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ABSTRACT: A series of studies have been conducted for mechanical behavior of elastic thin films on compliant substrates. Under tension, the film may fracture by growing channel cracks. The driving force for channel cracking (i.e., the energy release rate) increases significantly for compliant substrates. Moreover, channel cracking may be accompanied by interfacial delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. Alternatively, when the film is under compression, it tends to buckle. Two buckling modes have been observed, one with interfacial delamination (i.e., buckle-delamination) and the other without delamination (i.e., wrinkling). By comparing the critical stresses for the onset of buckling, we give a criterion for the selection of the buckling modes, which depends on the stiffness ratio between the film and the substrate as well as the interface defects. A general conclusion from these studies is that, whether tension or compression, the interfacial properties are critical in controlling the morphology and failure of elastic thin films on compliant substrates.
Thermal and Thermomechanical Phenomena in Electronic Systems, 2008. ITHERM 2008. 11th Intersociety Conference on; 06/2008
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ABSTRACT: A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a power-law scaling under uniaxial compression. More complicated dynamics is predicted under equibiaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a chaotic labyrinth pattern under equibiaxial stresses. Under stresses of the same magnitude, the two patterns have the same average wavelength, but different amplitudes. It is noted that the dynamics of wrinkling, while analogous to other phase ordering phenomena, is distinct and rich under the effects of stress and substrate elasticity.
Physical Review E 09/2006; 74(2 Pt 2):026214. · 2.26 Impact Factor
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ABSTRACT: This paper presents a nonlinear mathematical model for evolution of wrinkle patterns of an anisotropic crystal film on a viscoelastic substrate layer. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. Previously, theoretical studies on wrinkling have assumed isotropic elastic properties for the film. Motivated by recent experimental observations of ordered wrinkle patterns in single-crystal thin films, this paper develops a theoretical model coupling anisotropic elastic deformation of a crystal film with viscoelastic deformation of a thin substrate layer. A linear perturbation analysis is performed to predict the onset of wrinkling instability and the initial evolution kinetics. An energy minimization method is adopted to analyze wrinkle patterns in the equilibrium states. For a cubic crystal film under an equi-biaxial compression, orthogonally ordered wrinkle patterns are predicted in both the initial stage and the equilibrium state. This is confirmed by numerical simulations of evolving wrinkle patterns. By varying the residual stresses in the film, numerical simulations show that a variety of wrinkle patterns (e.g., orthogonal, parallel, zigzag, and checkerboard patterns) emerge as a result of the competition between material anisotropy and stress anisotropy.
Journal of the Mechanics and Physics of Solids.
