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Chapter
Chapter
is to identify these adhesional strains by using the radius of curvature and to find the stress in each material. We assume that the total strain (£tot)at any point of the system represented in Fig. 2, is: (Navier-Bemouilli’s hypothesis). Therefore, the effect of transverse shear (rxy = 0) is neglected, (ii) the radius of curvature is large compared with transverse dimensions [width (b) and thickness (h) of the three-layer system], leading to R\ b\, hh (iii) longitudinal elements of the beam are subjected only to simple tension or compression inducing stresses in the x direction, (iv) Young’s modulii of the coating having bulk properties, the interphase and the substrate have the same value in both tension and compression (flexural modulus). Based on these assumptions, final uni-axial residual stresses (a), in the x -direction of the three-layer system (bulk coating/interphase/substrate) are given by: of the zero deformation (y0)- Therefore, we consider two equilibrium conditions for the force (N) and the moment (M) for any cross section (area S) of the coating/interphase/ substrate system:
DOI link for is to identify these adhesional strains by using the radius of curvature and to find the stress in each material. We assume that the total strain (£tot)at any point of the system represented in Fig. 2, is: (Navier-Bemouilli’s hypothesis). Therefore, the effect of transverse shear (rxy = 0) is neglected, (ii) the radius of curvature is large compared with transverse dimensions [width (b) and thickness (h) of the three-layer system], leading to R\ b\, hh (iii) longitudinal elements of the beam are subjected only to simple tension or compression inducing stresses in the x direction, (iv) Young’s modulii of the coating having bulk properties, the interphase and the substrate have the same value in both tension and compression (flexural modulus). Based on these assumptions, final uni-axial residual stresses (a), in the x -direction of the three-layer system (bulk coating/interphase/substrate) are given by: of the zero deformation (y0)- Therefore, we consider two equilibrium conditions for the force (N) and the moment (M) for any cross section (area S) of the coating/interphase/ substrate system:
is to identify these adhesional strains by using the radius of curvature and to find the stress in each material. We assume that the total strain (£tot)at any point of the system represented in Fig. 2, is: (Navier-Bemouilli’s hypothesis). Therefore, the effect of transverse shear (rxy = 0) is neglected, (ii) the radius of curvature is large compared with transverse dimensions [width (b) and thickness (h) of the three-layer system], leading to R\ b\, hh (iii) longitudinal elements of the beam are subjected only to simple tension or compression inducing stresses in the x direction, (iv) Young’s modulii of the coating having bulk properties, the interphase and the substrate have the same value in both tension and compression (flexural modulus). Based on these assumptions, final uni-axial residual stresses (a), in the x -direction of the three-layer system (bulk coating/interphase/substrate) are given by: of the zero deformation (y0)- Therefore, we consider two equilibrium conditions for the force (N) and the moment (M) for any cross section (area S) of the coating/interphase/ substrate system:
ABSTRACT
To simplify writing we have adopted the following notation: the n order moment of a function / (y) is described as:
and
(13)
(14)
(15)
For the bending moment (M), the development and the rearrangement of equa tion ( 1 2 ), yields:
Then, equations (15) and (16) yield:
(16)
(17)