A spatial cylindrical model on nano-bearing constructed by double-walled carbon nano-tube (DWCNT) is established. Two motion equations are advanced to characterize the eccentric and deflective mode of the nano-bearing, respectively. On the basis of these equations, the coaxial stability of the nano-bearing under two axis-deviation perturbations is investigated. A characteristic parameter λ * governing the coaxial stability of the nano-bearing is determined. The influences of the angular velocity, interlayer spacing and axial length of the nano-bearing on the characteristic parameter λ * are analyzed and discussed in detail. It is found that when the angular velocity or interlayer spacing is smaller than a certain critical value, the parameter λ * keeps negative, and the coaxial stability of the nano-bearing is maintained. However, the axial length has very insignificant influence on λ * . In addition, for the two non-coaxial modes, the eccentric mode occurs more easily than the deflective one. The results of this paper provide a further insight into the coaxial stability of nano-bearing via the spatial model.
A pearlitic steel is composed of numerous pearlitic colonies with random orientations, and each colony consists of many parallel lamellas of ferrite and cementite. The constitutive behavior of this kind of materials may involve both inherent anisotropy and plastic deformation induced anisotropy. A description of the cyclic plasticity for this kind of dual-phase materials is proposed by use of a microstructure-based constitutive model for a pearlitic colony, and the Hill＇s self-consistent scheme incorporating anisotropic Eshelby tensor for ellipsoidal inclusions. The corresponding numerical algorithm is developed. The responses of pearlitic steel BS 11 and single-phase hard-drawn copper subjected to asymmetrically cyclic loading are analyzed. The analytical results agree very well with experimental ones. Compared with the results using isotropic Eshelby tensor, it is shown that the isotropic approximation can provide acceptable overall responses in a much simpler way.
