Prediction of Strain Hardening and Fatigue Life of Cyclically Unstable Materials

The data on cyclic deformation of materials with different cyclic properties are analyzed. The relationship between the level of additional strain hardening and the mechanical characteristics of a material is established. The proposed models take into account the influence of the form of stressed state on strain hardening and durability under conditions of nonproportional cyclic deformation. The models are constructed on the basis of the analysis of the experimental data on cyclic deformation of 304 stainless steel. The prediction of strain hardening and durability is performed with separate analysis of the influence of shape of the cycle and the form of stressed state. To take into account the influence of shape of the cycle, we use the coefficient of disproportionality of the cycle and the parameter of sensitivity to disproportionality. To take into account the form of stressed state, we use the coefficient of the form of stressed state and the corresponding parameter of sensitivity to the form of stressed state. The results of prediction of both strain hardening and durability of materials on the basis of the proposed phenomenological models reveal their fairly high efficiency. __________ Translated from Problemy Prochnosti, No. 5, pp. 118 – 130, September – October, 2005.     

Loss of stability for the process of plastic deformation with a complex stressed state

Basic preconditions are presented for considering the stability of the plastic deformation process in evaluating the ultimate deformation and strength properties of structural materials in tubular specimens under conditions of a complex stressed state. Calculated dependences are provided for calculating these characteristics. Results of experimental studies are analyzed for heat-resistant steels 15Kh2MFA, 15Kh2NMFA, and VK-2 (KP-100) (the latter simulates radiation embrittled steel 15Kh2NMFA) with different principal stress ratios in the temperature range 20–350°C. Calculated values of ultimate stresses and strains are compared with experimental data. The possibility of using the results of experiments carried out with stepwise loading as a basis for calculating the endurance under cyclic loading conditions with a complex stressed state is substantiated.Translated from Problemy Prochnosti, No. 10, pp. 3–8, October, 1991.     

Toward the description of uniaxial deformation of metals

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.Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev Polytechnic Institute. Translated from Problemy Prochnosti, No. 11, pp. 65–69, November, 1989.     

Version of the endochronic theory of plasticity for describing complicated cyclic loading histories

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.Translated from Probiemy Prochnosti, No. 5, pp. 3–12, May, 1993.     

Features of the development of mixed type cracks in titanium alloy OT4

The results of calculation and experimental study of the development of mixed type cracks in titanium alloy OT4 under uniaxial loading are presented. The values of T stresses and stress intensity factors are determined on the basis of the numerical analysis of the stress-deformed state of rectangular samples with a central inclined crack. The need to consider T stress in the constitutive relations of the stress-deformed state of the body with a crack is demonstrated as an example of trajectories of development of a curvilinear crack. The experimental data on the cyclic crack resistance of titanium alloy OT4 are interpreted with respect to the parameter of deformation energy density. The range of smaller values of the resistance of the material to the development of cracks in the mixed forms of destruction relative to the situation of normal fracture is established.     

Constitutive equation of plastic deformation of a zn-al alloy under tension-tension strain controlled cyclic loading

A constitutive equation of plastic deformation under tension-tension, strain controlled cyclic loading condition was derived from the transition state theory of rate processes. It was considered that the rate of plastic flow during the (tension-tension) cyclic deformation is controlled by a system of two consecutive energy barriers and that the material structural characteristics remain constant during cyclic deformation. The study revealed that within the stress, time, and temperature range, where the backward activations over the energy barriers are negligibly small, tension-tension, strain controlled cyclic deformation is essentially a stress relaxation process. The theory described well the cyclic deformation behavior of a near eutectoid ZnAl alloy. The constitutive parameters determined from the analysis of stress relaxation and tension-tension, strain controlled cyclic loading experimental results were identical. Consequently, it was recommended that stress relaxation can be used to determine the material structural characteristics which can then be used to predict the tension-tension, strain controlled cyclic deformation behavior of the alloy, using the constitutive equation derived in this report.     

An improved method for estimation of Ramberg–Osgood curves of steels from monotonic tensile properties

In the present study, first a method for estimating cyclic yield strength is improved and compared using the experimental data of 121 steels from literature. Correlations between cyclic deformation properties (K′ and n′) and monotonic tensile data are then investigated, and a simple method requiring only the monotonic tensile properties is developed for estimation of the Ramberg–Osgood curve. Prediction capability of the proposed method is not only evaluated using the aforementioned 121 steels, but also compared with several commonly used methods that are available in the literature. The proposed correlations are shown to predict the cyclic deformation properties of most of considered steels reasonable well.     

Studies on damage accumulation kinetics in a metal under cyclic loading in the multiaxial stress state

Results of experimental investigations of deformation behavior for 10GN2MFA steel under cyclic loading in the multiaxial stress state are presented. The effect of a stress state on homogeneity factor variations that represents a measure of metal damage is shown.     

Identification of the cyclic strain curve based on random test results

It is proposed to determine the characteristics of cyclic deformation according to the results of testing with variable amplitude and recording of the stress amplitude for a given law of deformation. The parameters established for 12010.3 steel are compared with the experimental data accumulated by M. Bily. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 107–109, March–April, 2008.     

Calculation and experimental examination of complex modes of elastoplastic deformation

A model is examined of elastoplsatic deformation based on the concept of plastic compliances, and one of the structural models of elastoplsatic deformation used for describing cyclic processes is studied. The form of equations suitable for both analytical calculations and numerical applications is proposed. The calculated results are compared with the experimental data obtained on tubular specimens.Translated from Problemy Prochnosti, No. 8, pp. 14–17, August, 1990.     

The equation of a contour and the form factor of a hysteresis loop

A procedure for the determination of the parameters of actual diagrams of cyclic deformation is developed on the basis of experimental and theoretical investigations of cyclic stress-strain diagrams for steels. This diagram characterizes the dependence of strains on stresses in a loading cycle in the region of the transition from low-cycle fatigue to multicycle and proper multicycle fatigues. The correspondence between the amplitudes of plastic and residual deformations is established and the formula for the determination of the form factor of a hysteresis loop is proposed. Numerical data are compared with experimental results for 45 and 15313 steels and with data obtained by other authors. Translated from Problemy Prochnosti, No. 3, pp. 30–38, May–June, 1997.     

Deformation and Life of Titanium Alloy VT9 under Conditions of Nonproportional Low-Cycle Loading

Results of experimental investigation of low-cycle fatigue of titanium alloy VT9 under nonproportional loading are presented. Tensile-torsional low-cycle fatigue tests were carried out on thin-walled tubular specimens under proportional and nonproportional cyclic deformation at room temperature. It has been found that cyclic hardening in a steady state at the same value of the equivalent von Mises strain range is the same in circular cycles and in torsion (or tension–compression) cycles. In the case of nonproportional loading of specimens, the life of titanium alloy VT9 shortens in comparison with proportional loading, but not as much as for stainless steels.     

Predicting damage and failure under low cycle fatigue in a 9Cr steel

Experimental data have been generated and finite element models developed to examine the low cycle fatigue (LCF) life of a 9Cr (FB2) steel. A novel approach, employing a local ductile damage initiation and failure model, using the hysteresis total stress–strain energy concept combined with element removal, has been employed to predict the failure in the experimental tests. The 9Cr steel was found to exhibit both cyclic softening and nonlinear kinematic hardening behaviour. The finite element analysis of the material's cyclic loading was based on a nonlinear kinematic hardening criterion using the Chaboche constitutive equations. The models’ parameters were calibrated using the experimental test data available. The cyclic softening model in conjunction with the progressive damage evolution model successfully predicted the deformation behaviour and failure times of the experimental tests for the 9Cr steels performed.     

Method for the evaluation of the service life under random loading based on the energy criterion of fatigue fracture

We propose a method aimed at the assessment of the service life of structural elements under random loads based on the energy criterion of fatigue fracture and the model of cyclic deformation of materials after overloading. The possibility of determination of the maximum amplitude of stresses according to the number of loading cycles prior to fracture is substantiated. The results of evaluation of the service life under conditions of uniform stressed state are compared with the experimental data obtained by Swanson, Raikher spectral hypothesis of summation of defects, and linear hypothesis of summation. The dependence of the right-hand side of the linear hypothesis equation on the dispersion of the random loading process is established. __________ Translated from Problemy Prochnosti, No. 2, pp. 82–97, March–April, 2008.     

Constitutive model for cyclic deformation of perfluoroelastomers

Observations are reported in uniaxial cyclic tensile tests with a strain-controlled program on perfluoroelastomer Hyflon MFA. A constitutive model is developed for its viscoplastic response and damage at three-dimensional deformations with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Numerical simulation demonstrates that the constitutive equations adequately describe the mechanical response of perfluoroelastomer in cyclic tests with complicated deformation programs.     

Effects of cyclic stress on the creep behaviour and dislocation microstructure of pure copper in the temperature range 0.4 to 0.5T m

The creep deformation behaviour of polycrystalline pure copper under static and cyclic stress was studied in the temperature range 0.4 to 0.5T _m. Both cyclic creep acceleration and retardation occurred depending on the condition of peak stress and temperature combination. The comparison of dislocation microstructures, developed during steady state static and cyclic creep deformation, has also been performed to determine the effect of cyclic stress on the dislocation microstructure and evidence for the enhanced recovery of the cell wall under cyclic stress was found. These effects of cyclic stress on the creep rate and dislocation microstructure were interpreted on the basis of diffusion-controlled recovery creep theory and the cyclic creep acceleration mechanism is suggested as the enhanced recovery of the cell wall with the help of athermally generated excess vacancies.     

Lifetime of Metals under Biharmonic Loading

A procedure for calculating the lifetime of metals under biharmonic loading is proposed, which is based on the energy-based criterion of fracture and the use of metal cyclic deformation and fatigue characteristics. The data obtained are compared with the known experimental ones.