Белла, Though I have seen multiple log chains after few HADR takeovers, I haven't taken interest in checking log chains for each TAKEOVER type , so unable to give a definitive answer.
TAKEOVER BY FORCE should most certainly create a new log chain. The standby at the point of TAKEOVER BY FORCE is not guranteed to have all log records from Primary, which is similar to a PIT recovery, thereby needing a new log chain.
A normal TAKEOVER, ideally should not require a new log chain as the Primary and Standby are guranteed to be in sync. But don't know how works is reality.
HTH