Consideration of the mechanical behaviour of small fatigue cracks

The mechanical behaviour of small fatigue cracks is investigated for a low, medium and high strength material. At first an elastic consideration is performed which give a good impression how the stress fields change with crack size. In part 2 a full elastic-plastic analysis of short cracks is performed using a new numerical scheme to simulate the growth of shear bands emanating from the crack tip. The influence of material and loading paramters as well as of the crack size on the plastic crack tip opening displacement is discussed. It is also investigated how it is possible to get a conservative estimate of the crack tip deformation at small cracks.     

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.     

Closure of part-through fatigue cracks at the notch root

This paper describes a study of fatigue closure of part-through cracks in notched, 5 mm thick, Al---Cu alloy sheet specimens. The study used a specially designed electron fractography technique which enables accurate assessment of closure and its development wit crack extension, as well as its variation across the crack front. The effect of prior overloads on notch root crack closure was also investigated.     

Ultrasonic diffraction technique for characterization of fatigue cracks

This paper describes an ultrasonic diffraction technique for characterizing fatigue cracks. The angular field of energy scattered from a crack tip was computed. Using the theoretically predicted and experimentally verified optimum range of angles, we measured the crack profiles by the ultrasonic diffraction technique. Ultrasonic measurements agreed very well with direct destructive measurements. In addition, fatigue crack closure was detected and information on crack surfaces was obtained.Oak Ridge National Laboratory; Oak Ridge National Laboratory is operated by Union Carbide Corporation under contract W-7405-eng-26 with the U.S. Department of Energy.     

Mixed-mode crack opening displacement measurements for small fatigue cracks growing in Astroloy at 20 °C

Crack opening displacements were measured for small fatigue cracks in Astroloy being grown with uniaxial stress application under high-cycle fatigue conditions. Four cracks were investigated including one that grew from 27 to 74 μm in three increments. Most of the cracks grew at an angle to the loading axis and all opened bimodally. Crack opening scaled with distance from the crack tip similar to an elastic crack, which allowed the calculation of a local stress intensity factor for both mode I and mode II. The proportion of mode II stress intensity factor was relatively large, varying as 0.06 < Δ K _II /Δ K _I < 0.42, with an average of ~0.3. Thus, uniaxial loading remote to the cracks resulted in a bimodal opening response on the scale of the cracks.     

The use of ΔK when examining microstructural effects on small fatigue crack growth

The behaviour of small fatigue cracks has been studied in the Al---Li---Cu---Mg---Zr alloy 8090. It was found that the crack inclination normal to the surface of the specimen made crack deflections and kinking in the plane of the specimen surface irrelevant to the crack driving force. The low closure levels associated with small fatigue cracks reduce the effect of microstructure on crack growth but this does not affect the ability of ΔK (stress intensity factor range) to detect microstructural influences. The use of ΔJ (J-integral range) as a correlating parameter reduced the differences between the data for long and short fatigue cracks. However, there was no evidence that ΔJ was superior at identifying microstructural effects. Similarly the effect of the higher-order terms on the value of ΔK was found to be minor. It is concluded that the use of ΔK is not likely to bias the microstructural effects and so ΔK may be used when examining microstructural effects on small fatigue crack growth.     

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.     

Propagation of short fatigue cracks from notches in a Ni base superalloy: experiments and modelling

A notched specimen containing a semicircular slot (0.1 mm deep) was designed to simulate the growth of three-dimensional short cracks under a stress concentration. Fatigue tests were performed on N18 superalloy at 650 °C with trapezoidal loading cycles. A high-resolution optical measurement technique proved to be capable of detecting half-surface crack increments as small as 10 μm, and the potential drop method was found to be inappropriate for very small crack lengths. The stress intensity factor, Δ K , was calculated using a weight functions method. Non-uniform stress fields were determined by FEM modelling using elasto-viscoplastic constitutive equations. The plasticity-induced crack closure effect was calculated within the specimen using viscoplastic FEM modelling. The prediction of crack aspect ratio was used to investigate differences of closure along the crack front. The role of notch plasticity on these differences is discussed. Using these calculations, it is shown that the apparent differences between the growth behaviour of short and long cracks can be largely accounted for.     

An investigation of crack closure and the propagation of semi-elliptical fatigue cracks in Q1N (HY80) pressure vessel steel

The results of an experimental investigation of the effect of crack closure on the propagation of semi-elliptical fatigue cracks are presented. Load-shedding fatigue threshold tests were carried out at stress ratios of 0.2, 0.35, 0.5 and 0.7. Crack closure was measured at the surface and depth positions using backface strain gauges, near-tip gauges, and a clip gauge. Differences between the surface and depth growth behaviour are explained by considerations of the effects of the transition from plane stress conditions at the surface to plane strain conditions at the depth. The effects of stress ratios are attributed largely to differences in the crack opening displacement, which result in asperities coming into contact to induce roughness-induced crack closure.     

Experimental investigations on the growth of small fatigue cracks in naval steel

The concept of damage tolerance is now largely employed to evaluate the fatigue life of structures. However, part of this fatigue relies on the initiation and growth of small cracks. The fatigue behaviour of a naval structural steel (S355NL) was investigated. In order to characterize the behaviour of short and long cracks, tests were performed under constant amplitude loading for several load ratios between –1.0 and 0.5. A major part of fatigue life is constituted by short crack initiation and propagation.     

Cyclic crystal plasticity analyses of stationary, microstructurally small surface cracks in ductile single phase polycrystals

ABSTRACT This paper explores the effects of microstructural heterogeneity on the cyclic crack tip opening and sliding displacements for stationary, microstructurally small transgranular surface cracks in a single phase metallic polycrystal using planar double slip crystal plasticity computations. Crack tip displacements are examined under plane strain conditions for stationary cracks of different lengths relative to grain size as a function of the applied nominal strain amplitude for tension-compression and cyclic shear. Nominal strain amplitudes range from well below to slightly above the nominal cyclic yield strength for each type of loading condition. Results indicate the complex nature of the crack tip sliding and opening displacements as functions of nominal strain amplitude and orientation of the nearest neighbour grains, the influence of the free surface in promoting the cyclic opening displacement even for cracks in the first surface grain, the rather restricted limits of applicability of linear elastic fracture mechanics, and very interesting crack tip plasticity effects which include crack tip displacement ratcheting or progressive accumulation, even for completely reversed, proportional applied loading. Results are compared for cases with and without crack face friction.     

A surface acoustic wave technique for monitoring the growth behavior of small surface fatigue cracks

The theory of Kino and Auld which relates the reflection coefficient of acoustic waves from a crack to its size is summarized. A scattering model is evaluated from this theory concerning the reflection of surface acoustic waves (SAW) from a small surface fatigue crack at a frequency such that the crack depth is much smaller than the acoustic wavelength. Acoustic predictions of crack depth are compared to postfracture measurements of depth for small surface cracks in Pyrex glass, 7075-T651 aluminum, and 4340 steel. Additionally, the minimum detectable crack depth as limited by the acoustic noise level is determined for several typical aluminum and steel alloys. The utility of SAW reflection coefficient measurements for inferring crack depth, crack growth, and crack opening behaviorin situ during fatigue cycling is discussed.     

Elastic correction of fatigue crack growth laws

Fatigue crack growth (FCG) is usually studied assuming that ΔK is the driving parameter. An effective ΔK is considered in the presence of crack closure. However, after crack opening, there is an elastic regime that does not contribute to FCG. The objective here is to quantify this elastic range of ΔK, ΔK_el, for different loading conditions and material properties. The yield stress was found to be the most important material parameter, followed by the hardening exponent. A linear decrease of ΔK_el with ΔK was found for the 7050‐T6, 6082‐T6, and 6016‐T4 aluminium alloys, while the 304L stainless steel presented a slight increase. On the other hand, the increase of K_max was found to increase the elastic fatigue range. Relatively high values of elastic range were obtained for the plane strain state, compared with the plane stress state.     

A perturbation solution for a crack in a power-law material under gross yielding

Abstract In order to develop an analytical method for quantifying the plastic-blunting behaviour of a short crack embedded in a notch plastic zone, the perturbation solution of He and Hutchinson is extended to include the effect of strain gradient. An edge-cracked plate subjected to a linearly varying remote strain is considered in this work to simulate the plastic deformation associated with a small crack at a notch root. The strain hardening of the material is assumed to obey a power-law. Comparison with finite-element (FE) computations demonstrates that this perturbation solution provides accurate values for the crack-tip opening displacement (CTOD) under gross-yielding conditions for a range of hardening parameters.     

Degradation of components and structures by fatigue

This note examines briefly fatigue as a degradation mechanism and how engineers compensate for the fatigue phenomenon. Design is generally based on the stress-lifetime concept, but this concept is not very useful for lifetime assessment of operating components; thus, fatigue crack initiation and the growth of fatigue cracks become important. The numerous factors related to fatigue crack initiation and growth are briefly mentioned, and the importance of including the growth of small fatigue cracks is emphasized through the use of an illustration.     

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.     

Theoretical and experimental study of fatigue growth of interacting cracks

Life assessment of structures weakened by interacting cracks represents an important and very challenging problem. Subsequently, the main objective of this paper is to address this problem by developing a new computational technique. It 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 are validated against an experimental study focusing on fatigue behaviour of two closely spaced collinear cracks in wide plates with different thicknesses. It is confirmed that non-linear effects associated with crack interaction have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components.     

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, S_max/₀. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from complete slip before opening to opening in mode I before mode II shear offset. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.     

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.     

Interaction effect of adjacent small defects on the fatigue limit of a medium carbon steel

Structural steels contain various material irregularities and natural defects which cause local stress concentrations from which fatigue cracks tend to initiate. Two defects in close proximity to each other may affect local stress distributions, and thus, begin to interact. In this paper, the effect of interacting small cracks on the fatigue limit is systematically investigated in a medium carbon steel. The growth of interacting cracks, as well as the characteristics of non-propagating cracks and microstructural aspects, was closely examined via the plastic replica method. It was found that although the fatigue limit is essentially controlled by the mechanics of interacting cracks, based on their configuration, the local microstructure comprised ferrite and pearlite has a statistical scatter effect on the behaviour of interacting cracks and non-propagating thresholds. With respect to the fatigue limit, when two defects were in close proximity, they behaved as a larger single defect. However, with greater spacing between defects, rather than mechanical factors, it is the local microstructure which determines the location and characteristics of non-propagating cracks.