T. Berstad

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.

Crashworthiness of aluminium extrusions : validation of numerical simulation, effect of mass ratio and impact velocity

Abstract Based on an experimental database obtained from static and dynamic tests on square aluminium extrusions in alloy AA6060 tempers T4 and T6, a numerical model using the LS-DYNA computer code was validated. Excellent predictions of the response of the tubes were found by using isotropic elasticity, the von Mises yield criterion, the associated flow rule and non-linear isotropic strain hardening. The plastic material parameters such as the initial yield stress and the strain hardening were determined from uniaxial tensile tests. The geometry was modelled using shell elements and a small trigger in the extrusion side-wall represented the initial geometrical imperfections. The validated model was used to study the response of square aluminium tubes, varying the mass of the projectile and the impact velocity. The simulations showed that the mean load was an increasing function with respect to an increase in the impact velocity and that the mass ratio between the projectile and specimen had no influence on this response parameter.

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.

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.

ERROR ESTIMATION AND ADAPTIVITY IN EXPLICIT NONLINEAR FINITE ELEMENT SIMULATION OF QUASI-STATIC PROBLEMS

Abstract A program module for error estimation with application to nonlinear finite element (FE) analysis of shell structures is coupled with the adaptive solution procedure in the explicit FE code LS-DYNA. The error estimation module provides estimates of the local and global errors and element-level refinement indicators. Hence, selective refinement of the mesh in areas where the local error is relatively large compared with a user-defined tolerance is made possible. Furthermore, the relative global error is estimated giving a measure of the overall accuracy of the FE model. Projection-type error estimators based on the L2-norm of the stress vector and the accumulated plastic strain are used to predict the discretization error by comparison of the FE solution with an improved C0-continuous solution obtained by the SPR-method. Three example problems including both material and geometric nonlinearities are provided. The numerical results show that the error estimates capture phenomena such as diffuse necking and local buckling, and give meshes with high resolution in areas with large deformations or high stress gradients.

Effects of the yield criterion on local deformations in numerical simulation of profile forming

Abstract Three anisotropic plasticity models are implemented in LS-DYNA3D for shell analysis using backward Euler integration algorithms. The models have different yield criteria (Hill, Barlat and Lian, and Karafillis and Boyce) but have all associated flow rules and non-linear isotropic strain hardening. The anisotropic models are applied in finite element analysis of a stretch bending process for aluminium extrusions. In addition, simulations with the von Mises yield criterion and a non-quadratic yield criterion for isotropic materials are carried out. Plastic anisotropy and the shape of the yield surface are found to have significant effect on the local deformations predicted in the simulations.

Effects of strain rate on the characteristics of PLC deformation bands for AA5083-H116 aluminium alloy

An experimental, theoretical and numerical investigation of the Portevin-Le Chatelier (PLC) effect in the aluminium alloy AA5083-H116 is described. Five different tests at different overall strain rates were carried out on smooth flat specimens in order to determine the effects of strain rate on the characteristics of the deformation bands and their propagation. Both digital image correlation and digital infrared thermography were used to capture and characterize the spatio-temporal features of the PLC behavior. Inhomogeneous deformation with various localization bands caused by the PLC effect was observed in all the tests and the formation, evolution and propagation of these deformation bands were visualized, allowing their characteristics to be measured. An elasto-viscoplastic constitutive model, developed for metals exhibiting dynamic strain ageing, is used to represent the material behavior. Linear stability analysis with the adopted constitutive model is shown to give the orientations of the bands, but fails to predict the critical strain at which serrated yielding occurs. Finally, the model is used in three-dimensional numerical simulations of the physical tests using explicit finite element analysis. The numerical results are compared with the experimental observations and the main deviations between tests and simulations are discussed.

Offset Impact Behaviour of Bumper Beam–Longitudinal Systems: Numerical Simulations

Abstract The paper presents the results from numerical simulations of bumper beam–longitudinal systems subjected to 40% offset impact loading. Numerical simulations were carried out with the non-linear finite element code LS-DYNA, searching for an efficient, numerically robust and accurate representation of the observed system behaviour. A comparative study of an industrial-like modelling procedure and another procedure incorporating a user-defined material model has been performed. In the latter procedure, the material model consists of state-of-the-art anisotropic plasticity, an isotropic strain and a strain-rate hardening rule as well as some ductile fracture criteria. Both shell and solid elements were utilized in discretizing the bumper beam–longitudinal set-up. Numerical crash results revealed good agreement with the experiments with respect to overall deformation mode and energy dissipation. The simulations were capable of giving relatively accurate prediction of the collapse mode found in the experimental tests, except for the bumper beam–longitudinal system with AA7003-T1 longitudinals. Sensitivity studies were performed considering both physical and numerical parameters. The physical parameters were strain-rate effects and the heat-affected zone, whereas the numerical parameter considered was adaptive meshing.

Strain-Rate Sensitivity of Aluminum Alloys AA1200 and AA3103

Tensile tests are carried out for the aluminum alloys AA1200 and AA3103 at various strain-rates in the range from 10 -4 s -1 to I s -1 . Tests with constant nominal strain-rate and strain-rate jump tests are conducted, and the instantaneous rate sensitivity and the rate sensitivity of strain hardening are investigated. For both materials, the instantaneous rate sensitivity is found to be rather independent of strain, while the rate sensitivity of the strain hardening is important and the saturation stress increases with increasing strain-rate. A phenomenological constitutive model is described that comprises a kinetic equation governing the instantaneous rate sensitivity of the flow stress and a structural parameter that determines the mechanical state of the material. The evolution of the structure parameter is assumed to depend on strain-rate. The model parameters are determined for the two materials using the available experimental information. It is found that the constitutive model provides a good representation of the experimental results.