Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 2. Action of external forces

We analyze the motion of a mechanical dissipative system containing a viscoelastic strain-hardening body with one degree of freedom under the action of an external tensile force depending on its controlling parameters and initial loading conditions. We construct periodic and aperiodic solutions of a nonautonomous third-order dynamical system taking into account transient processes of motion from the initial state. It is shown that the transient process of motion of the system is realized either as forced damped oscillations responsible for its acoustic activity or as an aperiodic process of damping. We also consider transient dynamic processes in a viscoelastic Maxwell body subjected to static loading in the case where strain hardening is absent. Frantsevich Institute for Problems in Materials Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 12–26, September–October, 1998.     

Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 3. Hydraulic loading of the system

We analyze the motion of an open mechanical system with one degree of freedom used as a model of uniaxial tension of a viscoelastic strain-hardening body in a machine with hydraulic drive creating a variable force and, at the same time, playing the role of a damping element. It is shown that a nonautonomous fourth-order dynamical system with stable periodic or aperiodic solutions (depending on its control parameters) may serve as a model of the transient processes of motion in the analyzed system. Due to a significant decrease in the viscous resistance of the system caused by the presence of the hydraulic drive, the aperiodic attenuation is typical of the transient process. It is shown that systems with hydraulic elements differ fundamentally from mechanical systems without elements of this sort. Frantsevich Institute of Problems in Materials Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 42–61, January–February, 2000.     

Numerical study of vibrations of a nonlinear mechanical system simulating a cracked body

The paper presents the results of a numerical study of forced and decaying vibrations of a system simulating a body with a closing crack under the action of various modes of a nonlinear restoring force and nonlinear viscous friction or the hysteresis-type energy dissipation. We obtained the general patterns of appearance of higher harmonics of the Fourier expansion of time dependence of vibration of a cracked body model. The sensitivity of the higher-harmonic method to the presence of a crack is compared with that of some other vibration damage indicators. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 65–80, November–December, 1999.     

Dynamics of Uniaxial Tension of a Viscoelastic Strain-Hardening Body in a System with One Degree of Freedom. Part 4. Action of an External Force on a Compound Body

A rheological model and the dynamics of an open mechanical system, comprising an elastic machine element and a compound body consisting of two irreversibly deformable bodies connected in series with one degree of freedom under the action of an external force are considered. If the system is subjected to a load below the elastic limit of both bodies, the motion of the mechanical system is described by a classical second-order dynamic system. If the system is subjected to a load above the elastic limit of one of the bodies, the motion of the mechanical system is described by a third-order dynamic system, and when it is loaded above the elastic limit of both bodies, the motion is described by a dynamic system of two third-order differential equations. The solutions of this dynamic system are damped oscillations in character, with the damping factor increasing with the ratios of the elastic stiffness and strain hardening values to the value of viscous resistance of deformable bodies.     

Effect of break of the elastic axis of a rotor with transverse crack on its vibrational characteristics

We perform a numerical analysis of the effect of break of the elastic axis on the characteristics of bending vibrations of a multispanned unbalanced rotor with transverse crack mounted on elastic damping supports. The break of the elastic axis in the cross section with crack is caused by local plastic strains. The solution of the problem is sought in the form of a sum of the contributions of the forces of gravity, residual disbalance, and the crack responsible for the break of the axis. The problem is reduced to the numerical analysis of the trajectory of the shaft with its subsequent improvement by the method of iterations. Amplitudes and phases of several first harmonics of vibrational displacements are found as functions of sizes, initial orientation of the crack, and the ratio of vibrational and static displacements. In the presence of the break of the elastic axis, the magnitudes of vibrational characteristics undergo significant changes. The amplitudes of vibrations induced by the crack are comparable with the amplitudes of vibrations caused by disbalance. It is shown that the behavior of the trajectory of motion regarded as a function of principal parameters is nonlinear. Institute for Problems in Mechanical Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 82–89, July–August, 1997.     

Structure and properties of high-modulus alloys of the Ti-B system

We study the influence of alloying with Al, Zr, and Si on the structure and mechanical properties (including the modulus of elasticity) of cast and deformed alloys of the Ti-B system. It is shown that, by optimizing the compositions of titanium alloys subjected to combined silicoboride hardening and additionally alloyed with aluminum, it is possible to get the modulus of elasticity E as high as 160 MPa with a strength σ of 1500 MPa and a level of plasticity δ of 2–5% at room temperature. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 3, pp. 27–32, May–June, 2006.     

Strain hardening of structural metals with metastable structure under complex loading

We investigated distinctive features of strain hardening under complex loading for quenched and low-tempered steels of ferritic-pearlitic (40KhN), martensitic (30Kh3NSMV), and maraging (Kh16N5D3) types and an Al-4Cu age-hardening alloy whose matrix phase is characterized by the metastable structure corresponding to supersaturated interstitial and substitutional solid solutions susceptible to disintegration in the process of plastic deformation. We analyzed structural indicators of the depletion of the matrix phase of supersaturating alloying elements forming carbides and intermetallic compounds and the mechanisms of hardening and softening influence of preliminary deformation (within reasonable ranges of its variation) on the value of the yield limit when repeated loading changes its sign. It is shown that, for the investigated type of metastable materials, in the analyzed range of preliminary deformations governed by alloying, the application of repeated biaxial tension leads to a uniform extension of the limiting yield curves. As the degree of supersaturation decreases (in the process of thermal treatment) and we observe the formation of equilibrium solid solutions of the matrix phase, the character of strain hardening evidently changes from predominantly isotropic to kinematic. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 85 – 94, January – February, 1998.     

Interparticle interaction in a deformed body. II. Theory of elasticity for a body of theN th coordination order

In the framework of the model of structurally continual media described in the first part of the work [Mat. Sci.33, No. 2, 125–134 (1997)], we construct the theory of elasticity for an anisotropic body of then th coordination order by using the thermodynamic approach. Unlike the classical theory of elasticity for anisotropic bodies, in the constructed theory, the role of bulk forces is played by the forces of interparticle interaction. We introduce matrices of new material constants which characterize the nanomechanical properties of the body from the macroscopic point of view and describe the field of natural elastic waves of a given anisotropic structurally continual medium. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 3, pp. 19–30, May–June, 1997.     

Longitudinal vibrations of a cross-cracked cantilever beam. Part 1. Small vibrations

Based on the analysis of solutions to differential equations of longitudinal vibrations of a macroelastic body whose nonlinearity is due to “breathing” of the damaged material under tension-compression cycling, we estimate the suitability of the deformation-cycle characteristic of a body under free and forced vibrations for the diagnostics of fatigue damage in structural elements. We consider the following problems: the construction of a simplified model of longitudinal vibrations of mechanical elements with cross cracks, the investigation of free vibrations of a cracked body including resistance forces, the forced vibrations of a cracked body taking into account a perturbation force including and excluding resistance forces, and the study of vibrations of a beam with resistance different from the linear one. We show that the presence of a macrocrack is responsible for the occurrence of representative higher harmonics in the deformation-cycle spectrum. They can serve as a sensitive and efficient vibration-diagnostic parameter to detect cracks in structural elements. Zaporozh'e State University, Zaporozh'e, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 23–34, March–April, 1999.     

Dynamic interaction of parallel cracks in elastic bodies

We study time dependences of the stress intensity factors in an infinite isotropic elastic body with parallel cracks whose faces are subjected to impact loads. The original problem is reduced to the solution of a system of boundary integral equations with a parameter corresponding to the wave number in the decomposition of the dynamic process into the set of monochromatic components. The numerical reconstruction of the dependences of unknown quantities on time is carried out for two circular cracks loaded by tensile forces in the form of the Heaviside function. The presence of stress intensity factors of all three types is a distinctive feature of the considered problem. Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 94–102, May–June, 1998.     

Special features of high-frequency loading of coated materials

We study the features of high-frequency loading of coated components: different combinations of stresses in the adhesive contact zone, which are caused by dynamic deformation of a base material and the action of body inertial forces, and the effect of cyclic loading on the adhesive and cohesive strength of a coating. We introduce the notion of “vibration strength” of a coating and show that it is essential to ensure an equal fatigue life of the base-coating system under cycling in an operating environment. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 134–138, September–October, 1988.     

Analysis of the aluminum alloy resistance to the penetration of a steel rod at impact velocities of up to 500 m/s

The penetration of a steel rod into aluminum alloy plates of various thicknesses is examined. The resistance to penetration at its initial stages prior to the rod fracture is found to be determined by the dynamic strength of the plate material, its viscous component (proportional to the plastic strain rate) prevailing at impact velocities of up to 500 m/s. The depth of penetration varies with the velocity and is conditioned by wave processes in the plate, their scale being dependent on its thickness. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 106–110, September–October, 1998.     

Dynamic stability of a viscoelastic cylindrical panel with concentrated masses

We discuss the problem of the dynamic stability of a viscoelastic cylindrical panel with concentrated masses in a geometrically nonlinear formulation that is based on the Kirchhoff-Love hypothesis. The effect of the action of concentrated masses is introduced into the equation of motion of a cylindrical panel using the Dirac δ-function. The problem is solved by the Bubnov-Galerkin method based on a polynomial approximation of deflections together with a numerical method based on the use of quadrature formulas. The choice of the Koltunov-Rzhanitsyn singular kernel is justified. Comparisons between the results obtained from different theories are presented. The Bubnov-Galerkin method convergence is investigated for all problems. The effect of the material viscoelastic properties and concentrated masses on the process of the dynamic stability of a cylindrical panel is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 132–147, July–August, 2008.     

Analysis of oscillations of a plate under harmonic excitations of various types with dissipation of energy in materials

We suggest a procedure for the analysis of forced transverse oscillations of thin rectangular plates with regard for the energy losses in cyclically strained materials for various types of exciting harmonic forces (concentrated and uniformly or nonuniformly distributed over the surface, in particular, according to the sinusoidal law) as well as for the case of kinematic excitation by plane-parallel harmonic displacements of the supports. The oscillations of nonconservative elastic laminated systems is studied analytically by applying the asymptotic methods of nonlinear mechanics. The indicated procedure enables one to evaluate the dynamic stressed state of a laminated engineering structure as a function of the applied load in the stage of design. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 117–129, July–August, 1997.     

Elasticity characteristics of molybdenum within the temperature range 400–1400 K

We present the results of high-precision investigations of the elasticity characteristics of MChVP commercially pure polycrystalline molybdenum within the temperature range 400–1400 K. The measurements were carried out by using the ultrasonic echo-pulse method. The frequency of the sounding signal was equal to 10 MHz. We establish correlations between the moduli of elasticity in tension and in shear and study the distinctive features of the break in the dependences of the elasticity characteristics of molybdenum near T=900 K. We propose to consider this temperature as one of the physical constants of molybdenum. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 126–129, May–June, 1999.     

Exact solution of flow theory problems with isotropic-kinematic hardening. Part 2. Setting of the deformation trajectory in the spaces of total and plastic strains

For an arbitrary isotropic and linear kinematic hardening and loading paths given in the form of arbitrary multisection polygonal lines in the five-dimensional deviatoric space of total strains, we have studied analytically an initially isotropic elastoplastic material with von Mises yielding and the associated flow rule. The solutions obtained are valid for arbitrary relationships that govern the variation of the spherical component of the stress tensor. For arbitrary isotropic and kinematic hardening, we have also obtained an analytical solution to an elastoplastic problem for an arbitrary deformation trajectory given in the deviatoria space of plastic strains Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 62–71, January–February, 2000     

Longitudinal vibrations of a cantilever beam with a transverse crack. Part 2. Piecewise-linear model

A model of vibrations of a cracked body that is based on the difference in the stiffness characteristics in tension and compression is represented as a linear system with piecewise-constant parameters. We determine the parameters of vibrations of this system. We plot the relative crack size as a function of the difference in amplitudes in tension and compression, which is related to the vibration amplitude of a crack-free body with account for the resistance. The approaches described are applicable to evaluation of the “survival” of a structure (i.e., evaluation of the residual durability of a cracked structure). Zaporozh'e State University, Zaporozh'e, Ukraine. Translated from Problemy Prochnosti, No. 5, pp. 78–85, September–October, 1999.     

Assessment of conventional elastic limit for a hard WC-Co alloy in tension

This paper presents an algorithm for the calculation of a conventional elastic limit for WC-Co alloy in tension considering residual thermal stresses in its phases. The algorithm is based on equations of thermoelasticity for two-phase composite materials. Comparison of theoretical and experimental results revealed their fair agreement. Residual thermal stresses were found to have an appreciable effect on the elastic limit of a hard alloy in tension. Institute of Superhard Materials, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 116–122, November–December, 1999.     

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 2. Bending vibrations, analytical solution

We discuss the possibility of efficient application of the harmonic analysis of strain cycles formed in an elastic rod in the process of natural or resonance vibrations to the evaluation of the degree of fatigue damage. Fatigue damage is simulated by discontinuities of the material resulting in different values of the modulus of elasticity in the processes of tension and compression. In determining the potential strain energy of a rod in the presence of a crack on the basis of linear fracture mechanics, this model enables us to deduce expressions for relative changes in the stiffness of the rod in the presence of edge and surface cracks. By using the asymptotic method of nonlinear mechanics, we find the second approximation to the solution of the differential equation of vibrations of the rod whose nonlinearity is explained by the effect of “breathing” of the discontinuity formed in the material. It is shown that the discontinuity of the material caused by fatigue damage is responsible both for changes in the natural frequency of vibrations of the rod and for significant contributions of the constant component and even harmonics to the spectrum of strain cycles in the rod. The values of the constant component and the amplitudes of even harmonics (mainly of the second one) may serve as an efficient parameter for the detection of fatigue damage to materials. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 9–22, November–December, 1998.     

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 1. analytical approach

We consider a perfectly elastic cantilever beam with a crack. The influence of the crack depth and location on the vibration mode of the beam is simulated by a local change in the cross section. This problem is solved by the Rayleigh method. Fairly simple formulas for the determination of the natural frequency of the first mode of bending and longitudinal vibrations of a cantilever beam with an open and closing crack are derived. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 35–44, March–April, 1999.