In situ investigation of small fatigue crack growth in poly-crystal and single-crystal aluminium alloys

Abstract   In situ scanning electron microscope observations of short crack growth in both a poly-crystal and a single-crystal alloy revealed that fatigue cracks may grow in a shear decohesion mode over a length that is several times the grain size, far beyond the conventional stage I regime. In the poly-crystal aluminium alloy 2024-T351, fatigue cracks were found to continue to grow along one shear band even after two mutually perpendicular shear bands had formed at the crack tip. For the single-crystal alloy specimen with the loading axis being nearly perpendicular to its main shear plane, mode I fatigue cracks were found to grow along the shear band. These two types of fatigue crack growth pose a significant challenge to the existing fatigue crack growth correlating parameters that are based on crack-tip opening displacement. In particular, it has been found that the cyclic crack-tip opening displacement, which accounts for both large-scale yielding and the lack of plasticity-induced crack closure, is unable to unify the growth rates of short and long cracks in aluminium 2024-T351, suggesting a possible dependence of crack growth threshold on crack length.     

The effect of compressive peak stress on fatigue behaviour

The effect of compressive peak stress on the maximum stress at the endurance limit, crack propagation rate, threshold stress intensity and crack closure was studied in a laboratory environment using two steels (SAE1045 and SAE1010) and two aluminium alloys (2024-T351 and 7075-T651).As the compressive peak stress, Scp, was increased in magnitude, the maximum stress at the endurance limit, Sfa, decreased linearly. Compression-compression cycling did not initiate any cracks in a centre-notched SAE1010 steel specimen but initiated cracks, which gradually became non-propagating, in the notched 2024-T351 aluminium alloy specimens. In compression-tension tests, the crack propagation rate increased, and the threshold and the crack opening stress intensities decreased linearly with increasing compressive peak stress. During compression-compression cycling the load/displacement curves were not linear, indicating that the crack was not fully closed.     

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.     

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.     

IN SITU SEM MEASUREMENTS OF CRACK CLOSURE FOR SMALL FATIGUE CRACKS IN ALUMINIUM 2024-T351

Abstract Crack closure has been measured for a range of small, self-initiated fatigue cracks using in situ SEM loading. Cracks were grown at positive R ratios in the aluminium alloy 2024-T351 and at nominal ΔK levels that extend substantially below the corresponding long crack threshold. The crack closure stress of the small cracks decreased and the K_cl level increased with increasing crack size until the long crack value near threshold was reached. For cracks of depth larger than about one grain size, a good correlation was obtained between small and long crack growth rate data in terms of ΔK_eff     

THE EFFECTS OF STRESS RATIO, COMPRESSIVE PEAK STRESS AND MAXIMUM STRESS LEVEL ON FATIGUE BEHAVIOUR OF 2024-T3 ALUMINIUM ALLOY

Abstract— Fatigue crack growth behaviour of 2024-T3 aluminium alloy is investigated as a function of stress ratio, compressive peak stress and maximum stress level. It is found that as the stress ratio and the magnitude of the compressive peak stress are increased, the threshold stress intensity range decreased linearly. Intermediate and near threshold growth rate data are analysed with different formulae for effective stress intensity range. The data covered different values of stress ratio, compressive peak stress and maximum stress level. A formula for the crack opening stress level is introduced as a function of stress ratio, compressive peak stress and maximum stress level. The formula permitted a good correlation between crack growth data for both positive stress ratio and negative compressive peak stress values. Using the new formula, intermediate and near threshold crack growth data for the 2024-T3 aluminium alloy yielded a unique crack growth rate vs effective stress intensity range curve for all stress ratio and compressive peak stress values investigated. This suggests that for the 2024-T3 aluminium alloy the crack growth rate vs effective stress intensity range curve does not depend on stress ratio, compressive peak stress, or maximum stress level. The significance of the new equation and the crack growth rate versus effective stress intensity range curve is that they allow a designer to find crack growth rate vs stress intensity range data for the 2024-T3 aluminium alloy in both intermediate and near threshold regions for the particular stress ratio, compressive peak stress and maximum stress level conditions of the component under investigation.     

A model for fatigue crack growth with a variable stress intensity factor

A model for fatigue crack growth, similar to that of Majumdar and Morrow, is proposed where the crack growth rate is determined from the low cycle fatigue and cyclic stress-strain response of the material. The model is for a constant stress range at infinity, but does allow for a variable stress intensity factor due to the changing crack length. The study also includes an analysis of the strain range in the neighborhood of the crack tip. Further it is shown that the model predicts the critical stress intensity factor. A prediction of the crack growth rate is made for 2024-T351 aluminium, copper and CU-6.3 AL alloy and is compared to the experimental observations.     

Long fatigue life critical crack lengths*

A model based on surface strain redistribution and crack closure is presented for prediction of the endurance or fatigue limit stress by determining the threshold stress and critical length of short cracks that develop under microstructural control. The threshold stress first decreases with crack size to a local minimum then increases to a local maximum corresponding to the fatigue limit stress. This occurs at the critical crack length corresponding to about four grain diameters. The model is capable of determining the threshold stress range and depth of propagating and non‐propagating surface cracks as a function of stress ratio, material and grain size. The microstructure is shown to be particularly significant in the very long life regime (N_f ≈ 10⁹ cycles). When the surface cracks become non‐propagating, internally initiated cracks continue growing slowly, eventually reaching the critical crack length with failure occurring after a very high number of cycles (10⁷ < N_f < 10⁹ cycles).     

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.     

Dislocation theory based short crack model and its application for aircraft aluminum alloys

This paper presents a study on dislocation theory based short/small crack modeling, and its application for short crack growth life analysis on 2024-T351 aluminum specimens. The dislocation theory was applied to determine the crack tip opening displacement (CTOD) of a microstructurally short crack by taking into account the effects of microstructural features, such as grain size, orientation, and grain boundary. The CTOD was then used as the parameter for calculating the short crack growth rate. In this work, an existing CTOD model was modified for estimating the short crack life of 2024-T351 single edge notch tension (SENT) specimens, which were tested in an Advisory Group for Aerospace Research and Development (AGARD) program [Newman JC, Edward PR. Short-crack growth behavior in an aluminum alloy: an AGARD cooperative test programme. AGARD-R-732, NATO, Advisory Group for Aerospace Research and Development; 1988]. The analytical results matched the test results reasonably well.     

Gel electrode imaging of fatigue cracks in aluminium alloys

Previous papers have described a gel electrode technique recently devised for detecting and imaging fatigue cracks in aluminium tested in simple bending. In this study, the technique is shown to be applicable to testing in both bending and torsion and to high strength aluminium alloys 7075-T6, 2024-T3 and 2024-T4. Fatigue cracks as short as 10 μm in length are consistently detected and located. The flow of charge during image formation under standard conditions provides a quantitative measure of crack length, which is independent of alloy composition. A crack 100 μm long can be reliably detected by charge flow measurement; thus, this approach is not as sensitive as the information contained in the actual images.     

Fatigue crack propagation in the threshold regime after rapid load reduction

In this work, the influence of rapid load reduction on fatigue crack growth in the threshold regime of the aluminium alloy 2024-T3 has been studied. It can be shown that fatigue crack growth may be severely influenced by crack closure due to oxide formation and fracture surface roughness. After rapid load reduction, crack arrest could be observed at K_max values 10–100% above the constant amplitude threshold, depending on the environment. With measurements in different environments (humid air and vacuum), the oxide-induced crack closure effect could be recognized as being mainly responsible for an increase of the stress intensity threshold. Using high-frequency fatigue testing equipment, it was possible to show that after rapid load reduction in a vacuum, cracks may begin to grow again after crack arrest of more than 5 × 10⁷ cycles.     

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (R_eff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved.     

DETERMINATIONS OF JIC FOR 2024-T351 ALUMINIUM ALLOY

Abstract— The J -integral is an elastic-plastic fracture mechanics parameter which can be regarded as a measure of the intensity of the crack tip stress and strain fields, irrespective of the plastic zone size. The value of J at the onset of stable crack extension, J _IC, has been suggested as a fracture criterion for both large-and small-scale yielding conditions. In this work the value of J _IC for an extruded, medium-strength aluminium alloy, 2024-T351 bar, was determined using; (i) the Hutchinson-Rice-Rosengren crack tip model and experimentally-determined crack tip strain profiles; and (ii) the ASTM standard multiple-specimen technique. Knowing the critical load for initial crack extension from the crack tip strain profile method also enabled J _IC to be computed using a finite element-hybrid contour method and a modified linear elastic fracture mechanics approach. Agreement between the J _IC values obtained by the various methods was good.     

Crack closure in fibre metal laminates

GLARE is a fibre metal laminate (FML) built up of alternating layers of S2-glass/FM94 prepreg and aluminium 2024-T3. The excellent fatigue behaviour of GLARE can be described with a recently published analytical prediction model. This model is based on linear elastic fracture mechanics and the assumption that a similar stress state in the aluminium layers of GLARE and monolithic aluminium result in the same crack growth behaviour. It therefore describes the crack growth with an effective stress intensity factor (SIF) range at the crack tip in the aluminium layers, including the effect of internal residual stress as result of curing and the stiffness differences between the individual layers. In that model, an empirical relation is used to calculate the effective SIF range, which had been determined without sufficiently investigating the effect of crack closure. This paper presents the research performed on crack closure in GLARE. It is assumed that crack closure in FMLs is determined by the actual stress cycles in the metal layers and that it can be described with the available relations for monolithic aluminium published in the literature. Fatigue crack growth experiments have been performed on GLARE specimens in which crack growth rates and crack opening stresses have been recorded. The prediction model incorporating the crack closure relation for aluminium 2024-T3 obtained from the literature has been validated with the test results. It is concluded that crack growth in GLARE can be correlated with the effective SIF range at the crack tip in the aluminium layers, if it is determined with the crack closure relation for aluminium 2024-T3 based on actual stresses in the aluminium layers.     

Weld residual stress effects on fatigue crack growth behaviour of aluminium alloy 2024-T351

The interaction between residual stress and fatigue crack growth rate has been investigated in middle tension and compact tension specimens machined from a variable polarity plasma arc welded aluminium alloy 2024-T351 plate. The specimens were tested at three levels of applied constant stress intensity factor range. Crack closure was continuously monitored using an eddy current transducer and the residual stresses were measured with neutron diffraction. The effect of the residual stresses on the fatigue crack behaviour was modelled for both specimen geometries using two approaches: a crack closure approach where the effective stress intensity factor was computed; and a residual stress approach where the effect of the residual stresses on the stress ratio was considered. Good correlation between the experimental results and the predictions were found for the effective stress intensity factor approach at a high stress intensity factor range whereas the residual stress approach yielded good predictions at low and moderate stress intensity factor ranges. In particular, the residual stresses accelerated the fatigue crack growth rate in the middle tension specimen whereas they decelerated the growth rate in the compact tension sample, demonstrating the importance of accurately evaluating the residual stresses in welded specimens which will be used to produce damage tolerance design data.     

THE GROWTH OF SMALL CORROSION FATIGUE CRACKS IN ALLOY 2024

Abstract— The corrosion fatigue crack growth characteristics of small surface and corner cracks in aluminium alloy 2024 is established. The damaging effect of salt water on the early stages of small crack growth is characterized by: (1) crack initiation at constituent particle pits, (2) intergranular microcracking for a≤100μm, and (3) transgranular small crack growth for a≥100μm. In aqueous 1% NaCl and at a constant anodic potential of −700 mV_SCE, small cracks exhibit a factor of three increase in fatigue crack growth rates compared to laboratory air. Small cracks exhibit accelerated corrosion fatigue crack growth rates at low levels of Δ K (< 1 MPa√m) below the long crack Δ K _th value. When exposed to Paris regime levels of crack tip stress intensity, small corrosion fatigue cracks exhibit growth rates similar to that observed for long cracks. Similar small and long crack growth behavior at various levels of R suggest that crack closure effects influence the corrosion fatigue crack growth rates of small cracks for a≥100 μm. Contrary to the corrosion fatigue characteristics of small cracks in high strength steels, no pronounced chemical crack length effect is observed for alloy 2024 exposed to salt water.     

Fatigue crack closure at positive stresses

Recently Elber proposed that fatigue cracks close at positive stress levels during constant amplitude stress cycling. To investigate this behaviour, centrally cracked 2024-T3 Aluminium alloy sheets were tested. Crack opening displacements and strains near the fracture surface were measured for a propagating fatigue crack. The experimental results confirm the presence of crack closure at significant positive stress levels during the unloading portion of the cycle.     

FATIGUE CRACK TIP PLASTIC STRAIN IN HIGH-STRENGTH ALUMINUM ALLOYS

Abstract— Plastic zone size and shape and the distribution of strain within the plastic zone are determined for the high-strength aluminium alloys 2024-T4, 6061 T6, and 7075-T6 using the technique of selected area electron channeling. Plastic zone size is found to correlate with the work done in creating a unit of new crack surface and the yield stress, rather than with the stress intensity factor and yield stress. Plastic strain distribution is found to be a logarithmic function of distance from the crack tip, in agreement with the mathematical analysis for a moving crack in plane strain.     

EFFECT OF SPECIMEN GEOMETRY ON FATIGUE CRACK GROWTH IN PLANE STRAIN—I. CONSTANT AMPLITUDE RESPONSE

Abstract— The influence of specimen geometry on crack growth and crack closure response was determined for BS4360 50B steel and 6082-T6 aluminium alloy. Specimens were sufficiently thick for plane strain conditions to prevail along most of the crack front. After an initial crack growth transient from the sharpened notch, and steady state conditions are attained, the growth rate and closure responses are independent of specimen geometry. At growth rates above the near-threshold regime the cyclic crack openings exceed the fracture surface roughness for the steel, but are much less than the surface roughness for the aluminium alloy. This suggests that roughness-induced crack closure plays a dominant role for the aluminium alloy but not for the steel. Finally, the effect of mean stress upon closure response is presented for the steel.