More about the cathode foil tension

[Eugene Chudakov <gen@jlab.org>]

We measured the cathode elongation perpendicular to the strips
(the same tight cathode).
It turns out that the strip pitch is 6mm (not 5mm), while the strip
width is 5mm.
The elongation in the central area, between the seams is 0.25%+/-0.08%.
This is 1/4 of the expected value from kapton alone. Apparently,
copper plating is important. Indeed, one can calculate that for the elastic
regime the effective Young's modulus is 8.7GPa instead of 2.5GPa for kapton.
The measured elongation of 0.25% would provide a tension of 540N/m, which
is reasonably close to the tension we measured of 660N/m.

Actually, copper provides 90% of the tension in the plated areas,
which is about 600N/m. The "yield limit" of copper is 70Mpa, or for
our 5um layer the tension limit is 350 N/m.
We seem to exceed this limit by nearly a factor of two, and I do not
know at the moment what are the implications.

In the direction along the strips the effective Young's modulus should be twice
larger, or about 17 GPa.

Eugene

On Tue, 29 Jul 2008, Eugene Chudakov wrote:

>
> Micah and I measured the foil tension of the tight copper
> plated sample, used for the flatness measurements, to be 660+/-30 n/m.
>
> We put a 1.9 kg aluminum disk, 266mm diameter on the top of the foil,
> at its center and measured the foil sagging with the laser, in 2 radial
> positions "r". The internal radius of the fiberglass ring is R=503 mm.
> The measurement was done along the copper stripes.
>
>   r          sagging           T
>  221+/-5mm     3.73+/-0.05mm  650+/-20 n/m
>  347+/-5       1.53+/-0.05    720+/-40 n/m
>
> The formula used: sagging=m*g/(2*pi*T)*ln(r/R)
>
> The Young modulus of kapton is 2.5 GPa. The relative elongation of the 25-um foil
> (neglecting the copper plating) is 1%.
>
> Eugene
>