Instead by the tension direction the stress might be specified by a stress tensor
Then the Schmid factor for the slip system sS and the stress tensor sigma is computed by
Active Slip System
In general a crystal contains not only one slip system but at least all symmetrically equivalent ones. Those can be computed with
The option antipodal indicates that Burgers vectors in opposite direction should not be distinguished. Now
returns a list of Schmid factors and we can find the slip system with the largest Schmid factor using
The above computation can be easily extended to a list of tension directions
We may also plot the index of the active slip system
and observe that within the fundamental sectors the active slip system remains the same. We can even visualize the the plane normal and the slip direction
If we perform this computation in terms of spherical functions we obtain
The Schmid factor for EBSD data
So far we have always assumed that the stress tensor is already given relatively to the crystal coordinate system. Next, we want to examine the case where the stress is given in specimen coordinates and we know the orientation of the crystal. Lets import some EBSD data and compute the grains
We want to consider the following slip systems
Since, those slip systems are in crystal coordinates but the stress tensor is in specimen coordinates we either have to rotate the slip systems into specimen coordinates or the stress tensor into crystal coordinates. In the following sections we will demonstrate both ways. Lets start with the first one
These slip systems are now arranged in matrix form where the rows correspond to the crystal reference frames of the different grains and the rows are the symmetrically equivalent slip systems. Computing the Schmid factor we end up with a matrix of the same size
Next we want to visualize the active slip systems.
We observe that the Burgers vector is in most case aligned with the trace. In those cases where trace and Burgers vector are not aligned the slip plane is not perpendicular to the surface and the Burgers vector sticks out of the surface.
Next we want to demonstrate the alternative route
This becomes a list of stress tensors with respect to crystal coordinates - one for each grain. Now we have both the slip systems as well as the stress tensor in crystal coordinates and can compute the Schmid factor