Quantitative re-examination of Taylor model for FCC polycrystals

Tadano, Yuichi; Kuroda, Mitsutoshi; Noguchi, Hirohisa

doi:10.1016/j.commatsci.2011.07.024

Cited by 29 publications

(18 citation statements)

References 34 publications

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“…The Taylor model also represent the S-D effect, however, evaluated flow stresses exceed values obtained using the proposed model, consistent with a previous study on face-centered cubic polycrystals. 15) Flow stresses under uniaxial tensions and compressions are shown in Fig. 2 for hydrostatic pressures of p = 0, 552, and 1 104 MPa along with experimental results.…”

Section: Model Validationmentioning

confidence: 99%

“…Initial crystal orientations are randomly distributed, and the number of crystal grains is set to 512, which is considered sufficient to represent the polycrystalline behavior of cubic metals. 15) …”

Section: Analysis Conditionmentioning

confidence: 99%

“…Although this approach was successfully used in a lot of previous studies, the Taylor model sometimes overestimates the flow stress because of its inability to represent the highly inhomogeneous deformation of individual crystal grains. 15) Modern polycrystalline models, such as those based on the homogenization-based finite element method, have also been suggested. 16,17) The homogenization-based finite element method produces the mechanical properties of materials with an arbitrary microstructure as long as the microstructure is represented by a finite element model.…”

Section: Hydrostatic Pressure Dependent Crystal Plasticity By Homogenmentioning

confidence: 99%

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Hydrostatic Pressure Dependent Crystal Plasticity by Homogenization-based Finite Element Method

Tadano

Hagihara

2016

ISIJ Int.

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A crystal plasticity model considering the hydrostatic pressure dependence is presented and validated using several numerical examples. Some metallic materials clearly show higher flow stress under uniaxial compression than that under uniaxial tension, and this phenomenon is called the strength-differential (S-D) effect. Since the S-D effect often occurs in iron-based materials, the understanding and modeling of its mechanical characteristics is important in industrial and engineering fields. The S-D effect may result from the hydrostatic pressure dependence of plastic deformation. Therefore, in this study, a crystal plasticity model is modified to account for this dependence. The proposed model is combined with the homogenization-based finite element method. This model adequately reproduces the S-D effect observed experimentally, thus its advantages over the previously introduced Taylor polycrystalline model, which overestimates the flow stress and fails to represent the strong inhomogeneity of hydrostatic pressure distribution at a crystalline scale, is highlighted. In addition, initial and subsequent plastic work contours are evaluated and a forming limit diagram is analyzed to characterize the new model.

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Section: Model Validationmentioning

confidence: 99%

Section: Analysis Conditionmentioning

confidence: 99%

Section: Hydrostatic Pressure Dependent Crystal Plasticity By Homogenmentioning

confidence: 99%

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Hydrostatic Pressure Dependent Crystal Plasticity by Homogenization-based Finite Element Method

Tadano

Hagihara

2016

ISIJ Int.

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“…Yield points were defined to correspond to the 0.2% equivalent plastic strain for each loading condition. 36 A comparison of the yield loci from the phenomenological theory and the locus from the crystal plasticity theory showed a recognisable difference in the spread towards the pure shear direction and in sharpness towards the equi-biaxial tension direction.…”

Section: Mechanical Characterisationmentioning

confidence: 98%

Forming-limit prediction of perforated aluminium sheets with square holes

Chiba

Takeuchi

Nakamura

2015

The Journal of Strain Analysis for Engineering Design

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The forming-limit strains of perforated aluminium alloy (AA5052-O) sheets with square holes were theoretically and experimentally estimated for two types of hole arrangements: square and triangular patterns. The theoretical forminglimit curves were obtained by finite-element analyses on a unit module of the perforated sheets using two different approaches: the phenomenological theory and crystal plasticity theory. Hill's quadratic anisotropic and von Mises yield functions were used for the phenomenological analysis, and the one-element-per-grain model was adopted for the crystal plasticity analysis. To determine the forming limits, two different types of plastic instability criteria were applied. The experimental forming-limit strains were also obtained through a Nakazima stretching test. The theoretical predictability of the forming-limit curves was assessed by comparing the theoretical and experimental results. The comparison demonstrated that (1) the plastic instability criterion based on the external force power predicted qualitatively the same forming-limit curves as the criterion based on the equivalent plastic strain of the ligament for both hole arrangement patterns and (2) although the shapes of the predicted forming-limit curves were in reasonable agreement with the experimental results, the level of the predicted limit strains was considerably higher than that of the experimental limit strains. Thus, it was found that neither of the plastic instability criteria previously proposed for perforated sheets is appropriate to characterise the formability of perforated aluminium sheets with square holes.

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“…12 to 15), which has been often considered as an upper bound for the stresses, may contribute to explain the associated higher predicted limit strains. Recent reexamination of the Taylor model(Tadano et al, 2012) also revealed that its predictions tend to underestimate the lattice rotations. Because the latter play a major role in inducing textural (geometrical) softening that is favorable to localization, this may bring some support to the aboveobserved differences.…”

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confidence: 99%

Strain localization analysis for single crystals and polycrystals: Towards microstructure-ductility linkage

Franz¹,

Abed‐Meraim

Berveiller

2013

International Journal of Plasticity

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In this paper, we performed a strain localization analysis for single crystals and polycrystals, with the specific aim of establishing a link between the microstructure-related parameters and ductility. To this end, advanced large-strain elastic plastic single crystal constitutive modeling is adopted, accounting for the key physical mechanisms that are relevant at the microscale, such as dislocation storage and annihilation. The self-consistent scale-transition scheme is then used to derive the overall constitutive response of polycrystalline aggregates, including the essential microstructural aspects (e.g., initial and induced textures, dislocation density evolution, and softening mechanisms). The resulting constitutive equations for single crystals and polycrystals are coupled with two strain localization criteria: bifurcation theory, which is also related to the loss of ellipticity in the associated boundary value problem, and the strong ellipticity condition, which is presented in full detail along with mathematical links allowing for hierarchical classification in terms of conservativeness. The application of the proposed coupling to single crystals and polycrystals allows the effect of physical microstructural parameters on material ductility to be investigated. Consistent results are found for both single crystals and polycrystals. In addition, forming limit diagrams (FLDs) are constructed for IF-Ti single-phase steels with comparison to the reference results, demonstrating the predictive capability of the proposed approach in investigations of sheet metal formability. The results of the self-consistent scheme are systematically compared to those of the more classical full-constraint Taylor model, both in terms of the impact of microstructural parameters on ductility and in terms of the predicted formability limits and the level of the associated limit strains. Finally, we investigated the impact of strain-path changes on formability through the analysis of the effect of prestrain on the FLDs.International audienceIn this paper, we performed a strain localization analysis for single crystals and polycrystals, with the specific aim of establishing a link between the microstructure-related parameters and ductility. To this end, advanced large-strain elastic plastic single crystal constitutive modeling is adopted, accounting for the key physical mechanisms that are relevant at the microscale, such as dislocation storage and annihilation. The self-consistent scale-transition scheme is then used to derive the overall constitutive response of polycrystalline aggregates, including the essential microstructural aspects (e.g., initial and induced textures, dislocation density evolution, and softening mechanisms). The resulting constitutive equations for single crystals and polycrystals are coupled with two strain localization criteria: bifurcation theory, which is also related to the loss of ellipticity in the associated boundary value problem, and the strong ellipticity condition, which is presented in full detail...

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Quantitative re-examination of Taylor model for FCC polycrystals

Cited by 29 publications

References 34 publications

Hydrostatic Pressure Dependent Crystal Plasticity by Homogenization-based Finite Element Method

Hydrostatic Pressure Dependent Crystal Plasticity by Homogenization-based Finite Element Method

Forming-limit prediction of perforated aluminium sheets with square holes

Strain localization analysis for single crystals and polycrystals: Towards microstructure-ductility linkage

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