A fretting fatigue crack growth model is proposed accounting for the effects of tribological parameters of the contacting materials and the biaxiality of contact together with bulk stresses, upon fretting fatigue crack growth rate and direction of growth in the fretting-zone subsurface layers. Based on this model a new technique is developed to determine fatigue life and predict the fatigue limit in an aluminium alloy, AMg6N. and a titanium alloy, VT9, under fretting conditions. For the above cases, fretting fatigue crack growth behaviour predicted by the proposed model is in good agreement with the experimental results. NOMENCLATURE a = crack length b = specimen width F = friction force in fretting zone p a x I, Kmax II --mode I and I1 maximum stress intensity factor, respectively r , KF = maximum tangential and maximum normal stress intensity factor, respectively KEP, K K , = threshold stress intensity factor maximum value for a mode I fatigue crack and a mode I1 fatigue crack, respectively N = number of cycles P = normal contact load applied to fretting pad Q = shearing force in cyclic shear test R = stress ratio S = amplitude of slippage in fretting zone f = specimen thickness 0 = angle between the crack growth direction and the line passing through the original crack rZ = crack length divided by specimen's width (A = a/b) p = cyclic coefficient of friction (p = P/F) uyc, ryc = cyclic yield strength in tension and shear rp = angle between the current crack growth direction and the specimen normal cross-section ua = bulk cyclic stress amplitude plane

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An ultimate hardening model of materials has been developed, which is based on allowance for hardening in the fatigue fracture zone. Using this model, the high-cycle life of materials is estimated. The hardening function and the relation of its parameters to fatigue life have been described. An original method for the determination of model parameters on the basis of fatigue curve by its characteristic points is proposed.Keywords: ultimate hardening model of material, life, high-cycle fatigue, local cyclic yield strength, numerical solution.Introduction. At the present time, there still exists the problem of the limit state attainment prediction and reliable determination of the life of structural elements under cyclic loading with an arbitrary load. The existing models and methods, which allow one to predict life both from complete failure and from the initiation of fatigue crack of definite length, include material characteristics which require special determination, which makes the use of reference data available in the data base difficult.The present paper discusses the possibility of constructing a computational hardening model of materials, which describes the kinetics of the high-cycle fatigue process, on the basis of characteristics available in the database [1]. In view of the deformation nonuniformity of material, it always has local zones, in which the level of plastic strains under cyclic loading is rather high despite elastic deformation of the major part of metal.In steels of ferrite-pearlite class, a decrease in hysteresis loop (inelastic-strain range) with operating time under the action of cyclic load under soft conditions is observed in the main loading portion (after the stabilization of inelastic strains), which corresponds to increase in the yield strength, i.e., to hardening of material [2]. Such deformation kinetics was taken as a basis of the proposed computational model. A computational model is adopted, which assumes fatigue fracture of material on its ultimate hardening in some local space, in which sliding under cyclic loading begins earliest.This model is based on a modified theory of fatigue crack initiation [3] with the use of the Orowan deformation scheme [4]. The model involves construction of a cyclic-hardening curve on the basis of the known initial experimental high-cycle fatigue curve. To describe analytically the hardening function of material, which determines the occurrence of its limit state, a system of two integral equations containing unknown parameters of hardening diagram must be solved. To this end, two characteristic points on the fatigue curve are used, which determine the validity region of this model. These points for the high-cycle fatigue region are the coordinates of the conditional transition to the gigacycle and low-cycle fatigue fracture regions.Description of the Computational Model of the Ultimate Hardening of Materials under High-Cycle Fatigue. Consider the following model of cyclic deformation of some local aggregate of grains belonging to the surface l...

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