CLOSURE BEHAVIOUR OF SURFACE CRACKS

Abstract— The fatigue crack closure response was investigated for a surface crack in BS4360 50B structural steel, subjected to (1) constant amplitude loading and (2) constant amplitude loading interrupted by a single peak overload. A variety of compliance techniques was employed to determine closure behaviour. The crack mouth gauge measured the bulk, plane strain closure load, while the near tip strain gauge indicated the surface, plane stress closure response. For constant amplitude loading it was found that the surface regions of a surface crack are closed for a greater portion of the load cycle than the maximum depth point. A single peak overload caused different closure and growth rate transients at the surface of the thumbnail crack and at the maximum depth point. For growth rates above 10^-6 mm/cycle, such behaviour agrees with the response of a through crack when subjected to constant amplitude loading, and a single peak overload.     

A MODEL FOR THE FATIGUE LIMIT AND SHORT CRACK BEHAVIOUR RELATED TO SURFACE STRAIN REDISTRIBUTION

A model based on surface strain redistribution and the reduced closure stress of short cracks is shown to successfully predict the fatigue limit and short crack growth behaviour for aluminium alloy 2024-T351. Using this approach, the length of non-propagating cracks can be anticipated. The local stress intensity range may be resolved into two components (first the linear elastic fracture mechanics component and the second is due to surface strain concentration). Consequently, the local stress intensity range of aluminium alloy 2024-T351 is a maximum at a depth of approximately half a grain diameter and a minimum at a depth slightly in excess of three grain diameters. The reduced closure stress for short cracks coupled with the increased applied stress intensity caused by surface strain redistribution accounts for the variation of the effective stress intensity parameter as a function of crack depth. This parameter is a maximum for the smallest possible crack (3 μm) and decreases as crack length increases.     

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.     

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 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.     

Surface-crack propagation in plane-bending fatigue of smooth specimen of low-carbon steel

Long-life fatigue tests of smooth specimens of low-carbon steel were conducted under cyclic plane bending with zero mean stress. The propagation rate of small surface cracks nucleated at the corner of the specimen was measured and analysed from the viewpoints of linear and elastic-plastic fracture mechanics. The rates of crack growth both on the surface and at the depth were higher at larger amplitudes of the applied stress, when they were correlated to the stress intensity range. The J integral range evaluated from the elastic-plastic stress-strain distribution in the depth of the specimen was found to be a unique parameter controlling the growth rate of fatigue cracks both on the surface and at the depth of the specimen, and it was also found that the relation between the growth rate and the J integral for small surface cracks agreed with that for long through-thickness cracks.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234     

FATIGUE CRACK GROWTH AND CLOSURE AT HIGH STRESS RATIOS

Abstract— Fatigue crack growth tests have been carried out on a medium carbon structural steel over a wide range of stress ratios, i.e. from 0 to 0.7. All tests were conducted under constant amplitude loading conditions corresponding to growth rates in the Paris regime. Crack closure behaviour was observed experimentally by a surface strain gauge technique, and numerically by a finite element analysis under plane stress condition. While the crack closure could not be detected by experimental measurements at stress ratios equal to or greater than 0.5, the numerical results showed that closure occurred even at high stress ratios up to 0.7. The differences between experimentally and numerically determined crack opening levels were found for each stress ratio. A cause for these differences is discussed. In addition, two new types of crack tip parameters which have been proposed recently are evaluated by finite element analysis and their relevance to fatigue crack growth are discussed. It is concluded that fatigue crack growth rates are substantially determined by the effective stress intensity factor range which is based on the crack closure concept.     

The effect of grain size on small fatigue crack growth in pure titanium

The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of −1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = −1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range ΔK_eff (after allowing for crack closure, the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, η, of growth rate in coarse-grained material were smaller than those in fine-grained material. The η values were significantly large at a/d 3 (a = crack depth, D = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size.     

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.     

PREDICTION OF THE FATIGUE LIMIT OF CRACKED SPECIMENS BASED ON THE CYCLIC R-CURVE METHOD

Abstract— The propagation behaviour of fatigue cracks emanating from pre-cracks was numerically simulated to evaluate the development of crack closure with crack growth. The crack opening stress intensity factor at the threshold was approximated as a function of the applied stress and the amount of crack extension. Pre-cracked specimens of a medium-carbon steel with a small surface crack and a single-edge crack were fatigued to investigate experimentally the initiation and propagation of cracks from pre-cracks. Crack closure was dynamically measured by using an interferometric strain/displacement gauge. The threshold condition of crack initiation from pre-cracks was given by a constant value of the effective stress intensity range which was equal to the threshold value for long cracks. The cyclic R -curve was constructed in terms of the threshold value of the maximum stress intensity factor as a function of crack extension approximated on the basis of the experimental and numerical results. The cyclic R -curve method was used to predict the fatigue thresholds of pre-cracked specimens. The predicted values of the fatigue limits for crack initiation and fracture, and the length of non-propagating cracks agreed very well with the experimental results.     

Near-threshold fatigue propagation of physically through-thickness short and long cracks in a low alloy steel

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.     

VARIABLE AMPLITUDE LOADING OF SMALL FATIGUE CRACKS IN 6261-T6 ALUMINIUM ALLOY

Abstract— Constant and variable amplitude (VA) loading fatigue studies were carried out on a 6261 aluminium alloy using cylindrical plain hour-glass specimens. Crack growth was monitored via surface replication using cellulose acetate.
Crack growth results at constant amplitude loading show the typical intermittent high and low periods of growth rate associated with crack-microstructure interactions. Acceleration in growth rate during an overload block depends on crack length and stress amplitude ratio. It appears to pass through a maximum at a crack length corresponding to the first microstructural barrier. Microstructural-based modelling is therefore required for small fatigue cracks, rather than solely closure-based modelling. The Navarro-de los Rios model of short fatigue crack growth appears able to provide good indications of crack growth rates under VA block loading, and gives reasonable life predictions.
For short cracks (surface length < 80 μm) and a small overload ratio (6.7%), crack growth may show severe retardation during the overload block. This is ascribed to crack tip blunting being more important than the increase in stresses when closure is low. It appears from a Miner's rule type exercise, that VA block loading has its major effect on growth at a surface crack length of 20 μm. This means that the crack initiation period cannot be ignored in life prediction models for small fatigue cracks.     

AN EXPERIMENTAL STUDY ON THE OPENING AND CLOSURE BEHAVIOUR OF FATIGUE SURFACE, CORNER AND THROUGH-THICKNESS CRACKS AT NOTCHES

Abstract— The opening and closure behaviour of surface, corner and through-thickness cracks in thin notched plates of FeE460 ( K _t= 2.5) and A15086 ( K _t= 3.4) was experimentally studied. The cracks were initiated and examined under uniaxial fully reversed constant amplitude and two-step loading. Crack opening load values were measured during crack growth in notch sections with a nonuniform stress distribution using small strain gauges glued to the specimen surface, very close to the crack tip. The results represent a comprehensive set of experimental data for crack opening load values in dependence on crack lengths a, c and load level including the influence of overloads and covering all types of cracks. The results indicate uniform relationships between crack opening load levels and all crack types. Crack opening and closure occur at nearly the same strain level, which depends on the applied load level. The crack opening load values measured at large notched specimens differ from those measured at similar smaller specimens because of the different local stress gradients.     

A STUDY ON FATIGUE CRACK GROWTH UNDER OUT-OF-PHASE COMBINED LOADINGS

Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

A CRITICAL REVIEW OF CRACK TIP STRESS INTENSITY FACTORS FOR SEMI-ELLIPTIC CRACKS*

Several crack tip stress intensity factor solutions have been published for semi-elliptic, surface breaking cracks in plates subjected to tension or bending forces. These solutions do not agree with each other particularly well and the basis for choosing which one is the best has not been established. In this paper, the development of fatigue crack shape is used as a diagnostic tool to test the accuracy of these theoretical stress intensity solutions in predictive fatigue crack growth calculations. Those solutions giving the best engineering estimate of crack tip stress intensity factors are identified. Single equations are also given for each loading case at the deepest point or surface intersection point of semi-elliptic cracks in order to facilitate calculations on programmable calculators. A rational basis for calculating the progress of a crack which snaps through the thickness and continues to propagate in a stable way by fatigue is suggested.     

Experimental evaluation of the effect of residual stress field on crack growth behaviour in C(T) specimen

The effects of the residual stress field resulting from shot peening and the indentation technique were investigated in relation to fatigue crack closure and crack growth behaviour. Compact Specimens of 20NiCrMo2 were used in this investigation. The regions of residual stress field were located behind the fatigue crack tip. Crack closure behaviour was measured with back face strain and crack mouth opening displacement gauges. Crack length was monitored by the compliance and microscopic methods. Residual stress was measured by the incremental hole-drilling method. Subsequently the closure level, propagation rate and resulting crack growth retardation were studied. Crack closure and attendant growth retardation were shown to be dependent on the residual stress field. Residual stresses produced by shot peening and indentation were both compressive. The maximum value of residual stress for both operations were on the surface and at the same intensity. However, the residual stress induced by the indentation technique was deeper. The results showed that the closure effect was stronger in the case of indentation technique.     

Sickle-shaped cracks in metallic round bars under cyclic eccentric axial loading

In the present paper, the fatigue propagation of an initial sickle-shaped surface crack in a metallic round bar under eccentric axial loading acting perpendicular to the crack plane is examined. Firstly, the stress-intensity factor (SIF) along the crack front is determined through a three-dimensional finite element analysis and the one-quarter point displacement method, for different values of the loading eccentricity. Then, the fatigue behaviour of the cracked bar is numerically analysed by a step-by-step procedure based on the Paris–Erdogan law. The results are plotted in terms of crack paths, intersection angle and crack depth evolution, by varying the loading eccentricity.     

Axial fatigue of a gas-nitrided quenched and tempered AISI 4140 steel: effect of nitriding depth

Fatigue testing under fully reversed axial loading (R=?1) and zero‐to‐tension axial loading (R= 0) was carried out on AISI 4140 gas‐nitrided smooth specimens. Three different treatment durations were investigated in order to assess the effect of nitriding depth on fatigue strength in high cycle fatigue. Complete specimens characterization, i.e., hardness and residual stresses profiles (including measurement of stabilized residual stresses) as well as metallographic and fractographic observations, was achieved to analyse fatigue behaviour. Fatigue of the nitrided steel is a competition between a surface crack growing in a compressive residual stress field and an internal crack or ‘fish‐eye’ crack growing in vacuum. Fatigue life increases with nitriding depth until surface cracking is slow enough for failure to occur from an internal crack. Unlike bending, in axial fatigue ‘fish‐eye’ cracks can initiate anywhere in the core volume under uniform stress. In these conditions, axial fatigue performance is lower than that obtained under bending and nitriding depth may have no more influence. In order to interpret the results, special attention was given to the effects of compressive residual stresses on the surface short crack growth (closure effect) as well as the effects of internal defect size on internal fatigue lives. A superimposed tensile mean stress reduces the internal fatigue strength of nitrided steel more than the surface fatigue strength of the base metal. Both cracking mechanisms are not equally sensitive to mean stress.