Issue 46

V. Rizov, Frattura ed Integrità Strutturale, 46 (2018) 158-177; DOI: 10.3221/IGF-ESIS.46.16 170 Eqn. (55) is used also to determine H  . For this purpose, d M , 1 n and L  are replaced, respectively, with M , n and H  . The strain energy cumulated in half of the shaft as a result of the bending is obtained as M ML MQ MH U U U U    (60) where ML U , MQ U and MH U are the strain energies in the internal crack arm, the external crack arm and the un- cracked shaft portion, respectively. Formula (16) is applied to determine ML U . For this purpose, FL U and 0 i FL u are replaced with ML U and 0 i ML u , respectively. The strain energy density, 0 i ML u , in the i -th layer of the internal crack arm as a result of the bending is obtained by formula (18). For this purpose, 0 i FL u and L  are replaced with 0 i ML u and  , respectively (  is expressed by formula (54)). Figure 8 : Two three-layered functionally graded circular shafts loaded in bending and torsion with cylindrical delamination crack located between (a) layers 2 and 3 and (b) layers 1 and 2. Formula (16) is used also to determine MQ U by replacing of FL U , 1 n and 0 i FL u with MQ U , 2 n and 0 i MQ u , respectively. 0 i MQ u is determined by replacing of L  with  . MH U is found by formula (19). For this purpose, FH U and 0 i FH u are replaced with MH U and 0 i MH u , respectively. The strain energy density, 0 i MH u , in the i -th layer of the un-cracked beam portion as a result of bending is obtained by formula (18). For this purpose, 0 i FL u and L  are replaced with 0 i MH u and b  , respectively. The distribution of the longitudinal strains, b  , in the cross-section of the un-cracked shaft portion is found by (54). For this purpose,  , L 