Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

Investigation of the elastoplastic deformation and the fracture criterion of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane

The stress-strain state and fracture of a transversally isotropic material subject to uniaxial compression in a direction parallel to the isotropy plane is studied. The deformation theory of the plasticity of a transversally isotropic body was used to analyze the stress-strain state. The fracture analysis of the material is carried out using a proposed variant of the strain-strength criterion. Theoretical and experimental data on the stress-strain state and the strength of a transversally isotropic material are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 67–71, March, 2000.     

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.     

Modeling Creep and Continuous Fracture Process Zones in Spatial Prismatic Bodies

The semianalytic finite-element method is used to develop a method for solving problems of creep and continuous fracture of complex spatial bodies. The method allows modeling the variation of the stress-strain state during creep, accompanying accumulation of dispersed microdamages, and development of macroscopic effects—continuous fracture process zones. The growth of a continuous fracture process zone is modeled. A criterion is formulated for determination of the applicability limits of continuum damage mechanics. The method is exemplified by the problem of deformation and continuous fracture of a gas turbine blade __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 70–86, September 2005.     

Plastic Constants of Fracture

Based on the theory of an ideal rigid-plastic body, an approach is formulated for determining fracture constants on the basis of standard mechanical tests on uniaxial extension of plane and cylindrical samples. Instead of the experimentally determined characteristics of fracture of materials (dimensionless elongation and constriction of the sample during its fracture), two invariant tensor characteristics of the degree of sample deformation are introduced, which correspond to the moment of origination of a macrocrack and critical strain at the crack tip determining the process of crack propagation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 147–155, March–April, 2006.     

Deformation and fracture of a spheroplast under low-cycle loading at various temperatures

This paper gives the results of an experimental study of the deformation and fracture of a spheroplast under uniaxial low-cycle loading (compression and unloading) at a temperature T = 25 and 100°C. Various mechanisms of damage accumulation at various temperatures and degrees of damage to the material are studied. The experimental results are compared with the well-known dependences taking into account damage accumulation for metals. It is established that the basic propositions of these theories are suitable for the low-cycle fracture of spheroplast — a ductile material of complex structure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 197–204, January–February, 2009.     

Deformation of physically nonlinear stochastic composites

The studies of the deformation of physically nonlinear homogeneous and composite materials are systematized. Algorithms to determine the effective elastic properties and stress–strain state of particulate, laminated, fibrous, and laminated fibrous composite materials with physically nonlinear components are outlined, and their deformation patterns are studied. Composites are considered as two-component materials of random structure. Their effective properties are determined using the conditional averaging method. The nonlinear equations that allow for the physical nonlinearity of the components are solved by an iterative method. The relationship between macrostresses and macrostrains is established. Macrostress–macrostrain curves of homogeneous and composite materials are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 7–38, December 2008.     

Allowance for complex loading in transversely isotropic solids

A model of plasticity for a transversely isotropic material with allowance for complex loading is developed, based on results of experiments with homogeneous cylindrical specimens of isotropic materials. An empirical model of plasticity for isotropic metals is constructed with allowance for vector properties of the material. The model is extended to a particular case of anisotropy. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 128–133, January–February, 2009.     

On a mechanical analogy in the ideal plasticity theory

The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 74–80, July–August, 2008.     

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.     

Limit equilibrium of an orthotropic plate weakened by a periodic row of collinear cracks

A modified δ_c-model is used to study the limiting state of an orthotropic plate weakened by a periodic row of collinear cracks and satisfying a general failure criterion. The failure mechanism of the plate is analyzed.Astudy is made of the effects of the degree of orthotropy, the biaxiality of external loading, and the geometrical parameters on the fracture process zones at the crack tips and the limiting state of the plate. The safe loading of an orthotropic viscoelastic plate with a periodic row of collinear cracks is examined. The effect of the rheological parameters on the safe-load region is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 126–135, August 2008.     

Deformation and long-term damage of homogeneous and composite materials of stochastic structure (Review)

The studies of mathematical models for the coupled processes of deformation and long-time damage of stochastic composite materials are systematized. Damage is modeled by stochastically arranged micropores. The damage of a single microvolume is characterized by its stress-rupture strength determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises or Schleicher–Nadai criteria, and assumed to be a random function of coordinates. The equation of damage balance at an arbitrary time and the equations relating macrostresses and macrostrains constitute a closed system. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. The effect of temperature and nonlinearity on the curves is studied     

Thermodynamic criterion for predicting the brittleness and plasticity of metals

A brief comparative analysis of the various methods of evaluating the brittle fracture of metals is given. A plasticity index for metals is proposed and substantiated, and the relation describing its effect on the relative contraction at rupture is obtained. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 169–176, November–December, 1999.     

Strain Mapping of Al–Mg Alloy with Multi-scale Grain Structure using Digital Image Correlation Method

Al–Mg alloy powder was mechanically milled in liquid N₂ (cryomilling) to produce thermally stable powder with nanocrystalline (NC) microstructure for the manufacture of high-strength alloys. A multi-scale microstructure was achieved by blending unmilled coarse-grained (CG) powder with cryomilled powder and subsequently consolidating. The final bulk alloy was comprised of ultra-fine grained (UFG) regions and discrete CG bands. Dynamic observations of tensile deformation of the alloy were recorded using a micro-straining module attached to a light microscope, and the displacements were measured by digital image correlation (DIC). Strain inhomogeneity between UFG regions and ductile CG bands was observed in the micro-strain (strain order of 10⁻⁴–10⁻⁶) range, and the strain behavior was interpreted in terms of dislocation plasticity. Special emphasis was given to the distinct displacements between adjoining regions during deformation.     

Fracture resistance of materials with translational hardening in the presence of cyclic loading

We use the examples of two types of titanium alloys that are currently widely used to study the effect of translational hardening on the fracture resistance of materials subject to cyclic loading. We examine regularities in elastoplastic deformation, the stability of hardening over time, and critical values of crack length and fracture stress. Ukranian Scientific Research Institute for Civil Engineering, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 106–111, November, 1999.     

Experimental study of D16AT alloy deformation under periodic loading

An experimental procedure and results of an experimental study of the kinetics of the strained state of a material under periodic uniaxial loading are reported. Diagrams of the principal components of the total strain tensor for an asymmetric periodic “soft” regime of tension-compression of the samples are presented. Specific features of deformation revealed under periodic asymmetric loading of the samples can be used to formulate a criterion of fatigue fracture of materials and to identify the mechanism of strain hardening of pre-fracture zones in machine elements.     

On the threshold force pulses for spall fracture of materials

Spall fracture is considered using the classical one-dimensional model. Results of the analysis are used to predict the dynamic strength properties of some structural materials, in particular, rail steels. The dependence of the time of fracture of the material on the threshold amplitude and time of loading is obtained. A model for the comparative estimation of the dynamic strength of materials is proposed, and corresponding diagrams are constructed. It is shown that the fracture process can be optimized by choosing the duration of loading of the material. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 97–106, September–October, 2006.     

Study into the kinetics of a crack with a nonsmall fracture process zone in an aging viscoelastic plate

The subcritical growth of a mode I crack with nonsmall end zones in an aging viscoelastic plate under tensile loads applied at infinity is studied assuming that the fracture process zone is of constant length. The equations of incubation, transition, and major crack growth stages are obtained on the basis of the Volterra principle and critical crack opening criterion. The crack subcritical growth of a specific material is studied as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 92–101, August 2007.     

Experimental determination of the basic characteristics of heat and mass transfer upon thermoerosion fracture of materials

Using an original technique, heat and mass transfer in the interaction between a high-temperature heterogeneous jet with a high concentration of particles and the surface of structural materials was studied for the first time. The characteristics of heat and mass transfer were obtained under conditions of intense destruction of the materials under the action of a heterogeneous jet whose axis is perpendicular to the heating surface. Based on the results of experimental studies, some signs of high-temperature fracture of steel and cement grout under the action of a heterogeneous jet were revealed. Deceased. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 138–143, March–April, 2000.     

The kinetics of creep embrittlement under long-term static loading

The formulation and solution technique for the problem of construction of evolutionary equations of creep embrittlement of metal materials are considered. Embrittlement is regarded as loss of plasticity depending on the time to fracture. Experimental data for high-temperature steels and alloys are systematized and analyzed, and, on this basis, two main classes of materials, those that are subjected to ductile fracture and those that undergo embrittlement, are singled out. The kinetics of embrittlement is considered as regards the strain of instantaneous fracture and obeys the power law. The conditions of change in the nature of fracture are formulated, which allows one to calculate the coordinates of the inflection points on delayed-fracture curves. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 104–113, June, 2000.