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The effectiveness of predicting the strain hardening of metallic materials at low-cycle fatigue under nonproportional biaxial loading conditions has been analyzed. The cycle nonproportionality coefficient, which characterizes the geometry of a deformation cycle path, is used as the determining parameter. A comparative analysis of the effectiveness of using the most known nonproportionality coefficients to determine the levels of additional hardening of the material in the state of stabilization of its cyclic properties has been carried out.

An engineering approach to fatigue-life prediction is proposed on the basis of an analysis of experimental data on low-cycle fatigue in the case of uniaxial and biaxial (nonproportional) deformation of a wide range of metallic materials. The approach is based on the linear correlation between the reduced strain range and the number of cycles to fracture initiation. The above strain parameter takes into account both the orientation of the cycle path in the strain space and the degree of its nonproportionality. The use of the strain parameter as a criterion made it possible to obtain acceptable results in fatigue-life prediction.

We have analyzed experimental data on low-cycle fatigue in biaxial nonproportional deformation of various materials. To establish a correlation with the fatigue limit, we have proposed a strain parameter-the reduced range of strain. For most of the materials under consideration this correlation dependence can be obtained from uniaxial low-cycle fatigue experiments and can be represented by a linear function.

Abstract: We develop a version of the endochronic theory of plasticity for the description of the stress-strain state under stress-controlled asymmetric loading. We propose a new rule of kinematic hardening aimed at taking into account the unilateral accumulation of plastic strains. The reliability of the model is confirmed by good agreement between the numerical results and the well-known experimental dependence of the maximum level of strains on the number of cycles under conditions of uniaxial cyclic creep.

A new version of the engineering method of weight functions that combines the advantages of the existing versions is suggested. It is based on finding the dependence of the opening of the crack lips on the concentrated force applied at an arbitrary point of the crack lips and makes essential use of an approximate fundamental solution for a half plane with an edge crack in a combined method of weight functions. The high accuracy and simplicity of the method are illustrated by several examples.

Abstract: On the basis of theoretical analysis and numerical experiments, we study the efficiency of the endochronic theory of plasticity with regular kernel and isotropically kinematic law of hardening for the description of block loading. It is shown that the theory adequately predicts the kinetics of the stress-strain state in the case of strain-controlled loading. In the case of asymmetric stress-controlled loading, the model qualitatively predicts only the nonstationary stage of the process of cyclic creep of the material. To describe this effect more accurately, we propose a simple model of plasticity taking into account the anisotropy of cyclic properties of the material induced by the asymmetry of loading cycles.

We propose a cycle nonproportionality coefficient for a broad class of complex cyclic paths, allowing us to establish a clear relationship between the geometry of the strain path and the maximum hardening level attainable in the material in the steady state for a fixed value of the maximum plastic or total strain range. We discuss the effectiveness of using the proposed cycle nonproportionality coefficient compared with analogous parameters familiar from the literature. Based on a previously developed version of the endochronic theory of plasticity, we have numerically modeled the behavior of a material for cyclic loading along different planar nonproportional paths.

A model is constructed to describe the ductile fracture of a pipe with a rectangular three-dimensional defect. Upper and lower bounds are obtained for the burst pressure. The first is calculated for a rectangular crack, while the second is calculated for an axisymmetric three-dimensional defect. It is shown that if the half-width of the defect b0 is equal to 2(Rtn)1/2 — where R is the radius of the pipe and tn is the net thickness of the pipe wall—then the defect can be regarded as axisymmetric. Calculated values of burst pressure are compared with literature data from full-scale tests of pipes. The results can be used to analyze actual defects in pipelines (pitting, etc.), as well as in conducting full- scale tests of pipes and pressure vessels.

Equations of state for the endochronic theory of plasticity are suggested for describing processes of nonproportional cyclic deformation of materials. New rules are introduced for characteristics of isotropic and kinematic strengthening with regard to the nonproportionality parameter of the plastic deformation cycle path. Basic experiments are considered with the aim of specifying characteristic relationships. As applied to different complex plastic deformation paths, stress distribution is determined in single-crystal tubular specimens with the combined action of an axial force and torsional moment in relation to the number of loading cycles. Calculated and experimental data are compared.

Weighing-function expressions are given for an elliptic normal-detachment crack in an infinite body, which have been used to calculate K1 for uniform and linear load distributions in the range in a (ratio of the minor and major axes of the ellipse) from 0.2 to 1. These K1 are compared with theoretical values to judge the accuracy of the weighing functions. Good accuracy (about 6%) is provided by the weighing functions constructed with elliptic coordinates and on the bases of the Oore- Burns general treatment in combination with Rice's formula, apart from points on the major axis. An integral condition is derived for the weighing function, and this is used in refinement of the unknown weighing function.

A model is presented for strengthening of a body in order to describe processes of material nonproportional cyclic deformation on the basis of the approach of endochronous plasticity theory. New rules are introduced for isotropic and kinematic strengthening processes taking account of a nonproportionality factor for the plastic deformation cycle trajectory. Basic experiments are described for defining the equations of state. The distribution of stress fields in thin-walled tube specimens in relation to the number of the loading cycle is determined as applied to different plastic deformation trajectories. The adequacy of calculated and test data is confirmed. The values sought are compared with similar results obtained by the two-surface theory of flow.

On the basis of an analysis of the known solutions for a circular and for a semiinfinite normal-separation crack with straight front in an infinite body we constructed, in analogy to the method of Burns and Oore, a weight function for elliptical cracks. Its use for finding the stress intensity factors KI at the point of minimal curvature under conditions of uniform loading leads to a maximal error of 10%; at the point of minimal curvature of the crack front the error increases with decreasing ratio of the semiaxes of the ellipse. With the aid of this solution the weight function is found in bounded bodies with a quarter-elliptical, semielliptical, and elliptical crack. A comparison of the data obtained by this method with the values of KI calculated by the finite-element method under nonuniform loading showed that the suggested method is very accurate.

To evaluate the effectiveness of the previously proposed constitutive equations of the endochronic theory of plasticity, we examine the deformation of thin-walled tubular specimens along square paths in deviatoric strain space with the combined action of axial force and torque. We obtain the resolving system of equations in application to strain-controlled nonproportional cyclic loading. Good agreement of the modeling results with the experimental data is noted.

A procedure for approximate determination of a point weight function for partly elliptical type-I cracks is refined. It is proposed that the effect of the free surface of the body be considered by introducing a hypothetical load which is symmetric relative to the boundary of the body. Results of calculations of stress-intensity factors obtained by the above procedure and by other authors using the finite-element method are compared for semi- and quarter-elliptical cracks.

The effectiveness of the application of equations of state with a weak peculiarity of the endochronic theory of plasticity in describing complex processes is investigated. The influence exerted by the magnitude of the bend angle of the stress path and various plastic-strain paths on prediction of the material's mechanical behavior is analyzed. The results obtained are compared with the solution for a model employing a regular kernel.

Effectiveness of using the endochronic theory of plasticity for describing unidimensional deformation processes under cyclic loading is investigated. A method is developed for determining parameters of the equations of state which depend on the amplitude of plastic deformation and length of strain path. A sufficiently good agreement is shown between calculated and experimental data in describing the kinetics of the stress-strain state of specimens of steels 316 and 45 subjected to variable loads.

The method of the approximate weight function construction for a semi-elliptical crack was suggested. The weight function sought was written as the sum of asymptotic (weight function for an elliptical crack in an infinite body) and correction components. To take into account the influence of a body free surface on the asymptotic component behavior, fictitious forces symmetric with respect to the body free surface were introduced.