Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.     

Thermomechanics of elastoplastic and superplastic deformation of metals

Using the process theory of A. A. Il’yushin, we consider the problem of determining the thermomechanical parameters of a material element for specified deformation and temperature-variation processes with allowance for the elastic, plastic, and viscous properties of superplastic deformation. The relations obtained are applicable for the case of arbitrary stresses and finite strains. The strain and stress measures are decomposed into elastic, plastic, and viscous components by classifying the processes into reversible, irreversible equilibrium, and nonequilibrium processes. Tula State University, Tula 300600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 164–172, September–October, 1999.     

Elastic–plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic–plastic impact–contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic–plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results. The project supported by the National Natural Science Foundation of China (10532020).     

Erratum to: Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ ₃ = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.     

The velocity of ultrasound in low-carbon steel deformed at the low yield limit

The variation of a thin structure upon deformation of low-carbon steel at the yield limit is analyzed. The character of the interrelationship between the stage nature of a plastic flow of low-carbon steel and the velocity of ultrasound in it is established. It is shown that the velocity of ultrasound is a parameter for obtaining additional data on the development of plastic flow. The structural changes that exert an effect on the velocity of ultrasound in the deformation that corresponds to the yield site are studied. Institute of Strength and Materials Science Physics, Siberian Division, Russian Academy of Sciences, Tomsk 634021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 197–201, May–June, 2000.     

Types of Localization of Plastic Deformation and Stages of Loading Diagrams of Metallic Materials with Different Crystalline Structures

Macrolocalization, which accompanies the process of plastic deformation beginning from the yield point and ending by fracture, is determined by the staged character of material-loading diagrams. The evolution of localization patterns in a plastic flow of body-centered cubic vanadium alloy, hexagonal close-packed magnesium alloy, tetragonal tin, and face-centered cubic submicrocrystalline aluminum is analyzed within this concept. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 176–184, March–April, 2006.     

Elastic–plastic behavior of a semicircular frame being pressed against a rigid plane

As a simplified structural model, a semicircular frame is used to study the crashworthiness behavior of an aircraft fuselage. The quasi-static large elastic-plastic deformation of a semicircular frame in the process of its being pressed against a rigid ground is analyzed. First, based on the linear elastic assumption, the quasi-static large deformation contact process of the frame can be divided into three phases, i.e., point contact, line contact and post-buckling. By means of a shooting method, the relations between the displacement and contact force as well as the distribution of bending moment in the three phases are obtained. Then, by assuming an elastic, perfectly-plastic moment-curvature relationship for the semi-circular frame, the contact process is analyzed in detail to reveal the plastic collapse mechanism, the traveling of plastic hinge and the force-displacement relationship. In order to verify the analysis, a preliminary experiment was conducted, in which two types of half rings with clamped ends were pressed by a rigid plate. In addition, a numerical simulation is also conducted by employing ABAQUS to analyze both rectangular cross-sectional beam and I-beam. Finally, the theoretical predictions are compared with the experimental results and numerical solutions, showing that the elastic-plastic analysis can predict the contact process very well.     

Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes

A computational thermo-metallographic and thermoelastoplastic model for the analysis of the quenching process is developed and validated. The diffusive transfor-mations are modeled according to the Johnson–Mehl–Avrami–Kolmogorov model and the Scheil’s additivity rule. Two different models are investigated for the non-diffusive transformation—the Koistinen–Marburger model and the Yu model. A large displacement formulation is assumed for the deformation analysis, modeling the plastic behavior of the material according to the Prandtl–Reuss model. Two different bilinear hardening models—the isotropic and the kinematic hardening model—are used and compared. The model allows to evaluate the transient stress and strain distributions during the quenching process, the final phases and hardness distributions, and to predict the residual stress and the final deformation of the processed part. A good agreement between computational results and reference data is found     

Features of nonlinear deformation and critical states of shell systems with geometrical imperfections

Results from theoretical and experimental investigations into the nonlinear deformation (geometrical nonlinearity, plastic deformation, creep) and critical states (limit loads, buckling) of shell-frame systems with geometric imperfections are analyzed. The presence of prestresses is allowed. Diverse effects of various geometrical imperfections and plastic deformation for different load histories are studied. New qualitative effects of the mutual influence of these factors are established. Relevant experimental results are outlined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 3–47, December 2006.     

The use of the “trident” model in the analysis of plastic zones near crack tips and corner points

The paper deals with calculation of a plastic zone near a crack tip in a homogeneous elastoplastic solid and near a corner point of the boundary of this solid. The calculations are conducted for a solid subject to plane strain and within the framework of models with plastic strips. It is shown that in comparison with the widely used model with two straight slip-lines, the process of plastic deformation is described by the “trident” model more accurately. The results of calculations of the plastic zone by the “trident” model that correspond to different stages of the development of plastic deformation are given for a crack of normal separation in a quasibrittle material. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 95–100, March, 2000.     

One plasticity model for problems of plastic metal working

Scalar and tensor models of plastic flow of metals extending plasticity theory are considered over a wide range of temperatures and strain rates. Equations are derived using the physico-phenomenological approach based on modern concepts and methods of the physics and mechanics of plastic deformation. For hardening and viscoplastic solids, a new mathematical formulation of the boundary-value plasticity problem taking into account loading history is obtained. Results of testing of the model are given. A numerical finite-element algorithm for the solution of applied problems is described. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 159–169, November–December, 2008.     

Improved model of the griffith crack

The plane-stress state of a cracked continuous medium in tension is determined using relaxation elements. The stress state is analyzed at the tip of a crack surrounded by a plastically deformed material as a band of localized plastic deformation (LPD) shaped like an elongated ellipse. The plastic deformation considerably decreases the stress concentration at the crack tip. As the localization of the plastic deformation increases, the stresses at the crack sides decrease to zero. The decrease in stresses at the tip is accompanied by an increase in the concentration and gradients of the stresses at the end of theLPD band. Here the region of perturbation of the stress field is comparable with the width of the band. Institute of Physics of Strength and Materials Science, Tomsk 634055. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 132–141, November–December, 1998.     

Qualitative Distinctions in the Solutions Based on the Plasticity Theories with the Mohr-Coulomb Yield Criterion

The following two models of the plasticity theory are considered: the model with the Mohr-Coulomb yield criterion and the classical model of the plasticity theory with a yield criterion independent of the mean stress. The deformation problem of a plastic layer enclosed between two rotating plates is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 136–145, November–December, 2005.     

Numerical investigation of the plastic stress-strain state of laminated shells in axisymmetric deformation processes with small-curvature trajectories and allowance for geometric nonlinearity

Within the framework of the Kirchhoff-Love hypothesis, a procedure is developed for numerical investigation of the axisymmetric plastic stress-strained state of laminated shells with allowance for geometric nonlinearity. The process of deformation of isotropic materials is described by using the theory of deformation with small-curvature trajectories, while Hooke’s law is used to describe the deformation of orthotropic materials. The effect of inelastic complex deformation of two isotropic layers on an orthotropic layer is studied in an example of a three-layer shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 32, No. 8, pp. 80–86, August, 1996.     

Theoretical and experimental study of energy dissipation in the course of strain localization in iron

Plastic strain localization is studied with the use of a high-sensitivity infrared camera. Plastic strain localization in iron is demonstrated to be accompanied by the emergence of heat waves and their propagation over the sample surface. Constitutive equations that describe the energy balance in the material under plastic strains are derived, and the plastic flow of iron is analyzed. The results of research are compared with the data obtained by infrared scanning. The proposed model of strain localization in the form of soliton-like waves (phase triggering waves) is demonstrated to agree with the kinetics of temperature waves characterizing dissipation inherent in the development of plastic deformation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 153–164, January–February, 2009.     

Differential constitutive equations of incompressible media with finite deformations

A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids, and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic deformations of the material and deformations of elements of the medium at the structural level. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009.     

Dynamics of a rigid-plastic curvilinear plate of varying thickness with an arbitrary hole

A perfect rigid–plastic body is used as a model to develop a general procedure for analyzing the dynamic behavior of an arbitrary curvilinear plate of variable thickness with an arbitrary internal hole. The plate is subjected to an arbitrary, uniform, short-term dynamic surface load. Two plate deformation patterns are considered. Analytic formulas for plastic zones, ultimate loads, and residual deflections are presented. Numerical examples are given     

Generalized rheological model of shear deformation of structured condensed media

A relaxation-type macrorheological equation is constructed, which describes shear deformation of elastoplastoviscous media containing microvoids. The equation corresponds to regimes of steady-state creep and elastic and plastic strains, which pass to the regime of viscous flow with limited growth of voids at high shear strain rates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 87–95, September–October, 2007.     

Effect of an electric current on necking in a tensile rod

Necking conditions in a tensile thermoviscoplastic rod with passage through it of an alternating electric current are studied. Modeling is performed with allowance for the complex constitutive relations for the rod material, heat transfer in the rod, and the current distribution across the section of the rod as a function of the current frequency (skin effect). The stability of uniform tension is examined by linear analysis of perturbations using the Routh-Hurwitz theory. The results were refined by nonlinear analysis taking into account the effect of the amplitude curve of perturbations on the stability of plastic deformation. Institute of Mechanics and Applied Mathematics, Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 173–178, September–October, 1999.