Determining the thermal stresses in a hollow viscoelastic sphere

For a viscoelastic sphere with spherical cavity, solution of the quasistatic problem of the stresses produced by a nonstationary temperature field reduces to solution of an integral-differential equation whose right side depends on an unknown function of the time. A numerical solution method is described.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 2, pp. 300–305, August, 1969.     

Slow viscoelastic fluid flow past a rotating sphere

The problem of axially symmetric flow of a particular type of non-Newtonian fluid past a rotating sphere due to a uniform stream at infinity is investigated. The presence of a region of reversed flow is found under certain conditions depending on the angular velocity of the sphere, the speed of the uniform stream and radius of the sphere. This region which is attached to the rear portion of the sphere is found to depend strongly on the viscoelasticity of the fluid. The vortex is seen to move towards the sphere as the viscoelastic parameter increases while the other parameters are kept fixed. As this viscoelastic parameter approaches a critical value, the vortex is found to disappear.     

Axisymmetric wave propagation in a solid viscoelastic sphere

Two problems of linear wave propagation in a viscoelastic solid sphere are solved. The waves are generated by two types of impact on the surface of the sphere. The deformation has symmetry with respect to an axis through the center of the sphere. The solution is based on a superposition principle which reduces the general solution to a static elastic solution, an elastic solution of an eigenvalue problem and an integral equation of the Volterra type involving time only. The solutions are given in double infinite series involving spherical Bessel functions, Legendre polynomials and Legendre functions of the first kind and order one.     

Determination of the properties of viscoelastic materials using spherical nanoindentation

The article is devoted to determining the properties of linearly viscoelastic isotropic materials from the experiment on the introduction of a spherical indenter at a constant-rate displacement in a viscoelastic sample. The results are based on the Lee–Radok (J. Appl. Mech. 27:438–444, 1960) solution of the viscoelastic contact problem. An exact formula is obtained for calculation of the relaxation function using indentation load–displacement data. To illustrate the application of this formula, it is used to find the relaxation function of polymethyl methacrylate (PMMA). The relaxation function found in the article is compared with data measured in a conventional test to evaluate the suitability of the proposed method.     

Nanoscale mechanical characterization of PMMA by AFM nanoindentation: a theoretical study on the time-dependent viscoelastic recovery

Temperature-dependent indent recovery of polymethyl methacrylate is depicted by atomic force microscopy. The viscoelastic indent recovery is predicted by a numerical model based on the Boussinesq elastic theory. From the perspective of an elastic solution, viscoelastic solution for stress and displacement field is constructed through the analysis of the elasticity–viscoelasticity corresponding theory. The findings also illustrate the effect of loading condition, elastic modulus, and viscosity on the viscoelastic recovery rate.     

Luminous-flux measurements by an absolute integrating sphere

We present an original implementation of the absolute-sphere method recently proposed by Ohno. The luminous-flux unit, the lumen, is realized by means of an integrating sphere with an opening calibrated by a luminous-intensity standard placed outside. The adapted experimental setup permits one to measure luminous-flux values between 5 and 2500 lm with a significant improvement with respect to the simulated performances reported in the literature. Traditionally, the luminous-flux unit, the lumen, is realized by goniophotometric techniques in which the luminous-intensity distribution is measured and integrated over the whole solid angle. Thus sphere results are compared with those obtained with the Istituto Elettrotecnico Nazionale goniophotometer. In particular, a set of standards, characterized by luminous-flux values of ~2000 lm, has been calibrated with both techniques. We highlight some of the problems encountered. Experimental results show that the agreement between the two methods is within the estimated uncertainty and suggest promising areas for future research.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

Influence of surface energy on the nanoindentation response of elastically-layered viscoelastic materials

In the context of integrated nonlinear viscoelastic contact mechanics, a nonlinear finite element model is developed to predict and analyze the quasistatic response of nanoindentation problems of an elastically-layered viscoelastic materials considering the surface elasticity effects. Effects of surface energy are accounted for by employing the Gurtin–Murdoch continuum model for surface elasticity. The linear viscoelastic response is modeled by the Schapery’s creep model with a Prony’s series to express the transient component in the creep compliance. The viscoelastic constitutive equations are cast into a recursive form that needs only the previous time increment rather than the entire strain history. To satisfy the contact constraints exactly, the Lagrange multiplier method is adopted to enforce the contact conditions into the system. The equilibrium indentation configuration is obtained through the Newton–Raphson iterative procedure. The developed model is verified then applied to investigate the quasistatic nanoindentation response of two different indentation problems with different geometry and loading conditions. Results show the significant effects of surface energy and viscoelasticity on the quasistatic nanoindentation response.     

On evaluation of the green functions for harmonic line loads in a viscoelastic half space

Comparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw-Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numerically.     

Temperature fields due to thermomechanical coupling in a compressible viscoelastic sphere

Summary Internal cyclic loading of a viscoelastic hollow sphere is considered. The influence of the material properties in dilatation and shear on the heat generation and temperature distribution is analysed.For common polymeric materials the elastic and viscoelastic dilatational properties are found to be of less improtance than the temperature dependence in shear.

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Durch thermomechanische Kopplung hervorgerufene Temperaturfelder in einer kompressiblen viskoelastischen Kugel

Zusammenfassung Betrachtet wird eine viskoelastische Hohlkugel unter zyklischem Innendruck. Der Einfluß der Materialeigenschaften in Dilatation und Schub auf Wärmeentwicklung und Temperaturverteilung wird untersucht. Es zeigt sich, daß für gewöhnliche Polymere die elastischen und viskoelastischen Materialeigenschaften bei Dilatation von geringerer Bedeutung als die Temperaturabhängigkeit der Materialeigenschaften bei Schub sind.

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With 5 Figures     

Dynamic-contact stiffness at the interface between a vibrating rigid sphere and a semi-infinite viscoelastic solid

Vibration of a rigid sphere contacting a semiinfinite viscoelastic solid is studied theoretically. The rigid sphere is subjected to an oscillating force while being compressed in the vertical direction by a static force. The contact-pressure distribution and contact radius at the interface vary with the oscillation. Assuming sufficiently small oscillating force, we derive the dynamic-contact-pressure distribution with the constant contact radius, which establishes dynamic contact stiffness between the sphere and the viscoelastic solid. Numerical calculations show the influence of vibration frequency, contact radius, Poisson's ratio, and the damping characteristic of the solid.     

Stress and strain measurements in carbon-related materials impacted by a high-velocity steel sphere

To investigate the behavior of carbon-related materials damaged by the impact of a sphere, stress and strain measurements during the impact were carried out using a PVDF stress gauge and a constantan strain gauge. A spherical projectile having a velocity of ca. 150–1300 m/s was allowed to impact carbon fiber-reinforced plastics (CFRPs) with different carbon fibers, CFRPs with and without surface-treated fibers, polycrystalline graphites and a C/C composite. The maximum stress generated in the CFRPs depended on the reinforcing fibers; pitch-based fiber resulted in larger increase in stress with impact velocity. The CFRP without the surface-treated fiber resulted in lower strain and stress than the CFRP consisting of the surface-treated fiber. Polycrystalline graphites showed a very large strain, and then powdering; the movement of the powder was considered to affect stress and strain in the graphite materials.     

Depolarization measurements of an integrating sphere

Mueller-matrix polarimetry performed in the visible and near IR indicates that an integrating sphere acts as an ideal depolarizer to the 0.5% accuracy of the polarimeter. The integrating sphere emits unpolarized light regardless of the incident polarization state.     

The effect of work-hardening and pile-up on nanoindentation measurements

Nanoindentation is performed on the cross-section of copper samples subjected to surface mechanical attrition treatment (SMAT). The cross-section of the SMAT samples provides a unique microstructure with varying amounts of work-hardening depending on the distance from the SMAT surface. Results show that for a given indentation load the pile-up height decreases and the indentation depth increases as the distance from the SMAT surface increases, both following a power law relationship. Based on image analysis of the indented surface this increase in the pile-up height and decrease in indentation depth is attributed to the localization of plastic strain due to the increased resistance to dislocation motion in the work-hardened region. For a given amount of work-hardening (in terms of distance from SMAT surface), the indentation depth increased with the indentation load obeying a power law relationship with the exponent ranging from 0.58 to 0.68. However, the pile-up height increased linearly with the load, with the rate (slope) increasing with the amount of work-hardening. The observed linear increase in pile-up height with indentation load would naturally introduce an indentation size effect (ISE) if the hardness is corrected for the pile-up. Interestingly, this ISE associated with pile-up increased with an increase in indentation depth, in contradiction to the ISE associated with strain gradient. Deviation of the hardness values corrected for pile-up from the bulk behavior due to surface effect is highlighted and a method to obtain a bulk-equivalent hardness quantity representing the bulk behavior is proposed.     

On the use of nanoindentation for cementitious materials

Recent progress in experimental and theoretical nanomechanics opens new venues in materials science for the nano-engineering of cement-based composites. In particular, as new experimental techniques such as nanoindentation provide unprecedented access to micromechanical properties of materials, it becomes possible to identify the mechanical effects of the elementary chemical components of cement-based materials at the scale where physical chemistry meets mechanics, including the properties of the four clinker phases, of portlandite, and of the C-S-H gel. In this paper, we review some recent results obtained by nanoindentation, which reveal that the C-S-H gel exists “mechanically” in two different forms, a lowdensity form and a high-density form, which have different mean stiffness and hardness values and different volume fractions. While the volume fractions of the two phases depend on mix proportions, the mean stiffness and hardness values do not change from one cement-based material to another; instead they are intrinsic properties of the C-S-H gel.

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Résumé Les récents progrès en “nanomécanique”, aussi bien sur le plan théorique qu’expérimental, ouvrent de nouvelles perspectives en science des matériaux pour la nano-ingénierie des composites à base de ciment. Grace à de nouvelles techniques expérimentales telles que la ‘nanoindentation’, qui permet d’avoir un accès sans précédent aux propriétés micromécaniques des matériaux, il devient notamment possible d’identifier les effets mécaniques des composants chimiques élémentaires à l’échelle où la chimie rejoint la mécanique; cela inclut les propriétés des quatre phases de clinkers, de la portlandite et du gel de C-S-H. Dans le présent article, nous analysons quelques résultats récents obtenus par nanoindentation; ces résultats révèlent que le gel de C-S-H existe “mécaniquement” sous deux formes différentes, l’une à faible densité et l’autre à forte densité. La valeur moyenne du module d’élasticité, de la dureté, ainsi que la fraction volumique de ces deux formes sont différentes. Alors que la fraction volumique des deux phases dépend de la formulation du mélange, les valeurs moyennes du module d’élasticité et de la dureté sont identiques d’un composite à l’autre; il s’agit de propriétés intrinsèques du gel de C-S-H.

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Editorial Note Prof. Franz-Josef Ulm is a RILEM Senior Member. He was awarded the 2002 Robert L’Hermite Medal. He is Associate Editor forConcrete Science and Engineering.     

On the oblique water-entry problem of a rigid sphere

The case of oblique water-entry of a rigid sphere into an ideal incompressible fluid is studied analytically in order to determine the hydrodynamical loads acting on the body. We consider the motion imparted to the fluid by an impulsively-started partially-submerged sphere under the large-impact approximation, in which the free surface is assumed flat and equipotential. Asymptotic small-time expressions are derived for both the vertical and horizontal time-dependent added masses and analytical expressions for the hydrodynamic forces are obtained by differentiating these added masses with respect to the instantaneous submergence depth. The resulting expressions are also compared with corresponding numerical solutions and with a known solution for a two-dimensional profile.