In situ scanning electron microscopy study of fatigue crack propagation

The fatigue crack propagation rate is influenced by various mechanisms at the very vicinity of the crack tip, e.g., local plasticity and/or creep, microcracking, crack branching, and crack closure induced by plasticity and roughness. To study these mechanisms and their influence on crack propagation rate during different loadings, in situ scanning electron microscope studies have been performed. Throughout the load cycles images were taken and analyzed with an image analysis technique to measure the displacements around the crack tip. The obtained data can be used to determine compliance curves at any point along the crack, crack shapes, and the displacement field in the crack tip vicinity. The technique has been used to analyze which mechanisms of crack propagation are realized during, e.g., fatigue with overloads, and thermomechanical fatigue. The results were compared with results from measurements using the direct current potential drop technique, and it was found that various load conditions promote different mechanisms for crack propagation. __________ Translated from Problemy Prochnosti, No. 1, pp. 159–162, January–February, 2008.     

SEM study of overload effects during fatigue crack growth using an image analysing technique and potential drop measures

To study the mechanisms affecting the crack propagation rate for fatigue cracks exposed to an overload, an in situ scanning electron microscope technique was used, together with potential drop measurements. High‐resolution images were analysed with an image analysis program to measure the displacements along the crack, and the potential drop technique was employed to measure the electrical contact between the fatigue crack surfaces. The crack closure level could, by image analysis, be determined as close as 1 μm from the crack tip. The indications from the image analysis pointed towards a somewhat lower closure load as compared to the potential drop technique. The effect of an overload on the crack propagation rate was found to depend on the magnitude of the overload in combination with the steady‐state conditions. Both overload induced crack retardation and crack acceleration was noticed to occur.     

Fatigue crack closure: A myth or a misconception?

In this paper, we have extended our previous study on fatigue crack closure to examine the phenomenon of crack opening displacement (COD) and its impact on the crack tip fields in both 2D and 3D specimen geometries using full‐field experimental measurements and integrated finite element modelling. Digital image correlation (DIC) and digital volume correlation (DVC) were used to measure the near‐tip material responses on the surfaces (DIC) and the interior (DVC) of the specimens. Materials with elastic‐plastic and large plastic characteristics were chosen for the study, where plasticity‐induced premature contact between the crack flanks is known to occur. Displacement maps around the cracks were obtained using DIC and DVC at selected load increments and were introduced as boundary conditions into the finite element (FE) models to obtain the “effective” crack driving force in terms of J‐integral, and the results were compared with those “nominal” from the standard FE analysis. Both visual observation and compliance curves were used to determine the “crack opening” levels; whilst the impacts of the crack opening on the crack driving force J and the normal strains ahead of the crack tip were evaluated in 2D and 3D. The results from the study indicate that, crack closure, although clearly identifiable in the compliance curves, does not appear to impact on global crack driving force, such as J‐integral, or strains ahead of the crack tip; hence, it may well be a misconception.     

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.     

THREE-DIMENSIONAL CRACK-SHAPE EFFECTS DURING THE GROWTH OF SMALL SURFACE FATIGUE CRACKS IN A TITANIUM-BASE ALLOY

Abstract— A basic study was performed on the evolution of three-dimensional shapes of small surface fatigue cracks during fatigue, and the effect of this evolution on small-crack growth behavior of a titanium-base alloy. Specifically, the nature and the magnitude of variations in crack aspect ratio, a/c (a is the crack depth and c is the half-surface crack length), during cyclic crack growth and its impact on growth rates have been studied. Experiments were performed on naturally initiated micro-cracks in a microstructure consisting of equiaxed primary-α₂ phase in a Widmanstätten (transformed β) matrix. Several cracks under stress ratio (R) levels of 0.1 and ?1, were studied. A specialized experimental system, consisting of a laser interferometer (to measure precisely the small-crack surface displacements), and a photo microscope (to automatically and continuously photograph the fatigue micro-cracks) was employed in the study. Apparent aspect ratios of surface cracks were calculated from the compliance response and the surface crack length data as a function of fatigue cycles. These data enabled accurate calculations of growth rates at the surface crack tip as well as the tip at depth in the bulk over the entire crack growth period, thus giving an insight into the crack growth process. Measurements of closure levels of small cracks were also performed and were used to partly account for the differences in growth rates. In the comparisons of small-crack growth data with the large-crack data, surface growth rates correlated relatively well with the large-crack data. Growth rates at depth exhibited large variations due to the irregularity of crack fronts at this location, and these rates deviated significantly from the large-crack behavior. Additionally, these growth rates varied between different cracks. An attempt was made to rationalize these observations in terms of the effects of inhomogeneities present in the microstructure.     

Simulating small crack growth behaviour using crystal plasticity theory and finite element analysis

Predictions of small crack growth under cyclic loading in aluminium alloy 7075 are performed using finite element analysis (FEA), and results are compared with published experimental data. A double‐slip crystal plasticity model is implemented within the analyses to enable the anisotropic nature of individual grains to be approximated. Small edge‐cracks in a single grain with a starting length of 6 μm are incrementally grown following a node‐release scheme. Crack‐tip opening displacements (CTOD) and crack opening stresses are calculated during the simulated crack growth, and da/dN against ΔK diagrams are computed. Interactions between the crack tip and a grain boundary are also considered. The computations are shown to accurately capture the magnitude and the variability normally observed in small crack fatigue data.     

Plastic mismatch effect on plasticity induced crack closure: Fatigue crack propagation perpendicularly across a plastically mismatched interface

In the present work, comprehensive investigation of both theoretical analysis and numerical simulation was carried out to investigate the plastic mismatch effect on plasticity induced crack closure (PICC) behavior and effective fatigue crack tip driving force. During the process of crack tip approaching interface, crack tip load and crack tip load ratio will change, resulting in the change of PICC degree. When the crack propagates towards higher strength side, K_op/K_max increases; when the crack propagates towards lower strength side, K_op/K_max decreases firstly and then increases. The two mechanisms of “interface plastic mismatch effect on nominal fatigue crack tip driving force” and “interface plastic mismatch effect on PICC degree” were compared. The second mechanism must be considered when building crack tip driving force model for describing fatigue crack crossing plastically mismatched interface, because it is more physically factual and maybe more important than the first mechanism.     

A threshold fatigue crack closure model: Part I – model development

A fatigue crack closure model is developed that includes the effects of, and interactions between, the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out‐of‐plane cracking and multi‐axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two‐dimensional sawtooths, whose geometry induces mixed‐mode crack‐tip stresses. Continuum mechanics and crack‐tip dislocation concepts are combined to relate crack face displacements to crack‐tip loads. Geometric criteria are used to determine closure loads from crack‐face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. The CROP model is verified with experimental data in part II of this paper.     

Investigation of fatigue crack closure using multiscale image correlation experiments

Two full-field macroscale methods are introduced for estimating fatigue crack opening levels based on digital image correlation (DIC) displacement measurements near the crack tip. Crack opening levels from these two full-field methods are compared to results from a third (microscale) method that directly measures opening of the crack flanks immediately behind the crack tip using two-point DIC displacement gages. Of the two full-field methods, the first one measures effective stress intensity factors through the displacement field (over a wide region behind and ahead of the crack tip). This method reveals crack opening levels comparable to the limiting values (crack opening levels far from the crack tip) from the third method (microscale). The second full-field method involves a compliance offset measurement based on displacements obtained near the crack tip. This method delivers results comparable to crack tip opening levels from the microscale two-point method. The results of these experiments point to a normalized crack tip opening level of 0.35 for R ∼ 0 loading in grade 2 titanium. This opening level was found at low and intermediate ΔK levels. It is shown that the second full-field macroscale method indicates crack opening levels comparable to surface crack tip opening levels (corresponding to unzipping of the entire crack). This indicates that effective stress intensity factors determined from full-field displacements could be used to predict crack opening levels.     

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.     

Introducing the compliance ratio concept for determining effective stress intensity

Local crack tip strain measurements show that the conventional determination of ΔK effective may be misleading, especially when opening loads are relatively high as is often the case in the near-threshold regime. The conventional method assumes that K-opening can be directly related to a deviation in the linearity of a load vs crack mouth displacement curve (‘compliance offset method'). Although this deviation in linearity can be attributed to closure, local strain measurements show that significant crack tip strain can occur below the K-opening load. The redistribution of stresses associated with a partially open crack and the effect of this redistribution on the stress field in front of the crack cannot be determined simply on the basis of a change in the slope of the load–displacement curve. However, a recent addition to ASTM E-647 (Recommended Practice for Determination of Fatigue Crack Opening Load from Compliance) implies that it can. An alternative ‘compliance ratio' technique based on local crack tip strain is presented. A modification of this technique allowing the use of remote compliance measurements to account for crack tip strain below the opening load is suggested.     

Corrosion Fracture of Structural Metallic Materials: Effect of Electrochemical Conditions in Crack

Abstract: The work is a compressed review based on the summarised results and the original approach for study of corrosion crack growth, taking into account local electrochemical conditions in the crack tip, which was developed at the Karpenko Physico‐Mechanical Institute of NASU. The model scheme of the pre‐fracture zone in the corrosion crack tip, which can be defined by the local values of pH of solution, electrode potential of metal E and stress intensity factor K_I is proposed. For its realisation, the special method and testing equipment for corrosion crack growth study and local electrochemical measurements in the crack were developed. The variation of the electrochemical conditions in corrosion cracks was studied, and it has been found that some stabilised levels of the pH and E values can be achieved in the tip of a non‐propagating and a propagating crack under static and cyclic loading during of exposure time. On this ground, the method for forecasting of the threshold stress intensity factor K_ISCC under stress corrosion cracking was proposed using these characteristic values of pH and E. This method was also adopted for the determination of the threshold stress intensity factor K_th under corrosion fatigue. The special method for determining corrosion fatigue crack growth rate diagrams based on consideration of extreme electrochemical conditions in the crack tip was developed. It has been proven that such diagrams reflect the extreme influence of the environmental factor on corrosion fracture of material, and they may be recommended as the base for the remaining lifetime calculation of the structural elements exploited under environmental conditions.     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

Experimental investigation of crack growth direction in multiple cracks

In this paper, the interaction between multiple cracks in crack growth direction is studied in an aluminium alloy under static and fatigue loading. Self similar as well as non‐self‐similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the criterion for crack coalescence and crack growth direction are expressed in terms of the crack positions defined by crack offset and crack tip distances. The criterion presented in this study can be used to determine the limiting value of crack tip and crack offset distance and to determine the mode in which cracks coalesce during their growth process. Experimental results and crack interaction criterion presented under various crack positions and size conditions could be used to derive a new evaluation method of crack growth in multiple crack geometry.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

Fatigue limit evaluation of notches,small cracks and defects: an engineering approach

In this paper, the average stress method for the fatigue limit evaluation of stress raising geometrical features is revised and extended. In particular, an analytical close‐form approach was used and the linear elastic stress equations were modified by taking into account the effect of nominal stress on the local stress distribution. Hence, the average tangential stress was correctly evaluated over a distance of 2a₀, where a₀ was El Haddad's short crack constant, for long and small notches as well as for crack‐like notches. When this model is applied to a wide range of geometrical features subjected to mode I fatigue loading, the classical shape of the curves of the Kitagawa–Takahashi diagram was obtained for changes in crack‐like notch size. Similarly, notch sensitivity was estimated by reducing the notch tip radius. The accuracy of the proposed method in predicting fatigue limits was then checked by using experimental data taken from the literature and generated on testing specimens weakened by rounded and sharp notches as well as by small artificial defects.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

The effect of microstructures on fatigue crack growth in Q345 steel welded joint

It is a traditional that the fatigue crack growth behavior is sensitive to microstructure in threshold regime, while it is sensitive to R‐ratio in Paris regime. Fatigue test is carried out for welded joints of a Q345 steel where the compact tension specimens with 3.8 and 12.5 mm thickness are used, and comparisons of fatigue crack growth behavior between base metal and a few different locations in the welded joint are considered in Paris regime. Welding residual stresses are removed by heat treatment to focus the study on the microstructural effect. It is shown that fatigue crack growth rate (FCGR) in the base metal is not sensitive to R‐ratio, but the FCGR increases in the overheated zone, the fusion zone and the weld metal zone with R‐ratio increasing. To the low R‐ratio, FCGR in the three zones is smaller than that in the base metal, but they approximate the same with base metal under the high R‐ratio. The mechanism of fatigue crack growth is analyzed through crack path in microstructures and SEM fractograph. The coarse‐grained ferrite in the base metal is of benefit to relaxation of the average stress at the crack tip, and the fatigue crack growth predicts branching and deflection within above different locations in the welded joint. These tortuous crack paths with crack branching and deflection will promote crack closure as well as crack‐tip stress shielding and then resulted in higher crack growth resistance.