Dirk Steglich

Modeling of crack growth in round bars and plane strain specimens

The formation of cup-cone fracture in round bars and of slant fracture in plane strain specimens is studied using the finite element (FE) method. Constitutive models proposed by Rousselier [Nucl. Engng. Des. 105 (1987) 97] and by Gurson [Acta Metall. 32 (1984) 157] are used. The analysis takes into account viscoplasticity and void nucleation. Different indicators of localization are computed during FE calculations. The analysis shows that cup-cone is more easily formed using the Rousselier model than the Gurson model. Cup-cone fracture is inhibited in highly viscous materials. The use of the f* function in the Gurson model favors flat fracture. The crack path (flat or cup-cone/slant) can be correlated to the size of the localization zone which is formed ahead of the central penny shaped crack.

Modeling of plane strain ductile rupture

Abstract The formation of slanted fracture under plane strain conditions is studied using the finite Element (FE) method. Constitutive models proposed by Rousselier and by Gurson are used. Rices condition for localization is checked at every point of the FE mesh for each time step. The role of mesh design (element size, element aspect ratio, symmetry) is first studied. The different constitutive models are then compared. It is in particular shown that the use of the f ★ function in the Gurson model favors flat fracture.

Predicting crack growth resistance of aluminium sheets

Abstract The Gurson–Tvergaard–Needleman and the cohesive zone models are applied for modelling the ductile crack growth in thin aluminium sheets under monotonic loading. The material’s yield curve is obtained by standard tensile tests, whereas the remaining model parameters are fitted for a Kahn specimen. The transferability of these parameters from the small Kahn specimen to large centre-cracked panels is shown through numerical simulations. Both models were successfully applied to simulate the fracture resistance of a specimen, showing their ability to describe crack propagation of thin metal sheet. The effects of varying mechanical properties on fracture resistance are demonstrated by parameter studies. However, the transition from flat to slant fracture observed in real tests is not modelled at this stage. This requires rather laborious 3D calculations.

Ductile rupture of aluminum sheet materials

ABSTRACT This study deals with ductile tearing of Aluminum 2024 sheets. Tensile tests were conducted on smooth and notched specimens. They show that the plastic behavior is anisotropic. The crack path is slanted on moderately notched specimens whereas a normal to slant fracture transition is observed on severely notched samples. The damage behavior is modeled using the Rousselier model extended to account for plastic anisotropy. It is shown that the stress triaxiality can reach values up to 1.6. This shows, together with the slanted crack path, the importance of a 3D modeling. As these calculations require a large computational capacity, a relatively coarse mesh was used so that the load is overestimated. The experimental load could be reproduced changing the material parameters; in this case normal fracture is obtained. A finer mesh should be used to obtain simultaneously the correct crack path and load. To model cracking in large structures, a 2D plane stress cohesive zone model is used.

Modelling the Thermo‐Mechanical Behavior of Magnesium Alloys during Indirect Extrusion

One of the basic metal forming process for semi‐finished products is extrusion. Since extrusion involves complex thermo‐mechanical and multiaxial loading conditions resulting in large strains, high strain rates and an increase in temperature due to deformation, a proper yield criterion and hardening law should be used in the numerical modelling of the process. A phenomenological model based on a plastic potential has been proposed that takes strain, strain rate and temperature dependency on flow behaviour into consideration. A hybrid methodology of experiment and finite element simulation has been adopted in order to obtain necessary model parameters. The anisotropy/asymmetry in yielding was quantified by tensile and compression tests of specimens prepared from different directions. The identification of the corresponding model parameters was performed by a genetic algorithm. A fully coupled thermo‐mechanical analysis has been used in extrusion simulations for calculation of the temperature field by consi...

Crashworthiness of Magnesium Sheet Structures

A hollow rectangular profile, as an example of a typical structural component made of magnesium alloy sheets has been built, tested and evaluated in order to assess its behaviour during axial crushing. The profiles were joined from plane sheets of AZ31 and ZE10, respectively, by laser beam welding and were then tested in compression. Numerical simulations have been conducted to understand the complex interplay between hardening characteristics of the materials under investigation, profile cross-section variation and energy absorption. The results from the compression testing of the profiles show that the welds are not the source of damage initiation and failure. The performance of the magnesium profiles in terms of dissipated specific energy is confirmed for small and intermediate displacements to be comparable to that of aluminium profiles. For large displacements, however, the shear-type failure mode of magnesium causes a sharp drop of the crushing force and thus limits the energy absorption. These findings demonstrate the requirement for an alloy and wrought magnesium process development specifically for crash applications which aims at progressive hardening along with high ductility for improving the bending and shear behaviour.

Measurement and Analysis of the Biaxial Loading and Unloading Behavior of AZ31 Mg Alloy Sheet

A commercial AZ31 magnesium alloy sheet has been tested under proportional biaxial tensile loading using cruciform specimens. In order to quantitatively determine the elastic‐plastic deformation behavior of the test material, the contours of plastic work and the directions of plastic strain rates were measured over a range of equivalent plastic strain, 0.001 ⩽e0p⩽0.008. The measured work contours and the directions of plastic strain rates have been compared with those predicted using the von Mises, Hill’48 and the Yld2000‐2d yield functions. The validity of these yield functions is discussed from viewpoints of the yield surface shape and normality flow rule in the first quadrant of the stress space. The r‐value of AZ31 was found to increase with plastic strain. The effect of the changes in r‐value on the shape of the calculated yield locus has been discussed. Furthermore, biaxial unloading tests following biaxial loading were carried out for several stress ratios. The nonlinearity of the stress‐strain cur...

Modelling of Thermo-Mechanical Behaviour of Magnesium Alloys during Indirect Extrusion

A yield function for hexagonal closed packed (hcp) metals was modified with respect to strain rate and temperature and developed to capture the material behaviour during extrusion. Magnesium alloy ZEK100 was extruded indirectly at 300°C into a round bar. Compression tests were carried out at various strain rates, temperatures and sample orientation to characterise the material flow. These data were used as input data for fully thermo-mechanical coupled simulations of indirect extrusion. A successful prediction of the extrusion force and the temperature increase during extrusion is presented.

Forming of Magnesium — Crystal Plasticity and Plastic Potentials

Hexagonal close‐packed (hcp) metals show a deformation behavior, which is quite different from that of materials with cubic crystalline structure. As a consequence, rolled or extruded products of magnesium and its alloys exhibit a strong anisotropy and an unlike yielding in tension and compression. Microstructural mechanisms of deformation in pure magnesium are modeled by constitutive equations of crystal plasticity. Single crystals and textured polycrystals are analyzed numerically. By means of virtual mechanical tests of representative volume elements mesoscopic yield surfaces are generated and compared with phenomenological yield surfaces. The hardening behavior as well as deformation kinematics are accounted while fitting the respective model parameters for a plane stress state. The linking of micro‐ and mesoscale provides a procedure for the simulation of the yielding and hardening behavior of arbitrarily textured solids with hcp structure such as extruded bars or rolled plates.

Prediction of Crashworthiness for Extruded Magnesium Materials

To assess the crashworthiness of simple wrought magnesium structures, the axial deformation behaviour of different square tubes produced from magnesium alloys AZ31 and ZE10 were numerically investigated under quasi-static compressive loading conditions. Finite-element simulations were conducted to predict and assess the plastic buckling and crush behaviour. The necessary data to determine parameters for the plastic potential were taken from compression tests conducted along different orientations. The yield function Hill48 was selected, despite its inability to capture the strength differential effect. The modelling approach pursued is justified by considering the mechanical loading conditions, the fabrication process of the profiles and its implication on strain anisotropy, balancing achievable accuracy and computational efforts. The simulation results revealed that the material work hardening rates evidenced in uniaxial compression tests influenced the buckling modes as well as the energy dissipation.