Magnus Langseth

Validation of constitutive models applicable to aluminium foams

An extensive experimental database has been established for the structural behaviour of aluminium foam and aluminium foam-based components (foam-filled extrusions). The database is divided into three levels, these are: (1) foam material calibration tests, (2) foam material validation tests and finally (3) structural interaction tests where the foam interacts with aluminium extrusions. This division makes it possible to validate constitutive models applicable to aluminium foam for a wide spectrum of loading configurations. Several existing material models for aluminium foam from the literature are discussed and compared. To illustrate the use of the database, four existing material models for foams in the explicit, non-linear finite element code LS-DYNA have been calibrated and evaluated against configurations in the database.

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.

Close-range blast loading of aluminium foam panels

Full-scale field tests have been carried out in order to investigate the behaviour of aluminium foam panels subjected to blast loading. Charges were detonated at a given standoff distance in front of the foam panels, which were attached to the bob of a ballistic pendulum. Using this test set-up, the maximum swing of the pendulum after each test was used to calculate the energy and impulse transfer from the blast loading. Tests were carried out by varying the foam panel density and charge mass. Experiments were also done with an aluminium cover plate attached to the front of the foam panels. In general, it was observed that the energy and impulse transfer to the pendulum increased by adding a foam panel. In order to investigate this phenomenon, an analytical solution based on shock-wave theory was proposed in order to describe the deformation behaviour of a one-dimensional foam bar subjected to a linearly decaying blast loading. However, using this approach, it was found that the addition of a foam bar should not change the global response of the pendulum. On the other hand, similarities between the present case and recent investigations reported in the literature suggest that the observed increase in maximum swing of the pendulum when adding foam panels may be due to the continuous changing of the shape of the initially plane panel surface into a concave shape. In this way, surface effects could be controlling the energy and impulse transfer.

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.

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.

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.

Crashworthiness of aluminum extrusions subjected to oblique loading: experiments and numerical analyses

Oblique loading was studied through quasi-static experiments and numerical simulations. The behavior of square aluminum columns in alloy AA6060 subjected to quasi-static oblique loading was investigated experimentally for three different load angles. The square columns were clamped at one end and oblique load conditions were realized by applying a force with different angles to the centerline of the column. These tests were used to validate a numerical model. Numerical studies of oblique impact were carried out using the validated model, and the mean crush load was investigated through factorial analysis with parameters as load angle, thickness, length, and heat treatment of the alloy and impact velocity.

Square aluminum tubes subjected to oblique loading

The behavior and energy-absorbing capability of obliquely loaded square thin-walled aluminum columns in alloy AA6060 were studied through quasi-static experiments and FEM-analyses with LS-DYNA. The specimens were clamped at one end and oblique loading conditions were realized by applying a force with different angles to the centerline of the column. The primary variables were load angle, wall thickness and heat treatment of the alloy. The experimental results were compared with the numerical results, and the capacity was compared with Eurocode 9. LS-DYNA was able to predict peak loads with very good accuracy, while the mean loads were conservative compared to the experimental results. Furthermore, the study showed that Eurocode 9 is conservative, and that the moment capacity can be increased for temper T4 and cross-section class 1 and 2. The initial and subsequent failure loci are constructed from experimental and numerical results, and the failure loci shrink for increasing additional rotation from the initial position.

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.

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Abstract Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10 −3 and 10 0 /s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.