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12th International Conference on Magnesium Alloys and their Applications (Mg 2021): Modeling II; LPSO & MFS Structures III
Program Organizers: Alan Luo, Ohio State University; Mihriban Pekguleryuz, McGill University; Sean Agnew, University of Virginia; John Allison, University of Michigan; Karl Kainer; Eric Nyberg, Kaiser Aluminum Trentwood; Warren Poole, University of British Columbia; Kumar Sadayappan, CanmetMATERIALS; Bruce Williams, Canmetmaterials Natural Resources Canada; Stephen Yue, Mcgill University

Friday 10:50 AM
June 18, 2021
Room: Contributed I
Location: Virtual

Session Chair: Jian-Feng Nie, Monash University; Koji Hagihara, Nagoya Institute of Technology

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Numerical Modeling of the Forging Response of a Magnesium Alloy Control Arm: Bruce Williams¹; Tharindu Abesin Kodippili²; Jonathan McKinley¹; Stephan Lambert²; Hamid Jahed²; ¹Canmetmaterials, Natural Resources Canada; ²University of Waterloo
    The pronounced temperature and strain-rate sensitivity of magnesium alloys were apparent during full-scale forging of control arm components. To achieve the required fatigue resistance of ZK60 and AZ80 control arms, it was necessary to forge at a low temperature of 300 °C. At this temperature, a slow strain-rate was used to ensure the force required for forging was within the available load capacity of the equipment. The final forging sequence required to achieve complete material fill of the component was determined through a combination of experimental forging and numerical simulations. The temperature and rate sensitivity of the alloys and the material model utilized in the simulations will be detailed. Differences between adaptive remeshing, Adaptive-Lagrangian-Eulerian (ALE) and Combined-Eulerian-Lagrangian (CEL) FEA methods for predicting large deformation under isothermal conditions will be discussed. The challenges of forging a complex shaped magnesium component are highlighted.

First-principles Study on the Stability of Vacancy Formation in a Mg-Zn-Y Alloy with Long-period Stacking Ordered Structure: Takao Tsumuraya¹; Hiroyoshi Momida²; Tamio Oguchi²; ¹Magnesium Research Center, Kumamoto University; ²Institute for Science and Industrial Research, Osaka University
     A dilute Magnesium (Mg) based alloy with a nominal composition of Mg₉₇Zn₁Y₂ exhibit a remarkable high tensile yield strength of 600MPa. This strength is coupled with a unique atomistic structure where a concentration of solute atoms (Zn, Y) appears on the (0001) plane in a few hcp Mg matrix layers. Shockley’s partial dislocations occur in the concentrated solute atom layers. The stacking sequence is relatively long along the c-axis, and it refers to as long-period stacking ordered (LPSO) structure. In this study, to clarify the microscopic origin of the phase stabilities of LPSO structures, we calculate heats of formation and electronic structure of an Mg-Zn-Y alloy using first-principle calculations. We show how the geometry of solute clusters embedded in the Mg matrix affects electronic structure near the Fermi level that determines the structural stabilities. We also discuss the possible realization of vacancy formation in Mg-Zn-Y alloy using a convex hull.

Density Functional Theory Study of Solute Cluster Growth Processes in Mg-Y-Zn LPSO Alloys: Mitsuhiro Itakura¹; Masatake Yamaguchi¹; Daisuke Egusa²; Eiji Abe²; ¹Jaea; ²University of Tokyo
     To predict the distributions of interstitial atoms in the solute clusters in LPSO alloys, and to determine the kind of elements present, it is necessary to identify mechanisms by which interstitial atoms are created. In the present work, we use density functional theory calculations to investigate growth processes of solute clusters, in order to determine the precise atomistic structure of its solute clusters. We show that a pair of an interstitial atom and a vacancy are spontaneously created when a certain number of solute atoms are absorbed into the cluster, and that all full-grown clusters should include interstitial atoms. We also demonstrate that interstitial atoms are mostly Mg, while the rest are Y; interstitial Zn atoms are negligible. This knowledge greatly simplifies the atomistic modelingof solute clusters in Mg-Y-Zn alloys.

Mesoscale Modeling of Kinks : Pierluigi Cesana¹; ¹kyushu university
    Mg-based long-period stacking ordered (LPSO) alloys have attracted considerable attention over recent years due to their high strength, corrosion resistance and ignition temperature. Superior mechanical properties of LPSO depend strongly on a complex plastification pattern under loading and, in particular, on the formation of kinks, a mechanism that is yet to date largely elusive. In this talk we present recent advances in the modeling of kinks in the framework of non-linear elasticity. Our model consists of a Landau-type energy that is invariant under the full symmetry group of 2D (hexagonal or square) lattice. We perform FEM computations for rectangular (single-crystal) domains. We find the plastification pattern depends on the lattice symmetry and domain aspect ratio. Our results are in good agreement with a number of experimental observations of kinks both in LPSO structures and in single-crystals. This is a collaboration with G. Zanzotto (Padua) and E. Arbib (Milan).

FTMP-based Attempts Toward Kink Formation and Strengthening in MFS-Mg: Tadashi Hasebe¹; Yuta Nawa¹; ¹Kobe University
    Identification of the kink formation/strengthening mechanisms in LPSO-Mg systems is attempted based on Field Theory of Multiscale Plasticity, where FTMP-incorporated FE simulations are conducted aiming at reproducing kinking processes and the attendant strengthening. The incompatibility-based relevant underlying microscopic degrees of freedom for kinking are introduced, by projecting it on to that manifested as a variable crystallographically compatible condition for additional shear deformation, i.e., R-1 connectivity, in addition to that for the slip modes. The targeted phenomena also include scale-free-like energy release characteristics together with the specific return maps based on the combined ND–AE technique. The simulated results successfully reproduce not only the kink morphologies but also the energy-releasing characteristics. Further examinations about the choice of the measure for driving the R-1 connectivity relationship lead us to conclude that non-uniform formation of the kinking regions can play pivotal roles in raising the flow stress, in addition to the other features.

Higher-order Gradient Crystal Plasticity Analysis of LPSO-structured Magnesium Using Meshfree Approach: Yuichi Tadano¹; Daijiro Kamura¹; ¹Saga University
    Magnesium alloys with the long period stacking order (LPSO) structure show the superior strength and are expected as the next generation structural material. In the LPSO materials, kink deformation is an important deformation mechanism as well as slip deformation in the crystalline scale and may be the origin of the material strengthening. In this study, a higher-order gradient crystal plasticity analysis is conducted to evaluate the stress field around kink band to understand the strengthening mechanism due to kink. The finite element method sometimes provides an improper solution in the higher-order gradient crystal plasticity analysis; therefore, the reproducing kernel particle method, which is a kind of meshfree method, is introduced into the higher-order gradient crystal plasticity analysis. A numerical analysis of a specimen with kind band is demonstrated using the present method, and it is shown that kind band increases the macroscopic flow stress of material.

Numerical Evaluation of Kink Banding in Mg-based LPSO Single Phase Alloy: Tsuyoshi Mayama¹; Koji Hagihara²; Tetsuya Ohashi³; Yoji Mine¹; Michiaki Yamasaki¹; Yoshihito Kawamura¹; ¹Kumamoto University; ²Osaka University; ³Kitami Institute of Technology
    Kink banding in magnesium (Mg)-based long-period stacking ordered (LPSO) single phase alloy is studied by crystal plasticity finite element analysis, where basal and prismatic slip systems are taken into account. The numerical analysis reproduces formation processes of kink bands in single- and poly-crystals under various loading history including tensile, compressive or shear loading. While dominant kink-mode slip localization is developed by accumulation of basal slip, prismatic slip also produces slight kink bands under the conditions where basal slip system is hardly activated. Based on the numerical results, development mechanism of kink bands in LPSO is discussed in terms of lattice rotation and non-uniform deformation.

A Neural Network Approach for Approximating Simulation Predicted State Variables in a Preform Optimization Process: Tharindu Kodippili¹; Stephan Lambert¹; Arash Arami¹; ¹University of Waterloo
    An artificial neural network (ANN) assisted optimization framework is developed to improve the preform design process of a cast-forged magnesium AZ80 I-beam component. An entirely simulation-based optimization process would be computationally expensive and resource-intensive, limiting the searchable design space. A set of ANNs are trained – using finite element method (FEM) simulation data – on a subset of preform designs that are intelligently sampled from an optimized design space to predict state variable responses throughout spatially varying regions of the forging. The prediction accuracy of the ANNs will be discussed and compared with FEM simulations. The influence of the preform design on the material flow behavior will also be addressed.

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