Numerical study and experimental validation of the size effect of smooth and mode I cracked semi-circular bend specimens

The edge-cracked semi-circular bend (SCB) specimen subjected to three-point bending loading is used in many applications to measure the fracture behavior of quasi-brittle materials. The main objective of the present work was to study the effect of the crack length to SCB specimen radius ratio (a/R), span to specimen diameter ratio (S/D), and specimen size on its flexural and mode I crack growth behavior. The contour integral method was implemented using the 3-D finite element method to determine the mode I stress intensity factor. In addition, high-strength concrete specimens were experimentally studied to validate the numerical results. The results show that the maximum compression stress is not sensitive to the S/D value, while the tensile stress is very sensitive. The value of S/D is the main parameter controlling the crack driving force (i.e., the crack mouth opening displacement (CMOD) and the normalized stress intensity factor, Y(I)). For the same S/D, the SCB specimen diameter value change has a marginal effect on CMOD and Y(I.) The specimen with S/D = 0.8 showed that it is the most compatible specimen with three-point bending test conditions, regardless of the SCB specimen size. A good agreement between the numerical and experimental results was achieved.