Edge-induced stress and strain in stripe films and substrates: A two-dimensional finite element calculation

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Abstract
Finite element calculations of stresses and strains in substrates and stripe films of thickness h and width 2l are reported. Both variation of the stress in the vertical direction (away from the interface) in the film and distortion of the substrate are taken into account. The calculations show that both the horizontal and vertical lattice planes are curved in the film as well as in the substrate. If the thickness of the substrate is infinite, the curvature in the substrate is maximum near the interface and decays rapidly with depth. Furthermore, the edges near the top are over‐relaxed, i.e., if the film is originally under compression, the stress becomes tensile because the free edge surfaces affect the relaxation. For a film with h/l=1 or greater, the stress is reversed throughout the top layer. The change from compression to tension takes place partly because of the Poisson effect and partly due to the bending of the lattice planes. The approximations made in the existing analytical models were examined and the conditions under which the models describe the stresses in the film or in the substrate were determined to a good approximation. Our finite element calculations agree with the available experimental data. Ours are the only theoretical results with which measured substrate stresses agree qualitatively.