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Solid propellant rocket motor is considered as hollow viscoelastic cylinder inserted in multilayered elastic shell-like case. The material of propellant is considered to be compressible. An estimation of maximum unsteady stresses on cylinder-shell boundary and shell under growing pressure on interior or external cylindrical surface were calculated by FEM. Four corner isoparametric finite element is utilized. Numark method to integrate by time the dynamic equations is used. The problem of linear viscoelasticity have been employing of the Schapery method. `In the case of internal pressure, the possibility of tensile radial stresses on the contact surface of the propellant-shell during the transition process has been established. The dependence of the maximum contact stresses as well as circumferential stresses in the shell on the shell thickness is established. In the case of external pressure pulse, the presence of significant tensile radial stresses on the propellant-shell interface is shown. Insignificant tensile circumferential stresses in the transient wave process are possible in the shell.

We consider a problem of axisymmetric forced resonant vibrations and dissipative heating of a viscoelastic cylindrical shell with piezoelectric sensors and actuators under monoharmonic loading. The viscoelastic behavior of the passive and piezoactive materials is described in terms of complex moduli depending on the temperature of vibration heating. On the basis of numerical calculations, we study the influence of the temperature dependence of the properties of materials on the dynamic characteristics, temperature of vibration heating, electric indications of a sensor, and active modal damping of the shell by the piezoactuator (with regard for the indications of the sensor).

We consider the axially symmetric problem of irradiation of the end face of a cylinder made of 35KhMA steel by heat pulses. To simulate the mechanical behavior of the material, we use the Bodner–Partom model of flow generalized to the case of influence of microstructure on the plastic properties of the material. The problem is solved by the finite-element method. We also present quantitative estimates of the influence of microstructure on the current and residual state of the cylinder.

A method for calculating the stress–strain state and the service life of hardfaced components subjected to the simultaneous effect of cyclic thermal and mechanical loading has been proposed. This method can be used to study the history of loading at every point of the hardfaced component, select the appropriate fracture models and use these models to localize the areas of failure and estimate the service life of the hardfaced component in service.

UDC 539.3 On the basis of experimental data for 35KhМА steel, we have generalized the unified Bodner–Partom model of flow to take into account the influence of the phase composition of the material on its plastic properties. To determine parameters responsible for the yield strength and ultimate strength of the steel in the multiphase state, the rule of mixtures has been used. The reliability of the developed model has been confirmed by comparing with experimental data and results of other authors.

We consider the problem of the forced resonance vibrations and dissipative heating of a viscoelastic beam with piezoelectric actuators with regard for geometric nonlinearity in the quadratic approximation. The viscoelastic behavior of passive (without the piezoelectric effect) and piezoactive materials is described in terms of instantaneous and complex moduli. To solve the nonlinear problem of electroviscoelasticity and heat conduction, we use the method of quasilinearization together with the numerical methods of discrete orthogonalization and finite differences. We have studied the influence of geometric nonlinearity on the dynamic characteristics, temperature of vibration heating, and active damping of a beam with using a piezoelectric actuator.

The Bodner–Partom model is modified to describe such features of deformation as nonmonotonic dependence of hardening rate on stored plastic strain. This effect is allowed for by representing the hardening rate, which is a constant in the Bodner–Partom model, as a functional of plastic strain and plastic work. The Bodner–Partom parameters are found for some low-alloyed steels. The experimental and calculated data are in satisfactory agreement. The uniaxial deformation model is generalized to the case of multiaxial deformation

UDC 539.3 Within the framework of the dynamic statement of the coupled problem of thermomechanics, we investigate the stress-strain state of a disk, caused by the action of a laser pulse or an electron beam, with regard for microstructural transformations, which accompany the heating and subsequent cooling of the material. The solution of axially symmetric problem is carried out numerically using the thermodynamically consistent theory of inelastic behavior of the material and finite element technique and taking into account the temperature dependence of physical and mechanical properties of the material. We also study the influence of microstructural transformations on the dynamic and quasistatic response of the material as well as on the residual stress-strain state in the irradiation zone.

The mathematical model and method for calculating the heat resistance of deposited metal are described. The method takes into account the effect on this characteristic of residual surfacing stresses and stresses formed during cyclic thermal loading in service of deposited components. It has been confirmed by experiments that the proposed mathematical model can be used to calculate this characteristic with sufficiently high accuracy.

The stress–strain state of a disk caused by a thermal pulse is investigated within the framework of a dynamic coupled thermomechanics problem accounting for microstructural phase transformations caused by the heating and subsequent cooling of the material. The solution of the axisymmetric problem is obtained numerically from a thermodynamically consistent theory for the inelastic behavior of the material which takes into account the thermal dependencies of the material properties using the finite element method. The influence of the microstructural transformations on the dynamic and quasistatic response of the material as well as the residual stress–strain state within the irradiated zone are also studied in detail.

The thermal instability of a rectangular prism under vibrational heating is studied solving a coupled problem of thermoviscoelasticity and using finite-element modeling. The prism has copper and polyethylene or polymethylmethacrylate layers and undergoes high-frequency mechanical or kinematic compression. It is established that in the case of polyethylene, thermal instability occurs under mechanical loading and does not occur under kinematic loading. In the case of polymethylmethacrylate, thermal instability occurs under both kinds of loading. This is because of the increase in the shear and bulk loss compliances with temperature for each of the polymers. At the transformation temperature, shear dissipation goes over into bulk dissipation, which is predominant in rather thin polymeric layers. Dynamicity influences the critical loads both qualitatively and quantitatively

Within the framework of a coupled problem of thermoviscoelasticity, using the method of numerical modeling, we have studied the thermal instability of a rectangular prism, composed of copper and polyethylene or polymethylmethacrylate layers, in the course of its dissipative heating. The prism is subjected to high-frequency force or kinematic shear. We have established that, in the case of polyethylene, thermal instability occurs under conditions of force loading and is absent under a kinematic one. However, for polymethylmethacrylate, thermal instability takes place for both cases of loading. This effect is attributable to the existence of temperature intervals where the shear and volume loss compliances for each of the polymers increases with the temperature. We have also revealed that the critical values of thermal instability for a prism with metal layers are substantially higher than those for a homogeneous prism. In addition to thermal instability, thermal resonance instability is also possible. It is caused by the jump of the thermal state from the low- to high-temperature branch of the soft-type resonance characteristic.

The residual stress-strain state of a disk caused by the action of a laser pulse or an electron beam is investigated within the framework of the dynamic statement of the coupled problem of thermomechanics. The axially symmetric problem is solved numerically using the thermodynamically consistent theory of the inelastic behavior of the material involving the finite-element method and taking into account temperature dependences of physical and mechanical characteristics of the material. The response of the material to thermal irradiation followed by gradual cooling is studied, and the possibility of formation of surface profiles with the use of only thermal treatment is considered.

The vibration and vibrational heating of a rectangular prism with copper and polyethylene layers is studied by solving numerically a coupled problem of thermoelasticity. The cases of kinematic and mechanical harmonic shear loads on a section of the prism surface are examined. Local heating regions are revealed. They are due to the stress fields in the neighborhood of the points at which the type of boundary conditions changes. The temperature–time curves have preresonance, resonant, and postresonance sections. The heating process reaches a steady thermal state under kinematic loading and may become avalanche-like (which is typical of thermal instability) under mechanical loading

The Bodner–Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strainand stress-controlled cycles of loading in the temperature range 20–400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence

By way of numerical simulation, a method is developed to determine the parameters of the thermomechanical Bodner-Partom model of flow under high strain rate deformation using a split Hopkinson bar. The classical method is generalized in two directions. To evaluate the kinematic hardening parameters, the wave reflected from the free end of the bar is used. The thermomechanical parameters that are responsible for the stored energy of cold work are calculated from measurements of temperature changes in the specimen

The dynamic coupled thermoelastic problem formulation and the thermodynamically consistent theory of inelastic behavior of materials are used to solve an axisymmetric problem for a steel disk subject to a heat pulse at the center. The temperature dependence of the physical and mechanical properties of the disk is taken into account. The problem is solved by the FEM. The evolution in time and features of the strain-stress and thermal states of the disk and the dynamic effects accompanying the processes of heating and gradual cooling are studied

A new model for the determination of the residual stress–strain and microstructural state of a cylinder subjected to layer deposition by welding is developed. The growing body of theory and unified the Bodner–Partom viscoplastic theory generalized for the case of coupled thermomechanic processes are involved to describe the mechanical behavior of the material. Continuous cooling transformation (CCT) diagrams are used to account for microstructural transformation. The concept of eigenstrains and temperature state is utilized to satisfy the boundary conditions on the growing surface. A time-stepping procedure and a finite-element technique are used to simulate both the instantaneous and the residual stress–strain and microstructural state of a deposited cylinder. The influence of initial temperature on the residual stress–strain and the structural states of the cylinder deposited by austenitic and martensitic steel layers is investigated. It is discovered that martensite and bainite shares in the heat-affected zone can be effectively controlled by the initial temperature of the cylinder. Numerical and experimental results are compared.

The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined

A numerical model of the Black Sea region (Northeastern Mediterranean) is presented in which it is regarded as a part of the mosaic plate ensemble consisting of the fixed East European platform; the active Arabian, Adriatic, and Pannonian plates; and passive East and West Black Sea and Mysian microplates, which are embedded in a plastically deformable regional orogenic matrix. The fields of displacements, stresses, and deformations in the region are calculated by means of the finite element method within the framework of a linear-viscous rheology approach to a system with nonhomogeneous viscosities. The velocity field obtained is in good agreement with published data of direct observations of plate displacements in the region. In the pressure field, areas of low pressure and decompression are established in the western part of Black Sea and in the south of the Mysian microplate. The poles of rotation of the East and West Black Sea microplates and of the Mysian microplate are computed. For the latter two microplates, significant rotational components are suggested. The East Black Sea microplate acts mostly as indenter, which transmits the collisional motion from the Arabian plate to the southern edge of the East European platform including the Crimea. According to the geodynamical model, the rates of the Cenozoic sedimentation in the Black Sea depression at the collision stage (Oligocene-Pliocene) result from the greater compression of the East Black Sea microplate as compared to the West Black Sea microplate, which, probably, experienced a kind of extension.

A thermomechanically generalized Bodner-Partom model is developed. It is used to determine the fraction of plastic work that is not dissipated into heat and is stored in the material and to find a numerical solution to the dynamic thermomechanical problem for a disk under radial impulsive loading and to analyze the change in temperature due to thermomechanical coupling

(2006). Calculation of residual stresses in multilayer helical surfacing of cylindrical components on the basis of the theory of growth of visco-plastic solids. Welding International: Vol. 20, No. 2, pp. 150-156.

The geometry of flexible beams that are made of a physically nonlinear material and have a nearly linear load-deflection characteristic is identified for a wide range of monotonic and harmonic loads. The geometrically nonlinear beam equations are used. The physically nonlinear behavior of the material is described using a unified viscoplastic theory. A beam thickness criterion is formulated to provide nearly linear stiffness characteristic of the beam in the case of significant deflections and physically nonlinear deformations of the beam’s outer layers

Nonstationary axisymetric waves in a disk excited by an impulsive radial load are analyzed numerically. The nonlinear deformation of the material is described by the Bodner-Partom model. The model parameters are derived from experimental data for samples subjected to tension followed by compression over a wide range of strain rates. The temporal and spatial characteristics of the wave process are studied. The influence of hardening on wave focusing and residual strain distribution is examined

The finite-element method is used together with the theory of growing bodies to model the residual stress-strain state of cylindrical bodies with built-up layers. The case of two built-up layers is analyzed. Numerical and experimental results are compared

A coupled dynamic problem of thermomechanics is formulated based on a thermodynamically consistent modification of the Bodner-Partom model. This formulation is used to analyze the thermomechanical state of an aluminum cylinder under axial impulsive loading. The problem is solved by the finite-element method. Time integration is performed by the Crank-Nicholson scheme. Reversible and irreversible thermal changes are studied

We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations

A coupled dynamic problem of thermoelectromechanics for thin-walled multilayer elements is formulated based on a geometrically nonlinear theory and the Kirchhoff–Love hypotheses. In the case of harmonic loading, an approximate formulation is given using the concept of complex moduli to characterize the cyclic properties of the material. The model problem on forced vibrations of sandwich beam, whose core layer is made of a passive physically nonlinear material, and face layers, of a viscoelastic piezoactive material, is considered as an example to demonstrate the possibility of damping the vibrations by applying harmonic voltage to the oppositely polarized layers of the beam. Substantiation is given for a linear control law with a complex coefficient for the electric potential, which provides damping of vibrations in the first symmetric mode at the linear and nonlinear stages of deformation. The stress–strain state and dissipative-heating temperature are studied

Within the framework of a coupled thermomechanical problem, a simplified approach is developed to the vibration and dissipative-heating analyses of metallic structural members under harmonic loading in both micro- and macro-inelastic domains. The mechanical behavior of a material is described by means of complex moduli that depend on the strain-range intensity and are determined in both micro- and macro-inelastic domains. By an example of the resonant vibrations and dissipative heating of a sandwich beam, the amplitude–frequency characteristics of the field quantities and the behavior of the heating temperature are analyzed over a range of loads that includes both micro- and macro-inelastic domains

A coupled thermomechanical behavior of a finite viscoelastic cylinder under harmonic kinematic excitation at its ends is investigated. The method of superposition is utilized to determine the stress-strain state of the cylinder. A refined asymptotic technique is developed to find the stress-strain state at each point of the body including the corner. Stiffness characteristics are examined over a broad range of cylinder-geometry parameters. By use of known stress components the function for the dissipation rate is constructed and the temperature field of vibration heating is calculated by solving the appropriate heat-conduction boundary-value problem. For the case of strong temperature dependence of loss modulus the phenomenon of thermal instability is examined.

A thermomechanical model of reconditioning worn-out hollow cylindrical machine parts by thermoplastic compression is developed. The scheme proposed takes into account the main stages and features of the process, in particular, the contact interaction between the cylinder and a rigid punch under compression. The ultimate and residual stresses and process parameters are determined

The thermomechanical state of a notched viscoelastic rectangular plate under cyclic planar bending is analyzed within the framework of a coupled thermoviscoelastic problem. It is shown that under sufficiently intensive loading a zone of melted polymer forms near the notch and moves deep into the body, which may cause thermal fatigue failure of the polymer.

An approximate formulation is given to a dynamic coupled thermomechanical problem for physically nonlinear inelastic thin-walled structural elements within the framework of a geometrically linear theory and the Kirchhoff–Love hypotheses. A simplified model is used to describe the vibrations and dissipative heating of inhomogeneous physically nonlinear bodies under harmonic loading. Nonstationary vibroheating problem is solved. The dissipative function obtained from the solution for steady-state vibrations is used to simulate internal heat sources. For the partial case of forced vibrations of a beam, the amplitude–frequency characteristics of the field quantities are studied within a wide frequency range. The temperature characteristics for the first and second resonance modes are compared.

The coupled thermomechanical dynamic behavior of an inhomogeneous body is investigated for a partial case where a laminated inelastic disc is subject to forced axisymmetric vibrations and dissipative heating. The problem is solved in complete and approximate formulations. In the former case, the behavior of the material is described using generalized flow theory. In the latter case, the behavior of the material is characterized by complex moduli. The spatial distributions of the field quantities and the temperature– and amplitude–frequency characteristics of the disc are analyzed. The results are compared.

A model is developed to investigate thermal effects in elastoviscoplastic bodies. It allows us to obtain some quantitative and qualitative information on the stress–strain state of a body and to carry out a nondestructive diagnostics of internal defects, which are stress and strain concentrators. The problem on the plane stress state of a rectangle with a hole is considered as an example. The plate is made of steel and aluminum alloy. The variation in the temperature on the external contour of the body under monotonous and cyclic tension in the elastic and plastic domains is studied

A prescribed distribution of residual radial displacements on the inside surface of a hollow cylinder is considered to be formed with the help of a mobile ring heat source. It is established that this goal can be achieved if the source velocity is variable and the source power is constant. The problem is subdivided into three subproblems. The dependence of the total displacement on the source velocity is determined in the first subproblem. The second subproblem is to determine a law for velocity control depending on the prescribed distribution of residual displacements. The third subproblem consists in homogenization of their end distributions. Approaches to the solution of each of these problems are developed

Models used to study thermal effects in elastoviscoplastic and viscoelastic bodies deformed under monotonic and harmonic loading are considered. They allow us to obtain qualitative and quantitative information on the thermomechanical state of the material. Numerical results can be used in a nondestructive analysis and in predicting thermal fatigue failure of inelastic bodies