Micromechanical Model of Polycrystalline Materials with Lamellar Substructure

Kowalczyk-Gajewska, K.

doi:10.2478/v10172-011-0055-3

Cited by 9 publications

(4 citation statements)

References 30 publications

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“…The scheme coincides with the additive tangent approach [23] for the case of the Mori-Tanaka scheme. The results for the case of the self-consistent case were presented in [24] and [14]. Details of the self-consistent formulation can be found in the aforementioned papers.…”

Section: The Evpsc Modelmentioning

confidence: 99%

Crystal Plasticity Parameter Optimization in Cyclically Deformed Electrodeposited Copper – A Machine Learning Approach

Frydrych,

Tomczak,

Papanikolaou

2024

Preprint

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The paper describes an application of machine learning approach for parameter optimization. The method is demonstrated for the elasto-viscoplastic model with both isotropic and kinematic hardening. It is shown that the proposed method based on long-short term memory networks enabled to obtain reasonable agreement of stress-strain curves for cyclic deformation in low-cycle fatigue regime. The main advantage of the proposed approach over traditional optimization schemes lies in the possibility to get parameters for a new material without the necessity to conduct any further optimizations. As the power and robustness of the developed method was demonstrated on the very challenging problem (cyclic deformation, crystal plasticity, self-consistent model, isotropic and kinematic hardening), it is directly applicable to other experiments and models.

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Section: The Evpsc Modelmentioning

confidence: 99%

Crystal Plasticity Parameter Optimization in Cyclically Deformed Electrodeposited Copper – A Machine Learning Approach

Frydrych,

Tomczak,

Papanikolaou

2024

Preprint

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“…The two scalars KL iso and ḠL iso will be next compared with the estimates of isotropic bulk and shear moduli obtained by two variants of the core-shell model. The error ζ 2 related to the proposed isotropic approximation is defined by a normalized difference between CL iso and the actual C. It is defined as [58] ζ…”

Section: The Closest Isotropic Approximation CLmentioning

confidence: 99%

Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline materials of cubic symmetry

Kowalczyk-Gajewska,

Maździarz

2019

Preprint

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Anisotropic core-shell model of a nano-grained polycrystal, proposed recently for nanocrystalline copper, is applied to estimate elastic effective properties for a set of crystals of cubic symmetry. Materials selected for analysis differ in the lattice geometry (face-centered cubic vs. body-centered cubic) as well as the value of a Zener factor: a ratio of two shear moduli defining elastic anisotropy of a cubic crystal. The predictions are verified by means of the atomistic simulations. The dependence of the overall bulk and shear moduli on the average grain diameter is analysed. In the mean-field approach the thickness of the shell is specified by the cutoff radius of a corresponding atomistic potential, while the grain shell is isotropic and its properties are identified by molecular simulations performed for very small grains with approximately all atoms belonging to the grain boundary zone. It is shown that the core-shell model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations. Performed study indicates that the variation of the bulk and shear moduli with the grain size changes qualitatively when the Zener anisotropy factor is smaller or greater than one.

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“…The second anisotropy measure ζ 2 is defined by a norm of difference between the closest isotropic approximation of C and the actual C. The difference is normalized by the norm of C. The closest isotropic approximation of C is established employing the Log-Euclidean metric as proposed in [52]. The anisotropy factor is then calculated as [53] ζ…”

Section: Continuum Mechanics Estimates Of Elastic Modulimentioning

confidence: 99%

Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline copper

Kowalczyk-Gajewska

Maździarz

2018

International Journal of Engineering Science

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The full elasticity tensor for nano-crystalline copper is derived in molecular simulations by performing numerical tests for a set of generated samples of the polycrystalline material. The results are analysed with respect to the anisotropy degree of the overall stiffness tensor resulting from the limited number of grain orientations and their spatial distribution. The dependence of the overall bulk and shear moduli of an isotropized polycrystal on the average grain diameter is analysed. It is found that while the shear modulus decreases with grain size, the bulk modulus shows negligible dependence on the grain diameter and is close to the bulk modulus of a single crystal. A closed-form mean-field model of effective elastic properties for a bulk nano-grained polycrystal with cubic grains, i.e. made of a material with cubic symmetry, is formulated. In the model all parameters are based on the data for a single crystal and on the averaged grain size without any need for additional fitting. It is shown that the proposed model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations.

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Micromechanical Model of Polycrystalline Materials with Lamellar Substructure

Cited by 9 publications

References 30 publications

Crystal Plasticity Parameter Optimization in Cyclically Deformed Electrodeposited Copper – A Machine Learning Approach

Crystal Plasticity Parameter Optimization in Cyclically Deformed Electrodeposited Copper – A Machine Learning Approach

Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline materials of cubic symmetry

Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline copper

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