Correlation between saturation of high current (power) transformer core and load
I can confirm that this phenomena was saturation of the core. Today I tried a bigger core and the triangle shaped wave form was gone and i could achieve currents of \$&gt;2000A_{pp}\$.

I think the reason why the core saturated at (1) at \$5A\$ and in (2) with \$14A\$ is because with two windings the output voltage is bigger and with the same resistance of the (not ideal) short circuit there could flow a bigger secondary current (\$500A\$). This induced a bigger "counter" flux in the core what prevented the saturation. But then also this voltage was to small to overpass the resistance and the secondary current could not grow further. With that also the counter flux could not grow and the core goes into saturation.