Abstract: The invention relates to a connection assembly (100) for drill collars or heavy drill pipes comprising: a male connection element which comprises, in its longitudinal direction, an at least partially threaded conical surface portion which tapers from the first portion towards its free end; a female connection element which comprises an at least partially threaded conical inner surface and a cylindrical inner surface (220), said two connection elements being complementary so that one can be assembled in the other by screwing, characterized in that the male connection element additionally comprises, between its free end and said conical surface portion, another surface portion whose conicity is less than that of said surface portion and which is dimensioned with respect to said cylindrical inner surface (220) such that there is a clearance by virtue of which these two surfaces bear one against the other when the assembly is subjected to a bending stress.