Surface Rayleigh Waves in the Determination of Near-Surface Stresses of Structural Elements

A supersonic nondestructive method for determining stresses in near-surface layers of solids is stated on the basis of the acoustoelastic theory of surface Raylegh waves. Examples are presented of how this method is used to determine the operating and residual stresses in materials and structural elements. Features of the mutual use of surface and volume waves to obtain additional information on the stress distribution over the cross section of a specimen are indicated     

The Physical Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids

Theoretical and experimental works on acoustoelasticity are briefly generalized. Studies conducted and scientific results obtained at the S. P. Timoshenko Institute of Mechanics and E. O. Paton Institute of Electric Welding of the National Academy of Sciences of Ukraine are highlighted. Special features of these works and their difference from those of other authors are pointed out. The basic principles and laws governing the propagation of longitudinal, shear, and surface waves in bi- and triaxially stressed bodies are briefly stated with regard for the orthotropy and nonlinear properties of the material. The experimentally proven principles and laws for elastic waves propagating in initially stressed bodies are formulated. The physical fundamentals of the ultrasonic nondestructive technique for determining bi- and triaxial stresses in solids are described. The determination of bi- and triaxial residual stresses in specimens and structural members is demonstrated by examples. The basic principles of the related (dielectric and electromagnetic) methods for stress analysis of polymeric materials are stated. The application of the electromagnetic method to the stress analysis of some polymeric materials is considered     

Elastic waves in compressible materials with initial stresses and a nondestructive ultrasonic method for the determination of biaxial residual stresses

Concise information is given on the theory of the propagation of elastic waves in bodies with initial stresses. This information provides the basis of a nondestructive ultrasonic method for the determination of biaxial residual stresses in isotropic and quasiisotropic materials. The basic acoustoelasticity relation for biaxial stresses is analyzed, and an instrument for the determination of biaxial residual stresses in electric welding is described, along with examples of its application.Adapted from the complete text of a paper submitted to the 18th International Congress on Theoretical and Applied Mechanics, Haifa, Israel, August 22–28, 1992, Session B-A2: Waves in Solids (August 24, 1992).S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 3–17, January, 1994.     

Elastic waves in bodies with initial stresses

Conclusions An analysis of research available on the problem under consideration shows that at this time: a) Wave propagation in unbounded, bounded, and composite laminar bodies with homogeneous initial states has been studied sufficiently extensively; b) methods to determine the third-order elastic constants have been developed on the basis of existing theories; c) an ultrasonic nondestructive method to determine the stress in solids has been developed, where the stresses averaged over the bulk of the body are determined.In light of the above, in the authors' opinion, the following should be considered the most urgent questions for further investigations on the problem: a) the investigation of wave propagation regularities in bodies with inhomogeneous initial states (it is hence important to execute quantitative and qualitative analyses of the phenomenon); b) development of an ultrasonic nondestructive method of determining the stress in the near surface layers of a solid, which will afford a possibility of determining not only the membrane stresses but also the bending stresses; c) an investigation of the wave propagation regularities in fibrous composites with initial stresses.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 15, No. 4, pp. 3–23, April, 1979.     

Contact interaction of an elastic punch and an elastic half-space with initial (residual) stresses

The contact interaction of an elastic punch of arbitrary cross-section and an elastic semi-space with initial (residual) stresses is studied. A general method to solve the problem is proposed. It allows solving contact problems for bodies with initial (residual) stresses when the solution of the corresponding elastic problem is known __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 28–40, December 2007.     

Influence of prestress on the velocities of plane waves propagating normally to the layers of nanocomposites

The paper is concerned with longitudinal and transverse waves propagating at a right angle to the layers of a nanocomposite material with initial (process-induced residual) stresses. The composite consists of alternating layers of two dissimilar materials. The materials are assumed nonlinearly elastic and described by the Murnaghan potential. For simulation of wave propagation, a problem is formulated within the framework of the three-dimensional linearized theory of elasticity for finite prestrains. It is established that the relative velocities of waves depend linearly on small prestresses. In some composite materials, however, the thicknesses of the layers may be in a ratio such that the wave velocities are independent of the prestress level __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 3–22, July 2006.     

The dynamics of a compressible viscous liquid (review). II

This article is the second part of a review of the dynamics of rigid and elastic bodies in a compressible viscous liquid in a linearized formulation. The following processes are investigated: the forced harmonic vibrations of rigid bodies in moving and resting compressible viscous liquids, the nonstationary motion of rigid bodies in a compressible viscous liquid at rest, the movement of rigid bodies in a resting compressible viscous liquid under the action of radiation forces that are due to the interaction with propagating acoustic harmonic waves, the propagation of harmonic waves in thin-walled cylindrical elastic shells containing a compressible viscous liquid, and the propagation of harmonic waves in hydroelastic systems consisting of a resting compressible viscous liquid and elastic compressible or incompressible bodies with initial stresses. Publications concerning the above problems are analyzed. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 3–30, March, 2000.     

Features of plane wave propagation along the layers of a prestrained nanocomposite

Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 3–26, April 2007.     

Thermomechanical Model of Growing Cylindrical Bodies Made of Physically Nonlinear Materials

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 __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 118–126, September 2005.     

Ultrasonic nondestructive methods of stress analysis in materials and structural members (review)

Results of the justification, development, and application of nondestructive ultrasonic methods of stress analysis are briefly outlined (summarized). These are the results of cooperative research by the S. P. Timoshenko Institute of Mechanics and the E. O. Paton Institute of Electric Welding. The nondestructive ultrasonic methods are intended to determine triaxial (including biaxial and uniaxial) stresses in structural members and biaxial (including uniaxial) stresses in near-surface layers of materials     

Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review)

Recent investigations of dynamic problems for bodies with initial stresses are reviewed. These are investigations carried out over the last six years using the piecewise-homogeneous body model and the three-dimensional linearized theory of elastic waves in initially stressed bodies. Emphasis is on the investigations performed by the author and his students. The research studies on the wave propagation and dynamic time-harmonic stress-state problems are reviewed separately. The areas for further investigations are pointed out Published in Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 3–27, December 2007.     

Dependence of the deformation of flexible cylindrical shells on their geometry and the orthotropy and nonlinear properties of the composite materials

A study is made of geometrically and physically nonlinear inverse problems concerning the axisymmetric deformation of cylindrical shells into conical shells. Results obtained from the numerical solution of the problems are used to determine the laws of distribution of the surface loads, stresses, strains, and displacements in relation to the initial parameters and nonlinearities of the shells. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 86–91, June, 1999.     

Longitudinal nonlinear oscillations of a gas in a closed pipe

Results of an experimental study of longitudinal nonlinear oscillations of a gas in a closed pipe are reported. Pressure waves in a broad range of excitation amplitudes and frequencies are studied. Strong nonlinear oscillations at a frequency thrice as low as the first natural frequency of the gas column are discovered. Institute of Mechanics and Mechanical Engineering, Kazan' Scientific Center, Russian Academy of Sciences, Kazan' 420503. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 60–62, November–December, 1999.     

Dynamic problems of the mechanics of brittle fracture of materials with initial stresses for moving cracks. 3. Transverse-shear (mode II) and longitudinal-shear (mode III) cracks

This paper is devoted to the study of dynamical problems for moving cracks in materials with initial stresses, taking into account the author's previous publications on this subject. Stresses and displacements in linearized theory are represented through analytic functions of complex variables in dynamical problems. Exact solutions of dynamical problems are obtained for moving cracks in materials with initial stresses in the case of transverse shear (Mode II) and longitudinal shear (Mode III); these results are obtained for general cases of equal and unequal roots of the basic equation. New mechanical effects are analyzed in the dynamical problems under consideration. The results are obtained for compressible and incompressible bodies with elastic potentials of arbitrary structure. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 3–14, February, 1999.     

Propagation of shock waves in a two-phase mixture with different pressures of the components

The process of propagation of shock waves in two-component mixtures is considered. The studies were performed within the framework of the two-velocity approximation of mechanics of heterogeneous media with account of different pressures of the components. The stability of propagation of all types of stationary shock waves (fully dispersed, frozen-dispersed, dispersed-frozen, and frozen shock waves of two-front configuration) to infinitesimal and finite perturbations is shown numerically, using the method of coarse particles. The problem of initiation of shock waves (the formation of different types of shock waves from stepwise initial data) is solved. Flows in the transonic range relative to the speed of sound in the first component are obtained. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 55–63, January–February 1999.     

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.     

An inverse elastoplastic problem for plates

We study an inverse elastoplastic problem of determining the residual stresses, the plasticity zone, and the external loads for a plate for known residual deflections which occur after removal of these loads and elastic unloading. Assuming that the deformation theory of plasticity is valid at the active stage of deformation, we prove the theorem of unique solution. An iterative method of solution is proposed and a variational formulation of the problem is given. Some simple examples are considered. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 186–194, July–August, 1999.     

On the types and number of plane waves in hypoelastic materials

General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted theoretically. One of such effects is blocking of certain types of plane waves by initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 96–107, November 2005.     

Elastic waves in prestressed bodies interacting with a fluid (survey)

Conclusion The above survey of different studies and analysis of results obtained widiin the framework of linearized three-dimensional theory show that use of the given model makes it possible to account for fluid viscosity and initial stresses in elastic bodies. Both of these factors play a significant role in actual media. The model also permits determination of the effect of fluid viscosity and initial stresses on the wave processes in hydroelastic systems. The use of an approach based on representations of general solutions of linearized problems of aerohydroelasticity for bodies with uniform initial strains and a compressible viscous fluid makes it possible to obtain dispersion relations in a general form diat is invariant relative to different types of elastic potential and valid for arbitrary compressible and incompressible materials. The approach also allows researchers to study the main classes of problems encountered in practice, conduct numerical experiments, and use the results to find new properties, laws, and mechanical effects that are characteristic of the investigated wave processes and reflect the mutual effects of the fields of initial and dynamic stresses, as well as the interaction of elastic bodies with viscous fluids. Translated from Prikladnaya Mekhanika, Vol. 33, No. 6, pp. 3–39, June, 1997.     

Evolution of long nonlinear waves on the interface of a stratified viscous fluid flow in a channel

The dynamics of disturbances of the interface between two layers of incompressible immiscible fluids of different densities in the presence of a steady flow between the horizontal bottom and lid is studied analytically and numerically. A model integrodifferential equation is derived, which takes into account long-wave contributions of inertial layers and surface tension of the fluids, small but finite amplitude of disturbances, and unsteady shear stresses on all boundaries. Numerical solutions of this equation are given for the most typical nonlinear problems of transformation of both plane waves of different lengths and solitary waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 49–61, July–August, 2007.