Keywords: {10bar(1)2}<bar(1)011>, twinning, pseudoelasticity, nonconvex strain energy, magnesium, crystal plasticity.

The model proposed by [1] is used in a simple compression simulation of an RVE, where the orientation distribution is similar to the one that is experimentally observed in extruded magnesium. It is found that the predicted twin structure displays the main features of experimentally observed twin structures. The twins form as plates inside the grains. Near the grain boundary, the twinning induced misfit strain causes the nucleation of a twin in the neighbouring grain, i.e. the twins are able to propagate across grain boundaries. The average twin volume fraction and the texture evolution correspond well to experimental findings of [2]. Due to the complicated hardening behaviour owed to twin-particle interactions, the hardening behaviour of magnesium alloy is underestimated. In the phase of extensive twinning, the model predicts a zero hardening plateau, which is in accordance to experimental observations on pure magnesium [3]. At the end of the phase of extensive twinning, the stresses are overpredicted in both cases. This is due to the lack of deformation mechanisms like secondary twinning, slip inside the twins and damage.

The presented modelling approach is able to predict the features of deformation twinning on the microscale [1] as well as on the macroscale. However, problems should not be concealed. First of all, to predict the macroscopic material behaviour, the numerical homogenisation via the RVE method needs to be employed. The computational effort is therefore too large for practical forming process simulations. There are as well some fundamental difficulties. The most problematic fact is that twinning is connected to the movement of partial dislocations. This induces a strain path-dependence and energy dissipation. Both are neglected by any pseudoelastic modelling. For example, the elastic modelling allows, in principle, phase changes from one twin variant to another one without passing through the parent phase as the intermediate configuration. Such behaviour is not realistic due to the kinetic process underlying to the twin formation. The conclusion is that the pseudoelastic modelling cannot be applied if severe strain path changes occur. For the same reason, higher order twinning has to be excluded from the model, as the higher order twins are only accessible by a specific series of twinning operations. This strain path dependence can not be reflected by an elastic modelling with a static strain energy. The latter may be resolved by proposing a non-static strain energy density. Moreover, the strain energy invariance of conjugate twins restricts the elastic modelling to crystallographically equivalent conjugate twins. An example for crystallographically distinct conjugate twins are the {01bar(1)1}<01bar(1)bar(2)> and the {01bar(1)bar(3)}<03bar(3)2> twins in the hcp lattice. In an elastic modelling approach as given here, the strain energy invariance forces us to include both twin systems or none of them, although they may display very different characteristics.

1

R. Glüge, A. Bertram, T. Böhlke, E. Specht, "A Pseudoelastic Model for Mechanical Twinning on the Microscale", Zeitschrift für Angewandte Mathematik und Mechanik, accepted for publication in the special issue "Phase Transitions in Deformable Solids and Structures", 2010. doi:10.1002/zamm.200900339

2

L. Jiang, J. Jonas, R. Mishrab, A. Luob, A. Sachdevb, S. Godetc, "Twinning and texture development in two Mg alloys subjected to loading along three different strain paths", Acta Materialia, 55, 3899-3910, 2007. doi:10.1016/j.actamat.2007.03.006

3

R. Reed-Hill, "The Inhomogeneity of Plastic Deformation", Chapter "Role of Deformation Twinning in Determining the Mechanical Properties of Metals", American Society for Metals, 285-311, 1973.

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