In regard to schmid factor the two different angles are complementary to each other?
That is completely wrong statement. If this would be the case, which is not ! any smart person having some simple notion in trigonometry could write the following set of equations.
İf φ+λ=90 Then
TC= σy cos φ cos λ.=σy cos φ cos (90-φ)=σy cos φ sin φ=σy/2 sin 2φ
In general the force acting on the dislocation line at any given point can be written in the following fashion:
F = t . sigma . b, [unit in cgs: dyne/cm] Where b is the Burgers vector, t is the local unit tangent vector of the dislocation line, sigma is local second order stress tensor or matrix, which is symmetric. In crystalline solids the directions of the Burgers vectors (or the slip directions) and the slip planes are not arbitrary, which are fixed by the crystal structures.
I wonder whether you know which angles phi and lambda describe, and why they should be related somehow?
There is no physical reason that these two angles have to be complementary.
But I think, in some geomertry, the sum of these angles φ+λ=90 can be verified. For exemple, it is possible that φ=45° and λ=45°.
Dear Gert:: One can find very through information about the Burgers vectors (i.e., stable and marginal stable); slip systems( at RT, low and High Temp etc) for FCC, BCC, HCP diamond , and NaCL structure with discussions at the presence of TEM observations in the book entitled as Theory of Dislocation by J.P Hirth and J. Lothe. Slip System: FCC {111} and {100} elevated Tmep. BCC {110} where {112} for stacking faults. Niobium is exception which has slip direction. at RT: HCP {0001} and 112-0> {101-0} elevated Temp.
As Dr, Noize suggested properly,the slip directions and slip plane are not arbitrary but they fixed by the crystal structure as well as by the energetic and stability considerations. But their orientations with respect to the applied stress system depends on the choice of the external agent. One should not forget in the case of curved dislocation still we have two free vectorial parameter, which are the tangent vector, and the local curvature argument ed by the normal unit vector.
Well, there is a 90° angle between the slip direction (b) and the normal of the slip plane. If we view this in a 2D sketch on a piece of paper, and the direction of the applied stress lies between these two directions, then yes, the two angles would sum to 90°.
However, this is one special case of the problem. The direction of applied stress need not be between these two directions even in a 2D drawing, and of course in 3D there are many more degrees of freedom which completely invalidates the idea that the two angles must sum to 90°.
@ M. Schnabel: This means that for an infinite number of possibilities there is only one which fulfills this condition (if the loading dierction is exactly in the plane defined by the glide plane normal and the glide direction. In so far it is more the exception rather than the rule.
Actually, I am dealing with the dislocation theory and its practical applications in every sophisticated level last fifth years or more, but it has never came over my mine to ask a question as such, probably it was trivial for me. Why? because there is no mathematical connections between these two angles even in the ordered space such as lattice. Happy New Years every body.
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