Odd Sture Hopperstad

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.

Static and dynamic axial crushing of square thin-walled aluminium extrusions

Abstract An experimental investigation was carried out to study the behaviour of square thin-walled aluminium extrusions in alloy AA6060 subjected to axial loading. Both static and dynamic tests were performed and the primary variables were the wall thickness and temper of the square tubes and the impact velocity of the projectile. The mass of the projectile in the dynamic tests was 56 kg, while the impact velocity was in the range 8–20 m/s. The experimental results show that a symmetric deformation mode is formed for the static tests with a lobe number that is a function of the temper. In the dynamic tests a mixture of modes is found. The experimental results also show that the dynamic mean force is significantly higher than the corresponding static force for the same axial displacement, which indicates a strong inertia effect. For initially straight square tubes, the mean load ratio between a dynamic and a static test is a decaying function with respect to the axial displacement. However, by introducing initial geometrical imperfections prior to dynamic testing an almost constant ratio is found.

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.

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.

Static crushing of square aluminium extrusions with aluminium foam filler

An experimental investigation was carried out to study the behaviour of square aluminium extrusions filled with aluminium foam under quasi-static loading conditions. Based on the experimental work, simple relations between dimensionless numbers governing the influence of the foam on the characteristics of the crush problem were identified. Furthermore, a simplified set of equations applicable for design of foam-filled components was proposed.

An evaluation of yield criteria and flow rules for aluminium alloys

Abstract The mechanical characteristics of two aluminium alloys, AA7108 and AA6063, have been investigated by means of uniaxial tensile tests. The experiments show that the alloys exhibit significant anisotropy in yield strength, plastic flow and ductility. Based on the experiments, some existing phenomenological models of elastoplasticity were examined. The ingredients of the models are a yield criterion, a flow rule and a strain-hardening rule. Three yield criteria proposed by Hill (1950) , Barlat and Lian (1989) , and Karafillis and Boyce (1993) were evaluated. None of these have been found to give a satisfactory description of the mechanical behaviour.

Crash behaviour of thin-walled aluminium members

In order to assess the crashworthiness of aluminium extrusions, a research programme was carried out in co-operation with the aluminium industry in Norway. The main objective was to study the behaviour of aluminium extrusions under axial loading conditions and to give experimental data for validation of a numerical model in the computer code LS-DYNA. In order to increase the energy absorbing capabilities of thin-walled aluminium members under axial loading, an experimental investigation was performed to study the combined behaviour of extrusions and aluminium foam.