Forming of Magnesium – Crystal Plasticity and Plastic Potentials

Abstract

Anomalies in the mechanical behaviour of magnesium like anisotropy and strength mismatch originate from its hexagonal close-packed (hcp) crystallographic structure. Hcp metals hold a reduced number of available slip systems compared to body-centred cubic (bcc) and face-centred cubic (fcc) lattices, making plastic deformation more difficult. With the asymmetric distribution of slip systems over the crystallographic reference sphere, various primary and secondary slip and twinning mechanisms can and have to be activated at the same time. Understanding the mechanisms of dislocation gliding and deformation twinning for single crystals and polycrystalline aggregates constitutes the foundation for modelling of the macroscopic mechanical behaviour. To this end, microstructural experimental observations, mechanical tests and numerical modelling are combined.Channel-die compression tests on Mg single crystals for various crystallographic orientations and on textured and polycrystals have been conducted by Kelley and Hosford. [1,2] Their data are used to identify the parameters of a crystal plasticity model. The model is then applied for predicting the mesoscopic deformation of polycrystalline representative volume elements (RVEs). In this way the microscopic features developing during plastic deformation of Mg are linked to the mesoscale and allow for predicting the yielding behaviour of arbitrarily textured solids, for example rolled plates.Due to limitations in computational power, simulations of the behaviour of macroscopic structures cannot be performed effectively based on models of crystal plasticity. They require constitutive equations to be used in the framework of phenomenological plasticity, i.e. a plastic potential and a flow rule. The presented method can be used to calibrate parameters of any plastic potential. Here, the plastic potential proposed by Cazacu and Barlat [3] is used for the simulation of a cup-forming process.

Cyclic behavior of AZ31B Mg: Experiments and non-isothermal forming simulations

“…Nguyen et al (2013) presented a phenomenological model that uses different kinematic hardening rules depending on the deformation mechanism. Steglich and collaborators (Ertürak et al, 2009;Graff et al, 2007a;Graff et al, 2007b;Mekonen et al, 2012;Steglich et al, 2011) utilized the yield function proposed by Cazacu and Barlat (2004) for material modeling and forming simulation of magnesium alloys. Recently, Revil-Baudard et al (2014) and Chandola et al, (2015) used the CPB06 yield function for the finite element analysis of tension, compression, and torsion of Mg alloys.…”

FTMP-Based Modeling and Simulation of Magnesium

“…They in common introduced a sort of mode transition condition from twin to slip in artificial manners (e.g. Graff, Steglich and Brocks, 2007;Zhang and Josh, 2012 As can be easily imagined, such models always behave similarly regardless of the sample geometry and dimensions, which is obviously unrealistic.…”

Two-Scale Finite Element Modelling of Microstructures

“…Appropriate hardening laws have still to be found, however. A phenomenological mesoscopic yield function will finally allow for simulations of magnesium forming [38] or the structural performance components. Thus, the modelling chain from micro to macro is complete, see Fig.…”