The effect of sheet thickness on fatigue crack retardation in 2024-T3 aluminum alloy

Variable-amplitude fatigue studies of 2024-T3 aluminum alloy were performed to examine the effect of sheet thickness on fatigue crack growth rate retardation. Results indicated that the amount of retardation increased with decreasing specimen thickness. This phenomenon was attributed to enhanced plastic strains under plane stress conditions (i.e. in a thin sheet) which formed ahead of the advancing crack tip as a result of a high load excursion. These strains are believed to produce both crack closure and a favorable compressive residual stress field around the crack tip. Evidence of increased crack surface interference under plane stress situations was verified with electron fractographic observations.     

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.     

FINITE ELEMENT ANALYSIS OF CLOSURE BEHAVIOUR OF FATIGUE CRACKS IN RESIDUAL STRESS FIELDS

An elastic-plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8-node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field.     

Deformation behaviour at the tip of a physically short fatigue crack due to a single overload

A two-dimensional elastic–plastic finite element analysis was utilized to investigate the transition behaviour of a physically short fatigue crack following the application of a single overload cycle. The deformation accommodated at the tip of a crack artificially advancing with a fully reversed load was considered. The development of the cyclic crack tip opening displacement was computed and then modelled to include the effects of the stress level of the base cycles, overload pattern and crack length at which the transient cycle was applied. The cyclic crack tip opening displacement was initially of a relatively high value. It decreased and then increased to match the behaviour under the base load cycles. The extent and location of both the minimum and matching points were dependent on the overload crack length and the stress compared with the material’s yield stress. In the case of the yield stress being exceeded by the overload, the minimum and the-return-to-normality points are identical. A previously developed crack tip deformation parameter was invoked to predict relevant experimental fatigue growth rates of short cracks reported in the literature.     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.     

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.     

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.     

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.     

A numerical study of plasticity induced crack closure under plane strain conditions

The level of plasticity induced crack closure (PICC) is greatly affected by stress state. Under plane strain conditions, however, the level and even the existence of PICC still are controversial. The objective here is to study the influence of the main numerical parameters on plane strain PICC, namely the total crack propagation, the number of load cycles between crack increments, the finite element mesh and the parameter used to quantify PICC. The PICC predictions were included in a parallel numerical study of crack propagation, in order to quantify the impact of plane strain values on fatigue life. The results indicate that literature may be overestimating plane strain PICC due to incorrect numerical parameters. The number of load cycles usually considered is unrealistically small, and its increase was found to vanish crack closure, particularly for kinematic hardening. This effect was linked to the ratcheting effect observed at the crack tip. The total crack increment, Δa, must be large enough to obtain stabilized PICC values, but this may imply a huge numerical effort particularly for 3D models. The size of crack tip plastic zone may be overestimated in literature, which means that the meshes used may be too large. Additionally, the crack propagation study showed that the plane strain PICC has usually a dominant effect on fatigue life, and plane stress PICC is only relevant for relatively thin geometries.     

Finite-element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

An elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.     

Numerical simulation of plasticity-induced fatigue crack closure with emphasis on the crack growth scheme: 2D and 3D analyses

In this paper a numerical simulation of plasticity-induced fatigue crack closure is performed using the finite element method. Emphasis is placed on the crack growth scheme usually adopted for modelling fatigue crack growth in crack closure problems. The number of load cycles between node releases usually reported in the literature has been, in general, one or two. The present work shows that increasing the number of load cycles between node releases has a strong effect on the opening stresses, particularly, under plane strain conditions and 3D fatigue cracks, in contrast plane stress shows little variation with increasing number of load cycles. This investigation also suggests that ratchetting may take place close to the crack tip in both plane strain and 3D crack problems. The problem of discontinuous crack closure under plane strain conditions, often reported in the literature, is also addressed.     

ARALL (Aramidfaserverstärkter Aluminiumschicht-Verbundwerkstoff) - Ein neuer Hybrid-Verbundwerkstoff mit besonderen Schwingfestigkeitseigenschaften

ARALL (Aramid Fibre Reinforced Aluminum Laminate)-A New Fatigue Resistant Hybrid Composite High fuel expenses and the tendency to build larger aircrafts are two main factors forcing the aircraft engineers to develop structures which allow for higher design stress levels. Higher design stress levels require an increasing concern with the fatigue behavior of the structure. One way to solve the problem is to develop new high strength fatigue resistant materials. In this paper a material of this type is presented: ARALL, an aramid fibre reinforced aluminum laminate. This hybrid material consists of thin sheets of a high strength aluminum alloy which are bonded together. Into the bond-line thin layers of aramid fibres are embedded. As soon as fatigue cracks are initiated in the metallic part of the hybrid composite material during the fatigue loading, the strong and fatigue insensitive aramid fibres remain unbroken behind the propagating crack. They hinder the crack opening and reduce the stress intensity factor at the crack tip in the metal part of the hybrid composite. This mechanism leads to a significant reduction of the crack growth and can be enhanced by introducing favourable residual stresses into the hyb- rid material. For an optimized ARALL material an aluminum sheet thickness of about 0.5 mm and an aramid layer thickness of about 0.25 mm (with a fibre volume content of about 40–50%) are chosen. ARALL decreases the crack growth rates by orders of magnitude, as compared to monolithic aluminum sheets, and is an extremely damage tolerant material.     

Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading

A new mixed-mode threshold stress intensity factor is developed using a critical plane-based multiaxial fatigue theory and the Kitagawa diagram. The proposed method is a nominal approach since the fatigue damage is evaluated using remote stresses acting on a cracked component rather than stresses near the crack tip. An equivalent stress intensity factor defined on the critical plane is proposed to predict the fatigue crack growth rate under mixed-mode loading. A major advantage is the applicability of the proposed model to many different materials, which experience either shear or tensile dominated crack growth. The proposed model is also capable to nonproportional fatigue loading since the critical plane explicitly considers the influence of the load path. The predictions of the proposed fatigue crack growth model under constant amplitude loading are compared with a wide range of fatigue results in the literature. Excellent agreements between experimental data and model predictions are observed.     

The residual strength characteristics of stiffened panels containing fatigue cracks

In heavy structural members, where plane strain conditions prevail, linear fracture mechanics can be used for predicting residual strength. Aircraft structures consist largely of sheet structures with plane stress conditions where linear fracture mechanics do not seem to apply. Yet it is in the aircraft main structure that large fatigue cracks can develop and that has to be designed fail-safe. The present paper describes a method to predict the residual strength of a cracked sheet structure.Contrary to an unstiffened sheet, the sheet structure contains stiffening elements that can act as crack stoppers. This crack arresting action and its consequences for the residual strength are considered in the analysis.The paper proposes a method that relates the crack resistance of a stiffened panel to that of an unstiffened sheet. It takes full account of sheet-stringer interaction in the cracked region. A criterion for crack arrest is put forward. Ultimate panel failure after crack arrest is initiated either by subsequent unstable crack growth or by stiffener failure. Critical load conditions for both failure modes are presented. In case crack arrest does not occur, the residual strength of the unstiffened panel constitutes a safe lower bound.Computational results of the interacting rivet forces by both analytical and numerical (finite element) methods are presented. From these the load concentration in the stiffener and the reduction of the stress intensity at the crack tip can be determined. This enables the complete residual strength characteristics to be predicted.The results of residual strength tests on bonded and riveted panels with symmetric strip stiffeners or eccentric Z-stringers fully substantiate the method proposed for residual strength calculations.     

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.     

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.     

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.     

Predicting fatigue crack growth from a preyielded hole

Linear elastic fracture mechanics and the principle of superposition are commonly used to predict fatigue crack growth through residual stress fields. Several researchers have shown that such predictions correlate well with experiments in specimens with well characterized residual stress fields. However, in the case of crack growth from a hole in an aluminum 2024-T351 sheet with surrounding residual stress introduced by tensile preloading, superposition based fatigue predictions have been significantly nonconservative in comparison with experimental data. We show that this discrepancy may be explained by the sensitivity of the fatigue prediction to the initial residual stress field and initial flaw size. Conservative estimates of these quantities result in fatigue predictions that correlate well with experimental data.     

A crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue loading

In this paper, a crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue (TMF) loading is proposed. The equation is derived from systematic calculations of the crack opening stress with a temperature dependent strip yield model for both plane stress and plane strain, different load ratios and different ratios of the temperature dependent yield stress in compression and tension. Using a load ratio scaled by the ratio of the yield stress in compression and tension, the equation accounts for the effect of the temperature dependent yield stress and the constraint on the crack opening stress. Based on the scaling relation established in this paper, Newman’s crack opening stress equation for isothermal loading is enabled to predict the crack opening stress under TMF loading.