Energy density zone model and fatigue life prediction considering microscopic effects

An energy density zone (EDZ) model is developed for the prediction of fatigue life. The microscopic effects can be involved in the EDZ model. Three scale transitional functions in the model are utilized to describe the trans‐scale behaviours of fatigue failure from micro‐scale to macro‐scale. Fatigue failure behaviours of a low‐alloy and ultra‐high‐strength steel material (i.e. 40CrNi2Si2MoVA steel) is investigated. Two fatigue parameters in the model are determined from the experimental S–N curves for the smooth cylinder specimens (the stress concentration factor, SCF, K_t = 1). Then, fatigue lives of notched specimens with SCFs K_t = 2 and K_t = 3 are predicted respectively by the proposed model. The predicted S–N curves are satisfactory in comparison with the experimental results. Scatter of the fatigue test data can be depicted when the microscopic effects are considered. Influences of microscopic effects on the fatigue behaviours are explored by means of numerical simulations.     

A genetic algorithm for unified approach-based predictive modeling of fatigue crack growth

This paper presents a framework to derive models of fatigue crack growth in real-life applications based on the unified approach.The unified approach enunciates that two parameters-namely, the stress intensity amplitude ΔK and the peak stress intensity K_max-drive fatigue crack growth. It captures and explicates the various fatigue phenomena coherently. However, its application for damage prediction is still in its infancy. Mathematical models that are consistent with the approach and the various observed characteristics under various environments are imperative for fatigue damage life prediction. These models will reduce cumbersome experimentation that is usually needed for the fatigue crack growth analysis. The framework presented in this paper consists of using the unified approach to design the structure of a model that relates fatigue crack growth with the specified microstructure, applied stress and environmental conditions. The fatigue growth model is derived by parametrizing, using a genetic algorithm, these structural relationships from the known experimental data. This model can quantitatively estimate crack growth rate under the given combination of microstructure, applied stress and environmental conditions. The initial research on modeling fatigue crack growth dynamics in Al-5052 under vacuum and air has revealed that the models resulting from the framework can capture the actual crack growth pattern to within 12% accuracy, and that an automatic rendering of ΔK^* vs. trajectories is possible for a given material and environmental conditions.     

An engineering method for reliability analyses of mechanical structures for long fatigue lives

Reliability analyses of mechanical structures designed for long fatigue lives require: some information on the probability distribution of material fatigue strength at long fatigue lives. In order to address this need, three-parameter P-S-N curves are adopted to represent the results of fatigue tests based on the conventional method. The parameters of the P-S-N curves are estimated by using the least squares fitting method and maximizing the correlation coefficient. The three-parameter P-S-N curves obtained are then used to estimate the fatigue strengths for different survival probabilities at an arbitrarily long fatigue life. These fatigue strengths are used to define the probability distribution of fatigue strength at the long fatigue life when a normal. distribution is used to approximate the probability distribution of fatigue strength. The method is illustrated by analyzing the results of fatigue tests of steel #45 (Chinese steel) notched specimens subject to axial loads with a stress concentration factor k_t = 2·0. Then, the method is applied to the fatigue reliability analysis of the runner of a hydraulic turbine. It is shown here that the reliability at long lifetimes can be easily estimated by the proposed engineering method and the conventional method may give a non-conservative design at long fatigue lives due to the assumption of bi-linear P-S-N curves.     

复合材料疲劳寿命预测

在疲劳载荷作用下,复合材料的弹性模量会随着载荷循环数的增加而不断下降,而材料中的内部损伤则不断增大。为此,本文提出复合材料的疲劳模量和累积应变的概念,并由此定义出三种预测复合材料疲劳寿命的疲劳损伤模型。文中应用这三种模型对单应力水平和多应力水平下的玻璃纤维增强环氧树脂复合材料的疲劳寿命进行了估算,并同实验结果进行了比较。     

FATIGUE LIFE PREDICTION IN BENDING FROM AXIAL FATIGUE INFORMATION

Bending fatigue in the low cyclic life range differs from axial fatigue due to the plastic flow which alters the linear stress-strain relation normally used to determine the nominal stresses. An approach is presented in this report to take into account the plastic flow in calculating nominal bending stress S_bending based on true surface stress. For a given surface strain ε_S, hence the surface life (N_S), an equation is derived to express S_bending in terms of axial fatigue stress (S_axial), involving material constants c, b, N_T which are obtained from axial fatigue information and f₁ and f₂ which are functions of strain hardening exponent and depend on the geometry of cross-section. These functions are derived in closed form for rectangular and circular cross-sections. The nominal bending stress and the axial fatigue stress are plotted as a function of life (N_S) and these curves are shown for some materials of engineering interest.     

Investigation on the Fatigue Behaviors of Maraging Steel at Different Stress Ratios

Herein, the high-cycle fatigue behaviors of 18Ni maraging steel with different tensile strength in the stress ratio range from 0.1 to 0.5 are investigated, and compared with those at the stress ratio of −1. It is found that the relationship between the fatigue strength at the stress ratios of −1 and 0.1 and tensile strength is nonmonotonic, while the fatigue strength at the stress ratio of 0.5 improves as the tensile strength heightens. The tensile strength corresponding to the optimal fatigue strength state would change with the variation of the stress ratio, which is related to the alteration of key factors affecting the fatigue damage. Moreover, it is found that the Walker equation: σ_aR = σ₋₁ ⋅ [(1 − R)/2]^β gives reasonable results for the influence of stress ratio on the fatigue strength of 18Ni maraging steel.     

A simple method to analyse the notch sensitivity of specimens in fatigue tests

A simple method to analyse the notch sensitivity of specimens in fatigue tests is presented. The parameter m, which can be used to measure the notch sensitivity, the nominal stress and the stress concentration factor (K_t) are used to establish the method. In order to verify the feasibility of the method, notch fatigue test results from our group and literatures were collected. The results reveal that an optimal value of parameter m does exist for each material. Life predictions indicated that the model is able to describe the life evolution for notched specimens under high cycle fatigue and low cycle fatigue tests. Because the geometry effect is accounted for K_t, the method is suitable for the conditions when the notch geometries and the absolute dimensions are similar to the tested specimens.     

A fracture mechanics and mechanistic approach to the failure of cortical bone

The fracture of bone is a health concern of increasing significance as the population ages. It is therefore of importance to understand the mechanics and mechanisms of how bone fails, both from a perspective of outright (catastrophic) fracture and from delayed/time‐dependent (subcritical) cracking. To address this need, there have been many in vitro studies to date that have attempted to evaluate the relevant fracture and fatigue properties of human cortical bone; despite these efforts, however, a complete understanding of the mechanistic aspects of bone failure, which spans macroscopic to nanoscale dimensions, is still lacking. This paper seeks to provide an overview of the current state of knowledge of the fracture and fatigue of cortical bone, and to address these issues, whenever possible, in the context of the hierarchical structure of bone. One objective is thus to provide a mechanistic interpretation of how cortical bone fails. A second objective is to develop a framework by which fracture and fatigue results in bone can be presented. While most studies on bone fracture have relied on linear‐elastic fracture mechanics to determine a single‐value fracture toughness (e.g., K_c or G_c), more recently, it has become apparent that, as with many composites or toughened ceramics, the toughness of bone is best described in terms of a resistance‐curve (R‐curve), where the toughness is evaluated with increasing crack extension. Through the use of the R‐curve, the intrinsic and extrinsic factors affecting its toughness are separately addressed, where ‘intrinsic’ refers to the damage processes that are associated with crack growth ahead of the tip, and ‘extrinsic’ refers to the shielding mechanisms that primarily act in the crack wake. Furthermore, fatigue failure in bone is presented from both a classical fatigue life (S/N) and fatigue‐crack propagation (da/dN) perspective, the latter providing for an easier interpretation of fatigue micromechanisms. Finally, factors, such as age, species, orientation, and location, are discussed in terms of their effect on fracture and fatigue behaviour and the associated mechanisms of bone failure.     

Experimental research on the behaviour of high frequency fatigue in concrete

Calculating the fatigue strength of concrete under the cyclic load of vehicles when designing bridges is an issue which is receiving more and more attention from many engineers and researchers. Based on this fact, fatigue tests of plain concrete under constant-amplitude and stepping-amplitude cyclic loads were conducted. The mechanism which damages plain concrete specimens under high frequency fatigue loads was analysed and a non-linear accumulative fatigue formula that causes the damage was proposed. A fatigue equation P–S–N that considers the failure probability p′ was given. The results of this research are a good preparation for further studies into high frequency fatigue tests of concrete cylinders reinforced with carbon fibre.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Standing contact fatigue

A novel experimental method for testing the resistance of a material to contact fatigue, called standing contact fatigue (SCF), is presented. It comprises a spherical indenter, repeatedly pressed onto a plane specimen in pure normal contact without lubrication, friction or wear. The SCF method is here applied to three case-hardened steels, and results in ring/cone cracks initiated at the surface. The connection between SCF and spalling is discussed. The experimental results are presented in the form of P–N curves, where P is the normal contact load and N the number of cycles required for fatigue crack initiation. The experimental results are supported by numerical simulations of the tests. The elasto-plastic properties of case-hardened materials are graded, i.e. functions of the depth from the carburized surface. The gradation is estimated from independent experiments and is included in the analysis.     

New method for determining P‐S‐N curves in terms of equivalent fatigue lives

A new method for determining the P‐S‐N curves is proposed by the probabilistic analysis of the mixed samples that are composed of the testing fatigue lives and equivalent fatigue lives. The equivalent fatigue lives at each level are converted from all the testing data at all the testing levels according to the equivalent fatigue failure probability, where the life distributions are determined by the medians of logarithmic fatigue lives at respective levels and a unified coefficient of variation. Comparison results of the P‐S‐N curves of 2024‐T3 and A356.0‐T6 alloys with the different methods indicate that the new method can determine the high‐precision P‐S‐N curves with different sample sizes of the S‐N testing data, and can save testing time and improve testing efficiency, especially for the situation of large‐scatter S‐N testing data.     

X-ray analysis of polycrystalline aluminium subjected to fatigue cycling

Variations in the halfwidth values of X-ray reflections from fatigue-cycled, polycrystalline aluminium samples have been analysed. An oscillatory variation of the halfwidths with fatigue cycling has been observed. Analysis of the diffraction line profiles indicates that broadening arises mainly because of the build-up of microstrains during fatigue cycling. The present data indicate that (i) broadening due to fatigue cycling increases with glancing angle; (ii) changes in halfwidth and integral widths, due to fatigue cycling, are comparable and (iii) (b/b ₀) versusN curves for fatigue cycling under constant stress amplitude and flight loading conditions are comparable.     

Influence of transverse load on the high cycle fatigue behaviour of low pressure cast AZ91 magnesium alloy

A new testing procedure, employing transverse load was adopted to investigate the high cycle fatigue behaviour of low pressure cast AZ91 magnesium alloy. The tests were conducted with an electro dynamic shaker system by employing specimens fabricated as per ASTM standard. S–N plot was generated from the test results and compared with that of gravity cast AZ91 alloy tested in identical ambience. The influence of transverse load on the fatigue behaviour of these alloys is discussed. As fatigue cracks were found to have initiated in pores in most of the tested samples, pores were assumed as initial cracks as per linear fracture mechanics and the critical stress intensity amplitude (K_cr) was estimated. Structure–fatigue property correlations are discussed using fractographs. Mean stress effect on the fatigue properties and effects of alloying constituents are also discussed.     

Relations between fatigue strength and other mechanical properties of metallic materials

The relations between fatigue strength and other mechanical properties especially the tensile strength of metallic materials are reviewed. After analyzing the numerous fatigue data available, the qualitative or quantitative relations between fatigue strength and hardness, strength (tensile strength and yield strength) and toughness (static toughness and impact toughness) are established. Among these relations, the general relation between fatigue strength σ_w and tensile strength σ_b, σ_w = σ_b(C ? P ? σ_b), where C and P are parameters, (hereafter, the general fatigue formula) can well predict the fatigue strength with increasing the tensile strength in a wide range for many materials such as conventional metallic materials, newly developed materials and engineering components. On the basis of the experimental results of many materials, the fatigue damage mechanism, especially for high‐strength steels, is proposed. It is suggested that the general fatigue formula can provide a new clue to predict the fatigue strength and design the materials by adjusting material parameters P and C adequately.     

Mechanical fatigue of Sn-rich Pb-free solder alloys

Recent fatigue studies of Sn-rich Pb-free solder alloys are reviewed to provide an overview of the current understanding of cyclic deformation, cyclic softening, fatigue crack initiation, fatigue crack growth, and fatigue life behavior in these alloys. Because of their low melting temperatures, these alloys demonstrated extensive cyclic creep deformation at room temperature. Limited amount of data have shown that the cyclic creep rate is strongly dependent on stress amplitude, peak stress, stress ratio and cyclic frequency. At constant cyclic strain amplitudes, most Sn-rich alloys exhibit cycle-dependent and cyclic softening. The softening is more pronounced at larger strain amplitudes and higher temperatures, and in fine grain structures. Characteristic of these alloys, fatigue cracks tend to initiate at grain and phase boundaries very early in the fatigue life, involving considerable amount of grain boundary cavitation and sliding. The growth of fatigue cracks in these alloys may follow both transgranular and intergranular paths, depending on the stress ratio and frequency of the cyclic loading. At low stress ratios and high frequencies, fatigue crack growth rate correlates well with the range of stress intensities or J-integrals but the time-dependent C* integral provides a better correlation with the crack velocity at high stress ratios and low frequencies. The fatigue life of the alloys is a strong function of the strain amplitude, cyclic frequency, temperature, and microstructure. While a few sets of fatigue life data are available, these data, when analyzed in terms of the Coffin–Mason equation, showed large variations, with the fatigue ductility exponent ranging from −0.43 to −1.14 and the fatigue ductility from 0.04 to 20.9. Several approaches have been suggested to explain the differences in the fatigue life behavior, including revision of the Coffin–Mason analysis and use of alternative fatigue life models.     

Fatigue crack growth from small defects under out-of-phase combined loading

A modified linear elastic fracture mechanics analysis is presented for the evaluation of the crack growth and threshold behavior of small cracks initiated from small defects under combined loading fatigue. For the detailed evaluation of the behavior of small fatigue cracks, the Kitagawa effect, the elastic–plastic behavior of cracks in biaxial stress fields and crack closure effects are taken into account. In-phase and out-of-phase combined tension and torsion fatigue tests were conducted using annealed carbon steel specimens containing small holes. The direction of crack propagation, S–N curves and fatigue limits were found to be in good agreement with the theoretical predictions.     

Low and high‐cycle fatigue properties of an ultrahigh‐strength TRIP bainitic steel

The scope of this study is to characterize the mechanical properties of a novel Transformation‐Induced Plasticity bainitic steel grade TBC700Y980T. For this purpose, tensile tests are carried out with loading direction 0, 45 and 90° with respect to the L rolling direction. Yield stress is found to be higher than 700 MPa, ultimate tensile strength larger than 1050 MPa and total elongation higher than 15%. Low‐cycle fatigue (LCF) tests are carried out under fully reverse axial strain exploring fatigue lives comprised between 10² and 10⁵ fatigue cycles. The data are used to determine the parameters of the Coffin–Manson as well as the cyclic stress–strain curve. No significant stress‐induced austenite transformation is detected. The high‐cycle fatigue (HCF) behaviour is investigated through load controlled axial tests exploring fatigue tests up to 5 × 10⁶ fatigue cycles at two loading ratios, namely R = ?1 and R = 0. At fatigue lives longer than 2 × 10⁵ cycles, the strain life curve determined from LCF tests tends to greatly underestimate the HCF resistance of the material. Apparently, the HCF behaviour of this material cannot be extrapolated from LCF tests, as different damage, cyclic hardening mechanisms and microstructural conditions are involved. In particular, in the HCF regime, the predominant damage mechanism is nucleation of fatigue cracks in the vicinity of oxide inclusions, whereby mean value and scatter in fatigue limit are directly correlated to the dimension of these inclusions.     

A method to develop a unified fatigue life prediction model for filled natural rubbers under uniaxial loads

Rubber components are widely used in many fields because of their superior elastic properties. Fatigue failures, commonly encountered in rubber components, however, remain a critical issue. In this study, the effect of strain ratio R on the fatigue life of filled natural rubbers used in automotive mounts is investigated experimentally and numerically. A uniaxial tension/compression fatigue experiment was conducted on dumb‐bell cylindrical rubber specimens subject to loads representing different R ratios. The experimental fatigue data are used to formulate two preliminary fatigue models based on peak strain and strain amplitude as the damage parameters. The deficiencies of these two models in predicting fatigue life over a wide range of R ratios are discussed, and an alternative life prediction model is proposed. The proposed model incorporates the effect of R ratio using an equivalent strain amplitude. It is shown that the proposed model could effectively predict fatigue life over a wide range of R ratios with an improved accuracy.