Modeling of deformation induced anisotropy in free-end torsion

Abstract

The main purpose of this work is to develop a phenomenological model, which accounts for the evolution of the elastic and plastic properties of fcc polycrystals due to a crystallographic texture development and predicts the axial effects in torsion experiments. The anisotropic portion of the effective elasticity tensor is modeled by a growth law. The flow rule depends on the anisotropic part of the elasticity tensor. The normalized anisotropic part of the effective elasticity tensor is equal to the 4th-order coefficient of a tensorial Fourier expansion of the crystal orientation distribution function. Hence, the evolution of elastic and viscoplastic properties is modeled by an evolution equation for the 4th-order moment tensor of the orientation distribution function of an aggregate of cubic crystals. It is shown that the model is able to predict the plastic anisotropy that leads to the monotonic and cyclic Swift effect. The predictions are compared to those of the Taylor-Lin polycrystal model and to experimental data. In contrast to other phenomenological models proposed in the literature, the present model predicts the axial effects even if the initial state of the material is isotropic.

Application of the maximum entropy method in texture analysis

“…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].…”

A micro‐mechanically based quadratic yield condition for textured polycrystals

“…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) …”

“…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…”

“…In Böhlke et al (2003) the evolution of the tensor V ′ during the deformation process is modeled by a macroscopic constitutive equation. Here, this tensor is calculated based on a discrete orientation distribution.…”

Texture simulation based on tensorial Fourier coefficients

“…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.…”