CRACK OPENING STRESS MEASUREMENTS OF SURFACE CRACKS IN 7075-T6 ALUMINIUM ALLOY PLATE SPECIMEN THROUGH ELECTRON FRACTOGRAPHY

Abstract— Crack opening stress measurements were carried out on 9.6 mm thick specimens of 7075-T6 aluminium alloy with semi-elliptical surface cracks. Measurements were made through a fractographic technique based on a load sequence which can produce distinct striation characteristics on the fracture surface. The crack opening stress S _op is deduced from the striation pattern. The variation of S _op along the crack periphery and during crack extension was measured. Close to the front surface S _op is higher due to plane stress condition. At a large crack depth a strong influence of plasticity in the ligament on S _op was found, i.e. S _op decreases as the crack extends to breakthrough. The agreement of d a /d N =Δ K _eff curves between surface cracks and through cracks data was only found for a limited range of crack depth of the elliptical cracks.     

CRACK CLOSURE EFFECT ON CRACK GROWTH RATE AT 650°C IN DOUBLE NOTCHED SPECIMENS OF A NICKEL BASE SUPERALLOY

Abstract— Creep-fatigue tests were performed at 650°C in air on a N18 nickel base superalloy, using double notched and smooth specimens. The deformation mechanisms observed by TEM at the notch root are shown to be compatible with the constitutive set of equations used in the finite element analysis which is presented. For a given K _max at the notch root, the crack growth rate is much higher in a notched specimen than in a smooth one. This effect can be explained by a variation of the crack closure stress level with the local R ratio and the local stress. A strong accelerating effect of the R ratio, especially for negative values, is found in smooth specimens. Introducing a K _op correction in the experimental results leads to a good agreement between the measured crack growth rate plotted versus K _eff in notched and smooth samples.     

FATIGUE CRACK GROWTH OF SILICON NITRIDE WITH CRACK WEDGING BY FINE FRAGMENTS

Abstract— Fatigue crack growth tests of silicon nitride Si₃N₄ were carried out under four-point bending using square bar specimens at room temperature. A pre-crack was introduced by a bridge indentation method. Decreasing K -type tests at stress ratios of R = 0.1 and 0.6 and also under static load were first carried out, and after observing the cessation of crack growth, K -increasing tests were performed except for the case of a static load. Crack closure was observed on most specimens by the elastic compliance method. Furthermore, SEM observations of the crack paths were made to see what was happening during crack growth. The threshold and the region of steady crack growth were observed more clearly under cyclic loading, and an effect of load cycling certainly existed which became more evident when the maximum stress intensity factor K _max approached the threshold. A wedge effect, caused by fine fragments on the crack surface, played an important role in crack closure behaviour of each specimen, and it is suggested that the crack growth rate is controlled by both the effective stress intensity range Δ K _eff and the effective mean stress intensity factor K _m,eff at least as a first approximation.     

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.     

AN ASSESSMENT OF CRACK CLOSURE AND THE EXTENT OF THE SHORT CRACK REGIME IN Q1N (HY80) STEEL

Abstract— The paper addresses some aspects of the differences in fatigue crack growth rate behaviour and threshold values obtained for long through-cracks, short through-cracks and surface cracks. Attention is focused on plasticity induced closure in the wake behind the growing crack tip. For long cracks at high K _max, closure is found to depend in a linear manner on K _max, i.e. K _op, increases with the size of the monotonic plastic zone. Closure increases at low δ K and this is primarily a consequence of the load shedding procedure. If short through-cracks are prepared by machining specimens containing long cracks, a substantial part of the plastic wake is removed and this can produce marked effects on the closure contribution during subsequent growth. The length of crack "closed" in a long crack threshold test was found to be of the order of 1 mm. Cracks less than this length exhibited "short crack" behaviour: greater than this length, they behaved as "long cracks", with plastic wake effects apparently fully operative. Small surface cracks exhibit "long crack" behaviour at lengths as short as 0.2 mm and reasons for this are discussed.     

Determination of the opening load for a growing fatigue crack: evaluation of experimental data reduction techniques and analytical models

In metallic materials, growing cracks will remain closed or partially closed for a portion of the applied cyclic load as a consequence of plastically deformed material left in the wake of a growing crack, surface roughness along the crack surfaces, or corrosion debris. Proper characterization of this crack closure and the subsequent opening load is required for accurate prediction of crack growth. In the laboratory, global load–displacement data are commonly used in conjunction with a data reduction technique to estimate the opening load for a growing crack. Different data reduction techniques will be compared, and the influence of data smoothing will be demonstrated, using AA 7075-T651 specimens tested under constant amplitude cyclic loading with load ratios R = 0.1, 0.2, and 0.3. The ratio of maximum stress intensity factor to plane strain fracture toughness was approximately K _max / K _Ic = 0.5. The measured crack opening loads are also compared with predictions obtained from two different strip-yield models and three-dimensional elastic–plastic finite element analyses. Results show the necessity of using smoothed data, and the poor behaviour of the compliance offset data reduction technique, when analysing high load ratio data. A modification to this technique is proposed which improves crack opening load estimates. Overall, the analytical model predictions compare well with the experimental results; especially those results generated using the modified compliance offset technique.     

FINITE ELEMENT ANALYSIS OF SPECIMEN GEOMETRY EFFECTS ON FATIGUE CRACK CLOSURE

Abstract— Elastic-plastic finite element analysis is used to study fatigue crack closure at three different crack length to width ratios for three plane stress specimen geometries: center-cracked plate, single-edge-cracked plate (tension), and single-edge-cracked plate (bend). The maximum stress to flow stress ratio, S_max/σ_O, which successfully describes closure results in many center-cracked plate configurations, does not correlate the effect of different geometries on the normalized opening stress, S _open/ S _max. Crack opening stresses for different geometries and crack lengths are successfully correlated by a normalized stress intensity parameter, K _max/ K ₀, where K ₀=σ₀φa. The quality of the correlation is very high at small K _max/ K ₀, and gradually deteriorates as K _max/ K ₀ increases beyond the small-scale yielding regime.     

EXAMINATION OF SHORT-CRACK MEASUREMENT AND MODELLING UNDER CYCLIC INELASTIC CONDITIONS

The opening and closure behaviour of short fatigue cracks is seen as one of the important phenomena which control fatigue life of components where a major part of life consists of the growth of short cracks. Therefore attempts are undertaken to experimentally assess and to model the behaviour of short cracks with respect to opening and closure. In this paper crack opening results obtained by Sunder et al. through SEM evaluation of striation patterns of 2000 series aluminium alloys are examined and compared to predictions using a model recently developed for fatigue life prediction based on fracture mechanics of short cracks. Sunder's technique for crack opening measurements involves particular load sequences with increasing and decreasing load ranges applied to notched specimens with naturally nucleated surface cracks where crack opening levels are identified by steady-state striation widths for increasing load ranges. A detailed review of Sunder's results, however, indicates a number of inconsistencies and contradictions which are discussed. Opening and closure behaviour of short fatigue cracks, in particular for inelastic conditions, is compared to predictions obtained with the above-mentioned model which incorporates a constant strain opening and closure assumption. For inelastic conditions that may develop at notches this assumption means that cracks would close at considerably lower stress levels as compared to the opening stress which becomes important when effective (local) stress-strain ranges are to be determined for fatigue life prediction under spectrum loading. The constant strain assumption is supported by a number of experimental observations from the literature as discussed in the paper. The approximative nature of this assumption and further details of the model are pointed out which show a need for further developments.     

AN ANALYTICAL PROCEDURE FOR PREDICTING OPENING LOADS OF CRACKS AT NOTCHES

Abstract— An analytical procedure for the prediction of opening load levels for cracks growing from notches is presented, and estimates are made using experimental crack opening load data. The procedure is based on McClung's original procedure for estimating the local elastic-plastic stress—strain situation at the point of a hypothetical crack tip in a notched but uncracked body. A crack opening stress value for a crack in an urmotched body under the same stress—strain condition is then predicted. The corresponding opening load level for the crack stress-strain configuration in the notched but uncracked body is then predicted with a simple backward calculation. For the evaluation of the elastic-plastic stress distribution, simple analytical relationships, such as Neuber's rule, are used. Estimation of the crack opening stress level is performed using various crack opening stress formulae reported in the literature for cracks in unnotched specimens under a uniform stress distribution. The accuracy of all the investigated crack opening stress formulae within the scope of the presented procedure is checked, and discussed in detail using experimental data sets for opening load levels of comer cracks and through-thickness cracks in notched specimens of FeE460 and A15086. The predicted results using Newman's crack opening stress formulae, simply modified in respect to the definition of the flow stress, have been identified to be qualitatively and quantitatively consistent with the trends observed in experimental crack opening data.     

CREEP-FATIGUE CRACK GROWTH BEHAVIOR IN 1Cr-1Mo-0.25V STEELS. PART I: ESTIMATION OF CRACK TIP PARAMETERS

Abstract— Non-linear finite element (FEM) analyses, involving various creep deformation laws, as well as experiments with hold times of 100 s and 15 min were performed on compact type specimens with stationary cracks. The work was aimed at developing accurate expressions for estimating the small-scale creep parameters, ( C _t)_avg, for 1Cr-1Mo-0.25V steel at 538°C (1000°F). Here ( C _t)_avg is a representative value for the small-scale creep parameter C _t, averaged over a hold period under the conditions of creep-fatigue loading. These expressions were then applied to crack growth data obtained from specimens tested under the various hold times. When an elastic-plastic-primary creep-secondary creep constitutive model was used in the FEM analyses, the calculated values of C _t compared well with the measured values. The FEM results also showed that the accumulated creep deformation during the hold time was not significantly reversed during the unloading portion of the creep-fatigue cycle for this material. Therefore, a new method of estimating (C_t)_avg is proposed on the basis of these numerical and experimental results.     

MECHANICALLY SHORT CRACK GROWTH FROM NOTCHES IN A MILD STEEL

Abstract— Two L-notched specimens made of mild steel (average grain size =30 μm) and having root radii of 0.1 mm and 3 mm, and also a smooth surface specimen were cyclically loaded at different stress levels at R =−1 and at R = 0. A technique based on miniature strain gauges was successfully used to monitor the depth and the opening level of mechanically short cracks of depths from 0.015 mm to 0.5 mm. Three dimensional FEM computations were made to obtain appropriate calibration curves for varying crack aspect ratios and gauge eccentricities as well as notch plastic strain distributions. The fracture of L-notched specimens having a root radius of 0.1 mm was characterized by an early and multiple crack initiation phase (defined by a crack depth of 30 μm), and the short crack growth rates showed a mechanical behaviour different from that of long cracks (large discrepancies at the same Δ K -value, crack deceleration at R =−1 even beyond the notch plastic zone). For smooth surface specimens both the initiation and the propagation of a single short crack represented important fractions of the total life; the short crack growth rates were high and continuously increasing. The notch influence was highly reduced when the stress singularity is truncated by a 3 mm radius. The cracking behaviour was, in several aspects, close to that at smooth surfaces. The evolutions of crack closure were analyzed in each condition (transient decrease and stabilized value of the closure ratio U =Δ K _eff/Δ K ) and were shown to have a strong influence on short crack growth. Most of the short crack growth rates obtained in the various geometry/loading conditions are well consolidated with LEFM long crack growth rates using the Δ K _eff parameter.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

RELATIONSHIPS BETWEEN THE J-INTEGRAL AND THE CRACK TIP OPENING DISPLACEMENT FOR STATIONARY CRACKS IN WELDMENTS AT PLASTIC COLLAPSE

Abstract— Slip line field and finite-element analyses for J and crack tip opening displacement, δ_t, at plastic collapse are performed for an idealised weldment. The relationship between these two quantities is shown to depend on the nature of the loading (tension or bending), the ratio of yield stresses in weld and base materials, and on the width of the weld compared to the remaining ligament ahead of the crack. Cases where the weldment behaves as a single weld material are determined. However, it is also shown that there is a significant range of cases where the base material yield stress governs the relationship between J and δ_t, at collapse, even when the crack is located in weld metal.
It is shown that the relationship between J and δ_t, at plastic collapse only occurs at loads very close to the collapse load unless the crack is located close to the weld/base boundary or the weld width is small compared to the remaining ligament ahead of the crack. More generally, the weldment behaves as a single weld material in terms of the relationship between J and δ_t, and conventional fracture assessments using J or δ_t, are equivalent.     

ON THE TRANSITION FROM NEAR-THRESHOLD TO INTERMEDIATE GROWTH RATES IN FATIGUE

Abstract— Evidence is presented that the cyclic stress intensity threshold for fatigue crack growth in A1 2219-T851 is associated with a critical maximum value of stress intensity, K _c. This relationship is discovered by measuring the local value of stress intensity at the crack tip which is less than the applied stress intensity because of fatigue induced compressive residual stresses in the plastic zone. Crack growth rates and values of the crack tip residual stress are measured as functions of load ratio. For local stress intensities greater than K _c, the growth rate follows a power-law relationship, increasing monotonically with δ K . For local stress intensities below K _c, growth rates are also sensitive to the cyclic stress range, δσ. If the stress range is small, a threshold to growth, typical of long cracks, is seen. When the cracks are short and δσ exceeds a critical value, growth rates are a complex function of both δσ and δ K . This behavior is attributed to the effect of δσ on the propagation of the crack front past obstacles such as grain boundaries.     

Parametric study of oblique edge cracks under cyclic contact loading

The problem of a two-dimensional elastic body, carrying an inclined edge crack and loaded by a cylinder rolling on the surface, is solved by the weight function method. The load induced by the cylinder on the cracked body was represented by the Hertzian pressure distribution, and the nominal stress distribution in the uncracked body was numerically evaluated by the superposition principle. The crack opening displacement components were obtained by an analytical Green's function. The partial crack closure was considered and the influence of the mutual forces between the crack faces included in the analysis, by which the effective stress intensity factors K _I and K _II could be evaluated. By considering different friction conditions between the crack surfaces and several crack inclinations, the evolutions of the effective K _I and K _II during typical loading cycles were analysed.     

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.     

A SIMPLIFIED LABORATORY APPROACH FOR THE PREDICTION OF SHORT CRACK BEHAVIOR IN ENGINEERING STRUCTURES

Abstract— Conventionally determined fatigue threshold information (ASTM E647) can lead to non-conservative estimates of fatigue lifetimes when these data are utilized in damage tolerant design assessments. The non-conservative nature of such data can be attributed primarily to the development of excessively large amounts of crack closure at low R -ratios, particularly at near threshold stress intensity factor levels. These high closure levels attenuate the effective stress intensity condition prevailing at the crack tip and confound attempts to predict the behavior of short cracks that exhibit limited crack closure. A modified test procedure, involving constant maximum stress intensity factor ( K ^c_max) test conditions, is described which identifies fatigue crack propagation (FCP) threshold behavior in the absence of detectable amounts of crack closure. These data have been generated with conventional long crack specimens for several aluminum, iron, and nickel-based alloys and which are shown to closely simulate the FCP response of short cracks in these engineering materials. As such, the modified threshold test procedure, incorporating constant K _max loading conditions, represents a valuable tool in the prediction of the cyclic lifetime of engineering components. The stress-cyclic lifetime (S-N) curve for aluminum butt-welded beams was computed based on K ^c_max data and found to be in excellent agreement with actual test results.     

ELASTIC-PLASTIC FRACTURE MECHANICS FOR INITIATION AND PROPAGATION OF NOTCH FATIGUE CRACKS

Abstract Initiation and propagation are considered to be controlled by the extent of total plastic shear deformation φ. Crack initiation and crack propagation occur when φ, exceeds a critical threshold value which can be equated to threshold conditions determined from linear elastic fracture mechanics analyses. When a crack is in a plastically deformed zone φ_t=φ _p +φ _e . where φ _p is the component of φ _t due to notch bulk plasticity and φ _e , is the component of φ _t due to a linear elastic fracture mechanics (LEFM) analysis of the crack tip plasticity field.
When cracks initiate at notch roots φ _t > φ_th. As the crack propagates in the notch plastic zone the rate of decrease of v _p will be different from the rate of increase of φ _e and it is possible for φ _t to decrease to a level below φ_th thereby creating a non-propagating crack.     

CLOSURE AND GROWTH OF MODE I CRACKS IN BIAXIAL FATIGUE

Abstract— —The closure behavior of mode I fatigue cracks under biaxial loading is studied with an elastic-plastic plane stress finite element model. Biaxial stresses are shown to have a significant impact on crack closure behavior at higher maximum stresses. In general, normalized crack opening stresses are highest for equibiaxial loading and lowest for pure shear loading. The differences are apparently negligible for maximum applied stresses less than about 0.4 σ₀. Experimental crack growth data are quantitatively consistent with these trends. Correlations of the experimental data with a simple Δ K _eff were successful as first-order engineering estimates. Changes in forward and reversed plastic zone sizes with biaxiality are not entirely consistent with trends in crack growth rates.