E. V. Lomakin

Postcritical deformation of steels in plane stress state

We study the laws determining the mechanical behavior of materials at the postcritical deformation stage. Proportional tension-torsion tests of thin-walled tubular specimens of structural steels were carried out for various deformation trajectories to obtain experimental data about the work softening of steels under plane stress state conditions. The obtained experimental data were analyzed to determine the instant of time in the deformation process at which the transition to the postcritical stage occurs.

Yield delay and space-time inhomogeneity of plastic deformation of carbon steel

The paper deals with experimental study of carbon steel plastic deformation laws at the stage of yield delay and yield plateau formation in uniaxial extension tests. The kinematics of formation and propagation of localized plastic flow bands of the material on the surface of solid cylindrical specimens of various length was analyzed by using the digital image correlation method. The influence of the rate of kinematic loading, unloading, and repeated loading on the processes of development of inhomogeneous elastoplastic deformation fields is estimated at the stage of formation of the yield plateau.

Torsion of cylindrical bodies with varying strain properties

We analyze the results of experimental studies of effective strain properties of damaged, porous, and other inhomogeneous materials and study the main laws of their behavior under strain. We consider the possible versions of constitutive relations taking account of the dependence of the properties of the media under study on the loading conditions or the strain conditions and the relations between the shear and bulk strains. Since the traditional statement of the torsion problems for bodies with such properties cannot be used, we analyze the strain consistency equations and the relations between the strains and displacements in cylindrical coordinates and obtain expressions for the displacements in an appropriate generalized form, which can be used not only for the torsion problems. We study how the distributions of displacements, strains, and stresses under torsion depend on the parameter characterizing the susceptibility of the material strain properties to variations in the stress state type. We show that, in the case of torsion of a cylinder of circular cross-section, there is no deplanation of the cross-section, just as in the classical solution, but the distributions of displacements, strains, and stresses significantly differ from the well-known solutions.

Development of inhomogeneous fields under postcritical deformation of steel specimens in extension

The paper deals with experimental studies of inhomogeneous strain fields in the “neck” region in extension of plane and cylindrical specimens at the postcritical stage, which directly precedes the fracture, by using a video system and a digital image correlation method. We consider the problems of interpretation of extension diagrams obtained for specimens of various length with strain inhomogeneity in the working section of the specimen with a “neck.”We obtain experimental data about the distribution of longitudinal, transverse, and shear strain fields and the displacement fields in the region of the plane specimen localization by using the digital image correlation method.

Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.

Thermovisco-hyperelastic behavior of elastomeric materials modified by filler nanoparticles

We present the results of experimental studies of hyperelastic and relaxation properties of polymer composites with elastomeric matrix made of hydrogenated nitrile butadiene rubber filled with nanoparticles of technical carbon in the temperature range 19–150° C. We present typical experimental diagrams of deformation of the material with constant strain rate and the stress relaxation curves at different strain levels under tension and compression conditions. We consider a possible version of constitutive relations for describing some singularities of the behavior of the material under study. We developed a method for determining all the parameters of the accepted relations on the basis of the results of uniaxial tests. We found a nonmonotone dependence of the relaxation modulus on the temperature and proposed a formula for describing this dependence in the temperature range under study. To justify the possible use of the considered constitutive relations to perform calculations under conditions of arbitrary compound stress state, we performed numerical modeling of the compression experiment for cylindrical samples. A rather satisfactory agreement between the computational results and experimental data was obtained.

Supercritical Deformation and Fracture of Bodies with Concentrators under Plane Stress State Conditions

The paper deals with experimental studies of inhomogeneous strain fields with regions of supercritical behavior of the material in the case of extension of plane specimens of steel 20 with concentrators of different geometry by using the method of digital image correlation. The use of a video system permits obtaining experimental data about the distribution of the fields of longitudinal, transverse, and shear components and the strain intensity. The previously considered criteria for the deformation process transition to the supercritical stage for different types of the stress–strain state were used to distinguish the regions of supercritical behavior and to analyze the evolution of the strain and temperature fields in their stable development.

Nonlinear effects in deformation of filled elastomers with nanodimensional fillers

Various nonlinear effects manifesting themselves in the deformation of filled elastomers are analyzed, and the advantages and restrictions in the use of several constitutive relations proposed to describe the nonlinear viscoelastic behavior of the materials under study are discussed. We also note that further development of models of nonlinear deformation of filled elastomers under finite strains, which would permit describing their deformation properties more completely, is highly desirable.

Study of viscoelastic properties of elastomers reinforced by nanoparticles

The results of experimental studies of hyperelastic and relaxation properties of polymer composites with elastomer matrix based on hydrogenated nitrile-butadiene rubber filled with technical carbon particles in the temperature range 20–125°C are presented. The characteristic experimental strain curves of materials in extension at a constant strain rate and the stress relaxation curves in materials at various tensile strain levels are given. A possible version of constitutive relations for describing some specific features of mechanical behavior of the considered materials under finite strains is considered. The obtained experimental data are used to verify the proposed constitutive relations experimentally. It is shown that the temperature-time analogy permits one to use the obtained constitutive relations to analyze nonmonotone variations in the relaxation properties of the considered materials as the temperature increases in the range under study.

Experimental Studies of Thermoviscohyperelastic Behaviour of Filled Elastomers

The viscohyperelastic properties of the hydrogenated nitril-butadien rubber containing the nano-size particles of technical carbon are studied. The stress–strain curves and the relaxation diagrams of the material under conditions both of tension and compression are presented. For the description of the viscohyperelastic behavior of filled elastomers, the constitutive equations are proposed. These equations represent the experimental values of stresses as the sum of two parts: hyperelastic part and viscoelastic one. The hyperelastic part is defined by the hyperelastic potential. The viscoelastic one is described by the nonlinear analogue of the equations of linear theory of viscoelasticity. The method for the determination of the parameters and the material functions is proposed. The comparisons of experimental data with the results of theoretical predictions are presented.