That's a interesting question with a simple answer and a longer explanation
First, the simple answer; in the mainstream use of the software the transition from liquid to solid happens at the transition temperature. You can find the Transition temperature in the material data, in the Rheological Properties tab. This temperature is not depending on pressure.
This is a slightly simplistic answer though'; evidence of the transition from Liquid to Solid can be found in a few different areas of the material data (particularly if you look at semi-crystalline material): the spike in specific heat graph (assuming it has multi-point data), the drop in multi-point thermal conductivity data, the angle change/drop in the PVT graph as well as in viscosity.
When the local temperature drops, the viscosity goes up a lot to the point where the materials realistically not going to move much, so though below Ttrans the material will literally no longer flow and is considered frozen, material may for all practical purposes have stopped flowing to a great extent.
To answer your question a bit better for at the transition temperature is at 50 MPa, the best answer (for reality) is to look at the PVT graph, follow the 50 MPa curve form a high temperature down, and you will find the transition for that material where the slope of the curve changes. A complication is that for amorphous material this is pretty straight forward, but for semi-crystalline material the transition is not happening at a specific temperature, fur it's more a transition region. In the standard code this solidification region is actually simplified to a point, which works reasonably well but is certainly a simplification.
We have a method of doing this better for semi-crystalline materials using the crystallization code. This more accurately follows the transition depending on cooling rate, pressure etc and is not using a single transition temperature. However there are not a lot of materials that have material data for this at this point.
If you are really interested in going deep in this I would recommend you have a look at ' Flow Analysis of Injection Molds 2E" from Peter Kennedy (link). It's a good reference book for fundamentals of flow simulation.
Hanno
Hanno van Raalte,
Product Manager - Injection Molding & Moldflow products