Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite

Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition.     

Solution of the Stochastic Boundary-Value Problem of Steady-State Creep for a Thick-Walled Tube Using the Small-Parameter Method

The physically and statistically nonlinear problem of steady-state creep for a thick-walled tube loaded by internal pressure is solved in the third approximation using the small-parameter method. The variances of random creep strain rates and displacements are calculated. The results obtained are compared with the solution of the same problem in the first and second approximations. A reliability assessment method for the tube using the strain failure criteria is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 161–171, January–February, 2006.     

Asymptotics of stresses and strain rates near the tip of a transverse shear crack in a material whose behavior is described by a fractional-linear law

An approximate solution of the problem of determining the fields of stresses and strain rates due to creep near the tip of a transverse shear crack in a material whose behavior is described by a fractional-linear law of the theory of steady-state creep is given. It is shown that the strain rates have a singularity of the type ∼ r^−α near the crack tip; the order of singularity α changes discretely, depending on the polar angle, and takes the values 1, 2/3, and 1/2. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 165–176, January–February, 2009.     

Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 140–146, March–April, 2007.     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

Using the perturbation method to solve the problem of separated incompressible flow past thin airfoils

A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006.     

Nonlinear creep and ductile creep rupture of perfectly elastoplastic rods under tension

The paper is concerned with the problem of predicting nonlinear creep strains and time to ductile rupture of prismatic rods under constant tension. The material of the rod is assumed isotropic, homogeneous, and perfectly plastic. The problem is solved using models that take into account the change in the geometry of the rod during creep, the finiteness of the creep strains, and the effect of the initial and actual elastic strains. The conditions whereby the characteristic dimension of the rod tends to infinity and the accumulated and real strains in the viscous flow are limited are used as a failure criterion. The calculated results are compared with experimental data for a number of steels and alloys to formulate the conditions for the ductile rupture and embrittlement of metallic materials under uniaxial creep __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 120–133, April 2008.     

Structure of the constitutive relations for hereditarily elastic materials reinforced by hard fibers

The problem of simplifying the nonlinear hereditary elasticity relations is considered for strongly anisotropic materials such as fiber-reinforced composites. This is done using their property that the material stiffness is high along the reinforcement and is low in the cross-sectional direction. The material is considered transversally isotropic. The simplification is performed by analyzing asymptotic representations of creep relations. Relations of various degrees of accuracy for various types of composites and stress states are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 120–127, May–June, 2005.     

Solving initial–boundary-value creep problems

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

Generalized rheological model of shear deformation of structured condensed media

A relaxation-type macrorheological equation is constructed, which describes shear deformation of elastoplastoviscous media containing microvoids. The equation corresponds to regimes of steady-state creep and elastic and plastic strains, which pass to the regime of viscous flow with limited growth of voids at high shear strain rates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 87–95, September–October, 2007.     

Creep of plates made of aluminum alloys under bending

Results of experiments dealing with the creep of a V95pchT2 aluminum alloy are presented. Constitutive equations of steady creep are constructed and used to solve the problem of pure twisting of a square plate. Calculated and experimental values of plate curvature are compared. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 156–159, September–October, 2007.     

Stress concentration in viscoelastic transversally isotropic hyperboloid

The stress redistribution over time in a viscoelastic transversally isotropic hyperboloid of revolution is studied. The material has the property of slipping creep in the planes perpendicular to the isotropy plane. The body is subjected to uniaxial tension. An analytical solution is obtained on the basis of the Boltzmann-Volterra principle and the operator chain-fraction method. In calculating the stress concentration in the hyperboloidal body, the properties of the material are described by integral operators with a Rabotnov kernel. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 3, pp. 33–41, March, 1999.     

Steady-state conditions of a nonisothermal film with a heat-insulated free boundary

The equilibrium shapes of a nonisothermal liquid film with a heat-insulated free surface for large Marangoni numbers are investigated in the long-wave approximation using a combination of analytical and numerical methods. It is proved that the two-dimensional problem of the equilibrium of a strip-shaped film has a steady-state solution for an arbitrary large temperature gradient on the boundaries of the strip. An increase in this gradient leads to an abrupt thinning of the film near the heated boundary, which can result in instability and rupture of the film. In the equilibrium problem for a film fixed on a circular contour, the nonuniform distribution of the heat flux on the contour was found to have a significant influence on the free-surface shape. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 59–73, July–August, 2008.     

Linear problem of a hydrofoil moving under the free surface of a finite-depth fluid

A method of solving the plane linear problem of a steady-state irrotational flow about a body under the free surface of a heavy fluid of finite depth is developed. The boundary-value problem is formulated for a complex perturbed velocity and is reduced to a singular integral equation relative to the intensity of a vortex layer that models the hydrofoil. The kernel of the equation is the exact solution of the corresponding boundary-value problem for a vortex of unit intensity. The equation is solved by the discrete-vortex method. The effect of the parameters of the problem on the hydrodynamic characteristics of the elliptical hydrofoil and the shape of the free surface are estimated numerically. Omsk Division of the Sobolev Institute of Mathematics, Omsk 644099. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 85–90, November–December, 1998.     

Applied creep theory for bodies with anisotropy due to plastic prestrain

Plastic strains in structures at the stages of manufacturing, testing, and approaching the operation regime cause anisotropic variations in the mechanical properties of materials, including creep strength. We consider the following special but practically important class of loading processes for originally isotropic materials: a simple active plastic strain is followed by a long-term steady-state loading within the elastic limits. To describe the second stage, we present the creep strain deviator in the form of an additive orthogonal decomposition in the directions of the repeated loading and the vector anisotropy. The coefficients in the decomposition are material functions of time, of the intensities of the preliminary and repeated loadings, and of the angle between the directions of these loadings. We obtain conditions on the material functions under which, at any given time instant, there is a one-to-one continuous correspondence between the stress and strain tensors for the model proposed and the boundary-value problem in the generalized statement has a unique solution; we also prove the convergence of the iteration method of elastic solutions used to find this unique solution. The model is identified according to the creep diagrams (under steady-state stresses of different values) determined for the material in the original state and after the plastic prestrain at an angle (zero, extended, and intermediate) to the direction of the repeated loading. We show that our results are in good agreement with the results available in the literature concerning experiments in this class of processes for stainless steel at high temperature. We propose an engineering version of the theory in which only the experimental data for uniaxial tension are used. We discuss the versions of the model for the cases in which the plastic preloading is cyclic (one-dimensional or circular) and the repeated loading is unsteady.     

Nonlinear creep of unidirectional fibrous composites tensioned along the reinforcement

Creep strains in unidirectional organic-fiber-and organic-glass-fiber-reinforced plastics subject to tension in the reinforcement direction are predicted. Based on homogeneity condition and statistical criteria, it is shown that the creep of the composites is essentially nonlinear. To predict creep strains, use is made of a nonlinear creep model based on a modified Rabotnov’s similarity hypothesis for isochrones and of material constants determined from tests on specimens made of a composite as a whole and specimens made of its separate components, the mixing rule applied in the latter case. The calculated results and the experimental data are in satisfactory agreement __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 20–34, May 2007.     

Modeling the effect of diffusion of the ambient medium on the long-term strength of a hollow cylinder under uniaxial tension

The problem of the long-term strength of an extended thick-walled tube containing a corrosive medium in the internal cavity is solved. The diffusion of this medium into the tube material is analyzed. The diffusion equation is solved approximately by introducing the diffusion front, and the error of the solution is estimated. The dependence of the time of fracture of the tube on the variable tensile stress and the concentration of the medium filling the cavity is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 88–93, July–August, 2007.     

Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account

Motivated by recent progress in viscoelastic indentation analysis, the identification of viscoelastic properties from nanoindentation test data taking the real tip geometry into account is presented in this paper. Based on the elastic solution of the indentation problem, the corresponding viscoelastic solution is obtained by the application of the method of functional equations. This general solution, which accounts for the real geometric properties of the indenter tip, is specialized for the case of a trapezoidal load history, commonly employed in nanoindentation testing. Three deviatoric creep models, the single dash-pot, the Maxwell, and the three-parameter model are considered. The so-obtained expressions allow us to determine viscoelastic model parameters via back calculation from the measured load–penetration history. The presented approach is illustrated by the identification of short-term viscoelastic properties of bitumen. Hereby, the influence of loading rate, maximum load, and temperature on the model parameters is investigated.     

Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations

We prove the existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler–Poisson (Euler–Poisson) equations in three spatial dimensions with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty–Beals paper. We prove the non-linear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove finite time stability of solutions where the perturbations are entropy-weak solutions of the Euler–Poisson equations. Finally, we give a uniform (in time) a priori estimate for entropy-weak solutions of the Euler–Poisson equations.