Abstract

Crystal Plasticity (CP) modeling is a powerful and well established computational materials science tool to investigate mechanical structure–property relations in crystalline materials. It has been successfully applied to study diverse micromechanical phenomena ranging from strain hardening in single crystals to texture evolution in polycrystalline aggregates. However, when considering the increasingly complex microstructural composition of modern alloys and their exposure to—often harsh—environmental conditions, the focus in materials modeling has shifted towards incorporating more constitutive and internal variable details of the process history and environmental factors into these structure–property relations. Technologically important fields of application of enhanced CP models include phase transformations, hydrogen embrittlement, irradiation damage, fracture, and recrystallization. A number of niche tools, containing multi-physics extensions of the CP method, have been developed to address such topics. Such implementations, while being very useful from a scientific standpoint, are, however, designed for specific applications and substantial efforts are required to extend them into flexible multi-purpose tools for a general end-user community. With the Düsseldorf Advanced Material Simulation Kit (DAMASK) we, therefore, undertake the effort to provide an open, flexible, and easy to use implementation to the scientific community that is highly modular and allows the use and straightforward implementation of different types of constitutive laws and numerical solvers. The internal modular structure of DAMASK follows directly from the hierarchy inherent to the employed continuum description. The highest level handles the partitioning of the prescribed field values on a material point between its underlying microstructural constituents and the subsequent homogenization of the constitutive response of each constituent. The response of each microstructural constituent is determined, at the intermediate level, from the time integration of the underlying constitutive laws for elasticity, plasticity, damage, phase transformation, and heat generation among other coupled multi-physical processes of interest. Various constitutive laws based on evolving internal state variables can be implemented to provide this response at the lowest level. DAMASK already contains various CP-based models to describe metal plasticity as well as constitutive models to incorporate additional effects such as heat production and transfer, damage evolution, and athermal transformations. Furthermore, the implementation of additional constitutive laws and homogenization schemes, as well as the integration of a wide class of suitable boundary and initial value problem solvers, is inherently considered in its modular design.

Highlights

  • Predicting, understanding, and controlling the mechanical behavior is critical when designing structural materials and using them during service

  • Lp = f around the indents strongly depends on the activated deformation systems and, the crystal orientation. It was the idea of Zambaldi and Raabe [216] to use the information provided by this pattern, i.e. the height profile around the indent, together with the force–displacement curve to determine the parameter set of a Crystal Plasticity (CP) constitutive model

  • It was found that the CP simulations can be very efficiently used to calibrate complex analytical yield surfaces that are commonly used in industrial manufacturing. These results show that the use of Düsseldorf Advanced Material Simulation Kit (DAMASK)-based numerical homogenization schemes in conjunction with the spectral solver and high resolution Representative Volume Element (RVE) can serve as a powerful VIRTUAL LABORATORY for meeting simulation challenges in advanced manufacturing involving complex forming operations

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Summary

Introduction

Predicting, understanding, and controlling the mechanical behavior is critical when designing structural materials and using them during service. An example where the interplay of compositional changes with various interacting deformation mechanisms has been studied in detail is the dependence of dislocation (cross-) slip, mechanical twinning, and the formation of - and -martensite on the Stacking Fault Energy (SFE) in face-centered cubic (fcc) Iron (Fe)Manganese (Mn) [18,19] Such development of chemical compositionsensitive constitutive models is of high relevance since practically all engineering materials are multicomponent systems. Other than previous overviews of the field of continuum modeling [4,16,44,45,46,47], this contribution places the focus on those kinematic and constitutive features available in DAMASK together with numerical and technical details of their implementation, which are complemented by illustrative application examples It should, be mentioned that the DAMASK package is steadily extended and improved—hopefully by contributors attracted by this work—so that this paper can only reflect the status at the time of writing. In the Appendix, the scheme of notation and other technical information is compiled

Concept
Background
Hierarchical structure
Modularization
Conservation laws
Formulation
Numerical solvers
Partitioning and homogenization
Mechanical fields
Thermal fields
Damage fields
Single constituent kinematics
Multiplicative decomposition
Time integration
Stress tangent
Constitutive laws
Plasticity
Atomistically-informed crystal plasticity for Tungsten
Temperature
Damage
Application examples
Advanced generation techniques for synthetic dual phase steel microstructures
Free surfaces in spectral solver simulations
Wedge indentation
Single crystalline pillar compression
Single crystalline cellular materials
Shear banding
Grain-scale micromechanics of Magnesium
7.10. Damage in martensitic steel
7.11. Dual phase steel micromechanics
C11 C12 C44
7.12. Texture evolution during plate rolling
7.13. The VIRTUAL LABORATORY
7.14. Deep drawing of dual phase steel
7.15. Continuum dislocation dynamics
7.16. Dislocation patterning during cyclic loading
7.17. Glissile junction formation
7.18. Thermo-mechanics of microelectronic devices
7.19. Mechanics of biological structural materials
Workflow and usage philosophy
Boundary value problem solver
Pre- and postprocessing
Summary and outlook
Findings
PFT detF det
Full Text
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