A NOTE ON MODELLING SHORT FATIGUE CRACK BEHAVIOUR

Based upon experimental short fatigue crack growth data and adopting the Brown–Hobson model, new crack growth equations have been derived in an attempt to describe more precisely short fatigue crack growth behaviour that separates the physically small crack regime from the long crack regime. An empirical model for physically small crack growth was developed by employing elastic–plastic fracture mechanics parameters.
By considering the proposed approach to short fatigue crack modelling, a new second 'microstructural' threshold condition has been established using only short fatigue crack growth data. In the case of fatigue in an aggressive environment it is suggested that three transition (threshold) conditions can be identified representing: (i) a stress-assisted pitting/pit-to-crack transition; (ii) a microstructurally short shear crack/physically small tensile crack transition; and (iii) a physically small crack/long crack transition.
A comparison of this approach with that of existing models has been made, and predictions of total fatigue lifetime using the model have been presented. A reasonable agreement has been observed between predicted and experimental crack growth rates.     

HIGH TEMPERATURE SHORT FATIGUE CRACK BEHAVIOUR IN A STAINLESS STEEL

Abstract— Continuous low cycle fatigue (LCF) tests with-and without-hold time in push-pull and torsion loading modes and sequential LCF tests in push-pull mode were carried out at 650°C in air on thin tubular specimens of 316 stainless steel; the sequential tests involving pure fatigue (PF) and creep-fatigue (CF) loadings. The growth of short fatigue cracks was studied by taking several replicas from the specimen surface which were subsequently observed under a scanning electron microscope. An analysis was done with respect to both crack density and the orientation of microcracks and macrocrack(s) which led to failure.
Crack density was higher on the surface of a CF tested specimen than that of a PF tested specimen. Mainly short cracks oriented at 45° to the specimen axis were observed on a torsion fatigue tested specimen surface. For push-pull specimens the microcracks propagated perpendicular to the specimen axis to form macrocracks that propagated in the same direction. On the other hand, for torsion specimens the microcracks which initially propagated at 45° to the specimen axis linked to form macrocracks oriented parallel and perpendicular to the specimen axis. However, the macrocrack responsible for the final fracture was always oriented parallel to the specimen axis.
Cumulative damage was dependent on the type of loading (PF or CF) in the first part of sequential tests. In particular microcracks initiated during an initial damage phase observed under sequential LCF tests in PF were found to be healed by oxide formation during the hold times applied in the subsequent CF loading and this produced a total damage summation significantly larger than one.     

CYCLIC FATIGUE CRACK GROWTH AND CLOSURE BEHAVIOUR IN ALUMINA CERAMICS

Cyclic fatigue crack growth behaviour in alumina ceramics is investigated and the effect of grain size discussed. Special attention is given to crack closure effects. Cyclic fatigue tests were carried out using four-point bend specimens, and the load–strain and load–differential strain curves were monitored. These curves show hysteretic behaviour probably related to frictional sliding of bridging grains, and also include non-linearities due to crack closure. The crack opening load is determined from the load–differential strain curve by using a method introduced in this study. Growth rates can be successfully described by the relationship da/dN = C[ΔK_{eff /(1 ? Kmax /KIC )]m} which is proposed in this study to account for the effects of crack closure and the maximum stress intensity factor. Irrespective of grain size, growth rates can be well represented by the above relationship, implying that the grain size exerts an influence on growth rates not only because of crack closure behaviour but also the material fracture toughness. The growth rate curve based on the proposed relationship shows a sigmoidal form for ceramic materials, which is similar to metals.     

金属材料低温疲劳性能的预测方法

本文总结了作者近来研究金属低温疲劳取得的进展,主要内容包括:疲劳极限的热激活模型、应变疲劳公式、疲劳始裂寿命和裂纹扩展速率的定量预测方法、疲劳裂纹扩展机制脆转模型。当室温下的疲劳极限和门槛植ΔK_(th)确定后,应用本文的方法可根据拉伸性能定量预测材料在低温下的疲劳极限、应变疲劳寿命、疲劳始裂寿命和裂纹扩展速率,并且不需要低温疲劳试验和经验修正。     

低温环境下桥梁钢Q345qD疲劳裂纹扩展行为研究

为了明确在寒冷地区服役桥梁钢的疲劳裂纹扩展行为,以16 mm厚桥梁钢Q345qD为研究对象,完成了室温和低温下的夏比冲击韧性试验、疲劳裂纹扩展速率试验和疲劳裂纹扩展门槛值试验。结果表明,夏比冲击功和试样断口剪切断面率随温度的降低而减少;在应力比0.1、0.2和0.5条件下,疲劳裂纹扩展速率均随温度降低而变缓,该桥梁钢的疲劳韧-脆转变温度点在-60℃以下;在室温~-60℃,其裂纹扩展速率均对应力比的变化不敏感;应力比0.1条件下的疲劳裂纹扩展门槛值随温度的降低有略微增大的趋势。该批次桥梁钢表现出了良好的抵抗低温疲劳裂纹扩展性能,防止低温脆性破坏成为疲劳设计的重点;试验数据能为钢结构桥梁的进一步抗低温疲劳和防低温冷脆断裂设计提供参考。     

OVERLOAD RETARDATION OF FATIGUE CRACK GROWTH IN A 9%Cr 1%Mo STEEL AT ELEVATED TEMPERATURES

This paper describes an investigation into the effects of a single-peak tensile overload on fatigue crack propagation in a 9%Cr 1 %Mo steel. Overloads were applied during cycling at a constant stress intensity range (ΔK), and any consequent transients in growth rate were recorded. The severity of retardation rises as the magnitude of the applied overload is increased. The effect of temperature is complex, but a 525?C retardation is significantly less marked than at 25 or 225?C. Signs of crack face contact are seen on post-overload fracture surfaces, but there is little crack branching. The dominant cause of overload retardation in this steel appears to be plasticity-induced closure. At 525?C, post-overload dwell periods significantly reduce the severity of retardations. This is not observed at lower temperatures, indicating that the residual clamping stresses that lead to closure are gradually relieved at 525?C.     

CREEP-FATIGUE CRACK GROWTH AND FRACTOGRAPHY OF METALLIC MATERIALS IN AIR AND VACUUM AT ELEVATED TEMPERATURES

Creep-fatigue crack growth behaviour of a Type 304 stainless steel, a quenched 21/4Cr-1Mo steel, Hastelloy X, a Ti-6242 alloy, and a low carbon steel under different reversed loading patterns (P-P, C-P and C-C) were investigated in air and a vacuum environment. The results are discussed in the light of fracture mechanics and fractography. Crack growth rates for all of the materials tested were successfully correlated in terms of the cyclic J integral range (Δ J ) irrespective of the loading patterns. In the low growth rate region, where fatigue fracture was predominant, crack growth rates of all the materials were about the same for the same value of Δ J. On the other hand, growth rates were somewhat different, depending on the creep ductility of the material in the region of high growth rate, where creep fracture was predominant. Materials with lower ductility exhibited higher growth rates for the same Δ J values. Differences were insignificant between the crack growth rates in air and vacuum and were consistent with the small differences observed in the fracture surface morphology in the two environments.     

TRANSIENT FATIGUE CRACK GROWTH BEHAVIOUR FOLLOWING SINGLE OVERLOADS AT HIGH STRESS RATIOS

Fatigue crack growth tests with constant amplitude loading and single overload have been performed on a long mode I crack in 2017-T3 aluminium alloy at various stress ratios from 0 to 0.7. Two crack tip parameters of σ_op and σ_tt were evaluated using a finite element analysis for a growing crack under these loading conditions. The former is the crack opening stress and the latter is the applied stress level at which the stress at the crack tip becomes tensile. It was found that transient crack growth behaviour following single overloads at high stress ratios was significantly different from that at a low stress ratio: at higher stress ratios, following the application of the overload, there was a rapid retardation which was followed by an acceleration in growth rate and then a faster return to the steady state level at baseline loading. The experimentally observed transient post-overload behaviour is discussed in terms of the two effective stress range ratios of U_op and U_tt, which are determined from σ_op and σ_tt, respectively. For the stress ratios and overload ratios studied, the results indicate that the changes in U_tt with crack extension after the overload are reasonably consistent with the crack growth rate trends. The stress distribution at minimum applied stress would account for the transient changes in U_tt.     

THE APPLICABILITY OF NEURAL NETWORKS IN MODELLING THE GROWTH OF SHORT FATIGUE CRACKS

This paper examines the use of a neural network to model the chaotic behaviour of the growth of short fatigue cracks which are characterized by a decreasing crack growth rate with increasing crack length. Fatigue crack growth is modelled in terms of the Hobson short fatigue crack growth law. The neural network is exclusively trained and tested on Hobson's experimental data of short fatigue cracks propagating in a 0.4% carbon steel. The empirical constants d, α and C of Hobson's growth law are determined from the neural network predictions and are found to be within the following approximate ranges 63 < d < 400 (μm), −0.27 < α < 0.08 and 1 × 10⁻⁴ < C < 509 × 10⁻⁴ with no proportional relationship observed between the constant C and the applied cyclic stress. It is shown that neural networks are a viable computational tool for modelling the chaotic behaviour of short fatigue crack growth.     

THE INFLUENCE OF AGEING AT INTERMEDIATE TEMPERATURES ON THE MECHANICAL BEHAVIOUR OF A DUPLEX STAINLESS STEEL: Part II. FATIGUE LIFE AND FATIGUE CRACK GROWTH

Abstract— The mechanical behaviour of AISI 329 steel has been investigated for ageing times up to 20,000 h at temperatures of 475, 425, 375, 325 and 275°C. The study has concentrated on the changes in the response to cyclic strains, in the low-and the high-cycle fatigue regimes, and in the resistance to fatigue crack propagation as a function of temperature and time of ageing.
It is shown that ageing increases the fatigue resistance in the high-cycle fatigue regime, but the opposite occurs in the low-cycle fatigue regime. Ageing increases the LEFM threshold stress intensity factor range for fatigue crack propagation which reaches high values in these alloys, and is influenced by the fatigue load ratio. Crack closure contributes to the LEFM threshold stress intensity factor range for crack propagation only in the annealed condition of the AISI 329 steel.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

CRACK CLOSURE EFFECT ON CRACK GROWTH RATE AT 650°C IN DOUBLE NOTCHED SPECIMENS OF A NICKEL BASE SUPERALLOY

Abstract— Creep-fatigue tests were performed at 650°C in air on a N18 nickel base superalloy, using double notched and smooth specimens. The deformation mechanisms observed by TEM at the notch root are shown to be compatible with the constitutive set of equations used in the finite element analysis which is presented. For a given K _max at the notch root, the crack growth rate is much higher in a notched specimen than in a smooth one. This effect can be explained by a variation of the crack closure stress level with the local R ratio and the local stress. A strong accelerating effect of the R ratio, especially for negative values, is found in smooth specimens. Introducing a K _op correction in the experimental results leads to a good agreement between the measured crack growth rate plotted versus K _eff in notched and smooth samples.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

CRACK INITIATION AND SMALL FATIGUE CRACK GROWTH BEHAVIOUR OF SQUEEZE-CAST Al-Si ALUMINIUM ALLOYS

Abstract— Fatigue strength, crack initiation and small crack growth behaviour in two kinds of squeeze-cast aluminium alloys, AC8A-T6 and AC4C-T6 were investigated using smooth specimens subjected to rotatary-bending fatigue at room temperature. Fatigue resistance of these alloys was almost the same as that of the wrought aluminium alloys because of their fine microstructure and of the decrease in defect size due to squeeze-casting. Fatigue crack initiation sites were at the eutectic silicon particles on the surface of specimens or at internal microporosity in the specimens. Crack initiation life, defined as a crack length of 50 μm on the specimen surface, was successfully estimated from an evaluation of initiation sites using fracture mechanics and the statistics of extrema. Small fatigue crack growth in the two kinds of alloys obeys the relation proposed by Nisitani et al. , namely that d(2c)/d N = C (σ_a/σ_B)ⁿ· (2 c ), where C is a constant and σ_B is the ultimate tensile strength. It is pointed out that an improvement in fatigue strength of cast aluminium alloys can be expected by refining the eutectic silicon rather than by an increase in static strength.     

残余应力与胶粘剂对ARALL层板疲劳裂纹扩展特性的影响

研究了粘剂性质、含量及残余应力状态对纤维－铝合金胶接层板（ＡＲＡＬＬ）疲劳裂纹扩展特性的影响，分析了裂纹扩展过程中的分层状态的变化，结果表明，ＡＲＡＬＬ层板内富胶层的剪切形变和伴随裂纹扩展的分层区越大，即这两方面耗散能量越多，则疲劳裂纺扩展速率越低；胶粘剂含量的影响不明显，给层板施加预应力极大降低了层板的疲劳裂纹扩展速率，其本质在于裂尖在同样的疲劳载荷下实际所受到的有效应力降低。     

THE HIGH STRAIN-RATE FRACTURE CHARACTERISTICS OF DUCTILE METALS AT ELEVATED AND SUB-AMBIENT TEMPERATURES

Abstract— High strain-rate tensile tests have been carried out on pre-notched specimens of OFHC copper and Remko iron at both elevated and cryogenic temperatures. When properly expressed as a function of stress triaxiality at the centre of the notch (as predicted by numerical simulations of the experiment), the ductility of copper was found to be independent of temperature over a range from —190°C to 300°C. The specially-processed Remko iron was found to undergo a ductile-to-brittle transition at a temperature dependent on the stress triaxiality and the particular batch of the material. Otherwise the fully ductile strains-to-failure (when expressed as a function of stress triaxiality) for iron were found to decrease with increasing temperature up to 400°C; this being the maximum temperature tested.