Texture simulation based on tensorial Fourier coefficients

Böhlke, Thomas

doi:10.1016/j.compstruc.2006.01.006

“…However, Equation (27) consists of a system of nonlinear equations with the unknown variables sitting in the position of the exponential terms; therefore, it is nearly infeasible to be solved by the regular mathematical methods. Up to now, researchers still make unceasing progress in exploring the possible paths for resolving the problem of MEM [42][43][44].…”

Section: B Analysis Of the Complete Odf(c-odf) Via The Maximum Entromentioning

confidence: 99%

An Evolutionary Algorithm for the Texture Analysis of Cubic System Materials Derived by the Maximum Entropy Principle

Wang

¹

,

Wang

²

,

Wu

³

et al. 2014

Entropy

0

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Based on the principle of maximum entropy method (MEM) for quantitative texture analysis, the differential evolution (DE) algorithm was effectively introduced. Using a DE-optimized algorithm with a faster but more stable convergence rate of iteration, more reliable complete orientation distribution functions (C-ODF) have been obtained for deep-drawn IF steel sheets and the recrystallized aluminum foils after cold-rolling, which are both designated as the macroscopic cubic-orthogonal symmetry. With special reference to the data processing, no more other assumptions are required for DE-optimized MEM except that the system entropy approaches the maximum.

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“…Here, this tensor is calculated based on a discrete orientation distribution. For a set of N crystal orientations and corresponding volume fractions {Q α , ν α }, the tensor V ′ is given by (Böhlke, , 2006. In the last equation, the orthogonal tensor Q α represents the orientation Q of the α-th crystal.…”

Section: Elastic Lawmentioning

confidence: 99%

“…If we neglect the lattice distortions, which is an assumption reasonable for small elastic strains, then the anisotropic part of the stiffness tensor C A e can be described in terms of the 4th-order texture coefficient V ′ (Böhlke, , 2006 C A e = ζV ′ .…”

Section: Elastic Lawmentioning

confidence: 99%

A micro‐mechanically based quadratic yield condition for textured polycrystals

Böhlke

¹

,

Risy

²

,

Bertram

³

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.

show abstract

“…If we neglect the lattice distortions, which is an assumption reasonable for small elastic strains, then the anisotropic part of the stiffness tensor C A e can be described in terms of the 4th-order texture coefficient V ′ (Böhlke, , 2006)…”

Section: Elastic Lawmentioning

confidence: 99%

A micro-mechanically based quadratic yield condition for textured polycrystals

Bertram¹,

Böhlke

²

,

Risy³

2008

View full text Add to dashboard Cite

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.

show abstract

Texture simulation based on tensorial Fourier coefficients

Cited by 27 publications

References 20 publications

An Evolutionary Algorithm for the Texture Analysis of Cubic System Materials Derived by the Maximum Entropy Principle

An Evolutionary Algorithm for the Texture Analysis of Cubic System Materials Derived by the Maximum Entropy Principle

A micro‐mechanically based quadratic yield condition for textured polycrystals

A micro-mechanically based quadratic yield condition for textured polycrystals

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