This is what happens when you apply a DC voltage across a Josephson junction.

It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.

By looking at the Josephson equations, we see that $V(t)=k$ a positive constant, then $φ$ just increases linearly without bound.

Therefore, from the first equation:
we see that the current will just vary sinusoidally between $±I_{c}$.

$I(t)=I_{c}sin(φ(t))$

This meas that we can use a Josephson junction as a perfect voltage to frequency converter.

Wikipedia mentions that this frequency is $484GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.

Also it is likely not going to be very useful for many practical applications in this mode.

An I-V curve can also be seen at: Figure 4. "Electron microscope image of a Josephson junction its I-V curve".