Eshelby's method is used in this paper to evaluate approximately the e
nergy released when a fiber, which is embedded in a stressed infinite
matrix, is ''cut'' by the development of cracks in the matrix. The rel
eased energy can be considered as a measure of the toughness of a fibe
r against matrix cracks. As numerical examples, the energies released
by breaking an embedded isotropic glass fiber and an embedded transver
sely isotropic carbon fiber are evaluated and the effects of the fiber
geometry, material properties, as well as the stress field on the ene
rgies released are demonstrated.