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.     

STRESS STATE-RELATED FATIGUE CRACK GROWTH UNDER SPECTRUM LOADING

Abstract— The fatigue crack growth behaviour in aluminium alloy sheets of 2024-T3 and 7475-T761, subjected to standardized spectra (TWIST and FALSTAFF), was investigated using centre-cracked specimens. A strip crack closure model was used to interpret experimental data, and to make predictions for the crack growth.
The strip model is based on the Dugdale concept, but modified to keep plastically-stretched materials on the crack surface so that the crack opening load can be determined, and the fatigue crack growth can be analysed according to Elber's crack growth assumption. Differing from other models of the same kind, a variable constraint factor was introduced to account for the gradual transition of stress state at the crack tip resulting from the crack growth. It has been shown that the transition of stress state at the crack tip causes the unusual behaviour of the fatigue crack growth in sheets. Both experiments and predictions show that a crack may grow faster at a low load than at a higher one in a certain applied load range due to the crack tip stress state transition. The crack tip stress state also contributes to the thickness effect observed for the crack growth in sheets. In agreement with experimental results, it has been shown that a plane stress state will prevail at the crack tip in a thin sheet compared to that in a thick sheet. The plane stress state results in a higher crack opening level which leads to a longer fatigue life for thin sheets.     

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.     

FATIGUE BEHAVIOUR OF FIBRE ALUMINIUM LAMINATES WITH DIFFERENT RESIDUAL STRESSES

In this study two kinds of fibre aluminium laminates (aramid aluminium laminates, ARALL and glass aluminium laminates, GLARE) with different residual stresses in the aluminium layers were prepared. Fatigue crack propagation tests were performed. It is found that the residual stress condition plays an important role in the fatigue behaviour of fibre aluminium laminates. With a decrease of the tensile residual stress in the aluminium layers, the fatigue crack growth rate of the laminates is greatly reduced, and the shape of the curves of fatigue crack propagation rate as a function of the stress intensity factor changed. Compared to GLARE, the ARALL is more sensitive to the residual stress condition. The fatigue properties of non-prestressed GLARE are better than those of ARALL. The influence of the residual stress is discussed in detail.     

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.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Fatigue crack growth in hybrid boron/glass/aluminium fibre metal laminates

The crack growth behaviour of hybrid boron/glass/aluminium fibre metal laminates (FMLs) under constant‐amplitude fatigue loading was investigated. The hybrid FMLs consist of Al 2024‐T3 alloy as the metal layers and a mixture of boron fibres and glass fibres as the fibre layers. Two types of boron/glass/aluminium laminates were fabricated and tested. In the first type, the glass fibre/prepreg and the boron fibre/prepreg were used separately in the fibre layers, and in the second type, the boron fibres and the glass fibres were uniformly mingled together to form a hybrid boron fibre/glass fibre prepreg. An analytical model was also proposed to predict the fatigue crack growth behaviour of hybrid boron/glass/aluminium FMLs. The effective stress intensity factor at a crack tip was formulated as a function of the remote stress intensity factor, crack opening stress intensity factor, and the bridging stress intensity factor. The bridging stress acting on the delamination boundary along the crack length was also calculated based on the crack opening relations. Then, the empirical Paris‐type fatigue crack growth law was used for predicting the crack growth rates. A good correlation between the predicted and experimental crack growth rates has been obtained.     

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.     

Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre-metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values.     

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.     

Artgleiche und artverschiedene reibrührgeschweißte Verbindungen aus AA2124+25 % SiC und AA2024

Similar and dissimilar friction stir welded joints made from AA2124+25 % SiC and AA2024 An aluminium matrix composite (AMC) consisting of an AA2124 matrix reinforced by 25 vol.% SiC particles was used to produce similar AMC+AMC and dissimilar AMC+2024‐T3 joints by friction stir welding. When the particle reinforced composite was located on the retreating side, material mixing was less intense for dissimilar joints. Nevertheless, a higher strength has been determined for this arrangement due to a hook‐like interlocking of both materials. Tensile test and S‐N fatigue behaviour is shown to be compromised by alignment of the reinforcement particles perpendicular to loading direction already in the particle reinforced base material. Welding residual stresses were determined through the cut‐compliance method in terms of stress intensities acting at the crack tip. The underlying residual stress distribution in the un‐cracked structure was calculated by the weight function method. Longitudinal tensile residual stresses were found to be higher in the monolithic material as compared to the particle reinforced composite. This held true both for similar and within dissimilar joints. Growth behaviour of cracks crossing the joint line was described and correlated with residual stresses for similar joints.     

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.     

Damage tolerance assessment by bend and shear tests of two multilayer composites: Glass fibre reinforced metal laminate and aluminium roll-bonded laminate

The damage tolerance of an aluminium roll-bonded laminate (ALH19) and a glass fibre reinforced laminate (GLARE) (both based on Al 2024-T3) has been studied. The composite laminates have been tested under 3-point bend and shear tests on the interfaces to analyze their fracture behaviour. During the bend tests different fracture mechanisms were activated for both laminates, which depend on the constituent materials and their interfaces. The high intrinsic toughness of the pure Al 1050 layers present in the aluminium roll-bonded laminate (ALH19), together with extrinsic toughening mechanisms such as crack bridging and interface delamination were responsible for the enhanced toughness of this composite laminate. On the other hand, crack deflection by debonding between the glass fibres and the plastic resin in GLARE was the main extrinsic toughening mechanism present in this composite laminate.     

On the through-thickness crack with a curve front in center-cracked tension specimens

Three-dimensional finite element analyses are performed on through-thickness cracks with slightly wavy front in center-cracked plates. Considering there is an inherent relationship between the crack shape and the corresponding stress intensity factor (SIF) distribution of a crack, the curved configuration of the crack is determined using a heuristically derived iterative procedure if the SIF distribution function is known. Several simple SIF distribution functions, for instance the constant SIF distribution along the crack front, are assumed to determine the crack shape. Under the assumption that the rate of fatigue crack growth depends on the SIF range or the effective SIF range, possible effects of plate thickness, crack length and crack closure level gradient on the behaviour of crack tunneling are investigated. The stability of the curved shape of a through-thickness crack in fatigue is also discussed, i.e. whether a crack can maintain its shape satisfying the conditions of constant SIF distribution or other distribution along the crack front during fatigue growth. This study will be useful for a better understanding of the behaviour of crack tunneling and help to evaluate the validity of the two-dimensional linear elastic fracture mechanics in cracked plates.     

A modification of UniGrow 2‐parameter driving force model for short fatigue crack growth

In this paper, a modification of the UniGrow model is proposed to predict total fatigue life with the presence of a short fatigue crack by incorporating short crack propagation into the UniGrow crack growth model. The UniGrow model is modified by 2 different methods, namely the “short crack stress intensity correction method” and the “short crack data‐fitting method” to estimate the total fatigue life including both short and long fatigue crack propagations. Predicted fatigue lives obtained from these 2 methods were compared with experimental data sets of 2024‐T3, 7075‐T56 aluminium alloys, and Ti‐6Al‐4V titanium alloy. Two proposed methods have shown good fatigue life predictions at relatively high maximum stresses; however, they provide conservative fatigue life predictions at lower stresses corresponding high cycle fatigue lives where short crack behaviour dominates total fatigue life at lower stress levels.     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

The effects of corrosion on fatigue crack propagation in 2024‐T3 Aluminium

Abstract

The effects of salt water with 0.5 percent nitric acid on fatigue crack propagation in 2024‐T3 aluminium alloy are studied experimentally. First, the plastic zone size ahead of the crack tip is measured. It is found that the plastic zone size as well as the closure stress in corrosion fatigue is smaller than that in ordinary fatigue. Secondly, the crack propagation rate of corrosion fatigue is much higher than that of ordinary fatigue due to the creation of microcracks ahead of the main crack. Thirdly, the effective stress range governs the crack propagation rate in both ordinary and corrosion fatigue.     

Effect of impact damage on fatigue performance of structures reinforced with GLARE bonded crack retarders

Fibre-Metal Laminates (FML) such as GLARE are of interest as bonded crack retarders (BCR) to improve the fatigue performance of aircraft structures. The degradation of the performance of the crack retarder in service if subjected to damage is a critical factor in designing with this concept. Bonded assemblies of an aluminium alloy substrate reinforced with a GLARE strap were prepared, and were subjected to low velocity impact damage onto the GLARE, with impact energies ranging from 10 to 60 J. The thermal residual stresses developed during the bonding process of the GLARE to the aluminium were determined using neutron diffraction, and the change in the thermal residual stresses owing to impact damage onto the GLARE was evaluated. Pre- and post-impact fatigue performance of the BCR assemblies has been investigated. The results show that the BCR provides an improvement in fatigue life, but the reduction is impaired following impact damage. The results show that monitoring of impact damage will be critical in the damage tolerance assurance for aerospace structures containing bonded crack retarders.     

A two parameter driving force for fatigue crack growth analysis

A model for fatigue crack growth (FCG) analysis based on the elastic–plastic crack tip stress–strain history was proposed. The fatigue crack growth was predicted by simulating the stress–strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The fatigue crack growth was regarded as a process of successive crack re-initiation in the crack tip region. The model was developed to predict the effect of the mean stress including the influence of the applied compressive stress. A fatigue crack growth expression was derived using both the plane strain and plane stress state assumption. It was found that the FCG was controlled by a two parameter driving force in the form of: . The driving force was derived on the basis of the local stresses and strains at the crack tip using the Smith–Watson–Topper (SWT) fatigue damage parameter: D=σ_maxΔε/2.The effect of the internal (residual) stress induced by the reversed cyclic plasticity was accounted for the subsequent analysis. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351) and one steel alloy (4340) were used for the verification of the model.