Modeling of deformation induced anisotropy in free-end torsion

TLDR: In this article, a phenomenological model for the evolution of the elastic and viscoplastic properties of cubic polycrystals was developed, which predicts the axial effects in torsion experiments.

About: This article is published in International Journal of Plasticity.The article was published on 2003-11-01 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Anisotropy & Phenomenological model.

Figures

Fig. 4. Cyclic Swift effect: =kA0Ek (A0E ¼ F~ A~ 0 vs. shear number with =0.9 (phenomenological model).

Fig. 5. Cyclic Swift effect: percentage extension " vs. shear number K predicted by the phenomenological model for different values of (left: H25, right: H37).

Table 4 Material functions on the macroscale II (x 3 ffiffiffi 6 p Ip1=2)

Table 2 Material functions on the macroscale (non-symmetric velocity gradients)

Table 3 Material functions on the macroscale I

Table 5 Material parameters on the macroscale

Frequently asked questions

Q1. What are the contributions in "Modeling of deformation induced anisotropy in free-end torsion" ?

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. 

Q2. What is the scalar function of the tensor generators?

Due to the constraint that, similar to A~ 0, the function G~ 0 has to be symmetric and traceless with respect to all pairs of indices, the function G~ 0 is generally given by three 4th-order tensor generators G~ 0a and corresponding scalar functions Ga (Böhlke and Bertram, 2001)G~ 0 N~ 0p ¼ G1 Ip1 G~ 01 N ~ 0 p þ G2 Ip1 G~ 02 N ~ 0 p þ G3 Ip1 G~ 03 N ~ 0 p : ð13ÞThe tensor generators areG1 N 0ð Þ ¼ N0 N04 7 N02 The authorþ 2 35 tr N02 The authorIf g;G2 N 0ð Þ ¼ N02 N022 7 tr N02 N02 Iþ 2 N04 The authorþ 1 35 tr N02 2þ2tr N04 The authorIf g;G3 N 0ð Þ ¼ N02 N02 7 tr N02 N02 The authorþ 4 N03 Iþ 4 35 tr N03 The authorIf g: ð14ÞIn Table 1 the material functions are summarized. 

Q3. What is the viscoplastic flow rule for copper?

The viscoplastic flow rule (21) combines the assumption of elastic ranges and a rate-dependent inelastic flow which is typical for copper. 

Q4. What is the theory of isotropic tensor functions?

The 4th-order tensor function G~ 0 N~ 0p;M~ p and the scalar function d N~ 0p;M~ pcan be determined by means of the theory of isotropic tensor functions. 

Q5. What is the evolution of elastic and viscoplastic properties of a cubic crystal?

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. 

Q6. What temperature range did montheillet et al. (1984) test polycrystalline samples?

Montheillet et al. (1984) tested polycrystalline samples of Al, Cu, and a-Fe in fixed-end torsion over the temperature range 20–400, 500, and 800 C. 

Q7. What is the way to reproduce the monotonic Swift effect?

Montheillet et al. (1985) have shown that, if the ellipsoidal yield surface, proposed by von Mises (1928) and Hill (1948), is specified by the ideal orientations found in torsion textures, then the monotonic Swift effect can be reproduced. 

Q8. What is the main problem of a constitutive model?

Here the main problem of a constitutive model is the representing of the axial deformation behavior in a cyclic torsion test at large shear strains. 

Q9. What is the axial elongation of the cylinder?

With the aforementioned settings, the axial elongation of the cylinder corresponds to a growth of the F22 component of the deformation gradient. 

Q10. What is the shear direction of the cylinder?

The shear direction e1 represents the tangent of the circumference of the cylinder whereas the shear plane normal e2 is aligned with the longitudinal axis of the specimen.