A discrete dislocation analysis of near-threshold fatigue crack growth

Analyses of cyclic loading of a plane strain mode I crack under small-scale yielding are carried out using discrete dislocation dynamics. The formulation is the same as used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. The dislocations are all of edge character and are modeled as line singularities in an elastic solid. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Either reversible or irreversible relations are specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading as could occur in a vacuum or in an oxidizing environment, respectively. In accord with experimental data we find that the fatigue threshold ΔK_th is weakly dependent on the load ratio R when the reversible cohesive surface is employed. This intrinsic dependence of the threshold on R is an outcome of source limited plasticity at low R values and plastic shakedown at higher R values. On the other hand, ΔK_th is seen to decrease approximately linearly with increasing R followed by a plateau when the irreversible cohesive law is used. Our simulations show that in this case the fatigue threshold is dominated by crack closure at low values of R. Calculations illustrating the effects of obstacle density, tensile overloads and slip geometry on cyclic crack growth behavior are also presented.     

Discrete dislocation plasticity modeling of short cracks in single crystals

The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The fracture properties are specified through an irreversible cohesive relation. Under monotonic loading conditions, with the applied stress below the yield strength of the uncracked specimen, the initiation of crack growth is found to be governed by the mode-I stress intensity factor, calculated from the applied stress, with the value of K_init decreasing slightly with crack size due to the reduction in shielding associated with dislocations near a free surface. Under cyclic loading, the fatigue threshold is ΔK-governed for sufficiently long cracks. Below a critical crack size the value of ΔK_I at the fatigue threshold is found to decrease substantially with crack size and progressive cyclic crack growth occurs even when K_max is less than that required for the initiation of crack crack growth in an elastic solid. The reduction in the fatigue threshold with crack size is associated with a progressive increase in internal stress under cyclic loading. However, for sufficiently small cracks, the dislocation structure generated is sparse and the internal stresses and plastic dissipation associated with this structure alone are not sufficient to drive fatigue crack growth.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials

In this paper, a plasticity-corrected stress intensity factor range ΔK_pc is developed on the basis of plastic zone toughening theory. Using this new mechanical driving force parameter for fatigue crack growth (FCG), a theoretical correlation of Paris’s law with the crack tip plastic zone is established. Thus, some of the important phenomena associated with the plastic zone around the fatigue crack tip, such as the effects of load ratio R, overload and T stress on the FCG behavior, can be incorporated into the classical Paris’s law. Comparisons with the experimental data demonstrate that ΔK_pc as a single and effective mechanical parameter is capable of describing the effects of the load ratio, T stress and overload on the FCG rate. The FCG rate described as a function of ΔK_pc tested under a simple loading condition can also be used for other complex loading conditions of the same material.     

Discrete dislocation modeling of fatigue crack propagation

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small-scale yielding are carried out using discrete dislocation dynamics. Cracks along a metal–rigid substrate interface and in a single crystal are studied. The formulation is the same as that used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. The cyclic crack growth rate log(da/dN) versus applied stress intensity factor range log(ΔK_I) curve that emerges naturally from the solution of the boundary value problem shows distinct threshold and Paris law regimes. Paris law exponents in the range 4 to 8 are obtained for the parameters employed here. Furthermore, rather uniformly spaced slip bands corresponding to surface striations develop in the wakes of the propagating cracks.     

Scaling of discrete dislocation predictions for near-threshold fatigue crack growth

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small scale yielding are carried out using discrete dislocation dynamics. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. Calculations are carried out with different material parameters so that values of yield strength, cohesive strength and elastic moduli varying by factors of three to four are considered. The fatigue crack growth predictions are found to be insensitive to the yield strength of the material despite the number of dislocations and the plastic zone size varying by approximately an order of magnitude. The fatigue threshold scales with the fracture toughness of the purely elastic solid, with the experimentally observed linear scaling with Young’s modulus an outcome when the cohesive strength scales with Young’s modulus.     

Elucidating the variables affecting accelerated fatigue crack growth of steels in hydrogen gas with low oxygen concentrations

The objective of this study was to quantify the effects of mechanical and environmental variables on oxygen-modified accelerated fatigue crack growth of steels in hydrogen gas. Experimental results show that in hydrogen gas containing up to 1000 v.p.p.m. oxygen fatigue crack growth rates for X52 line pipe steel are initially coincident with those measured in air or inert gas, but these rates abruptly accelerate above a critical ΔK level that depends on the oxygen concentration. In addition to the bulk gas oxygen concentration, the onset of hydrogen-accelerated crack growth is affected by the load cycle frequency and load ratio R. Hydrogen-accelerated fatigue crack growth is actuated when threshold levels of both the inert environment crack growth rate and K_max are exceeded. The inert environment crack growth rate dictates the creation of new crack tip surface area, which in turn determines the extent of crack tip oxygen coverage and associated hydrogen uptake, while K_max governs the activation of hydrogen-assisted fracture modes through its relationship to the crack tip stress field. The relationship between the inert environment crack growth rate and crack tip hydrogen uptake is established through the development of an analytical model, which is formulated based on the assumption that oxygen coverage can be quantified from the balance between the rates of new crack tip surface creation and diffusion-limited oxygen transport through the crack channel to this surface. Provided K_max exceeds the threshold value for stress-driven hydrogen embrittlement activation, this model shows that stimulation of hydrogen-accelerated crack growth depends on the interplay between the inert environment crack growth increment per cycle, load cycle frequency, R ratio and bulk gas oxygen concentration.     

Micromechanisms of fatigue crack growth in a single crystal Inconel 718 nickel-based superalloy

The fatigue crack growth behavior of an experimental, single crystal alloy, of equivalent nominal chemical composition to Inconel 718 is presented. Fracture modes under cyclic loading were determined by scanning electron microscopy. The results of the fractographic analyses are presented on a fracture mechanism map that shows the dependence of the fatigue fracture mechanisms on the maximum stress intensity factor, K_max, and the stress intensity factor range, ΔK. Crack-tip deformation mechanisms associated with fatigue crack growth were studied using transmission electron microscopy. The relative effects of ΔK and K_max on the fatigue crack growth behavior of this material are discussed within the context of a two-parameter crack growth law. The influence of grain boundaries on the fatigue crack growth resistance of materials such as Inconel 718 is also discussed in light of the results of this investigation.     

（F＋M＋A）三相钢低周疲劳的扫描电镜动态研究SCIEI

用扫描电子显微镜疲劳加载台进行动态原位观察，研究了奥氏体（Ａ）在（Ｆ＋Ｍ＋Ａ）三相钢低周疲劳裂纹萌生和扩展过程中的作用．结果表明，在低周疲劳裂纹的萌生和早期扩展阶段，三相钢中的奥氏体会降低疲劳缺口敏感性，延长裂纹萌生期，使裂纹路径弯折并降低扩展速率．在高应变疲劳阶段，因奥氏体应变诱发相变生成马氏体，其边界是裂纹扩展的低能通道，从而加速裂纹的扩展．并提出了一个能量判据：当裂尖扩展功小于Ａ→Ｍ转变的能量时，奥氏体会提高材料的疲劳抗力，反之奥氏体会加速疲劳裂纹的萌生和扩展．     

Q960E热影响粗晶区疲劳寿命与ΔKth值的关系分析

基于模拟焊接热循环试验及疲劳裂纹扩展试验,对动载结构用高强钢Q960E热影响粗晶区进行了多种应力幅值作用下的疲劳寿命研究.通过得到Paris方程建立了不同焊接热模拟工艺下疲劳裂纹扩展门槛值（ΔK_th）随不同交变载荷下疲劳寿命值的近似线性关系.利用场发射扫描电镜中背散射衍射功能（EBSD）对疲劳裂纹扩展试样中的裂纹尖端进行了晶体学取向分析及扩展机制讨论.结果表明,在应力幅值ΔP固化后,疲劳寿命N随ΔK_th的增大而增加,其延寿微观机理在于组织中的亚结构取向存在差异,所形成的大角度晶界（≥15°）可有效迫使裂纹转向,从而提高材料的疲劳寿命.     

Fatigue crack propagation behavior of AZ31 Mg alloy in ultra-high vacuum

The fatigue crack propagation (FCP) behavior of extruded AZ31-F was examined in conjunction with crack closure phenomena. FCP experiments were carried out in an ultra-high vacuum system using a fatigue test machine under a constant load amplitude. To determine the effect of crack closure on the FCP rates, the crack closure levels were measured using the compliance method. The δK_th values of the AZ31-F decreased with increasing load ratio. It was found that ΔK_eff,th showed an almost constant value regardless of the load ratio.     

An intrinsic effect of hydrogen on cyclic slip deformation around a {1 1 0} fatigue crack in Fe–3.2 wt.% Si alloy

The effect of gaseous hydrogen on cyclic slip behavior around a fatigue crack tip introduced along the {1 1 0} plane in a Fe–3.2 wt.% Si alloy is precisely investigated by cross-sectional transmission electron microscopy and fractography. The results clearly suggest that the fatigue crack growth rate is promoted by hydrogen, whereas the number of dislocations emitted per load cycle is reduced. In addition, dislocation distribution is localized around the crack, causing quasi-brittle crack morphology. A sustained load test confirms that no subcritical crack growth caused by cleavage or micro-void coalescence exists along the {1 1 0} plane, which indicates that the observed increase in the fatigue crack growth rate is correlated solely to the intrinsic effect of hydrogen on the cyclic slip-off process around the crack tip.     

On the fatigue crack growth behavior of WC–Co cemented carbides: kinetics description,microstructural effects and fatigue sensitivity

The influence of microstructure and load ratio (R) on the fatigue crack growth (FCG) characteristics of WC–Co cemented carbides are studied. In doing so, five hardmetal grades with different combinations of binder content and carbide grain size are investigated. Attempting to rationalize microstructural effects, key two-phase parameters, i.e. binder thickness and carbide contiguity, are used. On the other hand, the effect of load ratio is evaluated from the FCG behavior measured under R values of 0.1, 0.4 and 0.7. Experimental results indicate that: (1) WC–Co cemented carbides are markedly sensitive to fatigue; and (2) their FCG rates exhibit an extremely large dependence on K_max. Furthermore, both fatigue sensitivity and relative prevalence of K_max over ΔK, as the controlling fatigue mechanics parameter, are found to be significantly dependent upon microstructure. As mean binder free path increases, predominance of static over cyclic failure modes diminishes and a transition from a ceramic-like FCG behavior to a metallic-like one occurs (conversely in relation to contiguity). Consequently, the trade-off between fracture toughness and FCG resistance becomes more pronounced with increasing binder content and carbide grain size. The observed behavior is attributed to the effective low ductility of the constrained binder and its compromising role as the toughening and fatigue-susceptible agent in hardmetals, the latter on the basis that cyclic loading degrades or inhibits toughening mechanisms operative under monotonic loading, i.e. crack bridging and constrained plastic stretching.     

不同疲劳载荷下工业纯钛再结晶热处理对疲劳裂纹扩展行为影响

本文开展热处理后工业纯钛TA2不同载荷水平下疲劳裂纹扩展实验,考虑裂尖塑性变形程度,研究疲劳裂纹扩展规律以及热处理状态对疲劳裂纹扩展不同阶段的适应性。结果表明,不同疲劳载荷下热处理对疲劳扩展速率产生不同的影响。A类加载热处理后的疲劳裂纹扩展速率下降是由于近门槛区有效载荷的降低,以及近门槛值的提高。B类加载下热处理对有效载荷以及裂尖塑性变形几乎没有什么影响。C类与D类加载下热处理后裂尖塑性变形受到限制,而导致疲劳裂纹扩展速率下降。     

喷射沉积SiC_P／Al-7Si复合材料的疲劳裂纹扩展

采用紧凑拉伸试样进行恒载和降K控制的拉--拉疲劳实验, 研究了喷射沉积SiC_p/Al-7Si复合材料及其基体的疲劳裂纹扩展行为. 通过金相显微镜和扫描电镜观察了复合材料及其基体的组织和疲劳裂纹扩展形貌, 研究了SiC颗粒对复合材料疲劳裂纹扩展机制的影响. 结果表明: 复合材料在任何相同的ΔK水平下其抗疲劳裂纹扩展能力优于基体材料, 并表现出较高的疲劳门槛值. 其原因是复合材料中裂纹裂尖遇到增强颗粒时, 裂纹发生偏转, 特别是SiC颗粒自身微裂纹萌生有效降低了裂纹尖端的应力强度因子, 复合材料的裂纹闭合效应也随之增大. 去除裂纹闭合效应的影响, 当有效应力因子ΔK_eff作为裂纹扩展的驱动力时, 复合材料的裂纹扩展速率却高于基体.     

疲劳裂纹尖端的位错结构

在双相钢物理短裂纹门槛区，观察到稳定的位错胞和墙结构；长裂纹门槛区，在铁素体／马氏体相界堆垛位错密度大，有形成位错胞的趋势．长裂纹扩展第二阶段，铁素体晶粒内具有单向滑移线（Ｒ＝０，－１）和正交网状（Ｒ＝－１）的位错结构，长裂纹扩展第三阶段，位错稀少，但单滑移、双交滑移位错线明显拉长，说明裂纹尖端位错组态是应变历史的产物．疲劳裂纹扩展门槛区形成的位错胞和墙是一亚稳态结构，与门槛循环应力应变处于动态平衡，也是一微观结构参数．     

Fatigue crack growth mechanism in cast hybrid metal matrix composite reinforced with SiC particles and Al2O3 whiskers

The fatigue crack growth (FCG) mechanism of a cast hybrid metal matrix composite (MMC) reinforced with SiC particles and Al₂O₃ whiskers was investigated. For comparison, the FCG mechanisms of a cast MMC with Al₂O₃ whiskers and a cast Al alloy were also investigated. The results show that the FCG mechanism is observed in the near-threshold and stable-crack-growth regions. The hybrid MMC shows a higher threshold stress intensity factor range, ΔK_th, than the MMC with Al₂O₃ and Al alloy, indicating better resistance to crack growth in a lower stress intensity factor range, ΔK. In the near-threshold region with decreasing ΔK, the two composite materials exhibit similar FCG mechanism that is dominated by debonding of the reinforcement–matrix interface, and followed by void nucleation and coalescence in the Al matrix. At higher ΔK in the stable- or mid-crack-growth region, in addition to the debonding of the particle–matrix and whisker–matrix interface caused by cycle-by-cycle crack growth at the interface, the FCG is affected predominantly by striation formation in the Al matrix. Moreover, void nucleation and coalescence in the Al matrix and transgranular fracture of SiC particles and Al₂O₃ whiskers at high ΔK are also observed as the local unstable fracture mechanisms. However, the FCG of the monolithic Al alloy is dominated by void nucleation and coalescence at lower ΔK, whereas the FCG at higher ΔK is controlled mainly by striation formation in the Al grains, and followed by void nucleation and coalescence in the Si clusters.     

循环载荷下裂尖形变规律的实验研究

应用散斑干涉技术，在常幅载荷下对疲劳裂纹扩展过程中的一个循环周期内，不同加载阶段的裂尖应变、裂纹张开位移进行了原位测量，给出了裂纹闭合对裂纹张开位移及裂尖形变的影响规律。结果表明：由于裂纹闭合和残余压应力的存在，疲劳裂尖应变与外加载荷的平方并不成正比，在加载初期，裂纹处于闭合状态，裂尖应变无明显变化，随着载荷的增加，裂纹逐渐由远离裂尖处张开并向裂尖发展，一旦裂纹完全张开，裂尖应变迅速增加，对裂尖应力-应变状态的分析表明，裂尖材料的应力-应变关系类似于光滑试样低周拉压疲劳应力-应变滞后关系。     

Methodologies to evaluate fracture toughness in lamellar grey cast iron

Fracture mechanics properties in lamellar grey cast iron were traditionally evaluated from parameters calculated at maximum load values from load vs. crack mouth opening displacement records. The evaluation was carried out in this way as a consequence of the difficulty in measuring stable crack growth. The chemical tinting technique presented in this paper permits stable crack growth in lamellar grey cast iron to be measured, and then, the determination of R-Curves by a multiple specimens technique. A good agreement between the measured compliances and the theoretical ones was also observed. This demonstrates that the unloading compliance method can be used in stable crack growth measurements to determine J-R Curves. In fact, the R-Curves obtained by both methods, unloading compliance and multiple specimens, are consistent. A technological toughness value corresponding to Δa = 0.5mm, J_.5 was proposed because the R-Curves set apart from the blunting line at a very early stage. Maximum load values (K_Pmax, J_max and K_Jmax) were also determined.     

Near-threshold propagation of mode II and mode III fatigue cracks in ferrite and austenite

The near-threshold behavior of mode II and mode III long fatigue cracks in ferritic (ARMCO iron) and austenitic (X5CrNi18-10) steel were experimentally studied using various samples specially prepared to obtain the effective threshold values ΔK_IIeff,th and ΔK_IIIeff,th. In both investigated materials, the effective thresholds for mode III were ～1.7 times higher than those for mode II. Three-dimensional topological data obtained by the examination of fracture surfaces using stereophotogrammetry were utilized to identify crack growth micromechanisms. In austenite, mode I branching of both the mode II and mode III cracks started at the very onset of crack growth. On the other hand, all cracks in ferrite propagated in crystallographically assisted local mixed mode I + II + III with mode II dominance. These experimental results can be understood in terms of crack growth micromechanisms according to a deformation model in ferrite and a decohesion model in austenite. The dissimilarity of growth mechanisms in ferrite and austenite may be attributed to a different number of available slip systems in body-centered cubic and face-centered cubic metals.     

Corrosion fatigue crack growth behaviour of naval steels

Fatigue crack growth behaviour of two varieties of HSLA steels used in naval structural applications have been evaluated in air and 3.5% NaCl solution. In air both the HSLA steels showed similar resistance to fatigue crack growth. However, in 3.5% NaCl, the fatigue crack growth resistance of HSLA-80 steel was superior to that of HSLA-100. The apparent inferiority of HSLA-100 to corrosion fatigue crack growth resistance is attributed to rapid film formation and rupture, and occurrence of planar modes of failure. Effect of R-ratio on air fatigue and corrosion fatigue crack growth behaviour is rationalised by the concept of crack closure. Effect of cyclic frequency on corrosion fatigue behaviour is examined. It is noted that the mechanism of corrosion fatigue crack growth for the two HSLA steels changes with attendant change in the Paris slope. This leads to increase or decrease of crack growth rates, depending up on the ΔK range of interest.