Prediction of fatigue crack growth rates using crack closure finite element analysis

A three-dimensional finite element fatigue crack closure model of a corner crack and of a through thickness crack has been developed to evaluate the range of effective stress intensity factor from the distribution of the range of stress ahead of the crack tip. The corresponding fatigue crack growth rate was evaluated from a Paris law fit to experimental data from high stress ratio tests. The point of origin for the range of stress distribution was adjusted in accordance with Irwin’s plastic zone correction. Encouraging comparisons of finite element predictions of fatigue crack growth rate incorporating closure effects with experimental measurements were obtained.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Plastic strain distribution at the tip of a fatigue crack. application to fatigue crack closure in the threshold regime

The fatigue crack growth rate behaviour of a Co-33 wt pct Ni alloy was investigated at room temperature down to the threshold regime using CT specimens for two load ratios 0.1 and 0.3. Cyclic equivalent plastic strain distributions along an axis normal to the crack plane were experimentally determined over the whole range of crack growth rates using two techniques microhardness and a quantitative metallographic technique applied to twins, both calibrated on low cycle fatigue specimens. These experimental values were compared with theoretical curves as obtained from the monotonic plane strain finite element analysis of Tracey and adapted to cyclic loading according to the procedure proposed by Rice. A good agreement was found in stage II crack growth in the vicinity of the crack tip but a discrepancy was observed in the low crack growth rate regime, indicative of crack closure. It was possible to determine the effective amplitude of the stress intensity factor which accounts for this discrepancy and an intrinsic crack growth law was obtained which obeys Paris equation and which applies in the whole crack growth rate range independently of the load ratio.     

加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟

采用不同应力比条件下的16MnR钢紧凑拉伸试样,设计了三种有限元分析模型,即不考虑加载历史效应的静态裂纹扩展模型,同时考虑加载历史和裂纹闭合的动态裂纹扩展模型以及仅考虑加载历史的伪动态裂纹扩展模型,对疲劳裂纹闭合过程、裂纹尖端的应力-应变迟滞环、疲劳损伤和裂纹扩展速率进行了数值模拟与分析,进而着重探讨了加载历史和裂纹闭合影响疲劳裂纹扩展行为的交互作用机制。结果表明:对于同类分析模型,应力比越大越不容易产生裂纹闭合;而在应力比相同的情况下,加载历史引起的残余压应力对裂纹闭合有明显的促进作用。裂纹闭合效应阻碍了平均应力的松弛,减小了裂纹尖端附近的应力-应变场强度、疲劳损伤和裂纹扩展速率,而加载历史引起的残余压应力则加快了平均应力的松弛和抑制了棘轮效应。与实验结果比较发现,只有同时考虑了裂纹闭合效应和加载历史影响的动态裂纹扩展模型,才能对疲劳裂纹扩展行为进行准确、定量的模拟。     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH-THICKNESS AND SURFACE FATIGUE CRACKS

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–^12–10–⁶m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

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.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Surface crack and cracks networks in biaxial fatigue

Semi-elliptical fatigue crack growth in 304 L stainless steel, under biaxial loading, was investigated. Compared to those of through-cracks under uniaxial loading, the growth rate of surface cracks is increased by a non-singular compressive stress and reduced by a tensile stress, when R = 0. Plasticity-induced crack closure under biaxial loading was investigated through 3D finite element simulations with node release. Roughness and phase-transformation-induced closure effects were also discussed. The interactions in two-directional crack networks under biaxial tension were investigated numerically. It appears that the presence of orthogonal cracks should not be ignored. The beneficial influence of interaction-induced mode-mixities was highlighted.     

Crack initiation under far-field cyclic compression and the study of short fatigue cracks

A procedure involving crack initiation under far-field cyclic compression is used to study the fatigue behavior of small flaws which are ˜0.3–0.5 mm in length and are amenable to linear elastic fracture mechanics (LEFM) characterization. This technique enables the determination of the threshold stress intensity range at which crack growth begins for small flaws and provides insight into some closure characteristics. Cracks were propagated in notched specimens of a bainitic steel subjected to fully compressive remote cyclic loads, until complete crack arrest occurred after growth over a distance of only a fraction of a mm at a progressively decreasing velocity. Following this, physically small flaws were obtained by machining away the notch. For the loads examined, the results indicate that the extent of damage left at the tip of the crack grown (and arrested) under remote compression is not large enough to affect subsequent tensile fatigue crack growth, when closure effects are not significant (e.g. at high load ratios). At high load ratios, the growth of small linear elastic cracks is identical to that of corresponding long flaws subjected to the same stress intensity range, which corroborates the similitude concept implicit in the nominal use of LEFM. At low load ratios, however, short tensile cracks propagate substantially faster than the longer flaws and exhibit lower threshold stress intensity range levels. Such apparent differences in their growth rates seem to arise, to a large extent, from the differences in their closure behavior, as indicated clearly from various aspects of the compression method. Global measurements of closure, with their inherent uncertainties, however, cannot account completely for the anomalous behavior of short flaws and for the effect of load ratio on short crack growth. Closure of short flaws begins to develop after growth over a minimum distance of about 0.5 mm in this steel. The significance and limitations of the compression technique are discussed and possible mechanisms responsible for the differences between long and short fatigue cracks are outlined.     

Fatigue life prediction of semi-elliptical surface crack in 14MnNbq bridge steel

The fatigue life prediction of semi-elliptical surface crack in 14MnNbq bridge steel is discussed in this paper. The FCG rates under different stress ratios R as well as FCG behavior under tensile and bending loading conditions are investigated experimentally. Moreover, an approach to predict surface crack growth is discussed, and the advantage of the approach is that the data used in the prediction is obtained from the testing of through-thickness cracks. The effects of crack closure on predictions are also considered and the data corrected by crack closure of through-thickness crack is used. Comparison results show that the corrected prediction with consideration of crack closure provides much better predictions than the normal ones. And reasonable agreement is obtained between the predicted and experimental results.     

CRACK GROWTH BEHAVIOUR IN A THERMAL FATIGUE TEST. EXPERIMENTS AND CALCULATIONS

Abstract— This study is concerned with the results of experiments in which thermal cycles have been repeatedly applied through the wall thickness of axisymmetrically cracked tubular specimens. The investigated material is a Cr–Mo steel used for the moulds when fabricating centrifugally cast iron pipes. Crack growth rates have been measured by using the interrupted tests technique. A methodology is proposed to model the crack growth rates under such thermal fatigue loadings. The elastic and plastic stress-strain fields are calculated on the uncracked specimen by means of a finite element code. Special attention was paid to reach a mechanical steady state regime. Fatigue crack growth rates data were obtained, both under isothermal and anisothermal conditions, on CT and SEN specimens. The latter specimens were tested under large-scale yielding in order to obtain the data appropriate to the cyclic stress-strain field calculated in the thermal fatigue specimens. An effective stress intensity factor, which takes into account both plastic strains and crack closure effect, was used to correlate the results of isothermal tests on CT and SEN specimens and to calculate the thermal fatigue crack growth rates in tubular specimens. It is shown that the use of the effective stress intensity factor gives a satisfactory agreement between the observed and the calculated crack growth rates.     

TRANSIENT FATIGUE CRACK GROWTH BEHAVIOUR FOLLOWING SINGLE OVERLOADS AT HIGH STRESS RATIOS

Fatigue crack growth tests with constant amplitude loading and single overload have been performed on a long mode I crack in 2017-T3 aluminium alloy at various stress ratios from 0 to 0.7. Two crack tip parameters of σ_op and σ_tt were evaluated using a finite element analysis for a growing crack under these loading conditions. The former is the crack opening stress and the latter is the applied stress level at which the stress at the crack tip becomes tensile. It was found that transient crack growth behaviour following single overloads at high stress ratios was significantly different from that at a low stress ratio: at higher stress ratios, following the application of the overload, there was a rapid retardation which was followed by an acceleration in growth rate and then a faster return to the steady state level at baseline loading. The experimentally observed transient post-overload behaviour is discussed in terms of the two effective stress range ratios of U_op and U_tt, which are determined from σ_op and σ_tt, respectively. For the stress ratios and overload ratios studied, the results indicate that the changes in U_tt with crack extension after the overload are reasonably consistent with the crack growth rate trends. The stress distribution at minimum applied stress would account for the transient changes in U_tt.     

FATIGUE CRACK GROWTH AND CLOSURE THROUGH A TENSILE RESIDUAL STRESS FIELD UNDER COMPRESSIVE APPLIED LOADING

Abstract— —Fatigue crack growth and closure through a tensile residual stress field under an applied compressive loading is investigated by carrying out various applied stress ratio tests ranging from R = 0 to R = It is found that even under applied compressive loading, fatigue crack growth rates are well correlated with the effective stress intensity factor range and the behaviour of crack closure through a tensile residual stress field is uniquely controlled by an effective stress ratio which takes account of residual stresses. Consequently, the method of predicting fatigue growth rates, using da/d N vs Δ K data from residual stress-free specimens, can be successfully applied to crack growth through a tensile residual stress field. However, previously used simple assumptions may lead to non-conservative estimates of crack growth rates.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

CRACK CLOSURE IN SMALL FATIGUE CRACKS—A COMPARISON OF FINITE ELEMENT PREDICTIONS WITH IN-SITU SCANNING ELECTRON MICROSCOPE MEASUREMENTS

Abstract— A three dimensional, elastic-plastic, finite element analysis of fatigue crack growth and plasticity-induced crack closure has been performed for a range of small, semi-circular cracks. Predicted crack opening displacements have been compared with data obtained from in-situ SEM measurements for a coarse-grained aluminium alloy 2024-T351. The magnitude of fatigue crack closure measured from in-situ SEM measurements was consistently higher than that predicted from the finite element analysis. It is deduced that the higher closure stresses obtained from in-situ SEM measurements are due to the contact of asperities on the fatigue crack surfaces. A simple mathematical model is suggested to describe the fatigue crack closure stress caused by the combination of both a plastic wake and asperities on the fatigue crack surfaces. The predicted fatigue crack closure stresses and their dependence on crack size are consistent with experimental measurement.     

Effects of mean stress and crack closure on fatigue life of spot welds

The effects of mean stress and crack closure on fatigue life of spot welds were investigated. A review showed that several of the previously proposed mean stress corrections give similar results. Fatigue tests on shear and peel loaded specimens were carried out, and the results agreed with the corrections reviewed. The present study shows that crack closure explains the mean stress effects observed. The crack opening force for spot welds was obtained, both experimentally from F–N curves with different load ratios and analytically from the available mean stress corrections. This was verified with detailed finite element simulations. Finally, the experiments and simulations indicate that the use of linear damage accumulation in fatigue life prediction of spot welds can be non‐conservative.     

The influence of cross-sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.