Carbon fiber reinforced composites are in favor by Grivel.   It has high modulus and high strength. Unfortuantely, it is really a poor choice for making the shaft for ice ax.  They use a polymer matrix  composite reinforced by carbon fibers.  The problem of the carbon composite are:  1) it is susceptible to mechanical impact which creates microcracks; 2) these microcracks later lead to catastrophic failure that can not be predicated in the field. 

http://www.grivel.com/products/ice/ice_axes/63-air_tech_carbon

This Grivel Airtech carbon is intended for low-angle snow and ice field.  The shaft of the ice ax will be constantly banged against snow, ice, or rocks.  Microcracks would develop at the point of impact.  Unlike aluminum alloys, which are extremely forgiving to this kind of impacts, the microcracks on the surface of  carbon composite became the high-stress points.  Repeated blows to the stress point enlarge the microcrack every time until it suddenly gives up.  

Imaging you are using the ice axe on a two-week trip to Denali, after ten days of use, the ice axe suddenly broke when you plunge into the frozen snow slope for a self-rescue.

Therefore, Carbon composite should NOT be used for ice ax or ice tools.