Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

On fatigue reliability under random loads

We consider the problem of estimating the probability of survival (non-failure) and the probability of safe operation (strength greater than a limiting value) of structures subjected to random loads. These probabilities are formulated in terms of the probability distributions of the loads and the material strength. For the material strength, the Weibull distribution is assumed, the parameters of which are estimated by a statistical analysis of the experimental tensile strength of steel specimens subjected to different periods of random loads. The statistical analysis shows that, with the application of random loads, the initial homogeneous distribution of strength changes to a two-component distribution, reflecting the two-stage fatigue damage. In the crack initiation stage, the strength increases initially and then decreases, while an abrupt decrease of strength is seen in the crack propagation stage. The consequences of this behaviour on the fatigue reliability are discussed.     

A statistical model for fatigue fracture under constant-amplitude cyclic loading

A statistical approach to fatigue fracture under constant load is presented. Crack initiation due to detrimentally-acting external factors is considered, with a time-dependent rate assumed for an ensemble of growing stochastically-independent fatigue cracks. For crack increments under cyclic loading, a proportional-effect model is applied. It is shown that at low rates of surface crack initiation and low scatter of the crack increments, the median value of the fracture stress appreciably exceeds the one predicted by the deterministic model, whose estimate is conservative. At high rates and high scatter, the picture is reversed.     

A stochastic approach to fatigue crack growth in elastic structural components under random loading

Summary A probabilistic analysis of fatigue crack growth, fatigue life and reliability of elastic structural components is presented on the basis of fracture mechanics and the theory of random process. Both the material resistance to fatigue crack growth and the time-history of the stress are assumed to be random. The stress in an elastic structural component is proportional to the corresponding displacement response that is governed either by a linear differential equation for a linear structural system or by a nonlinear differential equation for a nonlinear structural system due to the plasticity other components. Analytical expressions are obtained for the special case that the random stress process is narrow-banded. Numerical examples are given for the randomized Paris-Erdogan type crack growth law to illustrate the procedures and the results are compared with those obtained from simulation to validate the stochastic approach.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

A multiaxial fatigue criterion for random loading

ABSTRACT A multiaxial fatigue criterion for random loading is proposed. Firstly, the orientation of the critical plane, where fatigue life estimation is carried out, is determined from the weighted mean position of the principal stress directions. Then, the scalar value of the normal stress vector N (t) perpendicular to the critical plane is taken as the cycle counting variable since the direction of such a vector is fixed with respect to time (conversely to the time‐varying direction of the shear stress vector C (t)), and a nonlinear combination of normal and shear stress components acting on the critical plane is used to define an equivalent stress amplitude. Finally, a damage accumulation model is employed to process such an equivalent stress amplitude and to determine fatigue endurance. This criterion is herein applied to some relevant random fatigue tests (proportional bending and torsion).     

System for automated fatigue crack growth testing under random loading

Procedures have been developed for computer-controlled crack propagation testing under random load sequences. They include certain features which are not available in conventional systems, but which appear essential for random load testing. These include the capability to simulate any desired K-function on standard laboratory specimens and continuous on-line rainflow analysis of the test load sequence to exclude cycles falling below given values of threshold stress intensity, stress level or range. The system also includes a procedure for automated crack-opening displacement based crack opening/closing load level measurement. Experimental studies on AlCu alloy sheet material point to a requirement for development of standards for spectrum loading crack growth testing.     

A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading

Low‐cycle fatigue data of type 304 stainless steel obtained under axial‐torsional loading of variable amplitudes are analyzed using four multiaxial fatigue parameters: SWT, KBM, FS and LKN. Rainflow cycle counting and Morrow's plastic work interaction rule are used to calculate fatigue damage. The performance of a fatigue model is dependent on the fatigue parameter, the critical plane and the damage accumulation rule employed in the model. The conservatism and non‐conservatism of predicted lives are examined for some combinations of these variables. A new critical plane called the weight function‐critical plane is introduced for variable amplitude loading. This approach is found to improve the KBM‐based life predictions.     

Computer simulation of fatigue crack propagation under random loading conditions

The aim of this study is to simulate fatigue crack propagation under random loading conditions using a simple algorithm based on the Wheeler model [Wheeler O. Spectrum loading and crack growth. J Basic Eng D 1972;94:181–86]. To create the computer simulation, a model based on the mechanical properties of the material has been used. These properties include the yield stress (σ_y) and Paris’s constants C and m. The loading conditions (baseline loading ratio R, baseline stress intensity factor range ΔK and overload stress intensity factor K_ol, R_ol) are also required. The present model is validated with fatigue crack growth test data conducted on 12NC6 steel samples with four different heat treatments in order to have different types of mechanical behavior. The computer simulation and experimental results for crack propagation for different overload distributions (a single overload, a repeated overload, different overload magnitudes, random overload) are in good agreement.     

Spectral method of fatigue life calculation under random multiaxial loading

We develop a new spectral method for the evaluation of fatigue life under random multiaxial loading. This method is a generalization of the known formulas of Miles, Kowalewski, Raikher, and Bolotin based on the power spectral density function of stresses under uniaxial random loads. The power spectral density function of the equivalent stress determined according to a linear criterion of multiaxial random fatigue is introduced in the indicated formulas. It is shown that, in reducing the multiaxial state of loading to the uniaxial state according to linear criteria, the frequency bands of the components of the stress state are transformed into the frequency band of the equivalent stress without increasing its width. This favorable result cannot be obtained if the equivalent stress is calculated according to nonlinear multiaxial fatigue criteria. Technical University of Opole, Opole, Poland, Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 86–96, May–June, 1996.     

Effect of the loading spectrum and history length on fatigue life distribution under random loading

One major source of error commonly encountered in determining the fatigue life of a given element arises from the loads involved, which are usually of random nature. As a rule, resistance analyses, carried out by simulation or tests, are done by using a loading history accounting for the real loads involved that is repeated indefinitely until failure is encountered. The result is one of the many different lives that can be obtained with the various histories representing the same loading process. The life obtained with one of these loading histories is a random variable even if the other parameters influencing it are assumed to be constant. In studying fatigue crack growth one should therefore take account of the additional randomness introduced in defining a given loading history to be representative for the actual loads involved. In this work we studied the influence of the loading histories used to analyse lives in relation to the number of cycles and spectral density of the loading process. For this purpose, we performed fatigue crack growth simulations by using a model taking account of the sequence effect. Analyses were carried out on loading histories obtained from different spectral densities of the nominal stress and various loading history lengths for each.     

The prediction of fatigue life under random loading: a diffusion model

A diffusion model is used to analyze the growth of a fatigue crack under random loading. The randomness in loading is embedded in the coefficients of the diffusion equation, whose solution leads to the determination of fatigue life. To demonstrate the potential of this method, some calculations are made using typical values for material properties. The results show that fatigue life under random loading is governed, in addition to material properties, by such statistics as the mean and the mean square value of the loading.     

Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis

Life prediction for GH4169 superalloy thin tubular and notched specimens were investigated under proportional and nonproportional loading with elastic–plastic finite element analysis (FEA). A strain-controlled tension–torsion loading was carried out by applying the axial and circular displacements on one end of the specimen in the cylindrical coordinate system. Uniaxial cyclic stress–strain data at high temperature were used to describe the multi-linear kinematic hardening of the material. The comparison between FEA and experimental results for thin tubular specimen showed that the built model of FE is reliable. A fatigue damage parameter was proposed to predict the fatigue crack initiation life for notched specimen. The results showed that a good agreement was achieved with experimental data.     

Role of elasto-plastic analysis under cyclic loading in fatigue crack growth studies

Linear Elastic Fracture Mechanics (LEFM) has been widely used in the past for fatigue crack growth studies, but this is acceptable only in situations which are within small scale yielding (SSY). In many practical structural components, conditions of SSY could be violated and one has to look for fracture criteria based on elasto-plastic analysis. Crack closure phenomenon, one of the most striking discoveries based on inelastic deformations during crack growth, has significant effect on fatigue crack growth rate. Numerical simulation of this phenomenon is computationally intensive and involved but has been successfully implemented. Stress intensity factors and strain energy release rates lose their meaning,J-integral (or its incremental) values are applicable only in specific situations, whereas alternate path independent integrals have been proposed in the literature for use with elasto-plastic fracture mechanics (EPFM) based criteria. This paper presents certain salient features of two independent finite element (numerical) studies of relevance to fatigue crack growth, where elasto-plastic analysis becomes significant. These problems can only be handled in the current day computational environment, and would have been only a dream just a few years ago. The work presented in this paper is supported by sponsored research projects of the Aeronautics R & D Board, Government of India and their support is acknowledged.     

A method for predicting fracture resistance of material in cyclic loading under viscoelastoplastic deformation and neutron irradiation conditions

We analyze the available methods for prediction of fatigue fracture resistance, which allow for material creep in a deformation cycle and neutron irradiation. Benefits and drawbacks of the available methods are discussed. We present a new method for the fatigue fracture strength prediction, which suffers no disadvantages inherent to the well-known methods. The proposed method has been verified on austenitic steels tested at elevated temperatures. Translated from Problemy Prochnosti, No. 6, pp. 5–24, November–December, 2008.