Reaction-induced elastic strain

Reaction-Induced Elastic Strain and Its Relaxation Behavior 99... 

Purely viscous forces, unless augmented by other mechanisms, are not a dominant contributor to mechanochemical reactions. Inevitably, strains are necessary to provide sufficient energy storage within molecular bonds to induce bond rupture. In melts and concentrated solutions, the entanglement network can provide the elastic strains for mechanochemical reactions. In solid-state mechanochemistry, surfaces, friction, and cleavage planes are considered to be loci of such reaction sites. 

Frequently, a product becomes loaded when it is subjected to a defined deflection. The actual load then is a result of the structural reaction of the product to the applied strain. Unlike directly applied loads, strain-induced loads are dependent on the modulus of elasticity and, with TPs, will generally decrease in magnitude over time. Many assembly and thermal stresses could be the result of strain-induced loads. They include metal insert press fits in the plastic and clamping or screw attachments. 

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). 

---