- #1

Griffy11

- 27

- 0

I've taken a course at uni that may be a little bit over my head, and am pushing through an assignment for it at the moment in an attempt to do well. I've hit a bit of a roadblock on one question though, so am hoping that someone kind here can help me out! The question is structured like this:

1) As we know, slip in FCC crystals can occur on 12 independent {hkl}<uvw> slip systems.

i) Write down all systems.

I have {111}<110>, and there are 4 planes in this system, each with 3 directions in each plane <-1,1,0>, hence the 12. Is this right? This seems fine, but the real question I have issues with is below.

ii) A tensile load of 60kN is applied to a cylindrical FCC single crystal of iridium of diameter 10mm. If the centre of rotation of the cylindrical sample and the applied load are parallel to the [1,-2,1] direction, determine the resolved shear stress acting on the (1,-1,-1) plane in the [0,-1,-1],[1,0,1] and [1,-1,0] directions.

I've attempted to go about the problem by using:

Shear stress (t) is:

t = (F/A)*cos(phi)*cos(lambda)

The F is the force applied, given to us as 60kN. The A is the cross sectional area, which is easy to calculate for a cylinder with diameter of 10mm using pi*r^2, taking r to be 5mm.

I can also calculate cos(phi), the angle between the tensile axis (the axis upon which the force is applied, which I think is [1,-2,1], and the normal to this, which I am unsure of. I can also calculate cos(lambda), which is the angle between the tensile axis, again, which is think is [1,-2,1] and the slip direction, although I am also not sure of the slip direction. I assume it is one of the directions given.

My main issue stems from the miller index co-ordinates - I'm not sure how I should be using all 5 to calculate this. When I'm given a tensile axis coordinate, and a system of two coordinates I can work it out fine, but with 5 separate co-ordinates I'm quite confused.

Any help would be appreciated, and my apologies for the long post.