A regression model of fatigue crack propagation under flight simulation loading

A multi-variable regression analysis is made of crack propagation data under flight simulation loading for the 2024-T3 and 7075-T6 alloys. The study is made using an effective stress range concept based on cracl closure considerations. A two-variable regression model of the equivalent stress range is suggested. The model is used to calculate fatigue crack propagation lives. Predictions using the proposed model are compared with empirical results. It is shown that the model accounts for the influence of maximum, minimum and mean stress levels of the load spectrum.     

A stochastic model of fatigue crack propagation under variable-amplitude loading

This paper presents a stochastic model of fatigue crack propagation in ductile alloys that are commonly encountered in mechanical structures and machine components of complex systems (e.g. aircraft, spacecraft, ships and submarines, and power plants). The stochastic model is built upon a deterministic state-space model of fatigue crack propagation under variable-amplitude loading. The (non-stationary) statistic of the crack growth process for center-cracked specimens is obtained as a closed form solution of the stochastic differential equations. Model predictions are in agreement with experimental data for specimens fabricated from 2024-T3 and 7075-T6 aluminum alloys and Ti-6Al-4 V alloy subjected to constant-amplitude and variable-amplitude loading, respectively. The stochastic model of crack propagation can be executed in real time on an inexpensive platform such as a Pentium processor.     

Near-threshold fatigue crack propagation of welded joint under varying loading

The influence of varying loading on the fatigue crack propagation properties of HT80 steel welded joint and base metal was investigated by using center cracked specimens under two-step programmed test. The higher stress intensity range was slightly above the threshold level obtained by constant amplitude test and the lower one was 70% of the higher one. The fatigue crack propagated below the threshold level for the base metal at the stress ratio of 0 and 0.4. However, the fatigue crack did not propagate below the threshold level either for the base metal at the stress ratio of 0.9 or for the welded joint at the stress ratio of 0. These results mean that the use of the threshold level obtained under the constant amplitude test would be dangerous for assessing the fatigue performance of the base metal under varying loading. The use of the threshold level obtained for the center cracked welded joint specimens would be conservative even under the varying loading.     

Reliability degradation of structural components in the process of fatigue crack propagation under stationary random loading

Stochastic crack growth processes under stationary random loading are investigated by the use of an extended Markov approximation method. In order to reflect engineering reality of material inhomogeneity, the propagation resistance is also assumed to be random. A crack length distribution function is first derived in a closed form under some assumptions. It is found that so-called the cross effect does appear between the effect of randomness due to loading and that due to propagation resistance. Then, with the aid of this result, the discussion is made on how the reliability of structural components degrades with time in consideration of uncertainties associated with initial flaws. It is clarified that in the region of high reliability the influence of random loading becomes significant as the correlation time of the loading process increases. As an example, the results are applied to a problem on the determination of the inspection period.     

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.     

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 mathematical model of fatigue crack propagation under variable amplitude loading

A mathematical model of fatigue crack propagation based on the crack closure concept is proposed. It allows prediction of fatigue crack growth under complex loading sequences on the basis of data obtained under constant amplitude and simple Low-High, High-Low loading sequences. The model explains the influence of single and multiple positive overloads and the interaction of positive and negative overloads. An algorithm for cycle-by-cycle calculation of crack growth is proposed.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

Effect of load sequences on crack propagation under random and program loading

Crack propagation was studied in 2024-T3 Alclad sheet specimens under two types of random loading and under program loading with a very short period (40 cycles) and program loading with a longer period (40,000 cycles). In the program tests Lo-Hi, Lo-Hi-Lo and Hi-Lo sequences were employed. The loads were based on a gust spectrum. The crack rates were about the same under random loading and program loading with the short period. Under program loading with the longer period the crack rates were 2.5 times slower on the average, while a significant sequence effect was observed in these tests. Fractographic observations indicated different cracking mechanisms for the random tests and program tests with a short period on the one hand and the program tests with the longer period on the other hand. Implications for fatigue tests in practice are discussed.     

Computer simulation of fatigue crack initiation

Results of a Monte Carlo simulation of the initiation stage of fatigue failure of aluminum alloys are described. Initiation processes simulated are: (1) nucleation of cracks at particles at or near the alloy surface; (2) early growth of microcracks with lengths on the order of the grain size; and (3) microcrack coalescence. Analytic models which describe nucleation and microcrack growth form the basis of the simulation, and relate the fatigue failure processes to the alloy microstructure. Two types of simulation outputs are obtained: (1) predictions of microscopic cracking parameters such as crack density, length and closure stress; (2) predictions of the mean and scatter in alloy fatigue lifetimes. Examples of both types of predictions are shown for selected aluminum alloys, and are compared to experimentally determined values.     

Fatigue crack propagation under variable-amplitude loading

A finite-element analysis has been performed to investigate quantitatively the level at which fatigue crack surfaces come into contact during fatigue cycles. The results agreed well with experimental observations and suggest that quantitative design rules may be developed, based upon the crack-closure hypothesis.A summary of remarks made during a seminar held at the Institute for Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev, October 21, 1976.NASA-Langley Research Center, Hampton, Virginia 23665. Published in Problemy Prochnosti, No. 10, pp. 26–29, October, 1977.     

Stochastic loading and material inhomogeneity in fatigue crack propagation

The Gaussian stationary stochastic load process is considered to cause fatigue crack growth in randomly inhomogeneous materials. The Paris-Erdogan model is applied and the time when the crack length reaches a critical value (lifetime) is determined as a random variable. It is shown that random variations of the lifetime are not significantly affected by stochastic fluctuations of loading and material inhomogeneity. These fluctuations, however, affect significantly the mean value of the lifetime. An example is carried out to show quantitatively the influence of the load and material randomness on the structural lifetime.     

不同加载速率下PD3钢轨疲劳裂纹扩展行为研究

以往的研究已经证明加载速率会对铁磁性材料的力学行为和周围压磁磁场产生影响,为了进一步研究历史加载速率对后续压磁磁场演变规律的作用,对Q345工程结构钢进行了一系列循环拉伸试验,采用磁通仪对试件压磁磁场进行在线监测,研究试件在经历不同的历史加载速率后,其压磁磁场的演变规律。结果表明：加载速率历史是影响压磁磁场演变的重要因素之一。     

Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

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