A microstructure based analytical model for tensile twinning in a rod textured Mg alloy

A model for tensile twinning during the compression of rod textured magnesium is developed based on the idea that these twins nucleate at grain boundaries and that when the twin number density per grain is low these twins readily give rise to the formation of other ‘interaction’ twins in adjacent grains. Experimental observations of twin aspect ratios measured at a single grain size and twin number densities measured over four grain sizes were used to determine model material parameters. Using these, the model provides reasonable predictions for the observed magnitudes and trends for the following observations:1)Effect of grain size and stress on twin volume fraction, fractional twin length and the fraction of twin contact.2)Effect of grain size on the yield stress.3)Effect of grain size on the general shape of the stress-strain curve at low strains.A parametric study shows the model to be quite robust but that it is particularly sensitive to the value of the exponent assumed for the twin nucleation rate law. It is seen that preventing the formation of interaction twins provides an important avenue for hardening and that the flow stress is also particularly sensitive to the relaxation of the twin back stresses. The model shows the importance of taking microstructure into account when modelling twinning.