Regularized Yield Surfaces for Crystal Plasticity of Metals

Holmedal, Bjørn

doi:10.3390/cryst10121076

Cited by 6 publications

(4 citation statements)

References 37 publications

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“…Otherwise, the deformation is plastic and the return mapping should be employed to calculate the stress. The yield surface is the key function of the plasticity model, and this time the Holmedal model [ 36 ] is chosen:

where n is a material parameter. In Equation ( 19 ), the tensor

is the symmetric part of the Schmid factor in the

slip system, and it is constant in the lattice frame.…”

Section: Applications Of the Single-point Calculatormentioning

confidence: 99%

On the Single-Point Calculation of Stress–Strain Data under Large Deformations with Stress and Mixed Control

Wang

Chen

2022

Materials

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Stress–strain data with a given constitutive model of material can be calculated directly at a single material point. In this work, we propose a framework to perform single-point calculations under large deformations with stress and mixed control, to test and validate sophisticated constitutive models for materials. Inspired by Galerkin–FFT methods, a well-defined mask projector is used for stress and mixed control, and the derived nonlinear equations are solved in Newton iterations with Krylov solvers, simplifying implementation. One application example of the single-point calculator in developing sophisticated models for anisotropic single crystal rate-independent elastoplasticity is given, illustrating that the proposed algorithm can simulate asymmetrical deformation responses under uni-axial loading. Another example for artificial neural network models of the particle reinforced composite is also given, demonstrating that the commonly used machine learning or deep learning modeling frameworks can be directly incorporated into the proposed calculator. The central difference approximation of the tangent is validated so that derivative-free calculations for black-box constitutive models are possible. The proposed Python-coded single-point calculator is shown to be capable of quickly building, testing, and validating constitutive models with sophisticated or implicit structures, thus boosting the development of novel constitutive models for advanced solid materials.

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where n is a material parameter. In Equation ( 19 ), the tensor

is the symmetric part of the Schmid factor in the

slip system, and it is constant in the lattice frame.…”

Section: Applications Of the Single-point Calculatormentioning

confidence: 99%

On the Single-Point Calculation of Stress–Strain Data under Large Deformations with Stress and Mixed Control

Wang

Chen

2022

Materials

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“…Both the FC-Taylor and the Alamel model were implemented using the regularized single crystal yield surface (Holmedal, 2020). This approach enables activation of any number and type of slip systems in a very robust way.…”

Section: Crystal Plasticity Modelingmentioning

confidence: 99%

“…The FC-Taylor model ignores any grain interactions, whereas the Alamel model assumes grain interaction locally at the grain boundary by allowing relaxations of the strain constraints. Both models were formulated and implemented based on the regularized single crystal yield surface (Holmedal, 2020). This approach allows to introduce rate-sensitive behavior as well as activation of arbitrary number and type of slip systems in a robust way.…”

Section: Rate-sensitive Cp Models With Only the Octahedral Slip Systemsmentioning

confidence: 99%

Deformation Texture Evolution in Flat Profile AlMgSi Extrusions: Experiments, FEM, and Crystal Plasticity Modeling

et al. 2021

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In the present work, the deformation textures during flat profile extrusion from round billets of an AA6063 and an AA6082 aluminium alloy have been numerically modeled by coupling FEM flow simulations and crystal plasticity simulations and compared to experimentally measured textures obtained by electron back-scatter diffraction (EBSD). The AA6063 alloy was extruded at a relatively low temperature (350°C), while the AA6082 alloy, containing dispersoids that prevent recrystallization, was extruded at a higher temperature (500°C). Both alloys were water quenched at the exit of the die, to maintain the deformation texture after extrusion. In the center of the profiles, both alloys exhibit a conventional β-fiber texture and the Cube component, which was significantly stronger at the highest extrusion temperature. The classical full-constraint (FC)-Taylor and the Alamel grain cluster model were employed for the texture predictions. Both models were implemented using the regularized single crystal yield surface. This approach enables activation of any number and type of slip systems, as well as accounting for strain rate sensitivity, which are important at 350°C and 500°C. The strength of the nonoctahedral slips and the strain-rate sensitivity were varied by a global optimization algorithm. At 350°C, a good fit could be obtained both with the FC Taylor and the Alamel model, although the Alamel model clearly performs the best. However, even with rate sensitivity and nonoctahedral slip systems invoked, none of the models are capable of predicting the strong Cube component observed experimentally at 500°C.

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“…Further examples on crystal plasticity modeling involve a reaction stress model (Zhang et al [9]), statistical crystal plasticity constitutive models of polycrystalline metals and alloys (Shveykin et al [10]) or 3D representative volume element approach (Qayyum et al [11]). Furthermore, a theoretical work related to yield surfaces and slip systems has been provided by Holmedal [12].…”

mentioning

confidence: 99%