A.H. van den Boogaard

Strain in Shear, and Material Behaviour in Incremental Forming

This paper discusses some consequences of forming by shear, a situation that is sometimes claimed to occur in incremental forming. The determination of the principal strains and principal directions is discussed in detail. Two methods are presented: using a circular grid (although simulated on the computer), and by deriving formulae from the theory; both yield identical results. The strains assuming forming by shear are found to be (much) higher than in situations of forming by stretch. This affects notably more fundamental studies on material behaviour in incremental forming. The effects are illustrated using experimental data obtained with pre-stressed material.

A Metamodel Based Optimisation Algorithm for Metal Forming Processes

Cost saving and product improvement have always been important goals in the metal forming industry. To achieve these goals, metal forming processes need to be optimised. During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to designing feasible processes more easily. More recently, the possibility of coupling FEM to mathematical optimisation algorithms is offering a very promising opportunity to design optimal metal forming processes instead of only feasible ones. However, which optimisation algorithm to use is still not clear. In this paper, an optimisation algorithm based on metamodelling techniques is proposed for optimising metal forming processes. The algorithm incorporates nonlinear FEM simulations which can be very time consuming to execute. As an illustration of its capabilities, the proposed algorithm is applied to optimise the internal pressure and axial feeding load paths of a hydroforming process. The product formed by the optimised process outperforms products produced by other, arbitrarily selected load paths. These results indicate the high potential of the proposed algorithm for optimising metal forming processes using time consuming FEM simulations.

The ALE-method with triangular elements: direct convection of integration point values

The arbitrary Lagrangian-Eulerian (ALE) finite element method is applied to the simulation of forming processes where material is highly deformed. Here, the split formulation is used: a Lagrangian step is done with an implicit finite element formulation, followed by an explicit (purely convective) Eulerian step. The purpose of this study is to investigate the Eulerian step for quadratic triangular elements. To solve the convection equation for integration point values, a new method inspired by Van Leer is constructed. The new method is based on direct convection of integration point values without intervention of nodal point values. The Molenkamp test and a so-called block test were executed to check the performance and stability of the convection scheme. From these tests it is concluded that the new convection scheme shows accurate results. The scheme is extended to an ALE-algorithm. An extrusion process was simulated to test the applicability of the scheme to engineering problems. It is concluded that direct convection of integration point values with the presented algorithm leads to accurate results and that it can be applied to ALE-simulations

Experimental characterization of microstructure development during loading path changes in bcc sheet steels

Interstitial free sheet steels show transient work hardening behavior, i.e., the Bauschinger effect and cross hardening, after changes in the loading path. This behavior affects sheet forming processes and the properties of the final part. The transient work hardening behavior is attributed to changes in the dislocation structure. In this work, the morphology of the dislocation microstructure is investigated for uniaxial and plane strain tension, monotonic and forward to reverse shear, and plane strain tension to shear. Characteristic features such as the thickness of cell walls and the shape of cells are used to distinguish microstructural patterns corresponding to different loading paths. The influence of the crystallographic texture on the dislocation structure is analyzed. Digital image processing is used to create a “library” of schematic representations of the dislocation microstructure. The dislocation microstructures corresponding to uniaxial tension, plane strain tension, monotonic shear, forward to reverse shear, and plane strain tension to shear can be distinguished from each other based on the thickness of cell walls and the shape of cells. A statistical analysis of the wall thickness distribution shows that the wall thickness decreases with increasing deformation and that there are differences between simple shear and uniaxial tension. A change in loading path leads to changes in the dislocation structure. The knowledge of the specific features of the dislocation structure corresponding to a loading path may be used for two purposes: (i) the analysis of the homogeneity of deformation in a test sample and (ii) the analysis of a formed part.

Modelling of aluminium sheet forming at elevated temperatures

The formability of Al‐Mg sheet can be improved considerably, by increasing the temperature. By heating the sheet in areas with large shear strains, but cooling it on places where the risk of necking is high, the limiting drawing ratio can be increased to values above 2.5. At elevated temperatures, the mechanical response of the material becomes strain rate dependent. To accurately simulate warm forming of aluminium sheet, a material model is required that incorporates the temperature and strain‐rate dependency. In this paper simulations are presented of the deep drawing of a cylindrical cup, using shell elements. It is demonstrated that the familiar quadratic Hill yield function is not capable of describing the plastic deformation of aluminium. Hardening can be described successfully with a physically based material model for temperatures up to 200 °C. At higher temperatures and very low strain rates, the flow curve deviates significantly from the model.

Material-induced anisotropic damage in DP600

Plasticity-induced damage development in metals is anisotropic by nature. The anisotropy in damage is driven by two different phenomena: anisotropic deformation state i.e. load-induced anisotropic damage (LIAD) and anisotropic microstructure i.e. material-induced anisotropic damage (MIAD). The contribution of second-phase particles can be anisotropic in terms of shape as well as distribution. Most of the continuum anisotropic damage models mimic the phenomenon of LIAD only. Not much attention has been paid to MIAD. This work shows the existence of MIAD in a (pre-production) grade of dual-phase steel (DP600). The aim is to see the influence of MIAD on post-localization deformation behavior and final failure mode. The deformation in this material is almost isotropic up to localization but the post-localization deformation and final failure mode is different when loaded in 0° and 90° to rolling direction. Tensile specimens were deformed up to final failure. A few specimens were stopped just before the final failure. Scanning electron microscopic analysis was carried out to study martensite morphology and damage in these specimens. The martensite morphology showed anisotropy in shape and orientation in the undeformed specimens. Significant MIAD was observed in the deformed tensile specimens due to the anisotropic martensite morphology. MIAD explains direction-dependent post-localization deformation, final failure mode, and formability of this material. Lemaitres anisotropic damage model is modified to account for MIAD in a phenomenological manner. The MIAD parameters were determined from tensile tests carried out in 0°, 45°, and 90° to the rolling direction.

Influence Of The Plastic Material Behaviour On The Prediction Of Forming Limits

Prediction of the onset of necking is of large importance in reliability of forming simulation in present automotive industry. Advanced material models require accurate descriptions of the plastic material behaviour including the effect of strain rate [1, 3]. The usual approach for identifying the forming limits in industry is the comparison of a calculated strain map (major against minor strain) with a measured forming limit curve. This approach does not take into account the influence of strain path changes. Prediction of forming limit curves [4] with classical material models can already demonstrate that the forming limits are influenced by this strain path change effect. Including the effect of strain rate on the plastic material behaviour has a strong influence in prediction of onset of instability [2]. Neglecting this effect leads to underestimation of forming capacity of the material in stretch forming parts in particular. The shape of the yield locus [1, 2] will influence the predicted forming limit curves in the region from plane strain to bi-axial. Damage controlled failure will become more important using (advanced) high strength steels. This will affect the stress strain curve at high deformation grades. The work hardening is not only controlled by dislocation interaction, but also by void growth and possible presence of micro-cracks at the interface between the hard en soft phases.

A mixed elastoplastic / rigid plastic material model

A new integration algorithm is described for large strain plastic deformations. The algorithm degenerates to the Euler forward elastoplastic{plastic model for small strain increments and to the rigid{plastic model for large strain increments. The model benets from the advantages of both models: accuracy and fast convergence over a large range of strain increments.

Determination of flow curves under equibiaxial stress conditions

Three experimental methods have been used to establish flow curves for a low carbon steel under biaxial stress conditions: the hydraulic bulge test, the stack compression test and the biaxial tensile test. The individual tests are discussed and the results for a DC06 IF steel grade compared. Initially the results appear to be different but after compensation, including strain rate and temperature correction, the true hardening curves are coinciding.

Incremental Sheet Forming Analysed by Tensile Tests

To study material behaviour under conditions encountered in ISF operations tensile tests have been carried out on material taken from the walls of pyramidal products. The shape of the stress-strain curves depend on orientation. Tests in the direction of punch movement show an overshoot indicating a change in strain path, tests across that direction do not. From this it is concluded that the major direction of deformation in the walls is perpendicular to the direction of punch movement. There is no indication of a severe deformation in the direction of punch movement, either stretch or shear. The level of hardening in the material is less than expected from the macroscopic changes in dimensions. Apparently the forming operation in ISF causes additional softening of the material