Other excellent graphic sources, contemporary with those times, are the bass-relief of Tropaeum Traiani, from Adamclisi in Romania, where you can exactly see what you are looking for, I believe, scene fights with large falx between Romans and Dacians.
The sica is eventually a Dacian word, while falx (correctly "falx dacica" ) is a Latin one.
Here is a short, approximate translation from Roman work of FRONTO, named "PRINCIPIA HISTORIAE II”:
"He left for war with seasoned soldiers, him, (ann. Emperor Trajan)
that hated the Parts (ann. ancient Persians),
our enemies, and would not care much for their arrows, after the terrible wounds inflicted by the curved swords of the Dacians..." The translation is provided by me.
The changing in Roman armour in arder to respond the devastating blows of the falx dacica was adding transversal strips of thick metal on the shields and helmets of the Roman legionars and there are well mentioned.
The
falx dacica as we know it is probably a development, so proud to say it, a Northern Dacian development, inside the Carpathians, right in the Middle of my Transylvania.
Interesting to mention, so powerful was the myth of this weapon, that after the integration of Dacians in the Roman Empire, those who would leave their homelands and die somewhere else or fight as dispatched officers would use an image of a
falx next to their name and title, to mark their ethnical heritage.
Here is an excellent article on the matter, assuming you can read Romanian, if not, just enjoy the images :
http://www.gk.ro/sarmizegetusa/ranistorum/arma.html