Application of a semi-analytical method that accounts for constraint effects in the determination of resistance curves of mode I cracked specimens

Abstract In this study, a semi-analytical method concerning the constraint effects of fracture specimens is successfully used to determine J resistance curves of mode I cracks on the basis of equivalent energy principle. Further, a constraint effective factor f is introduced in order to obtain the J resistance curves given by specimens with different constraints, which is determined by finite element analyses (FEA). In addition, the semi-analytical method can also be used to determine the crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) of specimens with different constraints according to the growing crack sizes of sharp cracked specimens determined by a semi-analytical expression. Taking compact tension (CT) specimens and single edge-notched bending (SEB) specimens as examples, a series of numerical simulations were conducted in order to determine the rotational radii R of specimens with different thicknesses, crack lengths and hardening exponents of materials based on a plastic hinge model. Further, the CTOD resistance curves of CT and SEB specimens with different thicknesses and CTOA resistance curves of thin CT specimens were determined by combining the equations of rotational radii and the semi-analytical method.