Size effect on tensile softening relation

Tensile softening essential to the well-known fictitious crack model should be independent of specimen size and test methods. Commonly observed size effect (SE) on tensile softening relations measured from direct tensile specimens with smooth surface needs to be explained in order to determine the size independent tensile softening behaviour. In this paper, SE on tensile softening from direct tensile tests is elucidated by considering a boundary region where the key tensile softening mechanisms such as aggregate interlocking and frictional pull-out activities are limited in comparison with the inner region where those crack-bridging activities can be fully developed. SE on the tensile softening relation and the closely related specific fracture energy Gf is inevitable if the boundary and inner regions are comparable. The same SE is gradually diminished with the increasing specimen size simply because the relative contribution from the boundary region is reduced in comparison with that from the increasing inner region. In principle, the size independent tensile softening relation and the size independent specific fracture energy GF in the inner region can be obtained by separating the influence of the boundary region from the test results.