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.     

A probabilistic model for fatigue crack growth under random loading

A model for predicting fatigue crack growth rate and life probabilistically under random load history is presented. It allows for random growth per cycle, and is based on experimental results of constant amplitude cyclic loads. Predictions of the model are on the conservative side at the same time avoiding overdesigning. The reliability is included in the model thereby avoiding the need for using a factor of safety or ignorance in estimating a fatigue life or a crack length after N cycles of load application. The model is computer-oriented.     

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.     

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 model for predicting the creep-fatigue life under stepped-isothermal fatigue loading

A model is developed herein for predicting the fatigue life of creep-fatigue damage interaction, which is induced by combined high frequency mechanical loading and low frequency temperature variation, i.e. stepped-isothermal fatigue loading. The model is derived from continuum damage mechanics. In the model, the interaction between creep and fatigue damage is considered to be nonlinear. To validate the proposed model, a cast aluminum alloy is fatigue tested at 200–350 °C and 350–400 °C. The results show that good agreement can be achieved between predicted life and experimental data.     

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.     

Novel analytical model for fatigue cumulative damage estimation under random loading

A newly nonlinear cumulative damage model associated with the S‐N curve, which preserves the compatibility conditions established for S‐N plane, was proposed and assessed by Eskandari and Kim in 2015. The model requires one exponent, in addition to the S‐N curve, to calculate the residual strength. A methodology is established to determine analytically the lower bound value of the exponent. However, this value proved to be too low for a quasi‐isotropic glass‐fibre laminate, based on published residual strength data. Further on, good predictions are obtained for ascending and descending ordered block spectrum. Yet it failed at fully random spectrum. The model was modified by imposing a very small decrease on model exponent towards the lower bound value, each time an increase in peak stress occurs. This modified model has been found to give good agreement with fatigue experimental data at different spectrum loads.     

A new approach of fatigue life prediction for metallic materials under multiaxial loading

Based on experimental data found in literatures, four traditionally multiaxial fatigue life criteria are analyzed and verified. It is discovered that these conventional criteria cannot reflect well the combined effect both under tension and torsion loadings for some materials, such as 6082-T6 and AlCu4Mg1, due to lack of enough consideration about the influence of stress amplitude ratio and stress level on fatigue life even under proportional loading. In order to solve this problem, a new approach of fatigue life prediction, based on the equal-life curve, is proposed and it is composed of three parts: the multiaxial fatigue life surface, a new path-dependent factor for multiaxial high-cycle fatigue and a material parameter describing material sensitivity to non-proportional loading. Finally, the precision of the presented approach is systematically checked against the experimental data found in literatures for four different materials under proportional and non-proportional loadings.     

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.     

Microcrack propagation and fatigue lifetime under non-proportional multiaxial cyclic loading

Non-proportional multiaxial fatigue tests of tubular specimens were performed under purely alternating strain-controlled loading. Different loading paths with different phase shifts were applied. With increasing phase shift at the same equivalent load, the lifetime was found to increase. For lifetime prediction a model based on the Manson–Coffin law was developed. By including the hydrostatic loading part, it was possible to compare the results of the multiaxial fatigue tests with uniaxially ascertained results. To obtain more information about the microcrack behaviour under multiaxial non-proportional loading, sonic emission studies and fractographic analyses were performed. The results suggest a discontinuous microcrack propagation. Motivated by the good agreement between these observations and some microcrack propagation models known from literature, a simplified model was proposed for micro and short crack propagation. This model which is based on the J-integral range ΔJ yields a quite good agreement between the experimentally observed and the calculated lifetimes.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.