Analysis of the influence of aggressive environment on creep and creep rupture of rod under pure bending

Summary A method for modelling the influence of an aggressive environment on creep and creep rupture is suggested. This method is based on the introduction of a notion of structural elements and postulating elementary creep properties of these elements. The equations of behavior of a specimen as a whole are based on the behavior of the elements.A probabilistic approach is used for the analysis of creep and creep rupture of solids. Pure bending of a long thin rod in an aggressive environment is studied. It is supposed that the fracture of structural elements takes place only under tensional stresses. A system of integral-differential equations is derived; this system characterizes the process of damage accumulation and change of stress-strain state at times,which is caused by rod bending. It is demonstrated that rupture of any structural element in a tension area causes stress redistribution. This redistribution leads to a motion of the neutral lines at which stresses and strains equal zero. The numerical investigation of a derived system of equations is developed.This work has been partially supported by the Russian Foundation of Fundamental Researches (Grant No. 02-01-00289) and INTAS (Grant No. 03-51-6046).     

Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression

Stability analysis of noncircular shells is performed with allowance for nonlinear subcritical deformation. Explicit expressions for the rigid displacements of elements of noncircular cylindrical shells are obtained and used to construct shape functions of an effective quadrilateral finite element of natural curvature. A finiteelement algorithm for solving problems of nonlinear deformation and stability of shells is developed. Stability problem of an elliptic cylindrical shell is considered. The effect of the ellipticity and subcritical nonlinear deformation of the shell on the critical load is studied. Results obtained are compared with available experimental data.     

The stability of the flow of a layer of a viscous liquid with moment stresses along an inclined plane

The stability of the flow of a layer of liquid over an inclined plane, taking account of the spin of the molecules and the internal moment stresses, was discussed in [1], However, in [1], a number of errors were allowed to creep in, which led the authors to untrue qualitative and quantitative results. In the present work, the stability of the flow of a layer with respect to long-wave perturbations is investigated by the method of successive approximations [2, 3] under the assumption that the coefficient of rotational viscosity nr is considerably less than the coefficient of Newtonian viscosity . It is shown that, in a first approximation, internal moment stresses do not affect the stability of the motion, and that the rotation of the particles exerts a destabilizing effect on the flow of the layer with respect to three-dimensional periodic perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, pp. 149–151, September–October, 1977.     

Studies of nonlinear deformation and stability of stiffened oval cylindrical shells under combined loading by bending moment and boundary transverse force

The finite-element statement of stability problems for stiffened oval cylindrical shells is presented with the moments and the nonlinearity of their subcritical stress-strain state taken into account. Explicit expressions for the displacements of elements of noncircular cylindrical shells as solids are obtained by integration of the equations derived by equating the linear deformation components with zero. These expressions are used to construct the shape functions of the effective quadrangular finite element of natural curvature, and an efficient algorithm for studying the shell nonlinear deformation and stability is developed. The stability of stiffened oval cylindrical shells is studied in the case of combined loading by a boundary transverse force and a bending moment. The influence of the shell ovality and the deformation nonlinearity on the shell stability is investigated.     

Analysis of creep deformation and creep damage in thin-walled branched shells from materials with different behavior in tension and compression

A constitutive model for describing the creep and creep damage in initially isotropic materials with different properties in tension and compression has been applied to the modeling of creep deformation and creep damage growth in thin-walled shells of revolution with the branched meridian. The approach of establishing the basic equations for axisymmetrically loaded branched shells under creep deformation and creep damage conditions has been introduced. To solve the initial/boundary-value problem, the fourth-order Runge–Kutta–Merson’s method of time integration with the combination of the numerically stable Godunov’s method of discrete orthogonalization is used. The solution of the boundary value problem for the branched shell at each time instant is reduced to integration of the series of systems of ordinary differential equations describing the deformation of each branch and the shell with basic meridian. Some numerical examples are considered, and the processes of creep deformation and creep damage growth in a shell with non-branched meridian as well as in a branched shell are analyzed. The influence of the tension–compression asymmetry on the stress–strain state and damage evolution in a shell with non-branched meridian as well as in a branched shell with time are discussed.     

Description of creep within the framework of the field theory of defects

The creep laws are described within the framework of the field theory with the use of evolution equations for the density flux of uniformly distributed defects. For the case of uniaxial deformation under constant stress, it is shown that a certain critical stress that has the sense of creep stability limit exists and two deformation regimes can occur, depending on the magnitude of the external load. The unstable-creep rupture time is determined for the system in the case where the stresses are greater than the critical stress and the initial rate exceeds the unstable stationary rate. Institute of the Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634821. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 177–183, May–June, 2000.     

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

This paper describes the effect of thermal exposure (high-temperature exposure) (T = 675?C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675?C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress–strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.     

Effect of structural and mechanical characteristics of the composite material on the deformation of a reflector antenna

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundaryvalue problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundaryvalue problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.     

Approximate estimates of the high‐temperature creep of structural elements

The creep and longterm strength of structural elements under temperatures much higher than operational temperatures are studied. The actual nonuniform stress–strain state is reduced to a fictitious uniform state by averaging the specific dissipated power over the volume of the body. This allows one to estimate the intensity of creep and longterm strength of structural elements in terms of volumeaveraged energy parameters by using methods of ideal plasticity and considering statically possible stress fields and kinematically possible velocity and strain rate fields.     

Flow stability of viscous liquid layer with moment stresses on an inclined plane

The flow stability of a liquid layer on an inclined plane with account for molecular spin [1, 2] has been considered in [3] in the absence of moment stresses within the liquid. It was shown in [3] that molecular spin has a destabilizing effect on the flow. In the following we study the combined effect of molecular spin and internal moment stresses on the behavior of three-dimensional disturbances. The validity of Squire's theorem is established. The flow stability of a layer of relatively long-wave disturbances is studied by the method of sequential approximations [4, 5] under the assumption that the rotational viscosity coefficient _r is significantly smaller than the Newtonian viscosity coefficient .     

Example of exact solution of a problem of gas compression by a spherical shell

A study is made of the problem of isentropic compression of gas by a spherical shell of finite thickness on the exterior of which there is a vacuum. The complete solution to the problem with different boundary conditions and different equations of state for the shell and the compressible medium is possible only numerically. However, there exists a class of exact solutions to the equations of gas dynamics [1, 2] with linear radial distribution of the velocities of the particles in which contact discontinuities are allowed. For this it is necessary that both the shell and the compressible medium be described by the same equation of state p = ( – 1) E with the same specific heat ratio = c_p/c_v. There can be arbitrarily many such discontinuities in the solution, i.e., this class of solutions can describe the compression of matter by multilayer shells. In the present paper, a restriction is made to a single-layer shell with specific heat ratio = 5/3.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–179, November–December, 1982.     

Stability and Self‐Oscillations of a Rotor Containing a Conducting Liquid in a Magnetic Field

This paper considers the problem of the stability in the small of the steadystate spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the buttend boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was Dpartitioned into regions with different degrees of instability is constructed. Steadystate spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steadystate spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steadystate spinning can be subcritical or supercritical.     

Growth of Nonlinear Patterns in Binary-Fluid Convection,Analysis of Models

A recently proposed minimal model of the convection of binary mixtures in a Rayleigh–Bénard cell of aspect ratio 2 with realistic boundary conditions is invoked to study the transient dynamics from the entirely diffusive ground state to the convection state. The model was designed to reproduce the subcritical Hopf bifurcation found for negative Soret coupling in finite-difference simulations and experiments, but also performs well for the growth transients, including the competition between two counter-propagating waves. We prepared an initial state with only one wave, thus avoiding complicated wave competition. This allows us to elucidate the interaction of the concentration field with the pure-fluid fields, i.e., temperature and velocity, by means of modulus and phase equations. We explain the linear and nonlinear transient dynamics responsible for the strong decrease in frequency and concentration, and the feed-back loop responsible for propagation.     

Linearized equations of nonlinear elastic deformation of thin plates

A linearized system of equations governing elastic deformation of a thin plate with arbitrary boundary conditions at its faces in an arbitrary curvilinear coordinate system is proposed. This system of equations is the first approximation of a oneparameter sequence of equations of twodimensional problems obtained from the initial threedimensional problem by approximating unknown functions by truncated series in Legendre polynomials. The stability problem of an infinite plate compressed uniaxially is solved. The results obtained are compared with the existing solutions.     

Flow stability of a Grad-model liquid layer on an inclined plane

A study is presented of the flow of stability of a Grad-model liquid layer [1, 2] flowing over an inclined plane under the influence of the gravity force.It is assumed that at every point of the considered material continuum, along with the conventional velocity vector v, there is defined an angular velocity vector , the internal moment stresses are negligibly small, and in the general case the force stress tensor _kj is asymmetric. The model is characterized by the usual Newtonian viscosity , the Newtonian rolling viscosity _r, and the relaxation time = J/4 _r, where J is a scalar constant of the medium with dimensions of moment of inertia per unit mass, is the density. It is assumed that the medium is incompressible, the coefficients , _r, J are constant [2].The exact solution of the equations of motion, corresponding to flow of a layer with a plane surface, coincides with the solution of the Navier-Stokes equations in the case of flow of a layer of Newtonian fluid. The equations for three-dimensional periodic disturbances differ considerably from the corresponding equations for the problem of the flow stability of a layer of a Newtonian medium. It is shown that the Squire theorem is valid for parallel flows of a Grad liquid.The flow stability of the layer with respect to long-wave disturbances is studied using the method of sequential approximations suggested in [3, 4].     

Bi-stable states of initially stressed elastic cylindrical shell structures with two piezoelectric surface layers

A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method(FEM) simulation by using the ABAQUS code.     

Deformation and Failure of Aluminum Alloys from the Standpoint of the Kinetic Concept of Strength

A thermalactivation analysis was performed of experimental data on the strain and failure of 1201 T1, D16 T, and AK41 T1 aluminum alloys. The experiments were conducted under constant loads in creep conditions and under increasing loads. The duration of the tests was varied from fractions of a second to ten thousand hours, and the temperature ranged from 77 to 473 K. The rate activation parameters in the equations of steadystate creep and plastic strain were determined. Information was obtained on the relationship between plastic strain and failure. The plastic strain rate is shown to be affected by relaxation phenomena. The plastic characteristics of the alloys and their dependences on the temperature and time to failure are given.     

Stability of elastic bodies under omnilateral compression

Conclusions We have analyzed here the stability of the equilibrium of a simply connected isotropic compressible body with the elastic potential of arbitrary form and under uniform omnilateral deformation. A survey has been given here of earlier results obtained by other authors. The basic celations have been stated in a general form covering the theory of finite subcritical strains and two variants of the theory of small subcritical strains. For the latter theory new relations have been rigorously derived from which perturbations of tracking surface loads can be calculated, on the basis of corresponding expressions in the theory of finite subcritical strains. It has been proven that the sufficient conditions for the applicability of the static method of analysis are satisfied when the same boundary conditions are given over the entire body surface, as well as in several cases of different boundary conditions given at different segments of the boundary surface. It has been shown in a general form, for the theory of finite subcritical strains and for two variants of the theory of small subcritical strains, that the equilibrium of an elastic body under omnilateral deformation is stable, if a tracking load, is given over the entire boundary surface. As an example of problems with different boundary conditions at different segments of the boundary surface, we have considered the conventional problem concerning the stability of a bar on hinge supports and under uniform omnilateral deformation. It has been rigorously proven that in this case the equilibrium is stable when tracking loads are given at the lateral surfaces and is unstable when dead loads are given at the lateral surfaces. These conclusions apply to the theory of finite subcritical strains as well as to the theory of small subcritical strains, and they represent the complete version pertaining to compressible bodies.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 12, No. 6, pp. 3–27, June, 1976.     

Changes in the Seam-Filtration Mode with Stress Redistribution in Country Rock

A mathematical model for the mechanism of increasing oil output of productive seams is developed. The model involves a deliberate conversion of segments of the fault zone of the country rock to a supercritical state, which leads to a local redistribution of stresses in the block massif of rocks and an increase in contour and seam pressures. Based on solving the problem of restricted filtration, it is shown that the use of the proposed mechanism can ensure a relative increase in well production of 5–8%.