Size Evolution of the Surface Short Fatigue Cracks of 1Cr18Ni9Ti Weld Metal

Size evolution of the surface short fatigue cracks of iCrl8Ni9Ti weld metal was investigated. A local viewpoint is applied to be agreement with a so-called “effectively short fatigue crack criterion”. Attention was paid to the dominant effectively short fatigue crack (DESFC) initiation zone and the zones ahead of the DESFC tips. The results revealed that the evolutionary size shows a significant character of microstructural short crack (MSC) and physical short crack (PSC) stages. In the MSC stage, fatigue damage is due to mainly the initiation and irregular growth of the effectively short fatigue cracks (ESFCs). In the PSC stage, the damage is conversely due to mainly the DESFC growth and partially, the growth of the ESFCs and the coalescence of the ESFCs themselves with the DESFC. The process involves from a non-ordered/chaotic state in the initiation of MSC stage, gradually to an independently random state at the transition point between the MSC and PSC stages and then, to an ordered/history-dependent random state. Interactive effect of the collective cracks is stronger and shows an increase in the MSC stage. It reaches a maximum value at the transition point and then, tends to a decrease in the PSC stage. The DESFC acts as a result of the interactive cracks and thus, is deemed suitable to describe the behaviour of collective cracks.     

The evolution of short fatigue crack lengths and crack density: two approaches

The density and size of short cracks on the surface of 1Cr18Ni9Ti stainless steel smooth specimens during low cycle fatigue are investigated using a replica technique. The density and size data are analysed from two different observation policies, i.e. Policy I pays attention to the whole specimen test piece and Policy II is related to an ‘effective short fatigue crack criterion’, which pays attention to the dominant crack (DC) initiation zone and the zones ahead of the DC tips. The results reveal that both the crack density and crack size evolution exhibit a specific character during the microstructural short crack (MSC) and physical short crack (PSC) stages. The Policy I‐based observations exhibit an increasing density and little scatter of the density data. The increasing density violates the general test observation of decreasing collective crack effects in the PSC stage. The little scatter is too small to reflect the intrinsic scatter of fatigue properties. Both the crack density and crack size evolution from this policy show little relationship with the intrinsic localization of fatigue damage. However, Policy II‐based observations show an increasing crack density and an increasing density scatter in the MSC stage. The density and scatter reach their maximum values at the transition point between the MSC and PSC stages. Then, they decrease with fatigue cycling in the PSC stage and tend to their saturation values when the DC size is above about 500 μm. This behaviour shows a good agreement with the general test observations of decreasing collective crack effects and growth rate scatter in the PSC stage. Further, both approaches exhibit an evolutionary positively skewed crack size distribution, and an increasing difference between the average crack length and the DC length in the PSC stage, indicative of decreasing collective crack effects. A three‐parameter Weibull distribution (3‐PWD) is appropriately used to describe the crack sizes and a 6.5 to 7.6 μm value of location parameter of the distribution is obtained to reflect a minimum value for the initial cracks. It is worth noting that Policy I‐based observations show an increasing positively skewed crack size distribution, an increasing scatter of the size data and a decreasing shape parameter of the 3‐PWD. This represents an increasing collective crack effect and an increasing irregularity of interactive cracks, which violates the general test observations. In contrast, Policy II‐based observations exhibit a decreasing positively skewed size distribution shape and an increasing (from <1 gradually to >1) shape parameter of the 3‐PWD that is in agreement with the general test observations. The increasing shape parameter indicates that the collective crack effects act as an evolutionary process from an initial non‐ordered (chaotic) random state gradually to an independent random state at the transition point between the MSC and PSC stages and then, to a loading history‐dependent random state. This behaviour is in accordance with the evolutionary DC growth behaviour. Therefore, the evolutionary short crack behaviour associated with the intrinsic localization of fatigue damage should be appropriately revealed from the ‘effective short fatigue crack criterion’‐based observations.     

Interaction and evolution of short fatigue cracks

Distinguishing the different contributions to fatigue damage of short cracks having different sizes and locations on the specimen surface, three new concepts, referred to as effective short fatigue cracks (ESFCs), dominant effective short fatigue cracks (DESFC), and density of ESFCs, respectively, are introduced to facilitate an understanding of the mechanism of interaction and evolution of short cracks. These concepts are interrelated and in conjunction produce an 'effective short fatigue crack criterion'. Replica observations of 19 smooth axial specimens of 1Cr19Ni9Ti stainless steel weld metal during low-cycle fatigue tests reveal that the short cracks contribute to the fatigue damage of specimens due to the formation of a critical density of ESFCs. The density reflects the local microstructural growth conditions ahead of the DESFC tips. The DESFC behaviour is a result of interactive short cracks, and this behaviour is deemed suitable to describe the collective behaviour of short cracks. In the microstructural short-crack stage, the DESFC are located in the weakest zone. Due to an irregular microstructural barrier effect, the crack density is higher in this zone and increases with fatigue cycling to reach a maximum value at the transition point into the physical short-crack stage. Then, due to the effects of accelerating coalescence and the DESFC size shielding the formation of new cracks, the density decreases rapidly and tends gradually to a saturation value. This is why the short-crack growth rate is high initially and tends gradually to that of long-crack behaviour. The difference and change in local microstructural growth conditions ahead of DESFC tips are the intrinsic cause of the statistical behaviour of short cracks and the scatter of fatigue lives.     

Simulations and experiments of stochastic characteristics for collective short fatigue cracks in steels

ABSTRACT Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.     

Characterisation and quantification of multiple crack growth during low cycle fatigue

The collective growth of multiple microcracks (or short cracks) during low cycle fatigue of polycrystalline Cu–30%Zn, 316L and Fe–26Cr–1Mo is investigated. Scanning electron microscopy is employed to study the evolution of surface microcrack populations, as well as the growth of individual cracks, on smooth specimens cyclically deformed at constant plastic strain amplitudes. The damage accumulation process is quantified by construction of so-called damage accumulation (DA) profiles, which reveal important information about crack growth mode, crack initiation rates, strain localisation and crack coalescence. In addition, experimentally measured microcrack growth is quantified in terms of general crack growth relations. The uniformity of these relations for different materials indicates that growth barriers dictate the main differences in fatigue microcrack growth.     

基于微缺陷成核序列的岩石微裂纹生长和损伤演化模型

岩石在承载之初,由于微缺陷无序成核和有限生长,在材料内部形成大量分布性微裂纹。在该文中,这种演化机制被归结为:微缺陷随机、孤立成核生成最小微裂纹和微缺陷无重叠聚集成核、排列生长形成大尺度微裂纹,裂纹尺度生长是微缺陷成核数的函数。利用微裂纹尺度-频数分布分形以及微裂纹粗糙表面分形,建立基于微缺陷累计成核数序列的裂纹尺度生长模型和损伤演化模型。通过对二维岩石试件破坏过程的微裂纹尺度统计和损伤测试表明,模型的预测结果与观测值符合较好。由于微缺陷成核与声发射源机制具有相似性以及微缺陷成核数序列与声发射数序列具有相似性,所以该模型可用于通过声发射参数序列跟踪微裂纹生长和损伤演化。裂纹尺度生长对于完整认识材料宏观力学性质演化和预测材料灾变具有重要意义。     

Study on the accumulative fatigue damage rules under multiaxial two‐stage step spectra constructed by loadings with similar lives

In this paper, the influence on the multiaxial fatigue damage accumulation caused by loading path variation was studied. For 2024‐T4 aluminium alloy, the damage evolution during the entire life was first observed. On the basis of the observation, the stage I of fatigue damage evolution was further divided into two sub‐stages, and the dominant stress parameters of these two sub‐stages were proposed. Taking the dominant stress parameters into account, a phased accumulative fatigue damage model was proposed. Then, 12 multiaxial two‐stage step spectra constructed by loadings with approximately identical fatigue lives were carried out on 2024‐T4 aluminium alloy. The accumulative fatigue damage was calculated by the proposed model, and another five commonly used models and the calculated results were compared. According to the comparison, the newly proposed model had the most accurate results with the smallest scatter.     

Fatigue cracks nucleation on steel, acoustic emission and fractal analysis

In this paper, a new acoustic emission (AE) diagnostic technique, for the study of fatigue cracks nucleation and propagation on steel, was investigated. Using the fractal analysis, and the box-counting method (BCM) in particular, it is possible to characterize the spatial distribution of the prime AE sources through the fractal dimension (D) that evolve with the number of fatigue cycles (N) of the specimen. D–N curves were found useful to identify the condition of incipient collapse due to the nucleation and propagation of fatigue cracks on steel. It is possible to use the fractal dimension as a damage parameter. In all tested specimens, the crisis occurs within the same range of values of fractal dimension. The results suggest that it is possible to anticipate the detection of crack beginning relating to the other theoretical or experimental techniques.     

An investigation of the damage mechanisms and fatigue life diagrams of flax fiber-reinforced polymer laminates

In this paper we investigated the fatigue damage of a unidirectional flax-reinforced epoxy composite using infrared (IR) thermography. Two configurations of flax/epoxy composites layup were studied namely, [0]₁₆ unidirectional ply orientation and [±45]₁₆. The high cycle fatigue strength was determined using a thermographic criterion developed in a previous study. The fatigue limit obtained by the thermographic criterion was confirmed by the results obtained through conventional experimental methods (i.e., Stress level versus Number of cycles to failure). Furthermore, a model for predicting the fatigue life using the IR thermography was evaluated. The model was found to have a good predictive value for the fatigue life. In order to investigate the mechanism of damage initiation in flax/epoxy composites and the damage evolution, during each fatigue test we monitored the crack propagation for a stress level and at different damage stages, a direct correlation between the percentage of cracks and the mean strain was observed.     

Mechanical properties of concrete to cyclic uniaxial tensile loading using variable waveforms

The mechanical properties of concrete under cyclic tensile loading using square waveform, sine waveform and ramp waveform are studied. The experiments are performed on a closed-loop electro-hydraulic servo-controlled material testing system (MTS). The axial strain, dissipated energy per loading cycle, the damage evolution law and deformation modulus are mainly studied. The results show that the three-stage evolution law of axial strain and damage variable of concrete under ramp waveform and sine waveform are more obvious than those under the square waveform. The dissipated energy changes at different stages of fatigue life. At the beginning and end of the fatigue life, the rate of dissipated energy is higher than that at the medium stage of the fatigue time, which is attributed to the formation of cracks. The evolution of deformation modulus of concrete subjected to cyclic tensile loading using three loading waveforms also shows three stages: fast increase in the damage—increase at a slow constant rate—and accelerated increase in damage until failure.     

Evaluating formal properties of feature diagram languages

Feature diagrams (FDs) are a family of popular modelling languages, mainly used for managing variability in software product lines. FDs were first introduced by Kang et al. as part of the feature-oriented domain analysis (FODA) method back in 1990. Since then, various extensions of FODA FDs were devised to compensate for purported ambiguity and lack of precision and expressiveness. Recently, the authors surveyed these notations and provided them with a generic formal syntax and semantics, called free feature diagrams (FFDs). The authors also started investigating the comparative semantics of FFD with respect to other recent formalisations of FD languages. Those results were targeted at improving the quality of FD languages and making the comparison between them more objective. The previous results are recalled in a self-contained, better illustrated and better motivated fashion. Most importantly, a general method is presented for comparative semantics of FDs grounded in Harel and Rumpe's guidelines for defining formal visual languages and in Krogstie et al.'s semiotic quality framework. This method being actually applicable to other visual languages, FDs are also used as a language (re)engineering exemplar throughout the paper.     

Effect of retained austenite – Compressive residual stresses on rolling contact fatigue life of carburized AISI 8620 steel

In this study the rolling contact fatigue (RCF) of case carburized AISI 8620 steel was numerically and experimentally investigated. For the numerical study, a two dimensional finite element (FE) RCF model based on the continuum damage mechanics (CDM) was developed to investigate the fatigue damage accumulation, crack propagation and final fatigue life of carburized AISI 8620 steel under various operating conditions. A randomly generated Voronoi tessellation was used to model the effects of material microstructure topology. The boundaries of the Voronoi elements were assumed to be the weak planes where damage accumulates, cracks initiate and propagate to simulate inter-granular cracks. A series of torsional fatigue tests were conducted on carburized AISI 8620 steel specimens containing 0% and 35% retained austenite (RA) to determine fatigue load (S) vs. life (N) of the material. The S–N results were then used to determine the material parameters necessary for the rolling contact fatigue model. The torsional fatigue test results indicate that the carburized AISI 8620 specimens with higher RA demonstrate higher life than the specimens with lower RA. The RCF model also indicates that the material with higher level of compressive residual stresses (RS) and retained austenite demonstrates higher RCF life. In order to corroborate the results of RCF model, a three-ball-on-rod rolling contact fatigue test rig was used to determine the RCF lives of carburized AISI 8620 steels with different amounts of RA. The fatigue life and cracks evolution pattern from the numerical and experimental results were corroborated. The results indicate that they are in good agreement.     

Non-destructive assessment of the fatigue strength and damage progression of satin woven fiber reinforced polymer matrix composites

The aim of this study is to utilize infrared thermography to assess the critical damage states, and to capture the evolving damage processes, of 5HS and 8HS woven carbon fiber/epoxy composites subjected to uniaxial in-plane tensile quasi-static and fatigue loading. Quasi-static test results revealed that the dominant damage mechanisms were matrix cracks contained within the weft yarns, which initiated at the thermally-detected material thermoelastic limit and were confirmed through SEM observations. An established thermographic technique was also used to confirm the existence of a high cycle fatigue limit, which may in fact be a characteristic of all fabric reinforced polymeric composites. Temperature profiles captured during cyclic testing directly correlated with corresponding stiffness degradation profiles, providing support for thermography as an accurate fatigue damage metric. The infrared camera was able to detect the evolution of weft yarn cracking during the initial stage, as well as the initiation and growth of interply delamination cracking during the final stage of three-stage cyclic damage evolution. The reported results and observations provide an important step in the validation of thermography as a powerful non-destructive tool for assessing the development of damage, as well as predicting the critical damage states of fiber reinforced polymeric composite materials.     

含多处损伤宽板螺接搭接件疲劳寿命研究

对含多处损伤（Multiple Side Damage,MSD）宽板搭接件做了等幅疲劳试验和断口分析,得到搭接件的疲劳寿命和孔边MSD裂纹的形成特点、裂纹前沿形状及扩展历程。结果表明,搭接件的疲劳破坏具有一定的隐蔽性,其疲劳寿命的绝大部分消耗在螺栓头下裂纹扩展阶段,当孔间裂纹出现首次连通时,搭接件剩余寿命约为总寿命的0.7%~9.4%。基于有限元软件FRANC2D/L和裂纹扩展分析软件AFGROW,建立了考虑钉载、第二弯矩和孔间裂纹干涉等影响因素的含MSD宽板搭接件疲劳寿命计算模型,并对孔边多裂纹的扩展寿命进行了计算分析。计算结果与试验结果的对比表明,该文所建寿命计算模型具有一定的精度,能满足工程需要,计算结果和结论可作为该类结构损伤容限设计的参考依据。     

Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals

Threshold condition and rate of fatigue crack growth appear to be significantly affected by the degree of deflection of cracks. In the present paper, the reduction of the fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared to that for a straight counterpart is quantified via the Paris–Erdogan law modified according to some simple theoretical arguments. It is shown that such a reduction increases as the value of the kinking angle increases. Then, a so-called ‘continuously-kinked crack’ (the kink length tends to zero) is considered and modelled as a self-similar invasive fractal curve. The sequence of kinking angles in the crack is such that the fatigue crack path is ‘on average’ straight. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. It is shown that the fatigue crack growth rate in the Paris range depends not only on the above fractal dimension and in turn on the kinking angle, but also, in an explicit fashion, on the crack length. Some experimental results related to concrete and showing a crack size effect on the fatigue crack growth rate are analysed.     

Prediction of fretting fatigue crack initiation in double lap bolted joint using Continuum Damage Mechanics

In fretting fatigue, the combination of small oscillatory motion, normal pressure and cyclic axial loading develops a noticeable stress concentration at the contact zone leading to accumulation of damage in fretted region, which produces micro cracks, and consequently forms a leading crack that can lead to failure. In fretting fatigue experiments, it is very difficult to detect the crack initiation phase. Damages and cracks are always hidden between the counterpart surfaces. Therefore, numerical modeling techniques for analyzing fretting fatigue crack initiation provide a precious tool to study this phenomenon. This article gives an insight in fretting fatigue crack initiation. This is done by means of an experimental set up and numerical models developed with the Finite Element Analysis (FEA) software package ABAQUS. Using Continuum Damage Mechanics (CDM) approach in conjunction with FEA, an uncoupled damage evolution law is used to model fretting fatigue crack initiation lifetime of Double Bolted Lap Joint (DBLJ). The predicted fatigue lifetimes are in good agreement with the experimentally measured ones. This comparison provides insight to the contribution of damage initiation and crack propagation in the total fatigue lifetime of DBLJ test specimens.     

Analysis of fatigue crack behaviour based on dynamic response simulations and experiments for tensile-shear spot-welded joints

Fatigue crack initiation and propagation behaviours were studied based on the dynamic response simulation by the three‐dimensional finite‐element analysis (FEA) and dynamic response experiments for tensile‐shear spot‐welded joints. The entire fatigue propagation behaviour from the surface elliptical cracks at the initiation stage to the through thickness cracks at the final stage was taken into consideration during the three‐dimensional FEA dynamic response simulations. The results of the simulations and experiments found that the fatigue cracks of spot‐welded joint from initial detectable crack sizes to crack propagation behaviour could be described by three stages. Approximately one‐half of the total fatigue life was taken in stage I, which includes micro‐crack nucleation and the small crack growth process; 20% of the total fatigue life in stage II, in which the existing surface crack propagates through the thickness of sheet and 30% of the total fatigue life in stage III, during which the through thickness crack propagates along the direction of plate width to the final failure. According to the relationship between the crack length and depth and the dynamic response frequency during the simulated fatigue damage process, the definition of fatigue crack initiation and propagation stages was proposed. The analysis will provide some information for the fatigue life prediction of the spot‐welded structures.     

A statistical model of fatigue damage evolution in particulate-reinforced metal-matrix-composites

A statistical model of fatigue damage evolution has been developed for particulate-reinforced metal-matrix-composites (MMCs) by taking into considerations both the initial damage distribution and the effect of particulate reinforcement on fatigue damage development. The growth of microscopically fatigue-damaged regions in particulate-reinforced MMCs is considered as a stochastic process, and both the non-equilibrium statistical method and minimum strength principle are used to establish the evolution equation of fatigue damage. The fatigue damage evolution equation developed in the present study characterizes not only the kinetic process of fatigue damage evolution but also sets up the relationship between the mechanism of fatigue damage growth of the microscopically damaged regions and the result of fatigue damage, i.e. degradation of mechanical properties of particulate-reinforced MMCs. A new expression for calculating the cumulative fatigue damage and a new formula for predicting the average fatigue strength of the particulate-reinforced MMCs are derived. Experimental data of 2080Al/SiC_p composites are analysed and compared with results obtained with the present model. It is shown that the experimental results can be described well by the calculations.     

Microstructural effects on the short crack behaviour of a stainless steel weld metal during low-cycle fatigue

An experimental study into microstructural effects on short fatigue crack behaviour of 19 stainless steel weld metal smooth specimens during low-cycle fatigue is performed by a so-called ‘effective short fatigue crack criterion’. This material has a mixed microstructure in which it is difficult to distinguish the grains and measure the grain diameter. The columnar grain structure is made up of matrix-rich δ ferrite bands, and the distance between the neighbouring rich δ ferrite bands is an appropriate measurement for characterizing this structure. Particularly, the effective short fatigue cracks (ESFCs) always initiate from the bands of δ ferrite in the matrix in the weakest zone on one of the specimen surface zones which is orientated in accordance with the inner or outer surface of welded pipe from which the specimens were machined. These cracks exhibit characteristics of the microstructural short crack (MSC) and the physically small crack (PSC) stages. The average length of the ESFCs at the transition between MSC and PSC behaviour is ≈40 μm, while the corresponding fatigue life fraction is ≈0.3 at this transition. Different from previous test observations, the growth rate of the dominant effective short fatigue crack in the MSC stage still shows a decrease with fatigue cycling under the present low-cycle fatigue loading levels. A statistical evolution analysis of the growth rates reveals that the short fatigue crack growth is a damage process that gradually evolves from a non-ordered (chaotic) to a perfectly independent stochastic process, and then to an ordered (history-dependent) stochastic state. Correspondingly, the microstructural effects gradually evolve from a weak effect to a strong one in the MSC stage, which maximizes at the transition point. In the PSC stage, the effects gradually evolve from a strong to weak state. This improves our understanding that the short crack behaviour in the PSC stage is mainly related to the loading levels rather than microstructural effects.