S. K. Deb Nath

Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material

An analytical solution of the elastic field of a deep stiffened cantilever beam of orthotropic composite material is presented in the paper. The cantilever beam is subjected to a parabolic shear loading at its free lateral end and the two opposing longitudinal edges are stiffened. Unidirectional fibre-reinforced composite is considered for the present analysis where the fibres are assumed to be directed along the beam length. Following a new development, the present mixed-boundary-value elastic problem is formulated in terms of a single potential function defined in terms of the associated displacement components. This formulation reduces the problem to the solution of a single fourth-order partial differential equation of equilibrium and is capable of dealing with mixed modes of boundary conditions appropriately. The solution is obtained in the form of an infinite series. Results of different stress and displacement components at different sections of the composite beam are presented numerically in the form of graphs. Finally, in an attempt to check the reliability as well as the accuracy of the present solution, the problem is solved by using two standard numerical methods of solution. A comparison of the results shows that the analytical and numerical solutions of the present problem are in good agreement and thus establishes the soundness as well as the reliability of the present displacement potential approach to solution of the elastic field of orthotropic composite structures.

Study of the Spreading of Perfluoropolyether Lubricants on a Diamond-Like Carbon Film

Nonpolar perfluoropolyether (PFPE) Z and PFPE Zdol with polar end groups are widely used as hard disk lubricants for protecting carbon overcoats by reducing friction between the hard disk and head during movement of the head while reading and writing data on the hard disk. We investigate the spreading phenomenon of PFPE Z and PFPE Zdol on a thin diamond-like carbon (DLC) film adopting molecular dynamics (MD) simulations based on a coarse-grained bead-spring model to describe the thickness profiles and molecular movement, which evolve with time and temperature. In the present article, the hard disk surface was considered as a DLC and the position of its carbon atoms was obtained by heating and quenching the face-centered cubic (FCC) or body-centered cubic (BCC) diamond structures by MD simulation using the Tersoff potential. To simulate PFPE Z and PFPE Zdol on a thin DLC film using a coarse-grained bead-spring model based on finitely extensible nonlinear elastic potential and nonbonded potential, the original DLC thin film was compressed to half of its original configuration in all three spatial dimensions. How PFPE Z and PFPE Zdol on the DLC surface spread with time are briefly discussed. How the spreading profile of PFPE Z and PFPE Zdol on the DLC film spreads laterally and on the DLC film as a circular shape beyond its original position is also discussed. The effect of temperature on the film thickness and spreading area of PFPE Z and PFPE Zdol on the DLC film is also discussed. We show that the time dependence for the spreading of PFPE Z and PFPE Zdol droplets deviated from the expected proportionality to the square root of time in their spreading profiles with time. The model-calculated spreading rate of PFPE Z and PFPE Zdol on a thin DLC film increased inversely with absolute temperature as expected.

On the elastic, elastic-plastic properties of Au nanowires in the range of diameter 1-200 nm

In the present study, we obtain Youngs modulus and yield strength of 〈100〉 Au nanowire in the range of diameters 1-30 nm by tension and bending tests using molecular dynamics simulations. Double clamped Au nanowire is bended applying a point load at its middle span using cylindrical indenter by the atomistic approach. The superiority of the present bending technique is highlighted by analyzing the distribution of Von Misses stress of the present bending Au nanowire by 3D finite element modeling. First, Youngs modulus and yield strength of Au nanowires are determined using classical theory of continuum mechanics. Then the obtained Youngs modulus and yield strength of Au nanowires are corrected using 3D finite element modeling based on inverse technique [Deb Nath et al. Appl. Phys. A 103(2), 493 (2011) and Tohmyoh et al. Appl. Phys. A 103(2), 285 (2011)]. Effects of anisotropy on the tension and bending stiffness, tension and bending strength of Au nanowires are also discussed with graphs. Effects of tem...

Displacement Potential Based Finite Difference Solution to Elastic Field in a Cantilever Beam of Orthotropic Composite.

This paper concerns the finite difference solution to the elastic field in a cantilever beam of unidirectional orthotropic composite material. The mixed boundary value plane elastic problem is formulated in terms of a single displacement potential function. The numerical scheme developed is demonstrated for a particular case of a boron/epoxy cantilever beam for two different loading conditions. Numerical results of different stress and displacement components at different sections of the beam are presented in the form of graphs. With a view to verifying the finite difference results, solutions are also obtained by finite element method. The comparison of the results ensures that the present displacement potential based finite difference scheme is relatively simple, reliable, and accurate enough to analyze the elastic field in orthotropic composite structures under mixed boundary conditions.

Investigation of elastic field of a short orthotropic composite column by using finite-difference technique

Abstract The elastic field of a short column of orthotropic composite material under a linearly varying distributed load is analysed using displacement potential formulation. The finite-difference technique is used to obtain the numerical solutions of different parameters of the elastic field. The differential equations associated with the boundary conditions and the governing equation are approximated by their corresponding finite-difference forms, which are then applied, respectively, to the boundaries and the interior nodal points of the discretized column. To demonstrate the elastic behaviour of the fibre reinforced composite column, the results of displacements and stresses at different sections are presented in a graphical form.

Analytical solution of a stiffened orthotropic plate using alternative displacement potential approach

Abstract Analytical solution of elastic fields of a stiffened composite plate subjected to axial tension and pure bending is obtained using alternative displacement potential approach. In this approach, the problem is formulated in terms of a single potential function, defined in terms of the displacement components, which satisfies a single differential equation of equilibrium. All the parameters of the elastic field are expressed into algebraic equations using Fourier series. Assuming a trigonometric function as the displacement potential solution to the present problem, the mixed-boundary conditions at the stiffened edges are automatically satisfied. The resulting states of stress and displacement in the composite plate due to axial tension and pure bending are discussed in details. The effect of fibre orientation on the elastic field is also investigated.

Study of the Nanomechanics of CNTs under Tension by Molecular Dynamics Simulation Using Different Potentials

At four different strain rates, the tensile stress strain relationship of single-walled 12-12 CNT with aspect ratio 9.1 obtained by Rebo potential (Brenner, 1990), Airebo potential (Stuart et al., 2000), and Tersoff potential (Tersoff, 1988) is compared with that of Belytschko et al. (2002) to validate the present model. Five different empirical potentials such as Rebo potential (Brenner, 1990), Rebo potential (Brenner et al., 2002), Inclusion LJ with Rebo potential (Brenner, 1990), Airebo potential (Stuart et al., 2000), and Tersoff potential (Tersoff, 1988) are used to simulate CNT subjected to axial tension differing its geometry at high strain rate. In Rebo potential (Mashreghi and Moshksar, 2010) only bond-order term is used and in Rebo potential (Brenner et al., 2002) torsional term is included with the bond-order term. At high strain rate the obtained stress strain relationships of CNTs subjected to axial tension differing its geometries using five different potentials are compared with the published results and from the comparison of the results, the drawback of the published results and limitations of different potentials are evaluated and the appropriate potential is selected which is the best among all other potentials to study the elastic, elastic-plastic properties of different types of CNTs. The present study will help a new direction to get reliable elastic, elastic-plastic properties of CNTs at different strain rates. Effects of long range Van der Waals interaction and torsion affect the elastic, elastic-plastic properties of CNTs and why these two effects are really needed to consider in bond-order Rebo potential (Brenner, 1990) to get reliable elastic, elastic-plastic properties of CNTs is also discussed. Effects of length-to-diameter ratio, layering of CNTs, and different empirical potentials on the elastic, elastic-plastic properties of CNTs are discussed in graphical and tabular forms with published results as a comparative manner to understand the nanomechanics of CNTs under tension using molecular dynamics simulation.

Analytical solution of short guided orthotropic composite columns under eccentric loading using displacement potential formulation

Abstract In this paper, short guided columns of orthotropic composite materials are considered in order to analyse their elastic field due to an eccentric compressive loading. The supporting edge of the column is rigidly fixed and fibres are directed along the axis of the column. By a new approach of displacement potential formulation, the present mixed boundary value elastic problem is expressed in terms of a single potential function. Displacement and stress components are derived into infinite series using Fourier integral with the coincided boundary conditions along with the physical boundary conditions. Some numerical results of different stress and displacement components at different sections of the column are presented in the form of graphs. The effect of column aspect ratio and material orthotropy on the solution of stresses and displacements at a particular section is also analysed. Finally, analytical results obtained by the present formulation are compared to those of finite-element and finite-difference methods.

Study of the thermal decomposition of PFPEs lubricants on a thin DLC film using finitely extensible nonlinear elastic potential based molecular dynamics simulation

Perfluoropolyethers (PFPEs) are widely used as hard disk lubricants for protecting carbon overcoat reducing friction between the hard disk interface and the head during the movement of head during reading and writing data in the hard disk. Due to temperature rise of PFPE Zdol lubricant molecules on a DLC surface, how polar end groups are detached from lubricant molecules during coating is described considering the effect of temperatures on the bond/break density of PFPE Zdol using the coarse-grained bead spring model based on finitely extensible nonlinear elastic potential. As PFPE Z contains no polar end groups, effects of temperature on the bond/break density (number of broken bonds/total number of bonds) are not so significant like PFPE Zdol. Effects of temperature on the bond/break density of PFPE Z on DLC surface are also discussed with the help of graphical results. How bond/break phenomenonaffects the end bead density of PFPE Z and PFPE Zdol on DLC surface is discussed elaborately. How the overall bond length of PFPE Zdol increases with the increase of temperature which is responsible for its decomposition is discussed with the help of graphical results. At HAMR condition, as PFPE Z and PFPE Zdol are not suitable lubricant on a hard disk surface, it needs more investigations to obtain suitable lubricant. We study the effect of breaking of bonds of nonfunctional lubricant PFPE Z, functional lubricants such as PFPE Zdol and PFPE Ztetrao, and multidented functional lubricants such as ARJ-DS, ARJ-DD, and OHJ-DS on a DLC substrate with the increase of temperature when heating of all of the lubricants on a DLC substrate is carried out isothermally using the coarse-grained bead spring model by molecular dynamics simulations and suitable lubricant is selected which is suitable on a DLC substrate at high temperature.

On the thickness-dependent diffusion coefficient of perfluoropolyether lubricants on a thin diamond-like film

Diffusion of perfluoropolyethers (PFPEs) lubricants on a hard disk surface is an important self healing characteristic to replenish PFPEs lubricants on their uncovered surface. In the present paper, we study the diffusion coefficients of non-functional PFPE Z and PFPE Zdol with functional end groups as a function of lubricant film thickness on a thin DLC (diamond-like) film. Diffusion coefficients of PFPE Z and PFPE Zdol molecules on a DLC film are calculated using the equation of Einstein’s law of diffusion (Guo et al. J. Appl. Phys 93:8707, 2003; Guo Ph.D. thesis, 2006; Chung et al. IEEE Trans. Magn. 45:3644, 2009) considering the movement of their center of mass to reach their equilibrium positions from their original configurations. And it is averaged with the film thickness to show the thickness dependence on the diffusion of PFPEs lubricants on a DLC substrate. Firstly diffusion coefficients of sub-monolayer of partially coverage PFPE Z and PFPE Zdol on a DLC substrate are studied briefly and secondly the diffusion coefficient of monolayer PFPE Zdol on a DLC substrate is also studied elaborately. To support our results, we compare our thickness-dependent diffusion coefficients of PFPE Z and PFPE Zdol with those of published theoretical (Guo Ph.D. thesis, 2006; Chung et al. IEEE Trans. Magn. 45:3644, 2009) and experimental results (Chung et al. Tribol. Lett. 32:35, 2008; Ma et al. Tribol. Lett. 10:203, 2001). Here we study how lubricant film thickness plays an important role on its diffusion. Effects of polar end bead functionality, lubricant film thickness enhance the anisotropic behavior of diffusion coefficients of PFPE Zdol on the DLC substrate. But in the present analysis we consider hard disk carbon overcoat as a thin DLC film and we include all of their atoms within the force cut-off distance with PFPEs lubricant molecules for the interactions to study the thickness dependence on their diffusion coefficients.