Numerical Analysis On Buckling Of Nano-thin Film Under Dynamic Load

Thin film/substrate structure has been widely applied in engineering systems, andfit to achieve a variety of functions. The film/substrate structure is used in more andmore practice, so a large number of scholars are interested in the debonding andbuckling of thin film/substrate structure. There had been some mature theoreticalsystem in the buckling under static force, but the theoretical study of the dynamicbuckling problem is relatively little, so the main work of this paper is the study of thepreliminary theoretical explanation about axial impact buckling of the structure.Taking into account enormous differences in thickness between film and substrate,the specimen can simplify the substrate, and the Newton’s third Law is used tocalculate the top displacement of the substrate changing with time; and meanwhile thetop displacement of the substrate is simulated with finite element software, andcompare the experimental results, theoretical calculations and finite elementsimulation to search their difference. The results show that they are relatively closebetween the maximum displacement and the duration of the impact.In Tiersten model, the film is seen as impedance on the surface of the substrate, andthe original free boundary conditions become non-free boundary conditions, and theRayleigh type wave propagation velocity c in interface is calculated. Study thedisplacement and stress response which the displacement excitation is added at oneend and the other side tends to infinity of the film/substrate structure. Assume thatthey satisfy planar motion control differential equations, the Laplace and Fouriertransform methods are used to solve two-dimensional coupled differential equationswith initial and boundary conditions, the contact interface conditions are given byTiersten model. Since the numerical solution can not get the precise expression, thecorresponding u-t curve andσ x-t curve in the interface are solved by the numericalsolution. Due to numerical errors, the maximum displacement of the substrate is0.272mm less than0.3mm, the error is9.3%.Therefore need to study this particular film/substrate structure of the interface sideof the double-layer material stress distribution and singularity due to the stresssingularity of the double-layer material in the side of the interface can not be avoided.The calculation results showed that the interface side stress tends to infinity in therâ†'0，i.e., interface edge stress is singular, the singular zone range is r≤0.0005hf,h fis the thickness of the film, the result shows the scope of the singular zone is very small, and therefore the contribution of stress singularity to the buckling can beignored.Finally, study Rayleigh type wave propagation in the film/substrate interface, inthe impact process, the duration of the impact is far greater than the stress-waveone-way propagation time, the stress wave reflection have to be considered. Due tostress waves reflected back and forth between the impact end and fixed end, leading tostress constantly changing, Study the stress maximum and the stress distribution at themoment have a positive meaning to the study of the local buckling phenomenon. Thecalculation found that the buckling occurs at the fixed end of the specimen firstly.