Crack closure and surface microcrack thresholds — Some experimental observations

Threshold stress intensity data at several positive stress ratios are reported for surface microcracks in an EN8 designation 0.40% carbon steel. It is proposed that observed anomalies in short crack behaviour can be explained by using a crack closure argument, and an indirect method of measuring crack closure changes in the short crack regime (where the value of the threshold stress intensity is not constant) is used to rationalize threshold behaviour for all crack lengths.     

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.     

The effect of overloads on threshold and crack closure

The effect of tensile and compressive overloads on the threshold stress intensity level and crack closure behaviour of one aluminium alloy and three steels has been investigated. A few tensile overloads significantly decreased the crack propagation rate and increased the threshold stress intensity. An initially decreased and then increased opening stress was mostly responsible for the delayed retardation and crack arrest. Intermittant compressive overloads significantly accelerated the crack propagation and decreased the threshold stress intensity which was a function of the frequency of overloading. The opening stress was decreased to below zero after a large compressive peak load, and it took >10⁵ cycles for the opening stress to return to its stable level. During this period an initially high crack propagation rate also gradually decreased to the stable value.     

Plastic zone size estimation under cyclic loadings using in situ optical microscopy fatigue testing

An in situ optical microscopy fatigue testing is proposed in this paper to investigate the forward and reversed plastic zone size under cyclic loadings for Al‐7075‐T6. This experimental study is used to verify the hypotheses in a recently developed small time scale formulation of fatigue crack growth. During the testing, the entire cyclic loading cycle is divided into a certain number of steps. Images of the crack tip are taken at each step. The full strain field around the crack tip is determined using the digital image correlation (DIC) technique. The plastic zone size is obtained by combining the DIC results and the material constitutive relationship. Experimental measurements from the proposed study are compared with theoretical predictions. It is observed that the crack closure has a large effect on the reversed plastic zone size. The plastic zone size remains almost constant when the unloading path is below a certain stress level, which is one of the hypotheses used in a previous crack growth model. Discussions are given for the modelling of plastic zone size variation under cyclic loadings and several conclusions are drawn based on the current investigation.     

Influence of through-thickness crack shape on plasticity induced crack closure

In most of the previous three‐dimensional (3D) numerical studies of plasticity induced crack closure (PICC), ideal shapes have been assumed for the cracks. The aim of present paper is to study the effect of crack shape on PICC. With this objective a 3D numerical model was developed to predict PICC in middle‐tension (MT) specimens with different thicknesses and crack shapes. The radial size of crack tip elements and the stabilization of closure level were studied to ensure the quality of numerical predictions. Simultaneously, an independent numerical model was developed to predict crack shape evolution, stable crack shapes and corresponding K distributions. Crack closure was found to produce a significant tunnelling effect, with maximum values of ΔK and K_max at the surface. The curved crack presented significant plastic deformation near the free surface which has a high impact on the computation time, compared to the straight crack. The modification of ΔK and K_max with crack shape produced a variation of 38% in opening values at the interior positions, but relatively small variations at the surface. Considering the great influence of crack shape on PICC, it is fundamental to model realistic crack shapes.     

Plane problem of macro-microcrack interaction taking account of crack closure

The fracture stability of a macrocrack under the tensile and shear loading in the presence of a system of microcracks is analysed. Interaction of cracks leads to full or partial closure of the crack edges. The boundary problem is formulated and a solution is obtained by the small parameter method. Domains where microcracks are closed, and regions where microcracks cause full or partial closure of the macrocrack are found. The influence of crack contact on the stress intensity coefficient is analysed under the friction free assumption.     

The interaction of ultrasound with contacting asperities: Applications to crack closure and fatigue crack growth

The partial contact of two rough fatigue crack surfaces leads to transmission, reflection, diffraction, and mode conversion of an acoustic signal at those contacts. This paper reviews recent experimental and theoretical efforts to understand and quantify such contact on actual fatigue cracks in greater detail. It is shown that the size and density of individual contacts, or asperities, can be estimated from acoustic measurements. Furthermore, it is shown that this information is useful to provide the static stress across a partially closed crack as well as the effective stress intensity range which activates fatigue crack propagation.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique

We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, Δ, used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several—seemingly different—suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a Δ-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for Δ-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter ε.     

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.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

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.     

A threshold fatigue crack closure model: Part II – experimental verification

Predictions from an analytical model that considers contributions and interactions between plasticity, roughness, and oxide induced crack closure are presented and compared with experimental data. The analytical model is shown to correctly predict the combined influences of crack roughness, oxide debris, and plasticity in the near‐threshold regime. Furthermore, analytical results indicate closure mechanisms interact in a non‐linear manner such that the total amount of closure is not the sum of closure contributions for each mechanism.     

Measurement of fatigue crack closure through electron microscopy

A technique is proposed for estimating crack opening stress during fatigue crack growth. It involves electron fractography of fracture surfaces obtained under specially designed load sequences. The technique was experimentally validated on an AlCu alloy. The experimental data bear evidence of fatigue crack closure. They also indicate that fatigue crack closure is uneven across the specimen thickness.     

Dislocation emission criterion for a wedge crack under mixed mode loading

Dislocation emission criterion for a wedge crack under mixed mode loading was investigated using Airy stress function. The order of singularity at the wedge crack tip due to remote loading was found to vary with the loading mode. The plastic zones for plane stress and plane strain were studied based on von Mises' and Tresca criteria. The dislocation emission criterion was examined for both loading modes. The mechanism of crack propagation was believed to be controlled by dislocation emission. Under an action of Mode I loading, the wedge tip movement occurred when a pair of edge dislocations of Burgers vectors be ⁱ and –be ^–i were emitted from the wedge tip where b and were the magnitude of Burgers vector and the angle between the positive x axis and the line connecting from the tip to dislocation. Similarly, under an action of Mode II loading, the wedge crack tip moved as soon as either an edge dislocation of Burgers vector along the x direction was emitted from its tip or a pair of edge dislocations of Burgers vectors be ⁱ and be ^–i were emitted from the wedge tip. The conventional mechanism of crack propagation based on the energy release rate was not expected to occur. The calculated results for a few special cases were presented and compared with those reported in the literature.     

Monotonic and cyclic crack tip plasticity

Monotonic and cyclic plastic zone sizes were measured in a medium strength ferrite-pearlite steel (BM 45) tested in fatigue at 25 Hz at room temperature. Two methods were applied: microhardness and the recently developed ‘fatigue in compression’ technique. The results obtained are discussed in terms of accuracy and reliability.The retardation effect due to overloads was also studied in the same material and is illustrated experimentally as a $\text{d}\text{a}\text{d}\text{N}$ vs ΔK curve. This effect emphasizes the importance of an accurate evaluation of both the size and shape of the overall plastic zone. The shape and dimensions of the cyclic plastic zones seem to indicate that in ductile metals the steady state of fatigue crack growth occurs under plane strain conditions.     

Fatigue crack growth through a residual stress field introduced by plastic beam bending

We present predictions and measurements of fatigue crack growth rates in plastically bent aluminium 2024‐T351 beams. Beam bending and fatigue were carefully controlled to minimize factors other than residual stress that could affect the fatigue crack growth rate, such as large plastic strains or residual stress relaxation. The residual stress introduced by bending was characterized by a bending method and by the slitting method, with excellent agreement between the two methods. Crack growth rates were predicted by three linear elastic fracture mechanics (LEFM) superposition based methods and compared to experimental measurements. The prediction that included the effects of partial crack closure correlated with experimental data to within the variability normally observed in fatigue crack growth rate testing of nominally residual stress free material. Therefore, we conclude that crack growth through residual stress fields may be predicted using the concept of superposition as accurately as crack growth through residual stress free material, provided that the residual stress is accurately known, the residual stress remains stable during fatigue, the material properties are not changed by the introduction of residual stress, and that the effect, if any, of partial crack closure is taken into account.     

A numerical study of fatigue crack closure induced by plasticity

Crack closure delays the intrinsic mechanisms responsible for crack growth, therefore, it must be considered in fatigue crack growth modelling. The objective of this work is to develop a numerical procedure to predict crack closure induced by plasticity. First the crack closure was experimentally measured on M(T) 6082‐T6 aluminium alloy specimens of 3 mm thickness. A pin microgauge was used with the compliance technique. Then different parameters of the numerical procedure were analysed, namely the finite element mesh and the crack propagation scheme. The size of crack‐tip elements has an important influence and it is recommended to be of the same order of cyclic plastic zone. Crack‐opening levels only 10% lower than experimental results were obtained considering kinematic hardening and two load cycles in each increment.