Stress with interface elastic moduli

A more convenient method is not to decrease the elastic modulus of the whole adhesive but to form an elastic finish coat [182] not less than 30 pm thick [183] on the adhesive—substrate interface. With lower elastic modulus, the mobility of structural elements decreases. Application of an elastic sublayer decreased the internal stresses during the formation of coatings made of unsaturated polyester resins [185], epoxides [186], and polymer solutions [187]. The use of elastic finish coats found comparatively wide application for paint coatings but seems less promising for adhesive-bonded joints because of decrease of the adhesion strength due to the low cohesion strength of the finish coat itself and because of the labor requirements in producing the adhesive-bonded joints. 

The elasticity of the protein layer structure is supposed to act against the tendency of an emulsion or foam to collapse because it allows the stretching of the interface. This behaviour is most commonly observed for globular proteins, which adsorb, partially unfold, and then develop attractive protein-protein interactions (Dickinson, 1999a Wilde, 2000 Wilde et al., 2004). The strength of such an adsorbed layer, reflected in the value of the elastic modulus, and the stress at which the structure breaks down, can be successfully correlated with stability of protein-based emulsions and (more especially) protein-based foams (Hailing, 1981 Mitchell, 1986 Izmailova et al., 1999 Dickinson, 1999a). 

It can be seen from equations (8.10) and (8.11) that the contribution to the hardening comes mainly from the layers with a higher elastic modulus. However, differences in the elastic properties between the layers will cause the loops in the stiffer layers to be pulled across the interfaces, for the same reason that loops in the less stiff layers are repelled by the interfaces, greatly diminishing their contribution to the overall flow stress. 

Implant materials for coating. Prosthetic materials coated with HAp include titanium, Ti-6A1-4V, stainless steel, Co-Cr-Mo, and alumina (Jiang and Shi 1998). These materials are roughened by grit blasting for a mechanical interlock between the melted component of the particle and the substrate. The Ti-6A1-4V and Cr-Co-Mo alloys are the most common. Ideally, the elastic modulus and co-efficient of thermal expansion of the substrate and the coating material will be matched to minimize any residual stresses at the interface. Hydroxylapatite (E = 100 GPa and a = 12 x 10 °C (Perdok et al. 1987)) is... 

Suppose that a thin film is bonded to one surface of a substrate of uniform thickness hs- It will be assumed that the substrate has the shape of a circular disk of radius R, although the principal results of this section are independent of the actual shape of the outer boundary of the substrate. A cylindrical r, 0, z—coordinate system is introduced with its origin at the center of the substrate midplane and with its z—axis perpendicular to the faces of the substrate the midplane is then at z = 0 and the film is bonded to the face at z = hs/2. The substrate is thin so that hs R, and the film is very thin in comparison to the substrate. The film has an incompatible elastic mismatch strain with respect to the substrate this strain might be due to thermal expansion effects, epitaxial mismatch, phase transformation, chemical reaction, moisture absorption or other physical effect. Whatever the origin of the strain, the goal here is to estimate the curvature of the substrate, within the range of elastic response, induced by the stress associated with this incompatible strain. For the time being, the mismatch strain is assumed to be an isotropic extension or compression in the plane of the interface, and the substrate is taken to be an isotropic elastic solid with elastic modulus Es and Poisson ratio Vs the subscript s is used to denote properties of the substrate material. The elastic shear modulus /Xg is related to the elastic modulus and Poisson ratio by /ig = Es/ 1 + t s). 

A 1 jim thick diamond-like carbon film is deposited at 500 °C on a Ti alloy substrate. The film with elastic modulus Ef = 500 GPa and Poisson ratio Ui = 0.2, is essentially free of any internal stress at the deposition temperature. When cooled to the temperature 20 °C, however, an equibiaxial compressive mismatch stress of 5 GPa is expected to exist in the film as a consequence of thermal mismatch with the substrate. An unbonded circular patch, 30 gm in diameter, developed at the film-substrate interface during film deposition. Determine whether the film buckles upon cooling to 20 °C If so, determine the temperature at which buckling begins. 

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