Research Projects

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Research Projects

F. Rotersa,*, P. Eisenlohra, L. Hantcherlia, D. D. Tjahjantoa, T. R. Bielerb , D. Raabea  aMax-Planck-Institut für Eisenforschung, Düsseldorf, Germany bChemical Engineering and Materials Science, Michigan State University, East Lansing MI, USAAbstract
This article reviews continuum-based variational formulations for describing the elastic–plastic deformation of anisotropic heterogeneous crystalline matter. These approaches, commonly referred to as crystal plasticity finite element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media. Besides the discussion of the constitutive laws, kinematics, homogenization schemes, and multiscale approaches behind these methods we also present some examples including in particular comparisons of the predictions with experiments. The applications stem from such diverse fields as orientation stability, microbeam bending, single-and bicrystal deformation, nanoindentation, recrystallization, multiphase steel (TRIP) deformation, and damage prediction for the microscopic and mesoscopic scales and multiscale predictions of rolling textures, cup drawing, Lankfort (r) values, and stamping simulations for the macroscopic scale.

Basics of constitutive formulations, crystal kinematics, homogenization, multiple scales, and multiphysics approaches in crystal plasticity finite element modeling: theory, experiments, applications

F. Rotersa,*, P. Eisenlohra, L. Hantcherlia, D. D. Tjahjantoa, T. R. Bielerb , D. Raabea

aMax-Planck-Institut für Eisenforschung, Düsseldorf, Germany
bChemical Engineering and Materials Science, Michigan State University, East Lansing MI, USA

Abstract

This article reviews continuum-based variational formulations for describing the elastic–plastic deformation of anisotropic heterogeneous crystalline matter. These approaches, commonly referred to as crystal plasticity finite element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media. Besides the discussion of the constitutive laws, kinematics, homogenization schemes, and multiscale approaches behind these methods we also present some examples including in particular comparisons of the predictions with experiments. The applications stem from such diverse fields as orientation stability, microbeam bending, single-and bicrystal deformation, nanoindentation, recrystallization, multiphase steel (TRIP) deformation, and damage prediction for the microscopic and mesoscopic scales and multiscale predictions of rolling textures, cup drawing, Lankfort (r) values, and stamping simulations for the macroscopic scale.

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Creep of single crystal superalloys is governed by dislocation glide, climb, reactions, and annihilation. We use discrete 3D dislocation dynamics (DDD) simulations to study the evolution of the dislocation substructure in a γ/γ’ microstructure of a single crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with γ’ cubes.

Influence of dislocation climb on the creep rates in γ'-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study

Creep of single crystal superalloys is governed by dislocation glide, climb, reactions, and annihilation. We use discrete 3D dislocation dynamics (DDD) simulations to study the evolution of the dislocation substructure in a γ/γ’ microstructure of a single crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with γ’ cubes.
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We present crystal plasticity finite element simulations of plane strain compression of α-brass single crystals with different initial orientations. The aim is to study the fundamentals of mesoscale structure and texture development in fcc metals with low stacking fault energy (SFE). Shear banding depends on the initial orientation of the crystals. In Copper and Brass-R oriented crystals which show the largest tendency to form shear bands, an inhomogeneous texture distribution induced by shear banding is observed. To also understand the influence of the micromechanical boundary conditions on shear band formation, simulations on Copper oriented single crystals with varying sample geometry and loading conditions are performed. We find that shear banding can be understood in terms of a mesoscopic softening mechanism. The predicted local textures and the shear banding patterns agree well with experimental observations in low SFE fcc crystals. Keywords: fcc material; shear band; texture; crystal plasticity finite element analysis

Orientation dependence of shear banding in fcc single crystals

We present crystal plasticity finite element simulations of plane strain compression of α-brass single crystals with different initial orientations. The aim is to study the fundamentals of mesoscale structure and texture development in fcc metals with low stacking fault energy (SFE). Shear banding depends on the initial orientation of the crystals. In Copper and Brass-R oriented crystals which show the largest tendency to form shear bands, an inhomogeneous texture distribution induced by shear banding is observed. To also understand the influence of the micromechanical boundary conditions on shear band formation, simulations on Copper oriented single crystals with varying sample geometry and loading conditions are performed. We find that shear banding can be understood in terms of a mesoscopic softening mechanism. The predicted local textures and the shear banding patterns agree well with experimental observations in low SFE fcc crystals. Keywords: fcc material; shear band; texture; crystal plasticity finite element analysis
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This progress report discusses how physically based material models can contribute to the development and optimization of new materials. Using in addition enhanced simulation techniques such as density functional theory a true multi scale material development can be established.

Mechanism Oriented Steel Development

This progress report discusses how physically based material models can contribute to the development and optimization of new materials. Using in addition enhanced simulation techniques such as density functional theory a true multi scale material development can be established.
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Dual-phase (DP) steel is the flagship of advanced high-strength steels, which were the first among various candidate alloy systems to find application in weight-reduced automotive components. On the one hand, this is a metallurgical success story:

Dual-Phase Steels: Advances in Microstructure-Oriented Processing and Micromechanically Guided Design

Dual-phase (DP) steel is the flagship of advanced high-strength steels, which were the first among various candidate alloy systems to find application in weight-reduced automotive components. On the one hand, this is a metallurgical success story:
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Single crystalline copper beams with thicknesses between 0.7 and 5 μm are manufactured with a focused ion beam technique and bent in a nanoindenter. The yield strengths of the beams show a mechanical size effect (smaller-is-stronger).

The mechanical size effect as a mean-field breakdown phenomenon: Example of microscale single crystal beam bending

Single crystalline copper beams with thicknesses between 0.7 and 5 μm are manufactured with a focused ion beam technique and bent in a nanoindenter. The yield strengths of the beams show a mechanical size effect (smaller-is-stronger).
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In this project we pursue an approach for the computationally efficient and quantitatively accurate prediction of solid-solution strengthening. It combines the 2-D Peierls–Nabarro model and a recently developed solid-solution strengthening model. Solid-solution strengthening is examined with Al–Mg and Al–Li as representative alloy systems...

Computationally efficient and quantitatively accurate multiscale simulation of solid-solution strengthening by ab initio calculation

In this project we pursue an approach for the computationally efficient and quantitatively accurate prediction of solid-solution strengthening. It combines the 2-D Peierls–Nabarro model and a recently developed solid-solution strengthening model. Solid-solution strengthening is examined with Al–Mg and Al–Li as representative alloy systems...
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In this project we identify and analyze general trends governing solid solution strengthening in binary alloys containing solutes across the Periodic table using quantum-mechanical calculations. Here we present calculations for the model system of Al binary solid solutions.

Ab initio study of compositional trends in solid solution strengthening in metals with low Peierls stresses

In this project we identify and analyze general trends governing solid solution strengthening in binary alloys containing solutes across the Periodic table using quantum-mechanical calculations. Here we present calculations for the model system of Al binary solid solutions.
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In this project we study a new strategy for the theory-guided bottom up design of beta-Ti alloys for biomedical applications using a quantum mechanical approach in conjunction with experiments. Parameter-free density functional theory calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys...

Theory-guided bottom-up design of b-titanium alloys as biomaterials based on first principles calculations: Theory and experiments

In this project we study a new strategy for the theory-guided bottom up design of beta-Ti alloys for biomedical applications using a quantum mechanical approach in conjunction with experiments. Parameter-free density functional theory calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys...
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Designing light-weight bcc Mg-Li alloys by using ab initio calculations

Ab initio calculations are becoming increasingly useful to engineers interested in designing new alloys because these calculations are able to accurately predict basic material properties only knowing the atomic composition of the material.  In this project, single crystal elastic constants of 11 bcc Mg-Li alloys are calculated using density-functional theory (DFT) and compared with available experimental data. 
Bcc Mg-Li-based alloys are a promising light-weight structural material. In order to tailor the Mg-Li composition with respect to specific industrial requirements, systematic materialsdesign concepts need to be developed and applied. Quantum-mechanical calculations are increasingly employed when designing new alloys as they accurately predict basic thermodynamic, structural, and functional properties using only the atomic composition as input.

Using Ab Initio Calculations in Designing bcc MgLi-X Alloys for Ultra-lightweight Applications

Bcc Mg-Li-based alloys are a promising light-weight structural material. In order to tailor the Mg-Li composition with respect to specific industrial requirements, systematic materialsdesign concepts need to be developed and applied. Quantum-mechanical calculations are increasingly employed when designing new alloys as they accurately predict basic thermodynamic, structural, and functional properties using only the atomic composition as input.
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