Iron rope is a magical rope that, upon saying the command word, turns into solid iron (with no chain links). Thus, I have been trying to find an accurate break DC and Escape Artist check for breaking out of 1 inch iron bonds for when I entangle a creature using Animate Rope. The hardness and the Hit Points were easy enough, but I was having a hard time finding the DCs. I found bloodvine rope which was a break DC of 30 so I assumed it should be higher than that as it is just a vine with some alchemical treatments vs solid iron.
The Iron Bands of Binding have a Break DC of 30, as well as an Escape Artist DC of 30. Your Iron Rope is probably the same or a little worse.
If it were up to me, I would use the same Escape Artist DC that the rope had before it was frozen and add +2 to it, rather than a straight 30. Especially if someone was tied up with the rope before it was frozen.
There's no defined rule...
Iron Rope says that the resulting iron
has the hardness and hit points of a normal inch-thick iron bar...
which has no listed break DC, though it does have a bend DC of 24, here.
Making it up
Other similar items that have break DCs include manacles, chains and a 2 inch thick iron door.
Each of those DCs is from 26 to 28. The iron bar should be similar.
An entangled creature can slip free with a DC 20 Escape Artist check.
So even though the rope is iron and inflexible, it can be escaped, by the rules presented.
This DM might rule that the inflexibility of the rope-turned-iron-coil imparts the grappled condition, preventing movement. Escaping may or may not be any more difficult than escaping the animated rope.
In the table, Substance Hardness and hit points, an item made out of iron or steel has 10 hardness and 30 hit points per inch of thickness.
The description for iron rope also states:
When the end of this gray hemp rope is held and the command word is uttered, it is irrevocably transmuted into solid iron. The transmuted rope loses all magic and has the hardness and hit points of a normal inch-thick iron bar.
So once the command word is uttered the hemp rope turns into an iron rope. Gains 10 hardness, and 30 hit points.
Normal rope happens to be 0 Hardness, 2 hit points on the table Object Hardness and hit points. If we compare the new hardness and hit points to other objects on that table, we get a break DC at around the same level as Masterwork Manacles, which has a Break DC of 28, 10 hardness, and 10 hit points.
There's also a bit of information further down on the same page that mentions the DC to Burst chain bonds is 26.
So assuming that the iron rope has the properties of a chain or manacles, the break DC would be somewhere around 26-28.