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
.