steel sheets subjected to low velocity perforation by conical projectiles at different temperatures. Int. J. Solids Struct. 47 (2010) 1268-1284.] for TRIP 1000 steel sheets. The comparison reveals that the amount of specific energy absorbed by the aluminium targets is much lower than that corresponding to the steel targets. The role played by inertia on delaying plastic instabilities formation is determined as potential responsible for such behaviour.Publicad

Effect of plastic deformation and boundary conditions combined with elastic wave propagation on the collapse site of a crash box

21 pages, 22 figures.Several papers have been published recently on the crashworthiness studies. The main task was to predict the energy absorption Wp and average collapse force overbar-F in time of sheet steel structures. The main objective of this contribution is to design a component that allows absorbing and dissipating a high energy Wp allowing improvements of the survivability of passengers in vehicles. However, the range of applications is larger since it includes all civil and military applications related to safety of components, or more generally of construction elements being loaded by impacts or explosions. In the present 3D case, the aim of this numerical study on dynamic loading in adiabatic conditions of deformation is to analyze the effect of elastic wave propagation combined with plastic behavior on the collapse site of a rectangular tubular structure made of steel sheet. To demonstrate the strong coupling between the effects of strain-rate sensitivity, accounted for in the constitutive relation that is used in numerical simulations, with the process of elastic wave reflection on the boundary conditions, a series of numerical simulation was performed. It is shown in this numerical study that the strain-rate sensitivity influences the position of the first collapse site. Moreover, the first collapse initiation of a structure defines the level of power absorption. Since the process of folding may be combined with bending of the structure (in particular when a local buckling appears close to the opposite side of impact), in this non-axial case the energy absorption Wp decreases and the effectiveness of the structure to the energy absorption is insufficient.The researchers of the University Carlos III of Madrid are indebted to the Spanish Ministry of Education (project DPI2005-06769), and to the Region of Madrid (project CCG06-UC3M/DPI-0796) for the financial support that allowed to perform a part of the numerical simulations.Publicad

A constitutive model for analyzing martensite formation in austenitic steels deforming at high strain rates

This study presents a constitutive model for steels exhibiting SIMT, based on previous seminal works, and the corresponding methodology to estimate their parameters. The model includes temperature effects in the phase transformation kinetics, and in the softening of each solid phase through the use of a homogenization technique. The model was validated with experimental results of dynamic tensile tests on AISI 304 sheet steel specimens, and their predictions correlate well with the experimental evidence in terms of macroscopic stress–strain curves and martensite volume fraction formed at high strain rates. The work shows the value of considering temperature effects in the modeling of metastable austenitic steels submitted to impact conditions. Regarding most of the works reported in the literature on SIMT, modeling of the martensitic transformation at high strain rates is the distinctive feature of the present paper.The researchers of the University Carlos III of Madrid are indebted to the Comunidad Autónoma de Madrid (Project CCG10-UC3M/DPI-5596)) and to the Ministerio de Ciencia e Innovación de España (Project DPI/2008-06408) for the financial support received which allowed conducting part of this work. The authors express their thanks to Mr. Philippe and Mr. Tobisch from the company Zwick for the facilities provided to perform the tensile tests at high strain rates