The Relation Between Force-Law And Radius In Bubble Rafts

The Bragg bubble raft has been employed since it was first introduced by Bragg as a two-dimensional model of a crystalline structure of close-packed metals, and particularly defects in atomic packing such as voids, interstitials, dislocations and grain boundaries.Early work on fracture and more recent work on nanoindentation and nanoscale fracture have shown the success of bubble model for providing quantitative predictions of complex phenomena in real materials.Many educators such as Nicolson, Lomer and Shi et al have successively given a quantitative study of the mechanical and elastic properties of two–dimensional bubble rafts, the calculated values of Young's modulus and Poisson's are in good agreement the values measured in experiment. However, we can not give a great theory to explain the phenomena observed in experiment, which the dislocation widths changes greatly with the radius of the bubble raft until now. In order to solve the dislocation problem in bubble rafts,based on the study of former researches, this paper given a study on the relation between force-law and radius in bubble raft.Based on the analysis of inter-force among bubbles of the same size, got the distance between two bubble's center when the bubble rafts is in equilibrium .Then cut the infinite bubble rafts into two semi-infinite, consider the nonrigid slip between them, this is means that the bubble rafts will in equilibrium on the vertical direction by relaxation .Based on calculated the bubble raft of different radius , the relationship between the restoring force and relative displacement have calculated explicitly for the bubble raft. It is found that with the bubble radius increase, the maximum of the curve and the displacement which the restoring force reached maximum needed has gradually increased. In addition, the position where the upper semi-infinite bubbles is just losing contact with its lower semi-infinite left-hand neighbour, actually is the position the restoring force reached maximum .this is agreement with the theoretical analysis values by Bragg.According to the physical characteristics of the theoretical calculation curve, a new form of force law was found to replacement the sinusoidal law, it is found that the force law depended of the bubble radius.The curve plotted by this force law was similar to the theoretical calculation curve and the restoring force curve plotted by the generalized stacking faults energy .This show that a certain size of bubble rafts could as a model to simuliated some of the mechanical behavior of metal crystal.