The authors have earlier proposed a practical method of using a small cylindrical circumferentially notched and fatigue cracked specimen to measure K1c. This specimen has a machined "Vee" groove, from the root of which, is grown a fatigue crack using rotating bending. This specimen is then broken in tension and K1c thus established. In practice however a significant proportion of the final ligaments after fatigue cracking are eccentric and some are non-circular. Finite element analysis has been carried out on a spectrum of final ligament sizes and eccentricities, leading to a relationship for determining K1c from such eccentrically cracked specimens. The results using this relationship are compared with experimental data.