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.     

Effect of Compressive Mode I on the Mixed Mode I/II Fatigue Crack Growth Rate of 42CrMo4

Subsurface cracks in mechanical contact loading components are subjected to mixed mode I/II, so it is necessary to evaluate the fatigue behavior of materials under mixed mode loading. For this purpose, fatigue crack propagation tests are performed with compact tension shear specimens for several stress intensity factor (SIF) ratios of mode I and mode II. The effect of compressive mode I loading on mixed mode I/II crack growth rate and fracture surface is investigated. Tests are carried out for the pure mode I, pure mode II, and two different mixed mode loading angles. On the basis of the experimental results, mixed mode crack growth rate parameters are proposed according to Tanaka and Richard with Paris’ law. Results show neither Richard’s nor Tanaka’s equivalent SIFs are very useful because these SIFs depend strongly on the loading angle, but Richard’s equivalent SIF formula is more suitable than Tanaka’s formula. The compressive mode I causes the crack closure, and the friction force between the crack surfaces resists against the crack growth. In compressive loading with 45° angle, da/dN increases as K _eq decreases.     

A dislocation model for the two critical stress intensities required for threshold fatigue crack propagation

We have examined the variations, with decreasing load ratio, of threshold peak and cyclic stress intensities required for fatigue crack growth in stage I (mainly mode II loading) using a simple model simulating dislocation motion near a crack tip. In this model the crack grows by dislocations running into the crack during loading and unloading phases. Initially we have studied the behaviour of a crack with a dislocation source relatively far away from the crack tip. Crack propagation rates showed a Paris regime at high ΔK, and an abrupt threshold value ΔK_th below which no crack growth occurred. The variation with load ratio of the peak (K_th) and cyclic (ΔK_th) stress intensities at the fatigue threshold showed that two different processes controlled the behaviour. At high load ratios dislocations are generated readily during loading and the threshold is controlled by the need for sufficient unloading to allow dislocations to run back into the crack, so that the criterion ΔK ≥ ΔK∗ results. At negative load ratios it is the generation of dislocations during the loading phase that controls the threshold condition, since once generated, the large unloading and reversed loading easily forces dislocations back to the crack. Under these conditions the threshold criterion becomes K_max ≥ K∗.     

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.     

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.     

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.     

Fatigue lives of friction stir spot welds in aluminum 6061-T6 sheets

The fatigue lives of friction stir spot welds in aluminum 6061-T6 lap-shear specimens under cyclic loading conditions are investigated in this paper. The paths of fatigue cracks near friction stir spot welds in lap-shear specimens are first examined. The experimental observations suggest that under cyclic loading conditions, the fatigue crack is initiated near the possible original notch tip in the stir zone and propagates along the circumference of the nugget, then through the sheet thickness and finally grows in the width direction to cause final fracture. A fatigue crack growth model based on the Paris law for crack propagation and the local stress intensity factors for kinked cracks is then adopted to predict the fatigue lives of friction stir spot welds. The global and local stress intensity factors are used to estimate the local stress intensity factors of kinked cracks with experimentally determined kink angles. The results indicate that the fatigue life predictions based on the Paris law and the local stress intensity factors as functions of the kink length agree well with the experimental results.     

A7N01铝合金复合加载下的疲劳裂纹扩展行为

利用CTS试样,研究了A7N01P-T4铝合金母材在I-II型复合加载下,不同加载角度时疲劳裂纹的扩展行为,利用有限元数值计算复合加载下裂纹尖端的应力强度因子(SIF, stress intensity factor)得到了加载角度与裂纹开裂方向的关系,并与由最大周向应力准则导出的关系进行了对比,二者吻合良好;根据疲劳试验和有限元计算的结果,并引入当量应力强度因子,分析了不同加载角下疲劳裂纹的扩展速率. 结果表明,经当量化处理后,各加载角下的裂纹扩展速率曲线基本重合,并且满足Paris公式.     

Localised cyclic plastic deformation on translamellar fracture surfaces in a P/M γ-TiAl-based alloy

Large numbers of fine parallel steps are generated on translamellar fracture surfaces during slow crack growth (da/dN≤5.0×10⁻⁶ mm/cycle) under cyclic loading. These are seen only rarely during fast crack growth (da/dN≥1.0×10⁻⁴ mm/cycle) and are not seen during catastrophic fracture. These steps occur due to intense plastic deformation as a result of cleavage on {111} planes along twin boundaries and dislocation bands. Such action may promote an inherent resistance to crack growth owing to higher energy dissipation. TEM examinations show that the intense deformation structure consists of both microtwins and dislocation bands if the lamellae are orientated to allow easy glide. Conversely, microtwin activity dominates when easy dislocation glide is prevented. Crack initiation and growth resistance are sensitive to such microscopic features within the deformation zone. Lamellar volume fraction, the proportion and distribution of γ grains inside lamellae and lamellar interfacial strength may all influence the local plastic deformation through their interaction with underlying slip and twinning processes.     

Behaviour of mild steel under very low frequency loading in sea water

It is widely believed that the deterioration promoted by sea water is small in high stress, low cycle fatigue. Crack growth is faster than the penetration rate of the corrosive medium. This is probably true when the cyclic frequency is moderate (ca. 0.1 Hz). In ships large changes of the still water bending moment may occur when the loading condition goes from ballast to fully loaded and back. Wave bending is superimposed on the still water stresses. The absolute maxima and minima of the combined bending moments may occur only about once a week. Other very low frequency changes of stresses are connected to temperature changes (day/night) and, for offshore structures, changes of wind and wave directions. Experiments have been carried out with Fe 410 and Fe 510 at 0.05–0.0003 Hz. The crack growth curves for air and sea water remained practically parallel in a log da/dn-log ΔK plot. For simple programmed loading in sea water (one peak among 200 low stress cycles) the difference with results obtained in air was for Fe 410 about 1 : 20 in terms of da/dn; for Fe 510 it was 1 : 10. In air the peaks were very beneficial. In sea water there was no advantage.     

带斜裂纹模拟圆筒容器静压爆破和疲劳试验

本文提出了斜裂纹鼓胀效应修正系数公式.用该公式计算了带斜裂纹圆筒爆破载荷和开裂载荷,结果与实测大致相符,其平均误差在8%左右,可用于工程计算.本文还研究了斜裂纹疲劳扩展规律.采用直线法和投影法计算了疲劳扩展后的斜裂纹尖端应力强度因子。按照Paris 裂纹扩展方程整理了数据,然后获得了该钢种扩展速率方程,并论及了斜裂纹的扩展角问题.     

位错和位错偶沿单─滑移系从裂纹尖端的发射

采用计算机模拟了位错和位错偶沿单一滑移系从裂纹尖端的发射,考察了滑移面取向、外加载荷、晶格摩擦力以及位错发射的临界应力强度因子对所发射的位错数量、塑性区与无位错区大小以及裂关残余应力强度因子的影响研究表明,位错从裂纹尖端发射的临界应力强度因子对无位错区的存在和其大小起决定作用,而外加载荷与晶格摩擦力主要影响位错发射的数量以及塑性区大小．在Ｉ型载荷作用下,滑移面与裂纹面的夹角越大,从裂尖发射出的位错数量越多,位错对裂纹的屏蔽效应也越大当裂纹发射位错后的残余应力强度因子仍然较大时,位错偶就有可能在裂纹尖端附近产生井沿着几个滑移面发射,但发射出的位错偶对裂纹没有明显的屏蔽作用在滑移面不垂直于裂纹面时,发射出的位错或位错偶关于裂纹面呈不对称分布     

Fatigue crack retardation by silicon carbide powder paste infiltration under different cyclic stress conditions*

Fatigue crack retardation with infiltrated SiC paste into a crack is examined in low carbon structural steel. Two different sizes of SiC powders, whose average diameters are 15 and 53 μm, are used. The SiC powder mixed with oil is infiltrated into a through thickness fatigue crack from the crack mouth. Fatigue crack growth retardation is examined by the ΔK increasing test of R = 0.1, comparing with the base plate property, where ΔK is stress intensity factor range and R is stress ratio. Crack growth is retarded just after infiltrating SiC paste into the crack mouth, and the deceleration of crack growth rate to 1/50 of the base plate appears in the maximum. It is revealed that this crack retardation behaviour results from the crack closure induced by the wedge effect of the SiC particle into a crack. The crack retardation effect is investigated with several combinations of SiC particle size and cyclic stress conditions. The crack growth rate, da/dn and stress intensity factor, K_cl for the crack closure depend on both the maximum stress intensity factor, K_max, and the stress ratio, R. While the better retardation effect can appear in the higher K_max and the higher R ratio, it disappears in the R ratio over 0.7. The SiC paste with 15 μm powder brings the crack retardation effect in the wider cyclic stress condition more stable than in the SiC paste with 53 μm powder.     

Influence of specimen orientation and loading history on s.c.c. in an aluminium alloy

A contoured double cantilever beam specimen developed for linear elastic fracture mechanics (LEFM) studies was used in a stress corrosion cracking study of the Al Alloy RR 58. Subcritical s.c.c. tests were performed, in which a 3.5% NaCl solution, at 21°C, was drip-fed on to the crack surfaces with the crack propagating in the S-L orientation.Initial results showed three distinct regions of crack propagation when plotted as crack growth rate, da/dt, as a function of stress intensity K. Additional comparative tests showed that a faster-crack growth rate was obtained when the specimens had their longitudinal axis positioned vertically rather than horizontally, due to the better access of the corrodent to the crack tip. The present results were compared with data obtained under similar conditions on a range of 2000 series A1 alloys.The influence of loading history on the crack growth rate was studied. When the level of K was increased a temporary increase in crack growth rate was observed. Tests under decreasing K values showed an increase of the incubation time with decreasing values of the stress intensity. This latter effect is discussed in terms of the plastic zone size and an analytical solution suggested.     

Film rupture model for aqueous stress corrosion cracking under constant and variable stress intensity factor

A film rupture model for aqueous stress corrosion cracking is developed and used to predict kinetics of crack growth under constant and variable stress intensity factor. The model predicts that creep is necessary for sustained crack growth and creep rate limits crack velocity for constant K and dK/da loading. Contrary to recent thinking, the crack tip strain due to crack advance is viewed as a result, not a cause of crack growth. The crack tip strain gradient elevates and maintains crack tip stress as the crack propagates, which enables creep and sustained crack growth. The model provides a basis for understanding effects of positive and negative K - variation on crack growth.     

Effect of electromagnetic bulging on fatigue behavior of 5052 aluminum alloy

The effect of electromagnetic bulging on the fatigue behavior of the 5052 aluminum alloy was investigated through tensile–tensile fatigue testing. The intriguing finding is that the bulged specimens exhibited enhanced fatigue strength as depicted by maximum stress vs the number of cycles until failure (S–N) curves, by comparison with these original aluminum alloys. Although the fatigue process of the original and budged alloys follows the same mechanism with three distinct steps, namely, crack initiation at a corner of the tested samples, stable crack propagation with typical fatigue striations and finally catastrophic fracture with dimple fractographic features. The typical crack propagation rate vs stress intensity factor range (da/dN–ΔK) curves derived from the spacing of striations reveal a lower crack propagation rate in the bulged specimens. The enhancement of fatigue strength in electromagnetically bulged aluminum alloy is further rationalized in-depth on the basis of strain hardening and dislocation shielding effect.     

Effect of stress ratio on fatigue lifetime and crack growth behavior of WC–Co cemented carbide

Two types of fatigue tests, a rotating bending fatigue test and a three- or four-point bending fatigue test, were carried out on a fine grained WC–Co cemented carbide to evaluate its fatigue crack growth behavior and fatigue lifetime. From successive observations of the specimen surface during the fatigue process, it was revealed that most of the fatigue lifetime of the tested WC–Co cemented carbide was occupied with crack growth cycles. Using the basic equation of fracture mechanics, the relationship between the fatigue crack growth rate (da/dN) and the maximum stress intensity factor (K_max) was derived. From this relation, both the values of the threshold intensity factor (K_th) and the fatigue fracture toughness (K_fc) of the material were determined. The fatigue lifetime of the WC–Co cemented carbide was estimated by analysis based on the modified linear elastic fracture mechanics approach. Good agreement between the estimated and experimental fatigue lifetimes was confirmed.     

Cold hole expansion effect on the fatigue crack growth in welds of a 6061-T6 aluminum alloy

Compact test specimens were extracted from a 6061-T6 aluminum alloy welded plate with a thickness of 9 mm to analyze the cold hole expansion effect on fatigue crack growth tests conducted in mode I cyclic loading. At R = 0.1, a sharp crack in base metal, weld metal and heat affected zone was propagated from 17 to 24 mm. The fatigue crack growth at 24 mm (α = a/W = 0.3) was delayed by drilling a hole at the crack tip and applying a cold hole expansion of 4.1%. The residual stress fields due to cold hole expansion were determined with the finite element method. The fatigue crack growth testing was continued up to a crack length of 35 mm (α ∼ 0.43) at the same R, and crack opening displacements of the post-expansion crack were also determined with the finite element method. The results were expressed in terms of crack length versus number of cycles, as well as, fatigue crack growth rate as a function of applied and effective stress intensity factor range. The cold hole expansion contributed to delay the fatigue crack growth in base metal, and to a lesser extent in the weld metal and heat affected zone. A crack closure effect was determined by means of load versus crack opening displacement curves of the post-expansion crack, which was, completely or partially closed, in welded zones with compressive residual stress fields. The fracture surfaces of each welded zone were analyzed to elucidate the crack nucleation zone and its relation with the residual stress field. In all cases the crack was initiated at the surface of the specimen where the residual stresses were positive.     

Interaction of a screw dislocation with a thin-film-covered mode III crack

The present work models stress corrosion cracking by considering the interaction of a screw dislocation with a thin-film-covered mode III crack under an applied remote load. Exact solutions are derived from the proposed model. The results show that the crack stress field due to the applied load is enhanced by a harder film or abated by a softer film. When the crack length is much larger than the film thickness, the local stress intensity factor approximately equals the product of the nominal applied stress intensity factor times the ratio of the shear modulus of the film over that of the substrate. The critical stress intensity factor for dislocation emission from the crack tip is greatly influenced by the film stiffness and the film thickness. It is easier for a dislocation to be emitted from the crack tip if the covered film has a larger shear modulus than the substrate. The opposite is also true, a softer film makes the dislocation emission more difficult.