A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

[±20°]钢丝/橡胶复合材料的疲劳损伤累积

对 钢丝帘线增强的橡胶复合材料在拉伸循环载荷下的疲劳损伤累积进行了研究。结果表明:在载荷控制的疲劳过程中,材料的周期最大应变发展曲线呈现明显的三阶段规律。帘线端头处基体裂纹的出现是宏观疲劳损伤的初始,损伤的累积表现为裂纹数量增加、帘线/基体脱粘和层间裂纹的扩展。以动蠕变为参量建立了线性疲劳损伤累积模型,该模型能够较好地预报两级加载条件下材料的第二级疲劳寿命。     

Fatigue Damage Accumulation of Steel/rubber Composite

The fatigue damage accumulation of [±20°] laminated steel cord reinforced rubber composite under T-T loading was studied. Results indicate that the increase in the cyclic maximum strain exhibits three-stage tendency in the process of fatigue. The macroscopic fatigue damage initiates from the ends of steel cords in the form of cylindrical crack. Damage propagates along with the increase in crack numbers, the cord/matrix interface debonding and the growth of interply cracks. By using the dynamic creep as parameter, a linear fatigue damage accumulation model was established. This model can be used under dual loading conditions to estimate the residual fatigue life of the specimen.     

Stochastische Simulation der Schädigungsentwicklung in einem martensitischen Stahl

A probabilistic simulation model was developed for damage accumulation in the martensitic steel F82H‐mod under fatigue loading. Empirical relations for crack initiation, crack growth and coalescence of cracks are derived from an observation of experimental crack patterns and inserted in a stochastic simulation model based on a random cell structure. The simulation results are compared with the experimentally observed crack patterns.     

Simulation des Mikrorisswachstums unter Schwingbeanspruchung. Teil 1: Modell und Simulationsergebnisse,Mikrorisswachstum, Streuung,Einfluss von Beanspruchungsart und ‐höhe,Risskeimdichte und Korngröße

Simulation of fatigue microcrack growth. Part 1: Modelling and results of simulation, microcrack growth, scatter, effect of load condition, density of microcrack seeds and grain size Presented is a simulation of microcrack growth under alternating stresses. Microstructural barriers and the state of stress play a dominant role in the early stages of crack growth of metals. The polycristalline metal was modeled as an aggregat of hexagonal grains with a different crystallographic orientation of each grain. The effect of grain bounderies on stage I crack growth is considered in the model. The mode of shear crack growth is analyzed on the basis of microstructural crack growth within the first few grains, where the crack growth decelerates as the crack tip gets closer to the grain boundery. Normal stress crack growth has been considered for those cracks which are longer than microstructurelly short cracks, so‐called physically small cracks. Furthermore the transition from stage I to stage II growth is considered. The model is applied for thinwalled tubular specimens of the ferritic steel AlSI 1015 and the aluminium alloy Al Mg Si 1 subjected to tension and torsion as well as combined tension‐torsion loading. Also different load sequences are investigated. The microstructural crack pattern and crack distribution can sucessfully simulated with the model. The crack growth behaviour and the effect of lifetime until a crack length of 500 μm ist presented for numerous parameters.     

Microcrack growth and fatigue behavior of a duplex stainless steel

The kinetics of microcrack growth during cycling has been studied in a S32205 duplex stainless steel in the as-received and aged (100 h at 475 °C) conditions. Cylindrical specimens with a shallow notch were subjected to a constant plastic strain range of 0.3% in both thermal conditions. The characteristic features of surface damage and crack growth showed striking differences in microcrack density, nucleation location and propagation rate between the two thermal conditions even though the fatigue lives are comparable. In the as-received material, microcrack density is low and they nucleate mainly at grain and phase boundaries or second-phase particles. In the aged condition, slip markings first appear in the ferritic phase and they are the preferred site for microcrack nucleation. Crack propagation takes place along slip markings in adjacent grains for crack lengths less than 100 μm. A comparison between fatigue life and the relevant parameters of a microcrack growth law was made.     

Low-cycle fatigue model of damage accumulation - The strain approach

The paper presents a model of damage accumulation designed to analyse fatigue life of structural elements exploited in multiaxial, non-proportional, low-cycle loading conditions. The discussed approach consists of two calculation blocs. In the first bloc the components of stress and strain tensor are determined. This module, in which Mroz’s multisurface model was used, contains constitutive relations and the law of kinematic hardening. The second bloc contains the dependencies which determine the growth of anisotropic measure of damage accumulation (associated with the physical plane) and crack initiation criterion. The growth of the damage accumulation measure was associated with the loading damage accumulation function and the increment of non-dilatational plastic strain on the physical plane. It was assumed that crack initiation occurs when stress or a measure of damage accumulation on any physical plane reaches critical values.     

Damage evolution around white etching layer during uniaxial loading

Rolling contact fatigue cracks and thermally induced defects are common problems in the railway industry especially as demands for increasing loads, speeds, and safety continue to rise. Often, the two types of defects are found together in the field, however, whether one causes the other to occur is not completely agreed upon. The effect of thermal damage, in the form of a martensite spot on pearlitic steel test bars, on the fatigue life in uniaxial low cycle fatigue experiments was investigated by the authors. However, the focus of the current work was to characterize the damage evolution from the low cycle fatigue (LCF) tests and correlate the crack initiation and propagation with the initial thermal damage. Residual stress measurements, digital image correlation, and X‐ray tomography were used to characterize the effects of the thermal damage before, during, and after fatigue testing, respectively. It was found that the thermal damage causes strain accumulation and crack initiation at the interface between the two materials. The strain evolution was visualized using digital image correlation (DIC), clearly showing the strain concentrations at the top and bottom of the white etching layers (WEL), where the residual stresses are also most tensile. X‐ray tomography confirmed the planar crack growth from the martensite spot.     

THE EFFECT OF HYDROGEN ON SHORT FATIGUE CRACK GROWTH IN AN Al-Li ALLOY

Abstract— Experimental results are presented to illustrate the degree of susceptibility to hydrogen embrittlement in an Al-Li 8090 alloy. The ductility of the alloy (as recorded in slow strain rate tests) is reduced by hydrogen charging which induces microcrack formation on the surface of the hydrogen treated specimens. Results of fatigue tests show that small fatigue cracks propagate 1.5 to 10 times faster in specimens charged with hydrogen and fractographic evidence shows that short crack growth in hydrogen precharged specimens is transgranular, along persistent slip bands. The effect of hydrogen is reversible, the embrittlement effect being eliminated by holding the specimens for 24 hr at 470°C.     

Total Fatigue Life Estimation of Notched Structural Components Using Low‐Cycle Fatigue Properties

Abstract: In this investigation, an efficient fatigue life computation method under variable amplitude loading of structural components has been proposed. Attention in this study is focused on total fatigue life estimation of aircraft structural components. Flat specimens with central hole made of quenched and tempered steel 13H11N2V2MF were tested as representatives of different structural components. Total fatigue life of these specimens, defined as sum of fatigue crack initiation and crack growth life, was experimentally determined. Specimens were tested by blocks of positive variable amplitude loading. Crack initiation life was computed using theory of low‐cycle fatigue (LCF) properties. Cyclic stress–strain curve, Masing’s curve and approximate Sonsino’s curve were used for determining stress–strain response at critical point of considered specimens. Computation of crack initiation life was realised using Palmgren–Miner’s linear rule of damage accumulation, applied on Morrow’s curves of LCF properties. Crack growth life was predicted using strain energy density method. In this method, the same LCF properties were used for crack initiation life and for crack growth life computations also. Computation results are compared with own experimentally obtained results.     

Mikrorissentstehung und Mikrorisswachstum in Aluminiumlegierungen bei zyklischer Beanspruchung – Werkstoffliche Untersuchung und Simulation

Microcrack Initiation and Microcrack Growth in Aluminium Alloys Subjected to Cyclic Loading – Material Analysis and Simulation In this paper a model designed to simulate the growth of microcracks under the influence of cyclic loading is presented. Considering fatigue crack growth microstructural barriers as well as the state of stress play an essential role. The polycristalline metal was modelled as an aggregate of hexagonal grains with each of the grains showing a different crystallographic orientation. The crack growth is initially dominated by shear stresses leading to microstructurally short cracks (stage I). As the tip of the microcrack approaches a grain boundary the crack growth rate decreases. The transition from stage I to stage II crack growth is also considered in the model as the crack reaches a specific length and continues to grow under the influence of normal stresses (physically short cracks). The model is applied to tubular specimens of the aluminum alloy AlMgSi1 which are subjected to tension and torsion as well as to combined tension‐torsion loading cycles. In terms of the microcrack distribution as a function of their orientation the simulated crack growth behaviour reveals a close match with the experimental results.     

Analysis of fatigue damage evolution and associated anisotropic elastic property degradation in random short-fiber composite

A theoretical analysis of cyclic fatigue damage and associated anisotropic property degradation in a random short-fiber composite is presented. The fatigue damage takes various forms of microcracking, originated from microscopic stress concentrators in the highly heterogeneous material system. A probabilistic treatment of the microcracks is introduced to evaluate the statistical nature of the microscopic fatigue damage. Damage evolution and accumulation are analyzed through the development of probabilistic density functions of microcrack length and orientation during the cyclic loading history. Constitutive equations for the damaged fiber composite are then derived on the basis of a self-consistent mechanics scheme in conjunction with a three-dimensional elliptic crack theory and the microcrack density functions. Cyclic fatigue degradation and associated damage-induced anisotropy of composite material properties are determined and checked against experiments. The tensorial nature of material damage and composite stiffness changes during fatigue are evaluated explicitly. A power-law relationship between the rate of damage growth and the fatigue loading cycle is obtained. The rate of fatigue damage growth is found to decrease exponentially with load cycles—a phenomenon unique to the random short-fiber composite. This study provides a comprehensive analytical treatment of the homogeneous fatigue damage problem for random short-fiber composites. The fundamental mechanics and mechanisms of fatigue damage evolution and associated anisotropic property degradation of the composite are elucidated.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

基于微观结构的热喷涂WC/Co涂层裂纹生长模拟

涂层微观结构特征直接影响涂层的寿命,基于涂层微观结构研究涂层裂纹扩展特征成为评价热喷涂层性能的重要问题.本文基于WC/Co涂层微观结构建立了有限元模型,并采用XFEM方法研究了单应力状态预存裂纹行了模拟,获得了涂层微观裂纹扩展的损伤规律.研究表明:在拉应力作用下,沿着WC-Co边界产生的应力集中是涂层裂纹产生的根源;WC/Co涂层浅表面(0.125b,b为涂层厚度)的水平裂纹对垂直拉应力敏感、吸收能量快,0.78b处的裂纹扩展后对应力响应迅速,因此0.125b与0.78b是WC/Co涂层裂纹生长的关键深度;在0.78b处,当初始裂纹角度0°～45°时,扩展位移逐渐减小,扩展偏转角增大,45°时存在能量积累导致角度快速偏转.在周期应力作用时,WC/Co涂层的疲劳周期随应变幅值增加而减小;应变幅值相同时,WC/Co涂层的疲劳周期随频率增加而增加.     

Fracture analysis of turbine disks and computational–experimental background of the operational decisions

In this paper, fatigue crack growth under operation conditions for rotating disks of aircraft gas turbine engines is analyzed. Initiation and growth of surface cracks for compressor disks made from two-phase titanium alloy has occurred in a disk and blade attachment. Damage accumulation and growth for turbine disks made from steel took place on the inner surface of hole in a hub of wheel. Suggested approach of simulation modeling is used for an analysis and prevention of operation failures of engine rotating components. In the approach described, finite-element models (FEMs) in two and three dimensions were applied to the study of stress–strain state and stress intensity factors for the basic configurations of compressor and turbine disks and their operational damage. Proposed design modifications and repair technologies to existing in-service aircraft gas-turbine engine rotating components are analyzed and substantiated on a static strength and fatigue life basis.     

PLASTIC DAMAGE ANALYSIS FOR THE PROCESS ZONE OF A FATIGUE CRACK

The process zone of a mode I fatigue crack is described asymptotically with damage coupled plastic constitutive relations. A parametric study is conducted to obtain the orders and angular distribution modes of stress, strain and damage fields, as well as the profiles of the related process zones. The fatigue crack growth rate is also formulated theoretically.     

Off-axis fatigue crack growth and the associated energy release rate in composite laminates

Stable matrix crack growth behaviour under mechanical fatigue loading has been studied in a quasi-isotropic (0/90/-45/+45)_s GFRP laminate. Detailed experimental observations were made on the accumulation of cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finite element model of the damaged laminate has been constructed. This model has been used to relate the energy release rate of growing cracks to the crack growth rate via a Paris relation.     

Some Peculiarities of Fatigue Crack Growth at Various Stages of Its Development

The author considers some peculiarities of fatigue crack growth in metals at the stages of its initiation and initial development, and stable and unstable growth that precedes final fracture. It is shown that at the stage of initial growth of fatigue cracks, the stress state, nonlocalized fatigue damage that precedes initiation of the main fatigue crack, residual surface stresses, surface manufacturing and in-service defects, and contact interactions are the factors that determine the crack paths. Stable growth of a fatigue crack is primarily determined by the stress-strain state of a structure as a whole and by the stress-strain state at the crack tip with allowance for its variation due to crack propagation, which is evaluated by the criteria of fracture mechanics. The author also studied peculiarities of fatigue crack development in compressor blades of marine gas turbines. It is shown that for embrittled steels, when fatigue cracks develop under plane strain conditions, final fracture occurs at very small crack sizes. In this case, the characteristics of fatigue fracture toughness are appreciably lower than the static values. The paper also considers peculiarities of unstable fatigue crack propagation.     

Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone

As a composite material, cortical bone accumulates fatigue microdamage through the repetitive loading of everyday activity (e.g. walking). The accumulation of fatigue microdamage is thought to contribute to the occurrence of fragility fractures in older people. Therefore it is beneficial to understand the relationship between microcrack accumulation and the fracture resistance of cortical bone. Twenty longitudinally orientated compact tension fracture specimens were machined from a single bovine femur, ten specimens were assigned to both the control and fatigue damaged groups. The damaged group underwent a fatigue loading protocol to induce microdamage which was assessed via fluorescent microscopy. Following fatigue loading, non-linear fracture resistance tests were undertaken on both the control and damaged groups using the J-integral method. The interaction of the crack path with the fatigue induced damage and inherent toughening mechanisms were then observed using fluorescent microscopy. The results of this study show that fatigue induced damage reduces the initiation toughness of cortical bone and the growth toughness within the damage zone by three distinct mechanisms of fatigue–fracture interaction. Further analysis of the J-integral fracture resistance showed both the elastic and plastic component were reduced in the damaged group. For the elastic component this was attributed to a decreased number of ligament bridges in the crack wake while for the plastic component this was attributed to the presence of pre-existing fatigue microcracks preventing energy absorption by the formation of new microcracks.