On the “overlapping” problem in crack analysis

Abstract With the assumptions of classical elasticity, the displacement fields for certain crack configurations imply an “overlapping” of the crack faces and, thus, are physically unacceptable. An estimate of error in such solutions is illustrated by determining a physically acceptable solution for a central crack in an infinite sheet or a strip in pure bending. A solution which tolerates crack closure without overlapping is compared with the corresponding classical solution. The error in the classical solution is non-conservative and, for both the strip and the infinite sheet, underestimates the stress intensity factor at the crack tip in the tensile field by approx. 9%.