How to analyse slip transmission at grain boundaries

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Import Titanium data |

Taylor model |

From Mercier D. - MTEX 2016 Workshop - TU Chemnitz (Germany) Calculation and plot on GBs of m' parameter Dataset from Mercier D. - cp-Ti (alpha phase - hcp)

mtexdata csl % compute grains [grains, ebsd.grainId] = calcGrains(ebsd('indexed')); % make them a bit nicer grains = smooth(grains); % extract inner phase grain boundaries gB = grains.boundary('indexed'); plot(ebsd,ebsd.orientations) hold on plot(grains.boundary) hold off

% consider Basal slip sS = slipSystem.fcc(ebsd.CS) % and all symmetrically equivalent variants sS = sS.symmetrise; % consider plane strain q = 0.5; eps = strainTensor(diag([-q 1 -(1-q)])); % and compute Taylor factor as well as the active slip systems [M,b,ori] = calcTaylor(inv(grains.meanOrientation).*eps,sS);

sS = slipSystem mineral: iron (m-3m) size: 1 x 1 u v w | h k l CRSS 0 1 -1 1 1 1 1 computing Taylor factor: 100%

```
% find the maximum
[~,id] = max(b,[],2);
```

The variable `id` contains now for each grain the id of the slip system with the largest Schmidt factor. In order to visualize it we first
rotate for each grain the slip system with largest Schmid factor in specimen coordinates

sSGrain = grains.meanOrientation .* sS(id) % and plot then the plance normal and the Burgers vectors into the centers % of the grains plot(grains,M) largeGrains = grains(grains.grainSize > 10) hold on quiver(grains,cross(sSGrain.n,zvector),'displayName','slip plane') hold on quiver(grains,sSGrain.b,'displayName','slip direction') hold off

sSGrain = slipSystem CRSS: 1 size: 885 x 1 largeGrains = grain2d Phase Grains Pixels Mineral Symmetry Crystal reference frame -1 442 153261 iron m-3m boundary segments: 21799 triple points: 1444 Properties: GOS, meanRotation

We may also analyse the distribution of the slip directions in a pole figure plot

plot(sSGrain.b)

The same as a contour plot. We see a clear trend towards east.

`plot(sSGrain.b,'contourf')`

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