Size effect in compression fracture: Splitting crack band propagation

A simplified fracture-mechanics-based model of compression failure of centrically or eccentrically loaded quasi-brittle columns is presented and the size effect on the nominal strength of a column is predicted. Failure is modeled as propagation of a band of axial splitting cracks in a direction orthogonal or inclined with respect to the column axis. The maximum load is calculated from the condition that the energy released from the column due to crack band advance be equal to the energy consumed by the splitting cracks. The axial stress transmitted across the crack band is determined as the critical stress for buckling of the microslabs of material between the axial splitting cracks, and the work on the microslabs during postbuckling deflections is taken into account. The critical postbuckling deflection of the microslabs is determined from a compatibility condition. Under the assumption of small enough material inhomogeneities, the spacing s of the splitting cracks is calculated by minimizing the failure load and is found to decrease with structure size D as D^-1/5. The size effect on the nominal strength of geometrically similar columns is found to disappear asymptotically for small sizes D, and to asymptotically approach the power law D^-2/5 for large sizes D (where D = cross section dimension). However, when the material inhomogeneities are so large that they preclude the decrease of s with increasing D, the asymptotic size effect changes to D^-1/2. The size effect intensifies with increasing slenderness of the column, which is explained by the fact that a more slender column stores more strain energy. The predicted size effect describes quite well previous tests at Northwestern University of reduced-scale tied reinforced concrete columns of different sizes (with size range 1:4) and different slenderness (ranging from 19 to 53). Finally, a simple modification is pointed out for the case of shear loading of concrete, in which a system of parallel tensile cracks in the diagonal compression direction develops before the maximum compressive stress is reached.