Experimental data for AS 1405-180, AS 1204-350, HY 80 and C-Mn steels shows that the crack tip opening displacement (CTOD) elastic-plastic fracture toughness at initiation delta(c) decreases with increasing crack tip stress trifaxiality. This trend is confirmed by the continuum damage analysis in this paper. The dependence of the CTOD parameter at initiation on the local constraint, i.e. the stress triaxiality, provides the motivation to seek parameters that could rank the toughness of steels. Since the local effective plastic strain can be related to the CTOD, a relationship is described between the initiation CTOD toughness and the crack tip constraint, i.e. the stress triaxiality, on the basis of a new local damage theory for ductile fracture. Furthermore, a new constraint corrected toughness parameter delta(dc) (and corresponding criterion) for ductile fracture is proposed, in which both crack tip deformation and crack tip constraint intensity are taken into account. Several series of experimental data have shown that the parameter delta(dc) is nearly a constant or independent of the local constraint. It is found that the toughness variation with constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper. Copyright (C) 1996 Elsevier Science Ltd.