Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Analysis and modeling for time-dependent behavior of polymers exhibited in nanoindentation tests

Through the arrangement of the applied load, experimental nanoindentation results of polymethylmethacrylate (PMMA) and polyurethane (PU) employed to establish a mechanical model. The proposed model consists of irreversible delayed plastic (viscoplastic) deformation, irreversible viscous deformation, and reversible delayed elastic (viscoelastic) deformations. The phase lag exhibited between the responding depth and the oscillating load is found to be linear proportional to frequency in the range of 1-50 Hz. The residual cavity profile of the PMMA scanned by an atomic force microscope gives a validity of accommodation assumption applied in the present model. The effects of overshooting, which occurred in the dwelling process, are also discussed.     

A theory of coupled diffusion and large deformation in polymeric gels

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Electronic Structure and Magnetic Properties of SmCo7-xZrx

The electronic structure and magnetism of SmCo_7-xZr_x alloy are investigated using the spin-polarized MS-X. method. The results show that a few of electrons are transferred to the Sm(5d⁰) orbital due to orbital hybridization between Sm and Co atoms. The exchange interactions between 3d and 5d electrons are more important than the polarization effects of the conductive electrons, thus it is the main reason resulting in the long-range ferromagnetic order in SmCo_7-xZr_x. The Curie temperature of SmCo_7-xZr_x is generally lower than that of corresponding pure Co, which may be explained by the weaker average coupling strength between Co lattices due to some negative couplings mainly occurring of 2e site. The calculated results for the Sm₅Co₃₂Zr₂ cluster may lead to a better understanding of why SmCo_7-xZr_x is stable phase. Since the spin-up DOS peak of d electrons at E_F arises and the bonding of electrons at E_F strengthens with increasing Zr concentration, which results in the internal energy of the system decrease, the stable ferromagnetic order forms in SmCo_7-xZr_x.     

Behaviors of the positive temperature coefficient of resistance of poly(styrene‐co‐n‐butylacrylate) filled with Ni‐plated core‐shell polymeric particles

Conductive composite films of poly(styrene‐co‐n‐butylacrylate) copolymers filled with low‐density, Ni‐plated core‐shell polymeric particles were prepared and their behaviors of positive temperature coefficient of resistance (PTCR) were investigated. When the conductive fillers in the composite film were loaded beyond the critical volume, 10 up to 25 vol %, composite films exhibited a unique electrical resistant transition behavior, which the electrical resistance rapidly increased by several orders of magnitude at the critical temperature. The PTCR transition temperature, in general, occurred before the glass transition temperature of polymer matrix. Further increased the conductive filler loading to 30 vol %, the overpacked conduction paths were formed in the entire composite and the PTCR effects became blurred. While the composite film treated with thermal cycle several times from room temperature up to 120 °C, the electrical resistivity increased accompanied with the shift of the PTCR transition to lower temperature. The reason might have been caused by the formed interfacial cracks within the composite film. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 322–329, 2007