An analytical model to predict strain-hardening behavior and twin volume fraction in a profoundly twinning magnesium alloy


Strain hardening/work hardening occurs when a metal is strained beyond its yield point. In most engineering applications, this phenomenon is desirable as it increases the load carrying capacity of the material by making it resistant to deformation. Hexagonal closed packed magnesium alloys are considered as future materials for automobiles and aircraft applications. Unfortunately, their application potential is constrained mainly due to their limited strength and ductility at ambient temperature. Therefore, for one to successfully implement magnesium alloys in applications, they must first comprehend the deformation mechanism of the said material; particularly by means of consecutive experimental and modelling/simulation studies. Consequently, the mechanisms underlying the plastic deformation of polycrystalline magnesium alloys has been widely explored. A great deal of these studies investigating the deformation behavior of polycrystalline magnesium alloys have reported deformation twins, namely: extension twins and contraction twins. As such, it is important to provide analytical approaches that could readily predict the changes in strain hardening due to twinning. So far, five models have been presented. A thorough review of existing literature reveals that all the previous models were either developed for TWIP steel for larger strain by modelling only one feature or were restricted to very small strains for magnesium.

Indeed, even the most complete model recently reported still needs the twin volume fraction as an input for the polycrystal case. To address all these issues, Professor Laszlo Toth and Dr. Somjeet Biswas from the University of Lorraine together with Dr. Sudeep Sahoo from the Indian Institute of Technology Kharagpur developed a novel analytical approach that was designed to address several features relevant to the twin induced deformation behavior of polycrystalline metallic materials. The novelty of their study was it can accurately predict for the first time both the sigmoidal type flow curve and the twin volume fraction. Their work is currently published in the research journal, International Journal of Plasticity.

In brief, the experiments carried out in the course of the study mainly included uniaxial compression tests for two different cases at ambient temperature. Altogether, the microstructures were characterized at various strains up to fracture using the Electron Back-Scattered Diffraction technique in a Field Emission Gun – Scanning Electron Microscope. The model used was composed of three basic elements: Twin fraction prediction based on crystal plasticity elements, a two-phase composite model composed of the matrix and the twins by adopting the “Iso-work” hypothesis and a strain hardening approach inspired from a crystal plasticity model.

The microstructural investigation revealed the formation of a lamellar structure of alternated layers of matrix and the extension twin domains. Moreover, the authors reported that with progressive deformation, the twins broadened and consumed the entire microstructure prior to fracture. Overall, the applicability of the proposed analytical approach was verified for the present Mg-3Al-0.3Mn alloy. In fact, it was proved to be predictive with high precision for the stress-strain curve, and the twinning volume fraction.

In summary, the study presented a new analytical model which could accurately predict the strain-hardening behavior, the evolution of the twin volume fraction, and the partition of stress and strain between the matrix and twin phases in polycrystalline hexagonal closed packed materials where twinning is a relevant deformation mechanism. In a statement to Advances in Engineering, Professor Laszlo Toth further mentioned that their model could accurately reproduce the experimental twin-induced sigmoidal shaped flow curve together with the twin volume fraction evolution.


Sudeep K. Sahoo, Laszlo S. Toth, Somjeet Biswas. An analytical model to predict strain-hardening behaviour and twin volume fraction in a profoundly twinning magnesium alloy. International Journal of Plasticity, volume 119 (2019) page 273–290.

Go To International Journal of Plasticity

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