A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness
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ABSTRACT Fatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.Keywords:
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Many of the recent advances in the understanding of the fatigue crack growth process have resulted from an improved realization of the importance of fatigue crack closure in the crack growth process. Two basic crack closure processes have been identified. One of which is known as plasticity-induced fatigue crack closure (PIFCC), and the other is roughness-induced fatigue crack closure (RIFCC). Both forms occur in all alloys, but PIFCC is a surface-related process which is dominant in aluminum alloys such as 2024-T3, whereas RIFCC is dominant in most steels and titanium alloys. A proposed basic equation governing fatigue crack growth is (1) where where Kmax is the maximum stress intensity factor in a loading cycle and Kop is the stress intensity factor at the crack opening level. is the range of the stress intensity factor at the threshold level which is taken to correspond to a crack growth rate of 10-11 m/cycle. The material constant A has units of (MPa)-2, and therefore Eq. 1 is dimensionally correct. Eq.1 has been successfully used in the analysis of both long and short cracks, but in the latter case modification is needed to account for elastic-plastic behavior, the development of crack closure, and the Kitagawa effect which shows that the fatigue strength rather than the threshold level is the controlling factor determining the rate of fatigue crack growth in the very short fatigue crack growth range. Eq. 1 is used to show that The non-propagating cracks observed by Frost and Dugdale resulted from crack closure. The behavior of cracks as short as 10 microns in length can be predicted. Fatigue notch sensitivity is related to crack closure. Very high cycle fatigue (VHCF) behavior is also associated with fatigue crack closure.
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Abstract The effects of specimen thickness and positive stress ratio on the fatigue crack growth behavior of Ti-6Al-4V are discussed in this paper. Fatigue crack growth rates are shown to increase with increasing stress ratio. Stress ratio is shown to have a strong effect on fatigue crack growth behavior. However, for the range of specimen thicknesses examined in this study, the fatigue crack growth rates are shown to not be strongly affected by specimen thickness. A single intrinsic fatigue crack growth rate curve is obtained when the fatigue crack growth rates are plotted against the effective (closure-corrected) stress intensity factor range. Multiparameter extensions to the Paris law are also presented for the combined assessment of the effects of specimen thickness, stress ratio, and crack closure on the fatigue crack growth behavior of Ti-6Al-4V.
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This article studies plasticity-induced fatigue crack growth retardation in metals caused by crack path bifurcation in the near-tip region. To this end, the finite element method was used to model the crack with its bifurcated tip under several stress intensity factor (SIF) ranges. The results show the appearance of a retardation effect in the fatigue crack growth rate of the bifurcated crack in relation to the growth rate of the fully straight crack.
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Abstract Behaviour of fatigue crack growth and closure through a compressive residual stress field is investigated by performing fatigue crack growth tests on welded SEN specimens of a structural steel (JIS SM50A). Depending on the type of the initial residual stress in the region of crack growth, the growth and closure of the crack show different behaviour. In particular, in the transition region from a compressive residual stress field to a tensile residual stress field, the fatigue crack growth rates cannot be described by the effective stress intensity factor range Δ K eff , based on the measured crack opening stress intensity factor K op . Also it is found that the R'‐method using the data of d a /d N vs Δ K for residual stress‐free specimens, with the effective stress ratio R'[=( K max + K r )/( K min + K r )], gives non‐conservative predictions of the growth rates in the transition region. Observations of crack closure behaviour in this study indicates that partial opening of the crack occurs and this plays an important role in crack growth through a compressive residual stress field. Based on the concept of a partial opening point (defined and measured in this work), fatigue crack growth behaviour can be better explained.
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A fatigue crack initiated in welded structure propagates through the welded residual stress field. It is a very important problem to clarify the effect of welded residual stress on fatigue crack growth rate. For the butt welded joint of 600MPa grade steel, the effects of tensile and compressive residual stresses were investigated in association with the crack closure phenomenon. The results obtained are summarized as follows.(1) For the welded joint in which the fatigue crack propagated through the tensile residual stress field, the fatigue crack growth rate was accelerated by the tensile residual stress. But, the acceleration of fatigue crack growth rate was independent of the stress ratio and the intensity of residual stress.(2) For the welded joint in which the fatigue crack propagated through the compressive residual stress field, the fatigue crack growth rate decreased with increasing stress intensity range, and the crack arrested as the stress intensity range approached the threshold for crack growth, ΔK0. At the stress intensity range above ΔK0, the fatigue crack growth rate increased with increasing stress intensity range. The increase of stress ratio has given rise to increase in fatigue crack growth rate and decrease in ΔK0 value. Such a stress ratio effect was the same as the results of base metal.(3) It is considered that the welded residual stress has an effect on the fatigue crack growth rate to change the mean stress at the crack tip. This effect may be explained by the equivalent stress ratio, Req, defined by the following equation.Req=R-2Kres/Kmax
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Aluminum-lithium alloys exhibit similar environmental fatigue crack growth characteristics compared to conventional 2000 series alloys and are more resistant to environmental fatigue compared to 7000 series alloys. The superior fatigue crack growth behavior of Al-Li alloys 2090, 2091, 8090, and 8091 is due to crack closure caused by tortuous crack path morphology and crack surface corrosion products. At high R and reduced closure, chemical environment effects are pronounced resulting in accelerated near threshold da/dN. The beneficial effects of crack closure are minimized for small cracks resulting in rapid growth rates. Limited data suggest that the 'chemically small crack' effect, observed in other alloy system, is not pronounced in Al-Li alloys. Modeling of environmental fatigue in Al-Li-Cu alloys related accelerated fatigue crack growth in moist air and salt water to hydrogen embrittlement.
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This chapter contains sections titled: Special Features of the Propagation of Microstructurally Short Fatigue Cracks Definition of Short and Long Cracks Transgranular Crack Propagation Crystallographic Crack Propagation: Interactions with Grain Boundaries Mode I Crack Propagation Governed by Cyclic Crack-Tip Blunting Influence of Grain Size, Second Phases and Precipitates on the Propagation Behavior of Microstructurally Short Fatigue Cracks Significance of Crack-Closure Effects and Overloads General Idea of Crack Closure During Fatigue-Crack Propagation Plasticity-Induced Crack Closure Influence of Overloads in Plasticity-Induced Crack Closure Roughness-Induced Crack Closure Oxide- and Transformation-Induced Crack Closure ΔK*/K*max Thresholds: An Alternative to the Crack-Closure Concept Development of Crack Closure in the Short Crack Regime Short and Long Fatigue Cracks: The Transition from Mode II to Mode I Crack Propagation Development of the Crack Aspect Ratio a/c Coalescence of Short Cracks Intercrystalline Crack Propagation at Elevated Temperatures: The Mechanism of Dynamic Embrittlement Environmentally Assisted Intercrystalline Crack Propagation in Nickel-Based Superalloys: Possible Mechanisms Mechanism of Dynamic Embrittlement as a Generic Phenomenon: Examples Oxygen-Induced Intercrystalline Crack Propagation: Dynamic Embrittlement of Alloy 718 Increasing the Resistance to Intercrystalline Crack Propagation by Dynamic Embrittlement: Grain-Boundary Engineering
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