Issue 41

V. Rizov, Frattura ed Integrità Strutturale, 41 (2017) 491-503; DOI: 10.3221/IGF-ESIS.41.61 495   1 1 1 1 n z z     (12) where 1 1 n z is the coordinate of the neutral axis, 1 1 n n  , (the neutral axis shifts from the centroid since the material is functionally graded (Fig. 3)), 1  is the curvature of the lower crack arm. Figure 4 : Schematic of a non-linear stress-strain curve ( 0 u and * 0 u are the strain energy density and the complementary strain energy density, respectively). The following equilibrium equations of the lower crack arm cross-section (Fig. 3) are used in order to determine 1 1 n z and 1  : 1 2 2 1 1 1 1 2 2 h b h b N dy dz                   (13) 1 2 2 1 1 1 1 1 2 2 h b y h b M z dy dz                   (14) where 1 N and 1 y M are the axial force and the bending moment, respectively. It is obvious that 1 0 N  , 1 y y M M  (15) By using (2), the distribution of material property, B , in the lower crack arm cross-section is written as   2 2 1 1 0 1 2 2 2 4 r z y B B B B b h     (16) where 1 2 2 b b y    , 1 1 1 / 2 / 2 h z h    , 1 2 h r h   . (17) By substituting of (1), (12) and (16) in (13) and (14), one derives