Long-term strength of metals under an equiaxial plane stress state

This paper reports test results suggesting a significant dependence of the long-term strength of metals on the form of the stress state and the method of short-term loading. The experimental data obtained are described using a modification of the kinetic theory of long-term strength containing a vector damage parameter and taking into account strength anisotropy and the damage due to short-term loading. It is shown that the experimental and theoretical values of the time to rupture are in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 150–157, July–August, 2009.     

Nonlinear deformation of a particulate material in complex stress state

An algorithm is proposed to determine the effective deformation properties and stress-strain state of particulate composite materials with physically nonlinear components and complex stress state. The laws that govern the deformation of particulate composites are studied. A particulate composite is considered a two-component material of random structure. Its effective properties are determined by conditional averaging. The nonlinear equations that incorporate the physical nonlinearity of the components are solved by the method of successive approximations. The relationship between macrostresses and macrostrains is established. The effective deformation properties of a particulate composite as a function of the volume fractions of the components and stress state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 50–60, March 2006.     

Creep of a heat-resistant aluminum alloy in a complex state of stress

The article gives the results of experimental investigations of the creep of heat-resistant aluminum alloy AK4-1 with constant and variable loads, at a temperature of 175 °C and a duration of the tests equal to 100 h. Based on the experimental data, a verification of the theory of creep is adduced, based on the following hypotheses: 1) the change in the volume is elastic; 2) the deviator of the creep rates is proportional to the deviator of the stresses; 3) the intensities of the stresses, of the creep deformations, and their rates are connected by a relationship which does not depend on the type of the state of stress. It should be pointed out that the results of investigation of creep, under a complex state of stress, in carbon, low-alloy, austenitic steels, copper, and certain light alloys, are given in [1–6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 83–86, March–April, 1971.     

Vibrocreep of metals in uniaxial and complex stress states

The results of the creep tests with extension and torsion of tubular specimens made of D16AT and AD1 aluminum alloys, which were earlier obtained at the Institute of Mechanics, Lomonosov State University, were analyzed theoretically. Experimental data obtained with the author’s participation imply that a sharp increase in creep rate is observed under certain conditions when a vibration stress of small amplitude is added to the static stress. This effect (vibrocreep effect) is manifested only if the form of the stress state under the common action of static and dynamic stresses differs from the form of the static stress state. In this case, as the duration of the applied vibration stress increases, the vibrocreep effect gradually weakens. In this paper, we propose a model for describing the obtained experimental data containing the kinetic parameter; this parameter is nonzero only in the case of a complex stress state in the tubular specimens. As a positive measure of this parameter, we use the angle of rotation of the maximum principal stress vector when small vibrations are added to the basic stress state. The obtained experimental and theoretical creep curves are in a good agreement for different types of the stress states.     

Fracture of sedimentary rocks under a complex triaxial stress state

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.     

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.     

Evaluating the limiting state of materials with asymmetric cyclic loading and a complex stress state

Conclusion In order to construct models of the limiting state in asymmetric cyclic loading, it is best to use the representation of a unique limit curve that is invariant to the time to failure and type of stress state. Isotropic metallic materials were used as an example to show that such a curve does exist and is described satisfactorily by an exponential cosine function.The models constructed above were used to calculate the limiting state for several steels and alloys acted upon by the combinations of cyclic bending and cyclic torsion, static bending and cyclic torsion, and static torsion and cyclic bending. Results were also calculated for materials with stress raisers. The calculated data were compared with experimental findings and were shown to agree satisfactorily with the latter.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 2, pp. 67–79, February, 1995.     

Application of kinetic theory to the analysis of high-temperature creep rupture of metals under complex stress (review)

This paper gives an analytical review of the results obtained using the kinetic theory of creep and creep rupture to analyze the creep rupture of metals under complex stress. Special note is made of the outstanding contribution of Soviet scientists L. M. Kachanov and Yu. N. Rabotnov, who introduced the concept of material damage and developed the fundamentals of the kinetic theory. Different versions of this theory are used in studies of Russian and foreign scientists. The possibility of applying the kinetic theory to model the deformation and fracture of metals under creep conditions using scalar, vector, and tensor damage parameters and their combinations is considered.     

Limiting stress of metals and the limiting state under creep conditions

We show that, as long as one deals with a plane stress state, the Coulomb-Mohr fracture criterion traditionally used in soil and rock mechanics is in a rather good agreement with the results of fracture experiments for metal materials under the conditions of creep caused by a long-term action of a constant load. We perform statistical analysis to compare the proposed theoretical limiting-stress-fracture-time dependencies with the experimental results given in [1–3] and the results of computations by other authors [1, 4, 5]. Just as in [6], the limiting state arising under the conditions of creep caused by long-term loading is considered in the case of plane strain. We use the solutions of the rigid-plastic problems on the pressure exerted by a flat die on a half-plane and the extension of a strip with angular notches to find the fracture time for the corresponding problems in the setting of a perfectly rigid-creeping body.     

Stress-strain state of non-thin plates and shells. Generalized theory (survey)

Conclusions Thus, this part of our survey has presented the main approaches that have been taken to the construction of two-dimensional (in terms of the space coordinates) equations of a generalized theory of plates and shells. The solutions of these equations represent a certain approximation of the solution of the initial three-dimensional problem. They are based on expansion of the sought functions into Fourier series in Legendre polynomials of the thickness coordinate. Studies completed on the basis of the given variants of plate and shell theory were systematized and analyzed. In terms of the method of its construction, the theory involves a regular process of replacing the solution of the three-dimensional problem by the solution (or sequence of solutions) of two-dimensional boundary-value problems or initial-boundary-value problems. Numerical results illustrating the convergence of the successive approximation were presented. It should be noted that to make comparison with the results of classical or applied theories, several of the studies cited here presented solutions of problems for thin plates and shells with allowance only for the initial terms of expansions of the stress and displacement components into base functions (Legendre polynomials).S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 3–34, November, 1993.