MECHANISMS UNDERLYING TWO KINDS OF SURFACE EFFECTS ON ELASTIC CONSTANTS

Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample： elastic modulus either decreases or increases with decreasing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the microstructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, and the elastic moduli decrease with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coordination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair potential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface respectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk are located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one-dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.

CRACK PROPAGATION IN STRUCTURES SUBJECTED TO PERIODIC EXCITATION

In the present paper, asimple mechanical modelis developed to predict thedynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten （mimicking crack growth） if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

EQUIVALENT MODEL OF EXPANSION OF CEMENT MORTAR UNDER SULPHATE EROSION

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is results indicate that the model perfectly describes performed. The numerical and experimental the expansion of the cement mortar.

Evaluation of Young's Modulus and Residual Stress of NiFe Film by Microbridge Testing

Microbridge testing was used to measure the Young＇s modulus and residual stress of metallic films. Samples of freestanding NiFe film microbridge were fabricated by microelectromechanical systems. Special ceramic shaft structure was designed to solve the problem of getting the load-deflection curve of NiFe film microbridge by the Nanoindenter XP system with normal Berkovich probe. Theoretical analysis of load-deflection curves of the microbridges was proposed to evaluate the Young＇s modulus and residual stress of the films simultaneously. The calculated results based on experimental measurements show that the average Young＇s modulus and residual stress for the electroplated NiFe films are 203.2 GPa and 333.0 MPa, respectively, while the Young＇s modulus measured by the Nano-hardness method is 209.6：1：11.8 GPa for the thick NiFe film with silicon substrate.