Statistical aspects of some fatigue crack growth data

In this study, fatigue crack growth tests were performed for a considerable amount of specimens made of 2024T-351 aluminum alloy. In total, there are three data sets obtained, two of them are tested under constant-amplitude loading and the other under random loading. The results are reported in the present paper with special emphasis on the scatter and statistical aspect of these fatigue crack growth data. They are also compared with those of other available data sets. It is confirmed that the inhomogeneity of material does cause the scatter of fatigue crack growth. Whether the randomness of the applied load increases or decreases the scatter, however, needs to be investigated further since there is no unique result for all data sets compared. Crack exceedance probabilities of random crack size and cumulative distributions of random loading cycle obtained by solving probabilistic models of fatigue crack growth curves are also presented, and conclusions are drawn. Comments on chi-square goodness-of-fit test and equivalent loading investigation are made as well.     

An experimental investigation of fatigue crack growth of stainless steel 304L

A series of fatigue crack growth experiments were conducted using round compact tension specimens of AISI 304L stainless steel under Mode I loading. The influences of the R-ratio (the ratio of the minimum load to the maximum applied load in a cycle), notch size, the tensile and compressive overloads, and the loading sequence on crack growth were studied. The results show that the material displays sensitivity to the R-ratio. The application of a tensile overload results in a short period of acceleration in the crack growth rate followed by a significant retardation in the crack growth rate. A compressive overload (underload) produces a short period of acceleration in crack growth and the magnitude of such an acceleration depends on the value of the loading amplitude of the constant-amplitude loading. Results from the two-step high-low loading sequence reveal a period of crack growth retardation at the beginning of the lower amplitude step, an effect similar to that of a single overload. Two existing crack growth models which are based on the stress intensity factor concept are evaluated using the experimental results. A two-parameter crack driving force approach together with a modified Wheeler’s model is found to correlate well the crack growth experiments.     

Load interaction effects on fatigue crack propagation in 2024-T3 aluminum alloy

Variable amplitude fatigue studies have been conducted within a linear-elastic fracture mechanics framework in order to systematically examine the effect of complex loading on fatigue crack retardation in 2024-T3 aluminum alloy. Complex loading conditions were simulated by introducing a second tensile or compressive peak load after the crack had extended various distances, a', into the region affected by a previously applied high load excursion.

Maximum interaction between single peak overloads resulted when the two peak load cycles were separated by a small distance, a' _min, where the fatigue crack propagation rate resulting from a single overload reached a minimum. This behavior was attributed in part to interference of tensile displacements produced during the first peak load cycle which was verified from fractographic observations. Crack growth rate retardation was related also to the development of a favorable compressive residual stress at the crack tip. Peak loads were found to act as completely isolated events only when they were separated by a distance approximately three times the plastic zone size resulting from a single overload. Comparable findings resulted when 10 cycle block overloads were employed in place of single peak excursions.

When a single peak overload was followed by a compressive cycle, retardation was found to decrease to a minimum; however, when the loading sequence was reversed, the effect was less damaging. In addition, as the distance between positive and negative peak loads was increased, the number of delay cycles quickly approached that associated with a single high load excursion.     

FORMULATION OF A STOCHASTIC MODEL OF FATIGUE CRACK GROWTH

Based on a global/local energy balance a deterministic model of fatigue crack growth under constant amplitude loading is derived. The energy terms resulting from the continuous plasticity and localized fracture around the crack tip are determined for small scale yielding leading to the fatigue crack growth equation involving the stress intensity factor and its amplitude. Four material parameters which should be identified from experimental data have a physical interpretation; these are eventually assumed to be random variables and model the statistical scatter of the crack growth versus N curves observed in experiments. A Gaussian white noise random field is additionally assumed to describe the stochastic material non-homogeneity within a specimen. Its effect on the crack growth is derived and results in a positive non-stationary random function depending on the crack length. Statistical parameters of the random fields are identified. Verification of the model by comparison with experimental results is undertaken in a subsequent paper.     

Prediction of the fatigue crack delay due to an overload based on the short crack theory

It is well-known that a single tensile overload, during the fatigue crack growth under constant loading amplitude, can induce the delay phenomenon. One of the basic mechanisms for fatigue crack growth in ductile metals is based on the crack-tip blunting under tensile loads. In this article, we investigate the fatigue crack growth delay behavior due to the single overload in the case of 12NC6 steel through compact tension specimens. An analytical method based on properly modified εN concepts is presented to predict the delay lives. The combination knowledge of the short cracks and the 3D constraint effect is important for the analysis in the vicinity of the blunt crack tip after overload. The present approach provides an analytical means to quantify the crack delay cycles in fatigue following a single tensile overload. The experimental results are in good agreement with the analytical modeling for different overload distributions.     

COMPARISON OF A STOCHASTIC MODEL OF FATIGUE CRACK GROWTH WITH EXPERIMENTS

A stochastic model of fatigue crack growth under constant amplitude loading, derived from a global/local energy balance, is compared with experiment data. Four random variables and a Gaussian white noise random field were assumed to model, respectively the statistical scatter of the crack length versus N curves and their stochastic fluctuations reflecting the effect of stochastic material non-homogeneity within a specimen. The statistical analysis of the so called Virkler and Ghonem-Dore data sets is extensively used to identify the probabilistic characteristics of the random variables and random field and to verify the stochastic model. Based on the importance sampling integration technique the fatigue lifetime probability distributions are effectively calculated. The influence of the particular assumptions accounting for the random material properties is investigated and the quality of the model prediction is verified by comparison with empirical statistical characteristics of the lifetime.     

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.     

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.     

Random fatigue crack growth with retardation

On basis of a study of the literature concerning empirical findings in fatigue crack growth in metal specimens under constant amplitude loading with occasional overloads, the paper summarizes the reported qualitative effects of the overloads. The great scatter of the observations and the difficulty of setting up a clear physical mechanism, which in deterministic terms explains the crack growth retarding effects of the overloads, motivates attempts to formulate stochastic process models of phenomenological type. The paper shows that birth processes have features that make them applicable in modelling fatigue crack growth processes. In fact, this process type allows a time transformation that reduces the case of variable amplitude loading to the case of constant amplitude loading. The mean growth curve defined as the mean time of growth to a given crack length as function of this crack length may in the constant load amplitude case be calibrated to the Paris-Erdogan law. For the case of occasional overloads it may be further calibrated to the empirical results reported in the form of the Wheeler model of crack retardation based on the concept of a strengthening plastic zone at the crack tip caused by the overload.     

Fatigue crack growth simulation of aluminium alloy under spectrum loadings

Fatigue crack growth in structure components, which is subjected to variable amplitude loading, is a very complex subject. Studying of fatigue crack growth rate and fatigue life calculation under spectrum loading is vital in life prediction of engineering structures at higher reliability. The main aim of this paper is to address how to characterize the load sequence effects in fatigue crack propagation under variable amplitude loading. Thus, a fatigue life under various load spectra, which was predicted, based on the Austen, Forman and NASGRO models. The findings were then compared to the similar results using FASTRAN and AFGROW codes. These models are validated with the literature-based fatigue crack growth test data in 2024-T3 Aluminium alloys under various overload, underload, and spectrum loadings. With the consideration of the load cycle interactions, finally, the results show a good agreement in the behaviour with small differences in fatigue life compare to the test data.     

FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading

An analysis of fatigue crack closure under variable amplitude loading was made by using the finite element technique. Two basic types of variable amplitude loading were selected for the analysis; constant amplitude loading with a single overload and block loading. A characteristic variation of a crack closure level was found to exist for both types of loading: the trace of the crack closure level vs crack length rose to a maximum value and then decreased asymptotically. The characteristic behavior was explained in terms of the residual stress which had been induced by an overload or a load preceding to the variation. The predicted fatigue crack growth behavior which was obtained analytically was consistent with the experimental results, and it was concluded that the retardation and acceleration phenomena are closely correlated with the crack closure.     

Q345R钢多个过载作用下疲劳裂纹扩展行为研究

单一过载使得疲劳裂纹扩展速率减缓,可以提高疲劳寿命,但对于多个过载作用下疲劳裂纹扩展仍未明确,有待于进一步研究。针对Q345R标准紧凑拉伸试样,在常幅循环加载条件下引入多个拉伸过载,研究多个过载作用对疲劳裂纹扩展行为的影响。研究结果表明:在保持应力比、过载位置和过载比不变的情况下,随着过载间距增加,迟滞效应先增加后减小;过载间距循环数是单一过载迟滞循环数的一半时,da/dN_min达到最小,迟滞效应最明显。采用含有过载交互作用参数Ø_I的修正Wheeler模型对不同的过载间距疲劳裂纹扩展行为试验结果进行预测,预测的结果与试验结果能够很好的吻合。     

The significance of fractography for investigations of fatigue crack growth under variable-amplitude loading

Fatigue crack growth tests were carried out on 2024-T3 and 7075-T6 centrally cracked specimens. Variable-amplitude (VA) load spectra were used with periodic overload (OL) cycles added to constant-amplitude (CA) cycles. The fatigue fracture surfaces were examined in the SEM to obtain more detailed information on crack growth contributions of different load cycles. The striation patterns could be related to the load histories. SEM observations were related with (i) delayed retardation, (ii) the effect of 10 or a single OL on retardation, (iii) crack growth during the OL cycles, and (iv) crack growth arrest after a high peak load. Fractographs exhibited local scatter of crack growth rates and sometimes a rather tortuous 3D geometry of the crack front. Indications of structurally sensitive crack growth under VA loading were obtained. Fractography appears to be indispensable for the evaluation of fatigue crack growth prediction models in view of similarities and dissimilarities between crack growth under VA and CA loading.     

An experimental investigation on fatigue crack growth of AL6XN stainless steel

The crack growth behavior of AL6XN stainless steel was experimentally investigated using round compact tension (CT) specimens. The influences of the R-ratio (the ratio of the minimum load over the maximum applied load in a cycle), the tensile and compressive overloads, and the loading sequence on crack growth were studied in detail. The results from the constant-amplitude experiments show a sensitivity of the crack growth rate to the R-ratio. The application of a tensile overload has a profound effect on crack growth, resulting in a significant retardation in the crack propagation rate. A compressive overload (underload) leads to a short-lived acceleration in crack growth. Results from the two-step high-low loading reveal a period of crack growth retardation at the beginning of the lower amplitude step, an effect similar to that of a single overload. A crack driving force parameter together with a modified Wheeler model is found to correlate the crack growth experiments well.     

Study of underload effects on the delay induced by an overload in fatigue crack propagation

Many engineering structures are subjected to random loading. The problem of predicting crack growth rates in this case cannot be solved without an accurate knowledge of load-time history occurring in service. There are many calculating models of crack propagation under spectrum loading, such as Wheeler model [Wheeler O. Spectrum loading and crack growth. J Basic Eng D 1972;94:181–86], Huang et al. [Huang XP, Zhang JB, Cui WC, Leng JX. Fatigue crack growth with overload under spectrum loading. Theor Appl Mech 2005;44:105–15] which use different approaches trying to explain fatigue crack growth.In this paper we use Decoopman’s [Decoopman X. Influence des conditions de chargement sur le retard à la propagation d’une fissure de fatigue après l’application d’une surcharge. Thesis, Université de Sciences et Technologies de Lille; 1999] model. He has developed an empirical model which describes the fatigue crack propagation after an overload cycle on 12NC6 steel in fatigue. This model describes how the crack growth rate evolves during the delay induced by the overload.Nevertheless, it is limited to overload cycles. But, many authors [[4], [5]; Huang XP, Zhang JB, Cui WC, Leng JX. Fatigue crack growth with overload under spectrum loading. Theor Appl Mech 2005;44:105–15; Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng Trans Am Soc Mech Eng 1963; 528–34] have shown that an underload cycle occurring after an overload cycle reduces the delay.This study proposes to implement the underload effect in order to decrease the conservative results expected from this model. Decoopman’s model proposes a delay weighting factor after an overload cycle. In order to take into account of an underload cycle, we suggest an acceleration coefficient to correct the model. The main advantage of this model is that the delay weighting factor and the acceleration coefficient are only dependent on yield stress σ_Y, the crack length a, and the various plastic zone sizes. Many experimental results have been compared to simulated results. These comparisons show a good agreement.     

Fatigue life prediction of engineering structures subjected to variable amplitude loading using the improved crack growth rate model

It is a difficult task to predict fatigue crack growth in engineering structures, because they are mostly subjected to variable amplitude loading histories in service. Many prediction models have been proposed, but no agreed model on fatigue life prediction adequately considering loading sequence effects exists. In our previous research, an improved crack growth rate model has been proposed under constant amplitude loading and its good applicability has been demonstrated in comparison with various experimental data. In this paper, the applicability of the improved crack growth rate model will be extended to variable amplitude loading by modifying crack closure level based on the concept of partial crack closure due to crack‐tip plasticity. It is assumed in this model that the crack closure level can instantly go to the peak/valley due to a larger compression/tensile plastic zone resulted from the overload/underload effect, and gradually recovers to the level of constant amplitude loading with crack propagation. To denote the variation in the affected zone of overload/underload, a modified coefficient based on Wheeler model is introduced. The improved crack growth rate model can explain the phenomena of the retardation due to overload and the tiny acceleration due to underload, even the minor retardation due to overload followed by underload. The quantitative analysis will be executed to show the capability of the model, and the comparison between the prediction results and the experimental data under different types of loading history will be used to validate the model. The good agreement indicates that the proposed model is able to explain the load interaction effect under variable amplitude loading.     

Deformation behaviour at the tip of a physically short fatigue crack due to a single overload

A two-dimensional elastic–plastic finite element analysis was utilized to investigate the transition behaviour of a physically short fatigue crack following the application of a single overload cycle. The deformation accommodated at the tip of a crack artificially advancing with a fully reversed load was considered. The development of the cyclic crack tip opening displacement was computed and then modelled to include the effects of the stress level of the base cycles, overload pattern and crack length at which the transient cycle was applied. The cyclic crack tip opening displacement was initially of a relatively high value. It decreased and then increased to match the behaviour under the base load cycles. The extent and location of both the minimum and matching points were dependent on the overload crack length and the stress compared with the material’s yield stress. In the case of the yield stress being exceeded by the overload, the minimum and the-return-to-normality points are identical. A previously developed crack tip deformation parameter was invoked to predict relevant experimental fatigue growth rates of short cracks reported in the literature.     

变幅载荷下纤维金属层板的疲劳与寿命预测

文章建立了纤维金属层板等幅疲劳载荷下的疲劳裂纹扩展速率与寿命预测模型。在此基础上对玻璃纤维-铝合金层板（GLARE）的疲劳裂纹扩展与分层扩展行为进行了试验研究,探讨了层板过载疲劳行为的机理,提出了纤维金属层板变幅载荷下疲劳寿命预测的等效裂纹闭合模型,并在GLARE层板上得到了验证。