The evolution of Hooke's law due to texture development in FCC polycrystals

Böhlke, Thomas; Bertram, Albrecht

doi:10.1016/s0020-7683(01)00130-5

Cited by 58 publications

(24 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Application of the maximum entropy method in texture analysis

Böhlke

2005

Computational Materials Science

View full text Add to dashboard Cite

show abstract

“…In Equation 1, the current elastic law k p has been represented by a constant reference elastic law k 0 and a plastic transformation P [7], [10]. Equation 2 is the time-independent reference elastic law.…”

Section: Elastic Lawmentioning

confidence: 99%

Finite element simulation of lamellar copper–silver composites

Dodla

Bertram

Krüger

2015

Computational Materials Science

Self Cite

View full text Add to dashboard Cite

The mechanical behaviour and texture evolution of lamellar Cu-Ag polycrystals are numerically investigated for a uniaxial compression test by three dimensional finite element simulations. In the representative volume element (RVE), the lamellar structure is generated inside the grains. A crystal plasticity material model for large deformations is used at each integration point. In this work, two cold drawn textured Cu-Ag polycrystals are modeled by periodic Voronoi tessellations in the finite element (FE) software ABAQUS. The FE calculations use periodic boundary conditions to simulate the mechanical behavior of the textured polycrystals. The numerical model is validated by experimental compression tests for a constant strain rate of 10 −4 s −1 at room temperature. The numerical results in terms of texture of each phase and the mechanical behavior have been compared with the experimental results.

show abstract

“…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%

A micro-mechanically based quadratic yield condition for textured polycrystals

Bertram¹,

Böhlke

Risy³

2008

Int J Mater Form

Self Cite

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

The evolution of Hooke's law due to texture development in FCC polycrystals

Cited by 58 publications

References 27 publications

Application of the maximum entropy method in texture analysis

Application of the maximum entropy method in texture analysis

Finite element simulation of lamellar copper–silver composites

A micro-mechanically based quadratic yield condition for textured polycrystals

Contact Info

Product

Resources

About