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     

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.     

Modeling the deformability of a material

The high-temperature extension of metals to fracture is modeled for creep at constant stress or at constant strain rate. The dependence of the ultimate fracture strain on the loading factor (stress or strain rate) is studied. The nonmonotonic nature of this dependence with an internal maximum is described using the Rabotnov kinetic theory with one and two damage parameters. Available experimental data are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 183–188, September–October, 2007.     

Micromechanics modeling of strength for nanocrystalline copper

We present a model in this paper for predicting the inverse Hall–Petch phenomenon in nanocrystalline (NC) materials which are assumed to consist of two phases: grain phase of spherical or spheroidal shapes and grain boundary phase. The deformation of the grain phase has an elasto-viscoplastic behavior, which includes dislocation glide mechanism, Coble creep and Nabarro–Herring creep. However the deformation of grain boundary phase is assumed to be the mechanism of grain boundary diffusion. A Hill self-consistent method is used to describe the behavior of nanocrystalline pure copper subjected to uniaxial tension. Finally, the effects of grain size and its distribution, grain shape and strain rate on the yield strength and stress–strain curve of the pure copper are investigated. The obtained results are compared with relevant experimental data in the literature.     

On the forms of relationship between two noncoaxial second-order tensors (the case of plane strain or a plane stress state)

A relationship between noncoaxial tensors of stress and creep strain rate is established for the case of plane strain or a plane stress state. The basis is the experimentally substantiated hypothesis on the existence of a creep surface, which is a set of loading paths in the stress space that, at any time, ensure identical values of the creep intensity for a certain chosen measure and orthogonality of the creep strain rate vector to this surface. The relation obtained completely corresponds to available experimental data for complex loading. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 135–140, March–April, 1998.     

Numerical simulation of shock wave propagation in microchannels using continuum and kinetic approaches

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier–Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar–Gross–Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier–Stokes computations.      

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.     

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.     

Creep of axisymmetrically loaded plates with allowance for damage accumulation in their material

The Rabotnov kinetic creep theory was used to calculate the stress-strain state and damage accumulation in the material of axisymmetrically loaded circular and ring plates at any time before the beginning of fracture. It is shown that the solution of the problem can be reduced to solving the same problem under the assumption of steady-state creep of the material. The unsteady creep problem is solved by multiplying the known solution of the steady-state creep problem by certain functions of the coordinates and time, which are determined from a corresponding system of equations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 157–168, September–October, 2006.     

Mathematical model of creep for a microinhomogeneous nonlinearly elastic material

A mathematical model is proposed to describe the experimentally observed creep effect on the instantaneous elastic deformation of physically nonlinear elastic microinhomogeneous materials. Using a structural model of the medium, it is shown that, during unloading of a sample after creep at constant stress, the elastic strain can be both larger and smaller than the elastic strain during loading. It is shown that calculation results for a biocomposite material are in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 157–163, May–June, 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.     

Mechanical Performance of a Recycled Carbon Fibre/PP Composite

A composite made of recycled carbon fibres in recycled polypropylene matrix is studied experimentally to describe the features of the elastic and time dependent nonlinear mechanical behaviour. The properties of the developed material have a large variability to be addressed and understood. It was found that the stress-strain curves in tension are rather nonlinear at low strain rate and the strength is sensitive to strain rate. The elastic properties’ reduction for this composite after loading to high strains is rather limited. More important is that even in the “elastic region” due to viscoelastic effects the slope of loading–unloading curve is not the same and that at higher stress large viscoplastic strains develop and creep rupture is typical. The time and stress dependence of viscoplastic strains was analysed and described theoretically. The viscoelastic response of the composite was analysed using creep compliance, which was found to be slightly nonlinear.     

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.     

Modeling Creep and Continuous Fracture Process Zones in Spatial Prismatic Bodies

The semianalytic finite-element method is used to develop a method for solving problems of creep and continuous fracture of complex spatial bodies. The method allows modeling the variation of the stress-strain state during creep, accompanying accumulation of dispersed microdamages, and development of macroscopic effects—continuous fracture process zones. The growth of a continuous fracture process zone is modeled. A criterion is formulated for determination of the applicability limits of continuum damage mechanics. The method is exemplified by the problem of deformation and continuous fracture of a gas turbine blade __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 70–86, September 2005.     

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.     

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.     

Nonlinear regimes of variation of the shape of an elastic tube containing a flowing fluid

A linear and nonlinear analysis of the distributed oscillations of an elastic tube with a fluid flowing in it is developed. The critical flow velocity and the wavelength and oscillation frequency in the tube-flow system at loss of stability are found. The geometrical and physical nonlinearities, the latter related to increase in the Young’s modulus of the tube wall material with increasing strain, are considered. It is shown that four characteristic regimes of change of tube shape are possible: local dilatation, collapse, flexure, and distributed auto-oscillations. The tube oscillations are analyzed numerically for the nonaxisymmetric case. The conditions of existence of these effects in blood vessels are examined. Nizhni Novgorod, e-mail: klochkov@appl.sci-nnov.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 46–55, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 97-02-18612).     

Stress–strain state of nonthin orthotropic spherical shells of variable thickness

The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed. Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells with variable thickness is studied     

Contact problem for a ring plate on an elastic half-space. Variational approach

A contact problem of an axisymmetrically loaded flexible ring plate lying frictionlessly on an elastic half-space is considered. The plate subsidences are represented as a power series with unknown coefficients, which are determined by the Rayleigh-Ritz method using the minimum condition for the total strain energy of the plate and the elastic foundation. The method of orthogonal polynomials is used implicitly. Belarussian State Polytechnical Academy, Minsk 220027. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 193–198, January–February, 1999.     

Refined design of longitudinally corrugated cylindrical shells

A refined Timoshenko-type model based on the straight-line hypothesis is used to develop an approach to analyzing the stress state of longitudinally corrugated cylindrical shells with elliptic cross-section. The approach is to reduce the two-dimensional boundary-value problem that describes the stress–strain state of the shell to a one-dimensional one and to solve it with the stable numerical discrete-orthogonalization method. The solutions obtained using the straight-line hypothesis and the equations of three-dimensional elasticity are compared. The dependence of the stress–strain state of the shell on the number and amplitude of corrugations and the aspect ratio of the cross-section is analyzed