Modeling the deformability of a material

The high-temperature extension of metals to fracture is modeled for creep at constant stress or at constant strain rate. The dependence of the ultimate fracture strain on the loading factor (stress or strain rate) is studied. The nonmonotonic nature of this dependence with an internal maximum is described using the Rabotnov kinetic theory with one and two damage parameters. Available experimental data are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 183–188, September–October, 2007.     

Nonlinear stochastic creep problem for an inhomogeneous plane with the damage to the material taken into account

An analytical method for the solution of two-dimensional nonlinear creep problems is developed using as an example the biaxial extension of a plane from a stochastically inhomogeneous material with damage accumulation and the third stage of creep taken into account. The governing creep relation is adopted in accordance with the energetic version of the nonlinear theory of viscous flow. The stochasticity of the material is defined by two random functions of coordinates. Formulas for calculating the stress variance are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 140–146, March–April, 2007.     

Mechanical Performance of a Recycled Carbon Fibre/PP Composite

A composite made of recycled carbon fibres in recycled polypropylene matrix is studied experimentally to describe the features of the elastic and time dependent nonlinear mechanical behaviour. The properties of the developed material have a large variability to be addressed and understood. It was found that the stress-strain curves in tension are rather nonlinear at low strain rate and the strength is sensitive to strain rate. The elastic properties’ reduction for this composite after loading to high strains is rather limited. More important is that even in the “elastic region” due to viscoelastic effects the slope of loading–unloading curve is not the same and that at higher stress large viscoplastic strains develop and creep rupture is typical. The time and stress dependence of viscoplastic strains was analysed and described theoretically. The viscoelastic response of the composite was analysed using creep compliance, which was found to be slightly nonlinear.     

Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite

Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition.     

Mathematical model of creep for a microinhomogeneous nonlinearly elastic material

A mathematical model is proposed to describe the experimentally observed creep effect on the instantaneous elastic deformation of physically nonlinear elastic microinhomogeneous materials. Using a structural model of the medium, it is shown that, during unloading of a sample after creep at constant stress, the elastic strain can be both larger and smaller than the elastic strain during loading. It is shown that calculation results for a biocomposite material are in good agreement with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 157–163, May–June, 2008.     

Integral equation for stress concentration at the edge of a plane crack of arbitrary contour

Equations are derived for stress concentration near a crack of closed contour lying in a plane. A system of one-dimensional integral equations for the concentration factor is obtained. The right sides of the equations contain the initial approximation—a solution of the problem of a circular crack whose sides are acted upon by nonaxisymmetric loading. Mining Institute, Siberian Division, Russian Academy of Sciences, Novosibirsk 630091. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 143–148, September–October, 1999.     

Slow motion of a granular layer on an inclined plane

The shape of the free surface of a layer of granular material moving on an inclined plane is studied on the basis of a model of a non-Newtonian fluid with a nonlinear relation between the stress tensor and the shear rate of the flow. For small but finite elevations of the free surface, the governing equations are reduced to a quasilinear Burgers equation. Results of a numerical solution are presented for the case of arbitrary elevations. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 117–120, March–April, 1998.     

Stress–strain behaviour of poly(ethylene terephthalate) (PET) during large plastic deformation by plane strain compression: the relation between stress–strain curve and thermal history, temperature and strain rate

This study presents an experimental investigation of the large plastic deformation of poly(ethylene terephthalate) (PET) submitted to plane strain compression. PET samples, obtained by injection moulding, annealed and non-annealed, were deformed using a specific compression device developed for this purpose. The obtained stress–strain curves at different temperatures and strain rates are useful for engineering applications and show a significant temperature dependence and a minor dependence on the strain rate. A softening temperature as a minimum temperature necessary to initiate deformation when a minimum, almost zero, stress is applied is introduced. This temperature, at the zero stress and strain limit, we denominate “Stress–Strain independent softening Temperature (T _SOF)”. The T _SOF values, 104 and 113°C for non-annealed and annealed PET, respectively, have been obtained using three different strain rates, indicating that the property is sensitive to the thermal history of the material.     

Stress state of a transversely isotropic magnetoelectroelastic body with a plane crack under antisymmetric loads

The static equilibrium of a transversely isotropic magnetoelectroelastic body with a plane crack of arbitrary shape in the isotropy plane under antisymmetric mechanical loading is studied. The relationships between the stress intensity factors (SIFs) for an infinite magnetoelectroelastic body and the SIFs for a purely elastic body with the same crack and under the same antisymmetric loading are established. This enables the SIFs for a magnetoelectroelastic body to be found directly from the analogous problem of elasticity. As an example of using this result, the SIFs for penny-shaped, elliptic, and parabolic cracks in a magnetoelectroelastic body under antisymmetric mechanical loading are found Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 37–51, October 2008.     

Long-term strength of metals and creep equations based on the Coulomb-Mohr criterion

It is proposed to construct long-term strength and creep relations for metals on the basis of the Coulomb-Mohr criterion. The creep equations and the long-term strength criterion for plane stress are analyzed in detail. Results of long-term strength calculations are compared with data of experiments with metallic materials. It is established that theoretical and experimental results are in satisfactory agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 115–123, November–December, 2007.     

Influence of damage on properties of strain localization in geomaterials at plane stress and plane strain

Summary By regarding geomaterials under loading as a mixture of intact and damaged parts, we investigate the influence of damage on the properties of strain localization in elastoplastic geomaterials at plane stress and plane strain. Conditions for the onset of strain localization including the effects of damage are derived for the cases of plane strain and plane stress. Discussed are the inclination of the localized band and the hardening modulus corresponding to the onset of strain localization. It is shown that the properties of the strain localization are dependent on the damage and the capacity of bearing hydrostatic pressure by the damaged part, and that damage may induce an earlier onset of strain localization and lead to instability of a geomaterial.accepted for publication 11 March 2004     

An experimental study of uniaxial creep,cyclic creep and relaxation of aisi type 304 stainless steel at room temperature

Following previous work (Krempl, 1979), a servocontrolled testing machine and strain measurement at the gage length were used to study the uniaxial rate(time)-dependent behavior of AISI Type 304 stainless steel at room temperature. The test results show that the creep strain accumulated in a given period of time depends strongly on the stress-rate preceding the creep test. In constant stress-rate zero-to-tension loading the creep strain accumulated in a fixed time-period at a given stress level is always higher during loading than during unloading. Continued cycling causes an exhaustion of creep ratchetting which depends on the stress-rate. Periods of creep and relaxation introduced during completely reversed plastic cycling show that the curved portions of the hysteresis loop exhibit most of the inelasticity. In the straight portions, creep and relaxation are small and there exists a region commencing after unloading where the behavior is similar to that at the origin for virgin materials. This region does not extend to zero stress.The results are at variance with creep theory and with viscoplasticity theories which assume that the yield surface expands with the stress. They support the theory of viscoplasticity based on total strain and overstress.     

On the displacement potential solution of plane problems of structural mechanics with mixed boundary conditions

The present paper describes the advancement of displacement potential approach in relation to solution of plane problems of structural mechanics with mixed mode of boundary conditions. Both the conditions of the plane stress and the plane strain are considered for analyzing the displacement and stress fields of the structural problem. Using the finite difference technique based on the present displacement potential approach for the case of the plane stress and the plane strain conditions, firstly an elastic cantilever beam subjected to a pure shear at its tip is solved and these two solutions (plane stress and plane strain) are compared with Timoshenko and Goodier cantilever beam bending solutions (Theory of elasticity, 2nd edn. McGraw-Hill, New York, 1951); secondly the above-mentioned displacement potential approach for the case of the plane stress and the plane strain conditions are applied to solve a one-end fixed square plate subjected to a combined loading at its tip. Effects of plane stress and plane strain on the elastic field of the plate are discussed in a comparative fashion. Limitations of Timoshenko and Goodier cantilever beam bending solutions (Theory of elasticity, 2nd edn. McGraw-Hill, New York, 1951) over the displacement potential approach for the case of the plane stress and the plane strain conditions are not only discussed but also the superiority of the present displacement potential approach for the case of the plane stress and the plane strain conditions are reflected in the present research work.     

Experimental study on yield behavior of Daqing crude oil

The yield behavior of Daqing crude oil was studied by means of multi-mode controlled-stress tests with a high-precision stress controlled rheometer. Two experiments of creep and constant stress loading rate were performed. The yield stress of gelled crude oil was dependent on the test conditions such as the stress loading time and the stress loading rate, but the yield strain did not change with test conditions. The yield strain did exist objectively and it can be used as the criterion for the yielding of the structure of gelled crude oil. The yield strain of gelled oil was studied through experiments of creep, constant stress loading rate, oscillatory shear stress increase, and constant shear rate. The yield strain of gelled crude oil decreased with the increasing gel strength. The experiment of constant speed increase of stress showed the strain softening phenomena for low gel strength oil.     

Using a comparison theorem for evaluating the stress for plane cracks in transversally isotropic media

An established thermoelastic analogy for transversally isotropic media and the Hopf principle of the maximum are used to prove a comparison theorem for estimating the stress for plane cracks of complex shape (in the place perpendicular to the plane of isotropy) in the presence of force and temperature loading. This approach makes it possible to construct simple bounding contours and provide two-sided estimates forK ₁. The effectiveness of this approach is demonstrated on specific examples. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 7, pp. 85–94, July, 1999.     

Change in the stress intensity factors for plane cracks in a transversely isotropic medium due to thermal loads

The feasibility of controlling the stress intensity factors for plane cracks of arbitrary form (distributed in a plane perpendicular to isotropy axis in a transversely isotropic material) which are subjected to symmetric mechanical loading by heating the material is demonstrated by using the congruence theorem and making an analogy between isotropic and transversely isotropic materials based on the theory of thermoelasticity. It is shown that a thermal load which fully compensates for the mechanical load can be created within the range in which the material behaves linearly. If it turns out to be technically impossible to create the necessary thermal load, a simpler temperature regime can be chosen that will “cancel” the mechanical force field with a certain factor of safety. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 29–37, September, 1999.     

A non-linear uniaxial integral constitutive equation incorporating rate effects,creep and relaxation

A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.     

Effect of material compressibility on the solution of the elastoplastic plane strain problem

A model problem of plane strain of an elastoplastic material is considered. It is shown that the type of stress state in the loading plane affects the dependence of the solution on Poisson??s ratio. It is found that for the state in which the principal stresses in the loading plane are approximately equal, the effect of compressibility is significant, so that it must be taken into account. It is shown that if the principal stresses in the loading plane have different signs, the solutions for compressible and incompressible materials are almost the same.     

On the choice of coordinates in the analysis of plane plastic strain

The plane strain of an ideal rigid-plastic medium is studied in curvilinear coordinates. The methods used to solve the equations of plasticity were considered in [1–3]. Curvilinear orthogonal coordinates with the introduction of a metric function were used in [4, 5].