the Taylor factor, the shears of the slip systems and the plastic spin of a strain the crystal accommodates by slip alone

Syntax

M, b, W = calcTaylor(eps, sS)

Eps in the crystal frame, one or a list of strains.

M, b, W = calcTaylor(inv(ori) * eps, sS)

The strain of every orientation, one row of shears each.

oriNew = ori.exp(-W)

The orientation the spin turns the crystal to.

work, b, W = calcTaylor(inv(ori) * eps, sS, plasticWork=True)

The plastic work instead of the factor.

MFun, _, WFun = calcTaylor(eps, sS, bandwidth=32)

Eps in the specimen frame: functions of the orientation.

Description

Taylor’s model: every grain takes the macroscopic strain, which its slip systems must produce. Of all shears that do, the linear program takes those of least total shear, the absolute shears weighted by the critical resolved shear stresses. That sum divided by the size of the strain is the Taylor factor M.

The least total shear is often reached by a whole face of shears. The shears returned are the analytic centre of that face, which makes them and the spin unique and symmetric, as MATLAB’s; spinSelection takes another point of the face. The spin W is a spinTensor in the crystal frame, so ori.exp(-W) turns the crystal.

What comes back depends on the frame of the strain:

crystal frame, one strain or a list: the factor, the shears and the spin as numbers.
specimen frame: the factor as an SO3FunHarmonic and the spin as an SO3VectorFieldHarmonic of the orientation, fitted on a quadrature grid of the bandwidth (MATLAB’s ‘SO3Fun’ flag); the shears are None.

Input

`eps`	strainTensor, in the crystal frame of sS or in the specimen frame
`sS`	slipSystem, the systems in the crystal frame with their critical resolved shear stresses, symmetrised; or a TaylorModel prepared from them

Keywords

keyword	default	description
`plasticWork`	`False`	take the plastic work, the shears weighted by the critical resolved shear stresses, instead of the geometric Taylor factor
`spinSelection`	`None`	which shears of an optimal face: ‘centre’ its analytic centre, ‘basic’ a vertex, ‘minimumNorm’ the shears of least norm; by default the model’s, ‘centre’
`bandwidth`	`32`	the bandwidth of the functions for a strain in the specimen frame
`smoothing`	`0.0`	the halfwidth of a de la Vallee Poussin kernel the spin field is smoothed with; zero for none

Output

`M`	the Taylor factor, a number or an array of the shape of eps; SO3FunHarmonic for a strain in the specimen frame
`b`	the shear of every slip system, an array (…, number of systems); None for a strain in the specimen frame
`W`	spinTensor, the plastic spin in the crystal frame; SO3VectorFieldHarmonic for a strain in the specimen frame

References

G. I. Taylor, Plastic strain in metals, J. Inst. Metals 62 (1938) 307-324

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/strainTensor.calcTaylor_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

strainTensor.calcTaylor