Mechanical elastic constants and diffraction stress factors of macroscopically elastically anisotropic polycrystals: the effect of grain-shape (morphological) texture

Koch, N.; Welzel, U.; Wern, H.; Mittemeijer, E. J.

doi:10.1080/14786430412331284504

Cited by 32 publications

(37 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We have already demonstrated that: (33) and (34)). The satisfaction of that equation was demonstrated to be compatible with the traditional expression (40) employed for achieving the macroscopic stiffness determination.…”

Section: Checking the Compatibility Of The Geometric Version Of Eshelmentioning

confidence: 99%

“…Numerous, still recent, papers have actually dealt with the question of estimating the effective stiffness of single-phase (Kocks et al [34]) and two-phases (Fréour et al [20]) metallic bulk polycrystals, thin solid films (Welzel and Fréour [63]), or even metal / organic matrix composites (Fréour et al [24]), for instance. Scale transition models are also often used for calculating the (XEC) X-Ray Elasticity Constants (Hauk [29]; Koch et al [33]), required for achieving internal stress determination from X-Ray Diffracting peak-shifting measurements, since XEC are otherwise rather uneasy to deduce from experiments, even if some valuable experimental investigations have already been published (Singh et al [52]). The connected question of predicting the macroscopic Coefficients of Thermal Expansion or the Coefficients of Moisture Expansion of such heterogeneous materials has also (in most previously cited cases) been addressed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the meaning of the chosen set‐averaging method within Eshelby‐Kröner self‐consistent scale transition model: the geometric mean versus the classical arithmetic average

et al. 2011

View full text Add to dashboard Cite

Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. In the present work, the fundamental formalism historically introduced by Kröner is, for the first time, considered from the point of view of both the geometric and the arithmetic set averages methods. It is demonstrated in this paper that the polarization tensors describing the relations existing between the local and the macroscopic mechanical states do have a strong physical meaning when expressed using the geometric average, instead of the classical arithmetic mean.

show abstract

Section: Checking the Compatibility Of The Geometric Version Of Eshelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the meaning of the chosen set‐averaging method within Eshelby‐Kröner self‐consistent scale transition model: the geometric mean versus the classical arithmetic average

et al. 2011

View full text Add to dashboard Cite

show abstract

“…2.3 (Grain-shape / morphological texture) will be adopted. The effect of a grain-shape texture on the mechanical elastic constants has been considered by [23,27,28].…”

Section: Determination Of the Macroscopic Elastic Stiffness Accordingmentioning

confidence: 99%

“…the ellipsoidal grains are aligned along common axes (an ideal grain-shape texture occurs). Only an ideal grain-shape texture is considered in the following, as only in this case unique mechanical elastic constants and X-ray stress factors can be calculated employing the Eshelby-Kröner model (for a more detailed discussion of the effect of a non-ideal morphological texture, see [23]). …”

Section: Grain-shape/morphological Texturementioning

confidence: 99%

Eshelby‐Kröner self‐consistent elastic model: the geometric mean versus the arithmetic mean – A numerical investigation

Fréour

Fajoui

2012

Z Angew Math Mech

View full text Add to dashboard Cite

To cite this version:Sylvain Fréour, Jamal Fajoui. Eshelby-Kröner Self-Consistent elastic model: the geometric mean versus the arithmetic mean -A numerical investigation. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2012, 92 (4), pp.329-338. 10.1002 Key words Scale transition model, sets averages, geometric mean, arithmetic mean, Eshelby-Kröner self-consistent model.Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effec-tive behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corre-sponding macroscopic quantities, require the extensive use of set averages. The present paper is devoted to the comparison of the numerical results provided in pure elasticity by Eshelby-Kröner model depending on the average type chosen for achieving set average operations: either the traditional arithmetic mean or the geometric average. Various numerical applications of the model to the case of predicting either the effective stiffness or the lattice strains of singlephase polycrystals will be provided. The particular case when an extreme grain-shape occurs will also be investigated.

show abstract

“…Many studies have been conducted to characterize the mechanical properties of such materials. The classical Eshelby-Kröner self-consistent model enables to take into account non-spherical grains when certain conditions are fulfilled [1][2][3]. According to these restrictions, only an ideal morphological texture can be taken into account through (identical) ellipsoidal inclusions whose principal axes are aligned along specific directions in the specimen.…”

mentioning

confidence: 99%

Accounting for a Distribution of Morphologies and Orientations on Stresses Analysis by X-Ray and Neutron Diffraction: Normalized Self-Consistent Modeling

Hounkpati

Fréour

Gloaguen

et al. 2014

AMR

View full text Add to dashboard Cite

Abstract. The historical Eshelby-Kröner self-consistent model is only valid in the case when grains can be assumed similar to ellipsoids aligned preferentially along a same direction into the polycrystal. In this work, distributions of crystallites morphologies and geometrical orientations were accounted for, owing to the so-called normalized self-consistent model, in order to satisfy Hill's averages principles. Different nonlinear εϕψ-vs.-sin 2 ψ distributions were predicted in elasticity, even in the absence of crystallographic texture, in the case when several morphologies and geometrical orientations coexist within the same polycrystal. IntroductionPolycrystals with a morphological texture have macroscopic anisotropic properties in the absence of crystallographic texture. Many studies have been conducted to characterize the mechanical properties of such materials. The classical Eshelby-Kröner self-consistent model enables to take into account non-spherical grains when certain conditions are fulfilled [1][2][3]. According to these restrictions, only an ideal morphological texture can be taken into account through (identical) ellipsoidal inclusions whose principal axes are aligned along specific directions in the specimen. Such a microstructure is not generally observed in a real specimen; several morphologies or several grains with different morphological orientations could coexist within the same crystalline material. It is the case, for example, of titanium alloy Ti-17 polycrystal which consists of needle-shaped α crystallites mixed to slightly equiaxed prior β-grains [4]. Another example could be chosen among composite materials, made of epoxy resin and carbon-epoxy reinforcing strips, exhibiting an inplane distribution on the morphologies [5], the microstructure of which was successfully modeled through disc-shaped inclusions.It was recently numerically shown [5] that in such a situation, the Eshelby-Kröner self-consistent model does not simultaneously fulfil anymore both the so-called "Hill's average relations over the mechanical states", historically established in [6]. Therefore, this theoretical approach fails to represent a morphological texture featuring various grain shapes or a relative disorientation of the morphologies coexisting. The main interest of the present contribution is to show the possible influence of this morphological texture in the context of stress analysis by diffraction, in elasticity, using a normalized elastic self-consistent model. Then, we will be interested in the εϕψ-vs.-sin 2 ψ diagrams. If transversely isotropic grains are randomly oriented, the effective property of the polycrystal will be approximately isotropic, with values depending on the volume fraction and aspect ratio of the inclusions [7]. A random morphologic texture can then be neglected without consequence, within the context of modelling the multi-scale behaviour of heterogeneous materials consisting of quasi-isotropic elementary inclusions. This was demonstrated, at least numerically in [4]. Therefore, spec...

show abstract

Mechanical elastic constants and diffraction stress factors of macroscopically elastically anisotropic polycrystals: the effect of grain-shape (morphological) texture

Cited by 32 publications

References 16 publications

On the meaning of the chosen set‐averaging method within Eshelby‐Kröner self‐consistent scale transition model: the geometric mean versus the classical arithmetic average

On the meaning of the chosen set‐averaging method within Eshelby‐Kröner self‐consistent scale transition model: the geometric mean versus the classical arithmetic average

Eshelby‐Kröner self‐consistent elastic model: the geometric mean versus the arithmetic mean – A numerical investigation

Accounting for a Distribution of Morphologies and Orientations on Stresses Analysis by X-Ray and Neutron Diffraction: Normalized Self-Consistent Modeling

Contact Info

Product

Resources

About