Based on numerical studies of the influence of residual stresses on the constraint level and crack driving force, a new three parameter (CTOD, Q, R) approach has been proposed to characterise the crack tip stress field in the presence of residual stresses when the crack angle is zero.

While the well-established parameters CTOD and Q sets the size scale over which large stresses and strains develop, and characterise the constraint level due to geometry with no stresses present, respectively, the new R parameter provides a basis for more reliable fracture mechanics analyses in which the influence of external forces and residual stresses in front of a crack tip can be taken into account.

The difference between a solution accounting for residual stresses and the small scale yielding (SSY) field at r/(J/σ_{0}) = 2 and θ = 0 defines R:

where J stands for the so-called J-integral.

CTOD can be used as a fracture toughness parameter provided that the driving force (CTOD) is corrected for the residual stress induced constraint (R).

Since the geometry constraint (Q) and the residual stress induced constraint (R) are additive, the use of standardised constraint correction methods is possible.

Critical CTOD values established from small scale specimens can still be used as a fracture toughness parameter provided that the driving force (CTOD) is corrected for the residual stress induced constraint (R).