Fatigue Crack Growth Analysis Under Spectrum Loading in Various Environmental Conditions

The fatigue process consists, from the engineering point of view, of three stages: crack initiation, fatigue crack growth, and the final failure. It is also known that the fatigue process near notches and cracks is governed by local strains and stresses in the regions of maximum stress and strain concentrations. Therefore, the fatigue crack growth can be considered as a process of successive crack increments, and the fatigue crack initiation and subsequent growth can be modeled as one repetitive process. The assumptions mentioned above were used to derive a fatigue crack growth model based, called later as the UniGrow model, on the analysis of cyclic elastic–plastic stresses–strains near the crack tip. The fatigue crack growth rate was determined by simulating the cyclic stress–strain response in the material volume adjacent to the crack tip and calculating the accumulated fatigue damage in a manner similar to fatigue analysis of stationary notches. The fatigue crack growth driving force was derived on the basis of the stress and strain history at the crack tip and the Smith–Watson–Topper (SWT) fatigue damage parameter, D = σ_maxΔε/2. It was subsequently found that the fatigue crack growth was controlled by a two-parameter driving force in the form of a weighted product of the stress intensity range and the maximum stress intensity factor, ΔK ^p K _max ^1?p . The effect of the internal (residual) stress induced by the reversed cyclic plasticity has been accounted for and therefore the two-parameter driving force made it possible to predict the effect of the mean stress including the influence of the applied compressive stress, tensile overloads, and variable amplitude spectrum loading. It allows estimating the fatigue life under variable amplitude loading without using crack closure concepts. Several experimental fatigue crack growth datasets obtained for the Al 7075 aluminum alloy were used for the verification of the proposed unified fatigue crack growth model. The method can be also used to predict fatigue crack growth under constant amplitude and spectrum loading in various environmental conditions such as vacuum, air, and corrosive environment providing that appropriate limited constant amplitude fatigue crack growth data obtained in the same environment are available. The proposed methodology is equally suitable for fatigue analysis of smooth, notched, and cracked components.     

Inverse First-Order Reliability Method for Probabilistic Fatigue Life Prediction of Composite Laminates under Multiaxial Loading

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is based on a novel small timescale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics based on the geometric relationship between the crack-tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single-degree-of-freedom and multiple-degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated by using coupon testing data from open literature. Following this, the methodology is demonstrated by using a steel girder bridge. The proposed methodology shows that concurrent structural dynamics and material fatigue crack growth analysis can be achieved. Cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels shows a satisfactory accuracy by using the proposed coupled state-space model.     

Failure Diagram and Chemical Driving Forces for Subcritical Crack Growth

Kitagawa-Takahashi diagram that is modified for fatigue is now extended to the subcritical crack growth behavior under stress-corrosion crack growth. The analogy with the fatigue helps us to identify several regimes of interest from both the point of understanding of the material behavior as well as quantification of the failure process for structural design of components that are subjected to stress-corrosion and corrosion fatigue crack growths and failure. In particular, the diagram provides a means of defining the mechanical equivalent of chemical stress concentration factor and the chemical crack-tip driving forces to crack growth or its arrest. In addition, threshold stresses, crack arrest, and nonpropagating crack growth conditions can be defined, which help in developing sound design methodology against stress corrosion and corrosion fatigue. Chemical crack driving forces under corrosion fatigue can be similarly defined using the inert behavior as a reference.     

A theoretical model for creep crack growth

A theory of creep crack growth has been developed with the presumption that the crack growth occurs by the diffusion of vacancies along the grain boundaries. This is consistent with many experimental results that show that creep fracture is generally of intergranular type and the activation energies for crack growth rates fall within the range of grain boundary diffusion energies. The theory is based on the concept that creep crack growth results from a balance of two competing processes-the diffusion of point defects that contributes to the growth and the creep deformation process that retards the growth and causes even its arrest. The present analysis shows that crack growth via grain boundary diffusion occurs within some temperature range. The upper limiting temperature is determined by the bulk diffusion process which disperses the vacancies, that are diffusing to the crack tip, to the plastic zone ahead of the crack front. The lower temperature limit is set by the fact that the grain boundary diffusion rates decrease with the decrease in temperature and thus large stress intensities approaching the fracture toughness value are required to accomplish crack growth by the grain boundary diffusion. Outside these limits creep crack growth occurs via deformation which is significantly slower than growth by the grain boundary diffusion process. The importance of the present analysis rests on the fact that service conditions for many high temperature structural materials fall within the regime wherein creep crack growth occurs via grain boundary diffusion.     

Fatigue Fracture of Concrete Subjected to Biaxial Stresses in the Tensile C–T Region

In this paper cyclic quasi-static and constant amplitude fatigue responses of concrete subjected tensile compression–tension (C–T) biaxial stress are presented. In the tensile C–T region within the biaxial stress space, magnitude of the principal tensile stress is larger than or equal to that of the principal compressive stress. An experimental program consisted of subjecting hollow, cylindrical concrete specimens to torsional loading. Failure in both quasi-static and fatigue is due to crack propagation. It is shown that the crack propagation resulting from the biaxial loading can be predicted using Mode I fracture parameters. The fatigue crack growth is observed to be a two-phase process: an acceleration stage that follows a deceleration stage. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the quasi-static peak load. Analytical expressions for crack growth in the deceleration and acceleration stages are developed in terms of the mechanisms that influence quasi-static crack growth. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the biaxial fatigue response. Finally, a fracture-based fatigue-failure criterion is proposed, wherein the fatigue failure can be predicted using the critical Mode I stress intensity factor.     

A notch analysis of fracture approach to fatigue crack propagation

A model of fatigue crack growth is proposed that utilizes the recent developments in notch analysis of fracture and a concept of size effect that results from the changes in the critically stressed volume ahead of a crack tip. Accordingly, the fatigue crack growth mechanism involves local stresses reaching the theoretical cohesive strength and causing brittle fracture of atomic bonds at nominal stresses near the threshold, whereas slip-plane decohesion and plastic blunting and resharpening of the crack tip process may occur at stresses above the threshold range. The model contains three material parameters σFF nF, and ρF, that conveniently extend continuum analysis to situations where inhomogeneity of the material structure can influence the behavior appreciably. The analytical expression from the model was found to correlate fatigue crack growth data reasonably well in the low and intermediate stress ranges in Al 2024-T3, Al 7075-T6 and 250 grade maraging steel. The fracture modes observed are in agreement with the predictions from the model. The same fatigue crack growth model can be extended to estimating the threshold stress intensity factor range, ΔK_o and fatigue notch sensitivity of different materials.     

Reliability Analysis of Suspension Bridges against Fatigue Failure from the Gusting of Wind

A fatigue reliability analysis of suspension bridges due to the gustiness of the wind velocity is presented by combining overall concepts of bridge aerodynamics, fatigue analysis, and reliability analysis. For this purpose, the fluctuating response of the bridge deck is obtained for buffeting force using a finite-element method and a spectral analysis in frequency domain. Annual cumulative fatigue damage is calculated using Palmgren–Miner’s rule, stress-fatigue curve approach and different forms of distribution for stress range. In order to evaluate the reliability, both first-order second-moment (FOSM) method and full distribution procedure (assuming Weibull distribution for fatigue life) are used to evaluate the fatigue reliability. Probabilities of fatigue failure of the Thomas Bridge and the Golden Gate Bridge for a number of important parametric variations are obtained in order to make some general observations on the fatigue reliability of suspension bridges. The results of the study show that the FOSM method predicts a higher value of the probability of fatigue failure as compared to the full distribution method. Further, the distribution of stress range used in the analysis has a significant effect on the calculated probability of fatigue failure in suspension bridges.     

Theoretical model for FCGR near the threshold

A theoretical model for fatigue crack growth rate at low and near threshold stress intensity factor is developed. The crack tip is assumed to be a semicircular notch of radius ρ and incremental crack growth occurs along a distance 4ρ ahead of the crack tip. After analysis of the stress and strain distribution ahead of the crack tip, a relationship between the strain range and the stress intensity range is proposed. It is then assumed that Manson-Coffin cumulative rule can be applied to a region of length 4ρ from the crack tip, where strain reversal occurs. Finally, a theoretical equation giving the fatigue crack growth rate is obtained and applied to several materials (316L stainless steel, 300M alloy steel, 70-30 α brass, 2618A and 7025 aluminum alloys). It is found that the model can be used to correlate fatigue crack growth rates with the mechanical properties of the materials, and to determine the threshold stress intensity factor, once the crack tip radius α is obtained from the previous data.     

A model for creep-fatigue interaction in terms of crack-tip stress relaxation

A model was developed to explain the mechanism of the degradation of fatigue lives caused by the growth of transgranular crack without cavitational damage in spite of the creep-fatigue loading condition for some type 304L stainless steel and 1Cr-Mo-V steel. The model was developed by incorporating the stress relaxation effect during tensile hold time into the pure fatigue crack growth model based on the crack-tip shearing process. In the crack-tip region, the stress relaxation during hold time at the tensile peak stress reduces the maximum stress level but accumulates inelastic strain, which induces creep crack growth during hold time and enhances subsequent fatigue crack growth during subsequent loading by promoting the crack-tip shearing process. The predicted creep-fatigue lives by the model were in good agreement with the actual lives for type 304L stainless steel at 823 and 865 K and for 1Cr-Mo-V rotor steel at 823 K. The model was further expanded to explain the degradation of the life under the conditions of compressive hold cycling for 1Cr-Mo-V and 12Cr-Mo-V steels.     

Near-threshold fatigue crack growth properties at elevated temperature for 1Cr-1Mo-0.25V steel and 12Cr stainless steel

Near-threshold fatigue crack growth properties were investigated for a low-alloy steel 1Cr-1Mo-0.25V and a stainless steel SUS403 (13Cr) in the temperature range from 25 to 550°C. Fatigue tests were conducted at frequencies of 0.5, 5, and 50 Hz, in a manner designed to avoid crack closure. The effective value of threshold stress intensity range increased with increasing temperature and with decreasing frequency for the Cr−Mo−V steel, whereas the effective threshold stress intensity range was independent of temperature and frequency in the case of the SUS403 steel. At a given ΔK value, the fatigue crack growth rates accelerated with increasing temperature and with decreasing frequency for the Cr−Mo−V steel. However, although the rate of fatigue crack growth was independent of frequency at a given temperature for the SUS403 steel, the rate did increase with temperature. The observed threshold levels and crack growth behavior were closely related to the oxidation process of the bare surface formed at the crack tip during each load cycle.     

Temperature dependence of the intrinsic small fatigue crack growth behavior in ni-base superalloys based on measurement of crack closure

The effect of temperature on the small fatigue crack growth behavior of a single crystal and directionally solidified Ni-base superalloys was investigated at temperatures between 873 to 1123 K by measuring the crack closure. The results were also compared with those of the physically long crack. It was found that the propagation resistance and the fatigue threshold of the long cracks increased with temperature in all the materials. The long crack growth rates at three temperatures were approximately represented by an unique curve, after taking account of crack closure level and elastic modulus. In contrast, the small crack growth resistance decreased with temperature even when the crack closure phenomenon was taken into consideration. Furthermore, the small fatigue cracks exhibited considerably higher growth rates than the long cracks at a given effective stress intensity factor range and also grew under effective stress intensity factor ranges below the long crack threshold. The factors responsible for the lack of similitude in propagation rates between small and long cracks were also discussed, based on these observations and the chemical analysis near the crack tip using the electron probe microanalyzer.     

Crack Propagation in Flexural Fatigue of Concrete

In this paper the behavior of concrete subjected to flexural fatigue loading is studied. Notched concrete beams were tested in a three-point bending configuration. Specimens were subjected to quasi-static cyclic and constant amplitude fatigue loading. The cyclic tests were performed by unloading the specimen at different points in the postpeak part of the quasi-static loading response. Low cycle, high amplitude fatigue tests were performed to failure using four different load ranges. The crack mouth opening displacement was continuously monitored throughout the loading process. Crack propagation caused by quasi-static and fatigue loads is described in terms of fracture mechanics. It is shown that the crack propagation in the postpeak part of the quasi-static load response is predicted using the critical value of the mode I stress intensity factor (KIC). The ultimate deformation of the specimen during the fatigue test is compared with that from the quasi-static test; it is demonstrated that the quasi-static deformation is insufficient as a fatigue failure criterion. It is observed that crack growth owing to constant-amplitude fatigue loading comprises two phases: a deceleration stage when there is a decrease in crack growth rate with increasing crack length, followed by an acceleration stage where the rate of crack growth increases at a steady rate. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the peak load of the quasi-static response. Analytical expressions for crack growth in the deceleration and acceleration stages are developed, wherein the expressions for crack growth rate in the deceleration stage are developed using the R-curve concept, and the acceleration stage is shown to follow the Paris law. It is observed that the crack length at failure for constant amplitude fatigue loading is comparable to that of the corresponding load in the postpeak part of the quasi-static response. Finally, a fracture-based fatigue failure criterion is proposed.     

铸造奥氏体不锈钢的疲劳裂纹扩展

用紧凑拉伸试样研究了载荷比、单峰过载和两步高-低幅加载对Z3CN20-09M铸造奥氏体不锈钢疲劳裂纹扩展速率的影响.当应力强度因子范围相同时,疲劳裂纹扩展速率随载荷比的增大而增大.单峰过载使裂纹扩展速率先有短暂的增加后长距离的减速扩展,出现裂纹扩展迟滞现象.两步高-低幅加载时,若两步的最大载荷不同,第二步裂纹扩展也会出现迟滞现象.用两参数模型和Wheeler模型能够预测恒幅载荷和变幅载荷下的疲劳裂纹扩展行为.      

On the mechanism of fatigue crack growth in silicon nitride

The mechanism of fatigue crack growth in silicon nitride under the experimental conditions utilized is found to be of a cyclic nature, as contrasted to a form of static fatigue observed in some other ceramic systems. Conventional methods of analysis of the rate of fatigue crack growth in terms of ΔK_eff are not applicable, because the results of the experimental portion of this investigation show that ΔK_eff can decrease as the rate of fatigue crack growth increases. A mechanism which involves the formation of microcracks caused by a wedge effect which develops during the unloading portion of a cycle is discussed and evaluated. The wedge effect results from crack closure, which arises due to the roughness of the intergranular fracture surface as well as to debris trapped between the opposing fracture surfaces. In the proposed mechanism, the extent of crack advance per cycle is limited because of the decrease in stress intensity factor with crack advance in a given cycle associated with the wedge effect. The quantitative results of a semiempirical analysis of tests carried out in either air or vacuum are in agreement with some unusual experimental trends.     

Effects of temperature and environment on fatigue crack growth mechanisms in a 9% Cr 1% Mo steel

The environmental contribution of laboratory air to fatigue crack growth in a 9% Cr 1% Mo steel has been assessed by a comparison of crack propagation rates in air and vacuum over a range of temperatures (25–625°C). In the Paris regime, growth rates in air are generally higher than those in vacuum, where there is little variation of da/dN with temperature. In contrast, the enhancing effect of the air atmosphere on crack growth rates is strongly temperature dependent. A variety of environment-assisted crack growth mechanisms are found to be operative at different temperature ranges, and evidence of these is provided by both an analysis of activation energies and a fractographic investigation. The situation is different at lower stress intensities, where the threshold stress intensity range falls dramatically with increasing temperature in vacuum, and near-threshold growth rates at 525°C are higher in vacuum than in air. This effect is attributed to the occurrence of severe oxide-induced closure in air at elevated temperatures, where the crack is blocked with oxide at low stress intensities, reducing the crack driving force to a level below the intrinsic material threshold.     

Fatigue crack propagation at elevated temperatures in solid solution strengthened superalloys

The fatigue crack growth rates of three solid solution strengthened superalloys were measured at 25°C and from 538 to 871°C over a range of frequencies varying from 0.01 to 10.0 Hz. The three alloys were respectively nickel base, cobalt base and iron base alloys with approximately the same chromium content. The plots of crack growth ratevs AK, the range of the stress intensity factor, show three different regimes. At low ΔAK the crack growth rates are frequency independent and the fracture is strongly crystallographic. In the medium range of ΔK the fatigue crack growth rates are frequency and waveform dependent, indicating a strong creep-oxidation time dependent fracture mechanism. At high ΔK, nearK _c, the growth rates are again frequency independent and fracture proceeds by a void coalescence mechanism. The correlations between the fractographic features as seen in the SEM and the measured crack growth rates provide a good basis for the understanding of fatigue crack growth at elevated temperatures in the elastic-plastic range.     

Scaling laws for fatigue crack

A set of scaling laws has been developed for describing intermittent as well as continuous fatigue crack growth of large cracks in steels in the power-law regime. The proposed scaling laws are developed on the basis that fatigue crack growth occurs as the result of low-cycle fatigue (LCF) failure of a crack-tip element whose width and height correspond to the dislocation cell size and barrier spacing, respectively. The results show that the effects of microstructure on fatigue crack growth can be described entirely in terms of a dimensionless microstructural parameter, ξ, which is defined in terms of yield stress, fatigue ductility, dislocation cell size, and dislocation barrier spacing. For both discontinuous and continuum crack growth, the crack extension rate,da/dN, scales with ξ and(ΔK/E) ^m, where ΔK is the stress intensity range, m is the crack growth exponent, andE is Young's modulus. Application of the model to high-strength low-alloy (HSLA) and conventional ferritic, ferritic/pearlitic, and martensitic steels reveals that the lack of a strong microstructural influence on fatigue crack growth in the power-law regime is due to increasing yield stress and fatigue ductility with decreasing dislocation barrier spacing, which leads to a narrow range of ξ values and crack growth rates. Variation ofda/dN data with microstructure in HSLA-80 steels is explained in terms of the proposed model. Other implications of the scaling laws are also presented and discussed in conjunction with several fatigue models in the literature.     

A7085铝合金Ⅰ-Ⅱ复合型疲劳裂纹扩展及其数值模拟

为探究不同加载角度下A7085铝合金Ⅰ-Ⅱ复合型疲劳裂纹扩展机理,在MTS疲劳试验机上采用紧凑拉伸剪切试件（CTS）对A7085铝合金进行不同加载角度的疲劳实验;用有限元分析计算不同裂纹扩展长度的裂纹尖端应力强度因子,通过七点递增多项式法对数据进行处理,计算出A7085铝合金Paris公式中的参数C和m.结果表明不同加载角度的裂纹基本沿着与外载荷垂直的方向扩展,裂纹扩展路径近似为一条直线,裂纹扩展角测量结果基本符合最大环向拉应力理论;Ⅰ-Ⅱ复合型裂纹一旦发生扩展,Ⅱ型应力强度因子K_Ⅱ所占比例急剧减小,Ⅰ型应力强度因子K_Ⅰ不断增大,此后K_Ⅱ远远小于K_Ⅰ,有效应力强度因子（K_Ⅰ和K_Ⅱ的组合）基本等于K_Ⅰ,相当于裂纹扩展主要受Ⅰ型应力强度因子控制,研究结果有助于对Ⅰ-Ⅱ复合型疲劳裂纹扩展机理的理解.      

激光冲击强化技术研究及其在钛合金中的应用

激光冲击强化（LSP）通过高功率（GW／cm2级）、短脉冲（ns级）强激光诱导的冲击波在金属材料表层引入残余压应力,从而抑制疲劳裂纹的萌生和发展,是一种新型的金属表面强化技术。阐述了激光诱导冲击波的机理以及残余应力场的形成。分析了激光冲击的影响因素,论述了激光冲击强化的特点及其在钛合金中的应用,展望了激光冲击强化的应用前景和发展。     

Crack deflection: Implications for the growth of long and short fatigue cracks

The influences of crack deflection on the growth rates ofnominally Mode I fatigue cracks are examined. Previous theoretical analyses of stress intensity solutions for kinked elastic cracks are reviewed. Simple elastic deflection models are developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates. Experimental data are presented for intermediate-quenched and step-quenched conditions of Fe/2Si/0.1C ferrite-martensite dual phase steel, where variations in crack morphology alone influence considerably the fatigue crack propagation rates and threshold stress intensity range values. Such results are found to be in good quantitative agreement with the deflection model predictions of propagation rates for nonlinear cracks. Experimental information on crack deflection, induced by variable amplitude loading, is also provided for 2020-T651 aluminum alloy. It is demonstrated with the aid of elastic analyses and experiments that crack deflection models offer a physically-appealing rationale for the apparently slower growth rates of long fatigue cracks subjected to constant and variable amplitude loading and for the apparent deceleration and/or arrest of short cracks. The changes in the propagation rates of deflected fatigue cracks are discussed in terms of thelocal mode of crack advance, microstructure, effective driving force, growth mechanisms, mean stress, slip characteristics, and crack closure.