Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

Microstructural stability and nanoindentation of an electrodeposited nanocrystalline Ni-1.5wt.%P alloy

Microstructural stability of nanocrystalline Ni-1.5wt.%P alloy with an initial grain size of 3 nm processed by pulsed electrodeposition was studied using differential scanning calorimetry (DSC) and annealing. Microstructural characterization suggests that the observed exothermic peak during heating in DSC is related to both concurrent grain growth and Ni3P formation. Nanoindentation on samples with grain sizes from 3 to 50 nm revealed a breakdown in Hall-Petch strengthening in nano Ni-P alloy at grain sizes <= 10 nm, consistent with some previous observations. It is concluded that there is a grain boundary weakening regime for grain sizes < 10 nm, based on analysis which show that the data cannot be rationalized in terms of microstrain relaxation, variation in elastic modulus, texture evolution and duplex structure formation.

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Transient analysis of mammalian cell growth in hollow fibre bioreactor

A mathematical model describing the dynamics of mammalian cell growth in hollow fibre bioreactor operated in closed shell mode is developed. Mammalian cells are assumed to grow as an expanding biofilm in the extra-capillary space surrounding the fibre. Diffusion is assumed to be the dominant process in the radial direction while axial convection dominates in the lumen of the bioreactor. The transient simulation results show that steep gradients in the cell number are possible under the condition of substrate limitation. The precise conditions which result in nonuniform growth of cells along the length of the bioreactor are delineated. The effect of various operating conditions, such as substrate feed rate, length of the bioreactor and diffusivity of substrate in different regions of the bioreactor, on the bioreactor performance are evaluated in terms of time required to attain the steady-state. The rime of growth is introduced as a measure of effectiveness factor for the bioreactor and is found to be dependent on two parameters, a modified Peclet number and a Thiele modulus. Diffusion, reaction and/or convection control regimes are identified based on these two parameters. The model is further extended to include dual substrate growth limitations, and the relative growth limiting characteristics of two substrates are evaluated. (C) 1997 Elsevier Science Ltd.

Low temperature fabrication and impedance spectroscopy of PMN-PT ceramics

Single phase perovskite 0.9Pb(Mg1/3Nb2/3)O-3-0.1(PbTiO3) ceramics were prepared using the columbite precursor method after optimizing the synthesis conditions. X-ray diffraction (XRD) studies were carried out to verify the phase formation at each processing step. Scanning electron microscopy (SEM) was employed to observe the microstructure of the sintered ceramics. Impedance and modulus spectroscopic data were used to gain an insight into the electrical properties of the samples and with a view to observing the relaxations in them. (C) 1999 Elsevier Science Ltd.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

Solution grafting of maleic anhydride onto polyethylene and compatibilization of polyetylene-nylon blends

Maleic anhydride (MAH) has been grafted onto high density polyethylene (HDPE) with benzoyl peroxide (BOP) initiator in toluene solution. Maximum degree of grafting (12%) without crosslinking has been obtained using MAH/HDPE and BOP/HDPE weight ratios of 1.0 and 0.15 respectively, at 110 degrees C. The HDPE-g-MAH compatibilizer is found to drastically reduce the dispersed phase size and also to produce homogeneous blends for relatively low concentrations of dispersed phase in HDPE/nylon blends. Addition of this compatibilizer results in increase of tensile strength and modulus with increasing nylon content of HDPE/nylon blends, while the opposite is found for the blends without any added compatibilizer.

Synthesis and Degradation of Sorbitol-Based Polymers

A new class of biodegradable copolyesters was synthesized by the catalyst-free melt condensation of sorbitol with citric acid, tartaric acid, and sebacic acid. The resulting polymers were designated as poly(sorbitol citric sebacate) p(SCS)] and poly(sorbitol tartaric sebacate) p(STS)]. The synthesized polymers were characterized by Fourier transform infrared spectroscopy, H-1-NMR spectroscopy, and differential scanning calorimetry analysis. Porous spongelike scaffolds were prepared with a salt-leaching technique and characterized with scanning electron microscopy. Tensile testing of the p(SCS) and p(STS) polymers showed that they exhibited a wide range of mechanical properties. The Young's modulus and tensile strengths of the polymers ranged from 1.06 +/- 0.12 to 462.65 +/- 34.21 MPa and from 0.45 +/- 0.04 to 20.32 +/- 2.54 MPa, respectively. In vitro degradation studies were performed on disc-shaped polymer samples. The half-life of the polymers ranged from 0.54 to 38.52 days. The percentage hydration of the polymers was in the range 9.36 +/- 1.26 to 78.25 +/- 1.91, with sol contents of 2-14%. At any given polymer composition, the Young's modulus and tensile strength of p(SCS) was higher than that of p(STS), whereas the degradation rates of p(SCS) was lower than that of p(STS). This was attributed to the structural difference between the citric and tartaric monomers and to the degree of crosslinking. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 121: 2861-2869, 2011

Nanoindentation studies in NiTi films deposited on Si wafer

Nanoindentation tests were carried out at different locations in a Ti rich NiTi film deposited on a 3 `' silicon wafer by dc magnetron sputtering. The purpose of doing nanoindentation at different locations was to check the uniformity of the sample with respect to its mechanical behaviour and shape memory effect. The results showed that elastic modulus and hardness measured by nanoindentation was similar at different locations in the 3 `' wafer. Nanoindcntation coupled with depth profiling of residual indents using AFM also showed that the extent of shape memory recovery obtained by heating the film above its martensite to austcnite phase transformation temperature was also similar at different locations in the 3 `' wafer. However, the measured recovery ratio was lower than that predicted from theoretical calculations for indents made using Berkovich indenter. The results showed that the deposition process resulted in a NiTi film with uniform composition, mechanical properties and shape memory behaviour.

Dielectric Relaxation in CaO-Bi2O3-B2O3 Glasses

Glasses in the system CaO-Bi2O3-B2O3 (in molar ratio) have been prepared using melt-quenching route. Ion transport characteristics were investigated for this glass using electric modulus, ac conductivity and impedance measurements. The ac conductivity was rationalized using Almond-West power law. Dielectric relaxation has been analyzed based on the behavior of electric modulus behavior. The activation energy associated with the electrical relaxation determined from the electric modulus spectra was found to be 1.76 eV, close to that the activation energy for dc conductivity (1.71 eV) indicating that the same species took part in both the processes. The stretched exponent beta (0.5-0.6) is invariant with temperature for the present glasses.

Estimation of elasticity map of soft biological tissue mimicking phantom using laser speckle contrast analysis

Scattering of coherent light from scattering particles causes phase shift to the scattered light. The interference of unscattered and scattered light causes the formation of speckles. When the scattering particles, under the influence of an ultrasound (US) pressure wave, vibrate, the phase shift fluctuates, thereby causing fluctuation in speckle intensity. We use the laser speckle contrast analysis (LSCA) to reconstruct a map of the elastic property (Young's modulus) of soft tissue-mimicking phantom. The displacement of the scatters is inversely related to the Young's modulus of the medium. The elastic properties of soft biological tissues vary, many fold with malignancy. The experimental results show that laser speckle contrast (LSC) is very sensitive to the pathological changes in a soft tissue medium. The experiments are carried out on a phantom with two cylindrical inclusions of sizes 6 mm in diameter, separated by 8 mm between them. Three samples are made. One inclusion has Young's modulus E of 40 kPa. The second inclusion has either a Young's modulus E of 20 kPa, or scattering coefficient of mu'(s), = 3.00 mm(-1) or absorption coefficient of mu(a) = 0.03 mm(-1). The optical absorption (mu(a)), reduced scattering (mu'(s)) coefficient, and the Young's modulus of the background are mu(a) = 0.01 mm(-1), mu'(s) = 1.00 mm(-1) and 12kPa, respectively. The experiments are carried out on all three phantoms. On a phantom with two inclusions of Young's modulus of 20 and 40 kPa, the measured relative speckle image contrasts are 36.55% and 63.72%, respectively. Experiments are repeated on phantoms with inclusions of mu(a) = 0.03 mm-1, E = 40 kPa and mu'(s) = 3.00 mm(-1). The results show that it is possible to detect inclusions with contrasts in optical absorption, optical scattering, and Young's modulus. Studies of the variation of laser speckle contrast with ultrasound driving force for various values of mu(a), mu'(s), and Young's modulus of the tissue mimicking medium are also carried out. (C) 2011 American Institute of Physics. doi:10.1063/1.3592352]

Water ingression and the role of interface on the compressive properties of epoxy filled with treated fly ash

Polymer composites are generally filled with either fibrous or particulate materials to improve the mechanical properties. In choosing the fillers one looks for materials that are inexpensive and available in abundance, in order to realize a cost reduction also. Also, often these fibres/fillers are treated to improve the matrix adhesion and thereby mechanical properties. The present study is focussed on the influence of water ingression in such filler-modified composites and the attendant changes in the compressive properties. The changes in property effected following exposure to aqueous media and the influence interface modification has on the scenario is emphasized in the work. It is seen that for plain epoxy and fly ash filled systems the strengths are increased following exposure to aqueous media. The composites with surface-treated ash particles, on the other hand, record a drop in the values. Modulus values show are increased to varying degree in unfilled and filled systems. The study also includes a fractographic analysis of the tested samples with and without exposure to water.

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor $f$ is measured as a function of the Reynolds number $Re$. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the $f$–$Re$ curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of $16\ensuremath{/} Re$ in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

Stress induced phase transition in a monomolecular perfluroalkylsilane film self assembled on aluminium surface

We control the stiffnesses of two dual double cantelevers placed in series to control penetration into a perflurooctyltrichlorosilane monolayer self assembled on aluminium and silicon substrates. The top cantilever which carries the probe is displaced with respect to the bottom cantilever which carries the substrate, the difference in displacement recorded using capacitors gives penetration. We further modulate the input displacement sinusoidally to deconvolute the viscoelastic properties of the monolayer. When the intervention is limited to the terminal end of the molecule there is a strong viscous response in consonance with the ability of the molecule to dissipate energy by the generation of gauche defects freely. When the intervention reaches the backbone, at a contact mean pressure of 0.2GPa the damping disappears abruptly and the molecule registers a steep rise in elastic modulus and relaxation time constant, with increasing contact pressure. We offer a physical explanation of the process and describe this change as due to a phase transition from a liquid like to a solid like state.