Modeling of deformation induced anisotropy in free-end torsion

Böhlke, Thomas; Bertram, Albrecht; Krempl, E.

doi:10.1016/s0749-6419(03)00043-3

Cited by 39 publications

(21 citation statements)

References 38 publications

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“…The advantage of the tensorial representation is that it is coordinate-free. Therefore, the texture coefficients that occur in the tensorial representation can be used as micro-mechanically defined and measurable internal variables in continuum mechanics [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Application of the maximum entropy method in texture analysis

Böhlke

2005

Computational Materials Science

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The problem of estimating the crystallite orientation distribution function (codf) based on the leading texture coefficients is considered. Problems of such a type are called moment problems, which are well known in statistical mechanics and other areas of science. It is shown how the maximum entropy method can be applied to estimate the codf. Special emphasis is given to a coordinate-free formulation of the problem. The codf is represented by a tensorial Fourier series. The equations, which have to be solved for the estimate of the distribution function, are derived for all tensor ranks of the Fourier coefficients. As a numerical example, a model codf is estimated based on a set of discrete crystal orientations given by a full-constrained Taylor type texture simulation.

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Section: Introductionmentioning

confidence: 99%

Application of the maximum entropy method in texture analysis

Böhlke

2005

Computational Materials Science

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“…Here, we assume a linear relation between the 2nd-PiolaKirchhoff stress tensor and Green's strain tensor with respect to the undistorted state. In an Eulerian setting, this ansatz implies that the Kirchhoff stress tensor τ is given as a linear function of the Almansi strain tensor E A e (see, e.g., Böhlke and Bertram, 2001;Böhlke et al, 2003) …”

Section: Elastic Lawmentioning

confidence: 99%

“…For aggregates of cubic crystals, the Voigt bound and the Reuss bound can be represented as an additive split of the elasticity tensor into an isotropic and an anisotropic part (Böhlke and Bertram, 2001;Böhlke et al, 2003). Here, we apply such a split to the effective elasticity tensorC…”

Section: Elastic Lawmentioning

confidence: 99%

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A micro‐mechanically based quadratic yield condition for textured polycrystals

2008

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In the present paper a two-scale approach for the description of anisotropies in sheet metals is introduced, which combines the advantages of a macroscopic and a microscopic modeling. While the elastic law, the flow rule, and the hardening rule are formulated on the macroscale, the anisotropy is taken into account in terms of a micro-mechanically defined 4th-order texture coefficient. The texture coefficient specifies the anisotropic part of the elasticity tensor and the quadratic yield condition. The evolution of the texture coefficient is described by a rigid-viscoplastic Taylor type model. The advantage of the suggested model compared to the classical v. Mises-Hill model is first that macroscopic anisotropy parameters can be identified based on a texture measurement, and second that the anisotropy of the elastic and the plastic behavior is generally pathdependent, and that this path-dependence is related to a micro-mechanical deformation mechanism. An explicit modeling of the plastic spin is circumvented by the aforementioned micro-mechanical approach. The model is implemented into the FE code ABAQUS and applied to the simulation of the deep drawing process of aluminum.

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“…The tensorial Fourier coefficients or texture coefficients can be considered as micro-mechanically based tensorial internal variables [5,6,22]. They are defined in terms of the codf, which can be determined by texture measurements.…”

Section: Introductionmentioning

confidence: 99%

Texture simulation based on tensorial Fourier coefficients

Böhlke

2006

Computers & Structures

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The main result of the paper is the derivation of the evolution equation of the tensorial texture coefficients of the crystallite orientation distribution function (codf). The evolution equation of each coefficient depends on the complete codf and the lattice spin, which is a constitutive quantity. For the solution of the differential equation based on a finite number of coefficients, the codf has to be estimated. This estimate is obtained here by the maximum entropy method. By this approach the texture evolution can be described by modeling some low-order Fourier coefficients. It will be shown that such a low-dimensional approach yields a reasonable description of the texture evolution and of mechanical properties like the Taylor factor.

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Modeling of deformation induced anisotropy in free-end torsion

Cited by 39 publications

References 38 publications

Application of the maximum entropy method in texture analysis

Application of the maximum entropy method in texture analysis

A micro‐mechanically based quadratic yield condition for textured polycrystals

Texture simulation based on tensorial Fourier coefficients

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