The effect of grain size on small fatigue crack growth in pure titanium

The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = −1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range ΔK_eff (after allowing for crack closure, the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, η, of growth rate in coarse-grained material were smaller than those in fine-grained material. The η values were significantly large at a/d 3 (a = crack depth, D = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size.     

Small-crack growth and fatigue life predictions for high-strength aluminium alloys. Part II: crack closure and fatigue analyses

Small-crack effects were investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad aluminium alloys. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue and small-crack tests were conducted on single-edge-notch tension (SENT) specimens and large-crack tests were conducted on middle-crack tension specimens under constant-amplitude and Mini-TWIST spectrum loading. A pronounced small-crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite-element and weight-function methods were used to determine stress intensity factors, and to develop equations for surface and corner cracks at the notch in the SENT specimen. (Part I was on the experimental and fracture mechanics analyses and was published in Fatigue Fract. Engng Mater. Struct. 21 , 1289–1306, 1998.) This part focuses on a crack closure and fatigue analysis of the data presented in Part I. A plasticity-induced crack-closure model was used to correlate large-crack growth rate data to develop the baseline effective stress intensity factor range (Δ K _eff ) against rate relations for each material, ignoring the large-crack threshold. The model was then used with the Δ K _eff rate relation and the stress intensity factors for surface or corner cracks to make fatigue life predictions. The initial defect sizes chosen in the fatigue analyses were similar to those that initiated failure in the specimens. Predicted small-crack growth rates and fatigue lives agreed well with experiments.     

On the mechanism of fatigue crack propagation in ductile metallic materials

An overview of our research performed during the last 15 years is presented to improve the understanding of fatigue crack propagation mechanisms. The focus is devoted to ductile metals and the material separation process at low and intermedial crack propagation rates. The effect of environment, short cracks, small‐scale yielding as well as large‐scale yielding are considered. It will be shown that the dominant intrinsic propagation mechanism in ductile metallic materials is the formation of new surface due to blunting and the re‐sharpening during unloading. This process is affected by the environment, however, not by the length of the crack and it is independent of large‐ or small‐scale yielding.     

Estimation of the effects of plasticity and resulting crack closure during small fatigue crack growth

On the basis of a plastic-strip model and the method of singular integral equations, a closed-form analytical solution of the problem of an elastic-plastic plate containing a rectilinear fatigue crack is considered. The solution is used for the prediction of fatigue growth of `mechanically-small' crack by accounting for reverse plastic yielding and plasticity-induced crack closure in the material. The main effects of these factors on the crack-growth rate are analyzed, and the predicted results are compared with experimental data on small fatigue-crack growth in a aluminum-lithium alloy 2091-T351 and Fe-3% Si alloy.     

Micromechanical simulations of microstructure-sensitive Stage I fatigue crack growth

Simulations of dislocation dynamics at the tip of a Stage I crack are performed, taking into account the influence of the normal stress on the friction of the crack flanks and on the condition for dislocation emission at the crack tip. The interactions of the emitted dislocations with microstructural obstacles are analysed. The repeated decelerations and sometimes arrests that characterize Stage I crack growth are properly described by the model, and the differences in Stage I kinetics observed in reversed torsion and push–pull are analysed in terms of crack tip–grain boundary interactions.     

A cohesive model of fatigue crack growth

We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.     

The effect of stress ratio on fatigue crack growth rate in the absence of closure

A fractographic study¹ was performed on Al-alloy fatigue fracture surfaces produced by programmed load sequences. The load sequences included steps of constant amplitude cycles at three different stress ratios, each step is preceded by a small number of high amplitude cycles designed to avoid the influence of crack closure and to serve as fractographic markers. The experiments were conducted on different specimen geometries to produce conditions associated with a long crack under fully elastic conditions and a short crack in a notched coupon seeing high local post yield stress conditions. Crack sizes covered in the study ranged from 0.02 to 12 mm, and growth rates ranged from 2×10⁻⁷ to 4×10⁻⁵ mm cycle⁻¹. Fractographic evidence from the study suggests that the crack growth rate can vary by up to a factor of five with applied stress ratio change from 0.64 to 0.73. In the case of the long crack, the effect is less noticeable or totally absent. In the case of naturally initiating notch root cracks, the effect is more pronounced at higher stress level and lower crack growth rate.     

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.     

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.     

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

Prediction of crack growth following a single overload in aluminum alloy with sheet and plate microstructure

The fatigue crack growth behavior under constant amplitude and under single overload of 2024 aluminum alloy in sheet and plate product form has been investigated. Constant amplitude fatigue crack growth tests showed superior crack growth resistance of the plate attributed to a pronounced roughness induced crack closure as a result of the coarse and elongated grain structure. Crack growth tests with single overload showed that the retardation effect caused by the overload is not primarily influenced by roughness crack closure at the crack path. In this case, the sheet material with lower yield strength revealed a higher retardation effect than the plate material. The observed crack growth behavior has been simulated with the LTSM-F model, which accounts for retardation of crack growth after an overload due to material strain hardening at the crack front. Dissimilar strain hardening at the crack tip due to different yield strength for the sheet and plate has been considered by means of strength gradients inside the overload plastic zone. The analytical results confirmed the observed material crack growth trends.     

Three-dimensional finite element simulations of microstructurally small fatigue crack growth in 7075 aluminium alloy

Three‐dimensional finite element simulations were performed to study the growth of microstructurally small fatigue cracks in aluminium alloy 7075‐T651. Fatigue crack propagation through five different crystallographic orientations was simulated using crystal plasticity theory, and plasticity‐induced crack opening stresses were calculated. The computed crack opening stresses were used to construct small crack da/dN‐ΔK diagrams. The generated da/dN‐ΔK curves compared well with experimental small crack data from the literature. The variance observed among the da/dN‐ΔK results, which occurred as a consequence of the different crystallographic orientations employed, was found to be of the same order of magnitude as commonly observed variability in small fatigue crack growth data. This suggests that grain orientation is a major contributor to observed small fatigue crack data scatter.     

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.     

A study of fatigue crack growth of 7075-T651 aluminum alloy

Both standard and non-standard compact specimens were employed to experimentally study the crack growth behavior of 7075-T651 aluminum alloy in ambient air. The effects of the stress ratio (R), overloading, underloading, and high–low sequence loading on fatigue crack growth rate were investigated. Significant R-ratio effect was identified. At the same R-ratio, the influence of specimen geometry on the relationship between crack growth rate and stress intensity factor range was insignificant. A single overload retarded the crack growth rate significantly. A slight acceleration of crack growth rate was identified after a single underload. The crack growth rate resumed after the crack propagated out of the influencing plastic zone created by the overload or underload. A parameter combining the stress intensity factor range and the maximum stress intensity factor can correlate the crack growth at different stress ratios well when the R-ratio ranged from −2 to 0.5. The parameter multiplied by a correction factor can be used to predict the crack growth with the influence of the R-ratio, overloading, underloading, and high–low sequence loading. Wheeler’s model cannot describe the variation of fatigue crack growth with the crack length being in the overload influencing zone. A modified Wheeler’s model based on the evolution of the remaining affected plastic zone was found to predict well the influence of the overload and sequence loading on the crack growth.     

Determination of the length dependence of the threshold for fatigue crack propagation

A rising load amplitude crack growth test on specimens pre-cracked in cyclic compression is presented as a procedure to determine the length dependence of the threshold of fatigue crack propagation described by the R(resistance)-curve for the threshold of stress intensity factor range. The experimental results show that the residual stress field in front of the pre-crack can significantly influence the R-curve.In order to measure the material specific R-curve which is not affected by the pre-cracking condition it is important to use the smallest possible load amplitude. To achieve this goal, a very small notch root radius is essential. It is shown that at notches machined by razor blade polishing technique the load amplitude for pre-cracking can be reduced to values where the load history does not influence the R-curve for the threshold of stress intensity range.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

Effects of microstructure on fatigue crack propagation behavior in a bi-modal TC11 titanium alloy fabricated via laser additive manufacturing

In this study, the crack propagation behaviors in the equiaxed and equiaxed-columnar grain regions of a heat-treated laser additive manufacturing (LAM) TC11 alloy with a special bi-modal microstructure are investigated. The results indicate that the alloy presents a special bi-modal microstructure that comprises a fork-like primary α (α_p) phase surrounded by a secondary α colony (α_s) in the β phase matrix after the heat treatment is completed. The samples demonstrate a fast crack growth rate with larger da/dN values through the equiaxed grain sample versus across the equiaxed-columnar grain sample at low ΔK values (<13.8). The differences that are observed between the crack propagation behaviors (in the crack initiation stage) of the samples can be mostly attributed to the different size and morphology of the α_p lamellae and α_s colony within the grains in the equiaxed and columnar grain regions rather than the grain boundaries. The cracks prefer to grow along the α/β boundary with a smooth propagation route and a fast propagation rate in the equiaxed grain region, where the α_p and α clusters have a large size. However, in the columnar grain region, small and randomly distributed α_p lamellae generate a zigzag-shaped propagation path with a reduction in the da/dN value. Additionally, the change in the size of the α_p lamellae in the equiaxed grains (heat affected bands, HAB) is also observed to influence the propagation behavior of the crack during the crack initiation stage.     

Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads

It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the retardation of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history. However, studies of the combined effect of mixed-mode I+II constant amplitude fatigue loadings and a mixed-mode I+II single overload on fatigue behavior are still scant. In this study, fatigue tests were conducted under mixed-mode I+II constant amplitude loadings with a mixed-mode I+II single overload, with reference to the variation of fatigue crack retardation. The formation of the overload plastic zone (OPZ) ahead of the crack tip under a mixed-mode I+II single overload is studied experimentally by the measurement of the shape and size of the OPZ. The behavior of fatigue crack propagation under mixed-mode loading conditions is examined by changing the loading mode of a single overload, and the relationship between the mixed-mode I+II single overload and the behavior of fatigue crack propagation in terms of the characteristics of the OPZ is evaluated. The empirical modeling of the fatigue life under mixed-mode I+II constant amplitude loadings is proposed by considering the characteristics of both the OPZ and the combination of the mode-mixity of mixed-mode I+II constant amplitude loadings and a mixed-mode I+II single overload.