Yield point elongation due to twinning in a magnesium alloy

Fine-grained magnesium alloy AZ31 displays a yield elongation when deformed such that yielding occurs by twinning. That is, following yielding there is a plateau in the stress–strain curve. The present paper presents a microstructural analysis of the twins in deformed samples. A major aim is to explain the yield elongation and in particular why it decreases and eventually disappears with increasing grain size. It is shown that during the Lüders yield elongation twins initiate twinning events in neighbouring grains and in this manner twinning spreads its way progressively over the sample. This occurs at a twinning frequency of approximately one twin per grain. A criterion for the presence of a Lüders strain is developed based on twin transfer across boundaries. It is shown that higher Lüders strains and stresses are expected for finer grain sizes. The key to understanding the effect is that it arises from the condition for Lüders band propagation whereby the twins on the Lüders band front must stimulate, on average, one twin each within the fresh material ahead of the front, at a constant value of applied stress. An important part of the derivation followed here is that at the higher stresses seen in fine-grained samples, the twin aspect ratio is larger and consequently the strain at the grain level corresponding to a single twinning event is higher in finer-grained samples.