Mean stress effect correction using constant stress ratio S–N curves

This paper presents a stress based approach to take into account the influence of the mean stress value on fatigue strength of constructional materials. Elaborated model uses two S–N curves, i.e. for alternating stress (R = −1) and another one obtained under stress ratio R ≠ −1, for calibrating the equations of boundary condition. Two particular equations for the coefficient of intensification in stress transformations were proposed. The main advantage of the proposed solution is that the mean stress effect correction depends on the number of cycles to failure, what corresponds to the observed changes in experimental results presented in the literature. Proposed relations were compared with popular models for mean stress correction. The verification was made using selected series of experimental results taken from the literature. It was shown that the proposed solution is well correlated with experimental results.     

EFFECT OF BIAXIAL MEAN STRESS ON CYCLIC STRESS-STRAIN RESPONSE AND BEHAVIOUR OF SHORT FATIGUE CRACKS IN A HIGH STRENGTH SPRING STEEL

Abstract— Biaxial fatigue tests were conducted on a high strength spring steel using hour-glass shaped smooth specimens. Four types of loading system were employed, i.e. (a) fully reversed cyclic torsion, (b) uniaxial push—pull, (c) fully reversed torsion with a superimposed axial static tension or compression stress, and (d) uniaxial push—pull with a superimposed static torque, to evaluate the effects of mean stress on the cyclic stress—strain response and short fatigue crack growth behaviour. Experimental results indicate that a biaxial mean stress has no apparent influence on the stress—strain response in torsion, however a superimposed tensile mean stress was detrimental to torsional fatigue strength. Similarly a superimposed static shear stress reduced the push—pull fatigue lifetime. A compressive mean stress was seen to be beneficial to torsion fatigue life. The role of mean stress on fatigue lifetime, under mixed mode loading, was investigated through experimental observations and theoretical analyses of short crack initiation and propagation. Using a plastic replication technique the effects of biaxial mean stress on both Stage I (mode II) and Stage II (mode I) short cracks were evaluated and analysed in detail. A two stage biaxial short fatigue crack growth model incorporating the influence of mean stress was subsequently developed and applied to correlate data of crack growth rate and fatigue life.     

High cycle fatigue analysis in presence of residual stresses by using a continuum damage mechanics model

This study attempts to predict the high cycle fatigue life of steel butt welds by numerical method. At first, FE simulation of plate butt welding is carried out to obtain the weld-induced residual stresses employing sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. Then, a nonlinear damage cumulative model for multiaxial high cycle fatigue based on continuum damage mechanics (CDM), which can incorporate the effect of welding residual stresses, is derived using FE technique. The high cycle fatigue damage model is applied to the butt welds subjected to cyclic fatigue loading to calculate the fatigue life considering the residual stresses, and the computed total fatigue life which takes into account the fatigue crack initiation and the propagation is compared with the test result. In addition, the fatigue life prediction of the welds without considering the residual stresses is implemented to investigate the influence of welding residual stresses on the fatigue performance. The FE results show that the high cycle fatigue damage model proposed in this work can predict the fatigue life of steel butt welds with high accuracy, and welding residual stresses should be taken into account in assessing the fatigue life of the welds.     

Experimental and numerical study on crack initiation under fretting fatigue loading

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.     

Multiaxial fatigue reliability analysis of railroad wheels

A general methodology for fatigue reliability degradation of railroad wheels is proposed in this paper. Both fatigue crack initiation and crack propagation life are included in the proposed methodology using previously developed multiaxial fatigue models by the same authors. A response surface method in conjunction with design of experiments is used to develop a closed form approximation of the fatigue damage accumulation with respect to the input random variables. The total fatigue life of railroad wheels under stochastic loading is simulated, accounting for the spatial and temporal randomness of the fatigue damage. The field observations of railroad wheel fatigue failures are compared with the numerical predictions using the proposed methodology.     

Computational implementation of a non-linear kinematic hardening formulation for tension–torsion multiaxial fatigue calculations

The calculation of elastoplastic strains from stress histories, or vice-versa, is an important computational step in low-cycle fatigue analyses. This step is a challenging task for general multiaxial non-proportional (NP) loading histories, where the principal stress directions are not constant, requiring 6D incremental plasticity calculations to correlate the six stress with the six strain components considering plasticity effects. However, a large number of multiaxial fatigue problems only involve combined tension and/or bending and torsion loads, which are associated with only one normal and one shear stress component. The use of a special 2D formulation, instead of 6D, can greatly simplify the necessary incremental plasticity calculations for these practical problems. In this work, a new 2D tension–torsion incremental plasticity formulation is introduced, integrating non-linear kinematic (NLK) hardening models and NP hardening effects in a very efficient way, exactly reproducing tension–torsion calculations from more general 6D models, but with less than one fifth of the computational cost. The proposed 2D approach is validated by comparing NP strain-controlled tension–torsion experiments in 316L steel tubular specimens, a material that presents significant NP hardening effects, with experimental and predicted stress paths, calculated either with 6D or the proposed 2D formulation.     

Multiaxial fatigue life assessment of welded structures

Welded structures, such as welded pressure vessel components subjected to multiaxial cyclic loading, are particularly susceptible to fatigue damage. In this paper, a new path-length-based effective stress range is proposed to assess the fatigue life of weld joints under multiaxial fatigue loading. The path-length measure, a function of both normal and shear components on a critical crack plane, has a solid root in classic fracture mechanics and its application is validated by correlating nominal fatigue data including pure-bending, pure-torsion, in-phase, and out-of-phase loading. Path-Dependent Maximum Range (PDMR), a unique general-purpose fatigue life assessment package for multiaxial variable-amplitude loading, is introduced in this paper. Finally, the application of PDMR to multiaxial fatigue life assessment of complex loading cases is also discussed.     

Remarks on multiaxial fatigue limit criteria based on prismatic hulls and ellipsoids

This paper focuses on a class of multiaxial fatigue limit criteria where the equivalent shear stress amplitude is calculated by means of a scalar measure associated with a hypersurface enclosing the deviatoric stress history at a material point. We consider two hypersurfaces proposed by the authors, namely the maximum prismatic hull and the minimum Frobenius norm ellipsoid. Previous results obtained with elliptic and non-elliptic stress paths strongly suggested that such measures might always be the same. In this work we consider two counter-examples which show that these approaches are distinct. Fatigue limit criteria based on the linear combination of these measures with the maximum hydrostatic stress were applied to experimental data including: axial–torsional, biaxial tension and plane stress tests performed under harmonic and non-harmonic, synchronous and asynchronous waveforms. The predictions for both criteria fell within a 15% scatter band.     

A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

CRITICAL PLANE APPROACHES IN HIGH-CYCLE FATIGUE: ON THE DEFINITION OF THE AMPLITUDE AND MEAN VALUE OF THE SHEAR STRESS ACTING ON THE CRITICAL PLANE

Critical plane approaches are useful methods when designing against long-term fatigue of machine components made from metals. Somewhat surprisingly, the very basic problem of the evaluation of the amplitude and mean value of the shear stress acting on the critical plane is still not resolved satisfactorily for non-proportional cyclic loading conditions. In the present paper, existing proposals for solving this problem are briefly reviewed and their weaknesses highlighted. Then it is shown, through particular examples, that application of these proposals can lead to ambiguous results. Therefore, new definitions of the amplitude and mean value of the shear stress acting on the critical plane are formulated here. These new definitions are free from any ambiguity because they are based on the construction of the unique minimum-circumscribed circle to the path described by the shear stress on the critical plane. The centre of this circle defines the mean shear stress, whereas its radius provides the corresponding shear stress amplitude. The algorithm yielding this minimum-circumscribed circle is presented in some detail.     

Multiaxial creep–fatigue life prediction for cruciform specimen

This paper describes the high temperature multiaxial creep–fatigue life prediction for type 304 stainless steel. Finite element analyses were performed for determining the stress–strain state in the gage part of a cruciform specimen subjected to creep–fatigue loading under four strain waves at three principal strain ratios. Creep–fatigue lives of cruciform specimens were discussed in relation to the principal stress amplitude calculated by finite element analysis. Creep–fatigue damage was evaluated by linear damage rule and the suitability of three low cycle fatigue and three creep damage parameters was discussed.