Issue 47

V. Rizov, Frattura ed Integrità Strutturale, (2047) 468-481; DOI: 10.3221/IGF-ESIS.47.37 471 where da is an elementary increase of the delamination crack length. Figure 2 : Cross-section of the left-hand crack arm in the beam mid-span. Since the delamination crack is located in beam portion, 2 4 B B , the complementary strain energy cumulated in the beam portions, 1 2 B B and 4 5 B B , does not depend on the delamination crack length (Fig. 1). Thus, it is enough to calculate the complementary strain energy cumulated in beam portion, 3 4 B B , only. Since the two segments of the right-hand crack arm are free of stresses, the complementary strain energy, * U , is written as * * * L R U U U   (4) where * L U and * R U are the complementary strain energies cumulated in the left-hand crack arm and the un-cracked beam portion, 1 2 3 1 2 2 l l a x l l      . The complementary strain energy cumulated in the left-hand crack arm is expressed as 1 1 1 2 * * 0 1 1 1 1 0 2 i L i i h ya i n L L i h y U u dx dy dz          (5) where L n is the number of layers in the left-hand crack arm, 1 i y and 1 1 i y  are the coordinates, respectively, of the left- hand and right-hand lateral surfaces of the i -th layer, * 0 i L u is complementary strain energy density in the same layer, the axes, 1 x , 1 y and 1 z , are shown in Fig. 2. The Ramberg-Osgood stress-strain relation which is used to model the material non-linearity is written as 1 i m i i i i E H            (6) where  is the distribution of the lengthwise strains in the cross-section of the left-hand crack arm, i  is the distribution of the normal stresses in the cross-section of the i -th layer, i E is the modulus of elasticity in the same layer, i H and i m are