Tore Børvik

A computational model of viscoplasticity and ductile damage for impact and penetration

Abstract A coupled constitutive model of viscoplasticity and ductile damage for penetration and impact related problems has been formulated and implemented in the explicit finite element code LS-DYNA. The model, which is based on the constitutive model and fracture strain model of Johnson and Cook, and on continuum damage mechanics as proposed by Lemaitre, includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, non-linear isotropic strain hardening, strain-rate hardening, temperature softening due to adiabatic heating, isotropic ductile damage and failure. For each of the physical phenomena included in the model, one or several material constants are required. However, all material constants can be identified from relatively simple uniaxial tensile tests without the use of numerical simulations. In this paper the constitutive model is described in detail. Then material tests for Weldox 460 E steel and the calibration procedure are presented and discussed. The calibrated model is finally verified and validated through numerical simulations of material and plate perforation tests investigated experimentally.

Ballistic penetration of steel plates

This paper presents a research programme in progress where the main objective is to study the behaviour of Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles in the lower ordnance velocity regime. A compressed gas gun is used to carry out high-precision tests, and a digital high-speed camera system is used to photograph the penetration process. A coupled constitutive model of viscoplasticity and ductile damage is formulated and implemented into the non-linear finite element code LS-DYNA, and the material constants for the target plate are determined. The proposed model is applied in simulations of the plate penetration problem and the results are compared with test data. Good agreement between the numerical simulations and the experimental results is found for velocities well above the ballistic limit, while the ballistic limit itself is overestimated by approximately 10% in the numerical simulations.

Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses: Part II: numerical simulations

In Part I of this paper, projectiles with three different nose shapes (blunt, hemispherical and conical) were used in gas gun experiments to penetrate 12 mm thick Weldox 460 E steel plates. It was found that the nose shape of the projectile severely affected both the energy absorption and the failure mode of the target structure during penetration. This part of the paper describes numerical simulations of the problem investigated experimentally. A constitutive model of viscoplasticity and ductile damage for projectile impact has earlier been developed and implemented in the explicit finite element code LS-DYNA. Numerical simulations involving this model have been carried out, and the results are compared with the experimental data. However, numerical problems associated with the element mesh were detected, and adaptive meshing was found necessary in order to obtain reliable results for conical projectiles. From the numerical simulations it is found that the LS-DYNA code is able to describe the different failure modes without any predefined defects in the element mesh if special care is taken, and good agreement is in general obtained between the numerical simulations and experimental results.

Effect of Target Thickness in Blunt Projectile Penetration of Weldox 460 E Steel Plates

This paper describes an experimental, analytical and numerical investigation of the penetration and perforation of circular Weldox 460 E steel plates with different thicknesses struck by a blunt projectile at various impact velocities. In the experimental tests, a compressed gas gun was used to launch the sabot mounted projectile at impact velocities well above and just below the ballistic limit of the target plates. Nominal hardness, diameter, length and mass of the projectile were kept constant in all tests. The target plate was clamped in a rigid circular frame, and the thickness was varied between 6 and 30 mm: Measurements were made of the initial and residual velocities, and the ballistic limit velocity and the residual versus impact velocity curve were obtained for each target thickness tested. In addition, a digital high-speed camera system was used to photograph the penetration event. The experimental findings from the tests are presented and discussed, and the results are used to assess some empirical, analytical and numerical models. It is shown that especially the results obtained by the finite element approach are encouraging in terms of predicting the response of the plates examined. r 2002 Elsevier Science Ltd. All rights reserved.

Numerical simulation of plugging failure in ballistic penetration

A coupled computational material model of viscoplasticity and ductile damage has been developed and implemented in LS-DYNA. This model gives good agreement between numerical simulations and experimental observations of plugging failure in ballistic penetration, without the use of inverse modelling or predefined defects. However, even if the model constants can be determined from relatively simple uniaxial tensile tests, the computational model is rather comprehensive. In this paper numerical results obtained by using the fully coupled computational model are compared with results obtained from less sophisticated versions of the material model. The differences between the numerical results will be pointed out and discussed, and details from some of the simulations are shown. To validate the accuracy of the computational model, references will be made to experimental observations from gas-gun penetration tests on 8-mm thick Weldox 460 E steel plates.

On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical study

Non-linear finite element analyses of quasi-static and high-rate tensile tests with smooth and notched axisymmetric specimens of the structural steel Weldox 460 E have been carried out. The constitutive relation and fracture criterion of Johnson and Cook, which were adopted in the simulations, have previously been determined for Weldox 460 E steel. First, a validation study was completed to assess the accuracy of the constitutive relation and fracture criterion. The numerical results were compared with experimental data from tensile tests under quasi-static and dynamic loading conditions. Secondly, the use of Bridgmans analysis in the identification of the fracture criterion was evaluated, and the influence of adiabatic heating and inertia on the stress triaxiality in the tensile specimens was investigated. The results were finally used to discuss the identification of fracture criteria based on tensile tests with smooth and notched axisymmetric specimens.

On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part I. Experiments

Abstract Notched axisymmetric specimens of the structural steel Weldox 460 E have been tested at high strain rates in a Split Hopkinson Tension Bar. The aim was to study the combined effects of strain rate and stress triaxiality on the materials behaviour. It is further considered important to obtain experimental data that can be used in validation of constitutive relations and fracture criteria. The force and elongation of the specimens were measured by strain gauges during the high strain rate tests, while the fracture strain was calculated based on measurements of the fracture area in the microscope. Optical recordings of the notch deformation were obtained using a digital high-speed camera system. Using image processing of the digital images, it was possible to estimate the true strain against time at minimum cross-section. The strength of the material was found to increase with increasing strain rate, while for the ductility no significant effect of strain rate could be ascertained from the notched specimen tests. The ductility of the material was found to depend considerably on the stress triaxiality.

Empty and foam-filled circular aluminium tubes subjected to axial and oblique quasi- static loading

Tests on tubular columns made of the aluminium alloy 6060-T4 under axial and oblique, quasi-static loading have been performed. The columns were fixed at one extremity, while a concentrated force was applied at the other through a rigid collar. Empty and foam-filled columns were tested for load angles equal to 0, 5, 15 and 30 degrees with respect to the longitudinal direction of the column. The columns outer diameter was 80 mm and the thickness was 1.5 mm, while the distance from the point of load application to the fixed support was 245 mm. The aluminium foam density was about 0.3 g/cm 3 . The response parameters were the peak force, the absorbed energy and the mean crush force, in addition to visual observations of the deformation mode and fracture. Furthermore, LS-DYNA simulations of the experiments were performed. The columns were modelled with shell elements, while brick elements were used to model the aluminium foam core. The aluminium alloy was modelled using an isotropic elastoplastic model with isotropic strain hardening. Fracture in the aluminium column was not considered in the simulations. The aluminium foam was modelled using the Deshpande-Fleck model. In selected simulations, fracture was assumed to occur at a critical value of the plastic volumetric strain. The agreement between the experimental and predicted results was in general good.

Observations on shear plug formation in Weldox 460 E steel plates impacted by blunt-nosed projectiles

Shear plug formation in circular Weldox 460 E steel plates impacted by blunt-nosed cylindrical projectiles with striking velocities between 100 and 500 m/s has been investigated. Target thickness and projectile impact velocity were the primary variables, and for each target thickness the ballistic limit curve of the material was precisely determined. The test at an impact velocity just below the ballistic limit for each target thickness was selected for a microscopic examination of shear localisation and fracture. In these tests, the plug was pushed only partway through the target, and the localised shear zones outlining the fracture were easily recognised both in the optical and scanning electron microscope. Clear evidence of adiabatic shear bands and material damage due to void growth was found in several of the target plates. Analytical models available in the literature were compared with the results from the experimental and microscopic studies. Reasonable agreement was found between calculations and experiments. 2001 Elsevier Science Ltd. All rights reserved.

A numerical study on the influence of the Portevin–Le Chatelier effect on necking in an aluminium alloy

The constitutive relation proposed by McCormick (1988 Acta Metall. 36 3061–7) for materials exhibiting negative steady-state strain-rate sensitivity and the Portevin–Le Chatelier (PLC) effect is incorporated into an elastic–viscoplastic model for metals with plastic anisotropy. The constitutive model is implemented in LS-DYNA for corotational shell elements. Plastic anisotropy is taken into account by use of the yield criterion Yld2000/Yld2003 proposed by Barlat et al (2003 J. Plast. 19 1297–319) and Aretz (2004 Modelling Simul. Mater. Sci. Eng. 12 491–509). The parameters of the constitutive equations are determined for a rolled aluminium alloy (AA5083-H116) exhibiting negative steady-state strain-rate sensitivity and serrated yielding. The parameter identification is based on existing experimental data. A numerical investigation is conducted to determine the influence of the PLC effect on the onset of necking in uniaxial and biaxial tension for different overall strain rates. The numerical simulations show that the PLC effect leads to significant reductions in the strain to necking for both uniaxial and biaxial stress states. Increased surface roughness with plastic deformation is predicted for strain rates giving serrated yielding in uniaxial tension. It is likely that this is an important reason for the reduced critical strains. The characteristics of the deformation bands (orientation, width, velocity and strain rate) are also studied.