Numerical Analysis Of The Bifurcation Problem Of Nano-scale Thin Metal Film Under Tension

On the base of the past work, the paper has been studied the bifurcation problem of Nano-scale thin film under tension. At first, the nonuniform deformation of a freestanding metal loaded in tension is studied for the long and the short wavelengths, and make comparation to the result of linear perturbation analysis. Next the same work is done for the nano-scale thin film on the polymer substrate. The two groups of work show that, the existence of the substrate suppresses large-amplitude nonuniform deformation for both short and long wavelengths.The stiffness of the substrate and the rate of thickness of the substrate and the metal film perform an important effect on the metal film. To research the effect of the two factors, this paper designs three groups of simulation by the difference of the rate of thickness for the substrate and the metal film. And make comparations among the three simulations. In each group, three small groups are divided by the difference of the stiffness of the substrate. We get three modes of deformation of the metal film and substrate. When the substrate is stiff, the lowest critical strain approaches the short wave limit of the freestanding metal film. When the substrate is compliant, the lowest critical strain occurs at wavelengths about a few times the thickness of the film, and is not much above the long wave limit of the freestanding metal film. When the stiffness is same for the substrates, the thicker the substrate is, the higher the critical strain is. We use the cohesive element in ABAQUS to research the adhesion of the metal/polymer interface. We model the interface as an array of nonlinear springs, and model the metal and the polymer as elastic-plastic solids. Depending on the resistance of the interface to sliding, the metal film can exhibit three types of tensile behavior.We compare the effect of the interfacial shear strength and the interfacial tensile strength on the rupture strains. Consequently, the rupture strain of the metal films on polymer substrates is more sensitive to the interfacial shear strength, rather than the interfacial tensile strength.