Size effect on compression strength of fiber composites failing by kink band propagation

The effect of structure size on the nominal strength of unidirectional fibe r-polymer composites, failing by propagation of a kink band with fiber micr obuckling, is analyzed experimentally and theoretically. Tests of novel geo metrically similar carbon-PEEK specimens, with notches slanted so as to lea d to a pure kink band (not accompanied by shear or splitting cracks), are c onducted. They confirm the possibility of stable growth of long kind bands before the peak load, and reveal the existence of a strong (deterministic, non-statistical) size effect. The bi-logarithmic plot of the nominal streng th (load divided by size and thickness) versus the characteristic size agre es with the approximate size effect law proposed for quasibrittle failures in 1983 by Bazant. The plot exhibits a gradual transition from a horizontal asymptote, representing the case of no size effect (characteristic of plas ticity or strength criteria), to an asymptote of slope -1/2 (characteristic of linear elastic fracture mechanics, LEFM). A new derivation of this law by approximate (asymptotically correct) J-integral analysis of the energy r elease, as well as by the recently proposed nonlocal fracture mechanics, is given. The size effect law is further generalized to notch-free specimens attaining the maximum load after a stable growth of a kink band transmittin g a uniform residual stress, and the generalized law is verified by Soutis, Curtis and Fleck's recent compression tests of specimens with holes of dif ferent diameters. The nominal strength of specimens failing at the initiati on of a kink band from a smooth surface is predicted to also exhibit a (det erministic) size effect if there is a nonzero stress gradient at the surfac e. A different size effect law is derived for this case by analyzing the st ress redistribution. The size effect law for notched specimens permits the fracture energy of the kink band and the length of the fracture process zon e at the front of the band to be identified solely from the measurements of maximum loads. The results indicate that the current design practice, whic h relies on the strength criteria or plasticity and thus inevitably misses the size effect, is acceptable only for small structural parts and, in the interest of safety, should be revised in the case of large structural parts .