It is well known that the two-parameter

solution can well characterize the crack-tip fields and quantify the crack-tip constraint for different flawed geometries in variety of loading conditions. However, this solution fails to do so for bending dominated specimens or geometries at large deformation because of the influence of significant global bending stress on the crack-tip field. To solve this issue, a modified

solution is developed in this paper by introducing an additional term to address the global bending influence. Using the

flow theory of plasticity and within the small-strain framework detailed finite element analyses are carried out for the single edge notched bend (SENB) specimen with a deep crack in A533B steel at different deformation levels ranging from small-scale Yielding to large-scale Yielding conditions. The numerical results of the crack-tip stress field are then compared with those determined from the

solution and from the modified

solution at the same level of applied loading Results indicate that the modified

solution largely improves the

solution, and match very well with the numerical results in the region of interest at all deformation levels. Therefore, the proposed solution can effectively describe the crack-tip field and the constraint for bending dominated specimens or geometries.