Recent developments in fatigue crack growth assessment

This paper examines the fatigue crack growth histories, at low to mid range ΔK’s, for a range of aircraft aluminium alloys, test specimens and service loaded components. It concludes that the crack growth history shows that, as a first approximation, there is a log–linear relationship between the apparent crack length or depth and the life (N), respectively. This leads to the further observation that, for the range of materials and spectra considered here, there is a linear relationship between the crack growth rate and the crack length when plotted on a log–log scale.     

Application of inverse first-order reliability method for probabilistic fatigue life prediction

A general probabilistic life prediction methodology for accurate and efficient fatigue prognosis is proposed in this paper. The proposed methodology is based-on an inverse first-order reliability method (IFORM) to evaluate the fatigue life at an arbitrary reliability level. This formulation is different from the forward reliability problem, which aims to calculate the failure probability at a fixed time instant. The variables in the fatigue prognosis problem are separated into two categories, i.e., random variables and index variables. An efficient searching algorithm for fatigue life prediction is developed to find the corresponding index variable at a certain confidence level. Numerical examples using direct Monte Carlo simulation and the proposed IFORM method are compared for algorithm verification. Following this, various experimental data for metallic materials are used for model prediction validation.     

CRACK INITIATION AND SMALL FATIGUE CRACK GROWTH BEHAVIOUR OF SQUEEZE-CAST Al-Si ALUMINIUM ALLOYS

Abstract— Fatigue strength, crack initiation and small crack growth behaviour in two kinds of squeeze-cast aluminium alloys, AC8A-T6 and AC4C-T6 were investigated using smooth specimens subjected to rotatary-bending fatigue at room temperature. Fatigue resistance of these alloys was almost the same as that of the wrought aluminium alloys because of their fine microstructure and of the decrease in defect size due to squeeze-casting. Fatigue crack initiation sites were at the eutectic silicon particles on the surface of specimens or at internal microporosity in the specimens. Crack initiation life, defined as a crack length of 50 μm on the specimen surface, was successfully estimated from an evaluation of initiation sites using fracture mechanics and the statistics of extrema. Small fatigue crack growth in the two kinds of alloys obeys the relation proposed by Nisitani et al. , namely that d(2c)/d N = C (σ_a/σ_B)ⁿ· (2 c ), where C is a constant and σ_B is the ultimate tensile strength. It is pointed out that an improvement in fatigue strength of cast aluminium alloys can be expected by refining the eutectic silicon rather than by an increase in static strength.     

Application of fracture mechanics to estimate fretting fatigue endurance curves

This paper presents approximations to fatigue curves in fretting conditions with spherical contact in the alloy Al 7075. The curves are defined for a specific contact geometry and loads applied in the tests (axial load on the specimen, the normal and tangential contact forces). In order to obtain a curve of this type it is necessary to fix all parameters except for one and analyse its influence on life. The method used to estimate life in fretting fatigue combines initiation with propagation. Different approaches to the growth of short cracks are employed and in some cases a fretting fatigue limit is predicted. Various groups of fretting tests have been analysed, evaluating the suitability of each approximation.     

Fatigue life analysis of a cannon barrel

A steel cannon barrel was tested and analyzed in order to predict its lifetime. Mechanical properties, fracture toughness and fatigue behavior were determined experimentally. The cannon barrel was assumed to have a smooth inner surface. On that basis, finite element analyses were carried out in order to determine the stress intensity factor as a function of crack length for the case in which the cannon barrel contains two symmetrically located cracks. The fatigue data was assumed to follow the Paris–Erdogan law. A statistical Monte Carlo analysis for the fatigue life of the cannon barrel was carried out with many of the parameters assumed to be random variables.     

Fatigue crack propagation from a cold-worked hole

The cold expansion process is widely used to enhance the fatigue life of structures with fastener holes. Various studies assert that the cold expansion improves the fatigue strength of fastener holes; however, the improvement of fatigue life is difficult to quantify. Therefore, the influence on fatigue life of cold-worked process was studied by numerical and experimental tests. Then, a parametric study on material hardening behavior and Bauschinger’s parameter was performed for several loading conditions in order to determine their effect on crack growth propagation. The results of the numerical tests have exhibited a good prediction of the fatigue life of the component.     

Propagation of physically short cracks in a bainitic high strength bearing steel due to fatigue load

Physically short cracks in a bainitic high strength bearing steel were fatigue loaded. The rapid propagation rate of early open short cracks agreed with that of long closure free cracks. After some rapid growth, the short cracks entered a transition period to the rate of growth limited long cracks. Potential drop showed that the short cracks were open to the tip throughout the growth sequence, which excluded crack face closure in the wake as the growth limiting mechanism in this material. Instead the short crack effect was related to residual stresses and other mechanisms at the crack tip. Crack manufacturing procedures were determined for straight long and short start cracks in the present material. LEFM with effective material parameters and limit compensation predicted the short crack lives.     

A general model to estimate life in notches and fretting fatigue

Fatigue in notched specimens and fretting fatigue are two different phenomena but they have in common the existence of a stress gradient. In these cases fatigue life estimation is usually considered as a superposition of an initiation and propagation phase. One of the main problems to estimate the fatigue life is to define the crack length where one phase finishes and the other begins. The model employed in this paper combines both phases without defining a priori the separation between them. The proposed model is applied to uniaxial and multiaxial fatigue in specimens with stress gradient: a group of fretting fatigue tests with spherical and cylindrical contact and another group of tests with notched specimens. The comparison between life estimations and experimental results allows checking the validity of the model in different conditions.     

Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition

This work assesses the ability of linear elastic fracture mechanics (LEFM) with superposition to correlate the growth of one-dimensional fatigue cracks at cold-expanded open holes under constant amplitude loading. Care is taken in the work to accurately: control the test setup to ensure one-dimensional crack growth, determine residual stress in the coupons, measure crack growth, determine the fatigue crack growth rate (FCGR), compute stress intensity factors, and correlate fatigue crack growth rate with stress intensity factor range ΔK and stress ratio R. The work used long dog-bone coupons having a gage section 38.1 mm wide and a centrally located 7.09 mm diameter hole. The coupons were fabricated from 2.03 mm thick 7075-T6 sheet. The small coupon thickness and alignment of the loading fixture to eliminate bending resulted in one-dimensional crack growth. Residual stress due to cold expansion (CX) was measured using the contour method, as a function of position on the crack plane. Residual stress measurements gave typical results for the average residual stress field, with near-yield compression at the hole giving way to tension further out. Measurements on multiple coupons showed ±10% variability in residual stress. Crack growth behavior of multiple as-machined (AM) coupons (without CX) tested at R of 0.1 or 0.5 agreed with earlier results published in the literature. The scatter in lifetime, defined as the range of lifetime divided by the average lifetime, was less than 30% in the AM coupons. Crack growth behavior of multiple CX coupons tested at the same two applied stress ratios was consistent with predictions by linear superposition, where the predictions used a correlation for fatigue crack growth rate as a function of ΔK and R based on crack closure concepts and a piecewise log–log fit to FCGR versus ΔK_eff data from tests of non-residual stress bearing material and from the literature. Scatter in lifetime of CX coupons was 152% at R = 0.1 and 69% at R = 0.5. While the scatter in CX coupon lifetime is considerably greater than for AM coupons, it is found consistent with the observed 10% variability in residual stress. The work therefore demonstrates the ability of LEFM with superposition to accurately correlate the behavior of coupons with and without residual stresses.     

The generalised Frost–Dugdale approach to modelling fatigue crack growth

This paper summarises recent developments in the formulation and application of the generalised Frost–Dugdale crack growth law. We first reveal the relationship between the generalised Frost–Dugdale crack growth law, dislocation based crack growth laws, the two parameter crack growth model, and fractal fatigue concepts. We then show that a range of aircraft materials characterisation test data are consistent with this law and how it can be used to predict crack growth in a range of full-scale aircraft fatigue tests, and coupon tests including crack growth in aircraft fuselage lap joints.     

Analytical study of fatigue crack growth in AA7050 notched specimens under spectrum loading

An analytical study of fatigue crack growth in aluminium alloy 7050-T7451 notched specimens under a fighter aircraft wing root bending moment spectrum was conducted. The crack growth data were measured by quantitative fractography for three groups of specimens with different stress concentration geometrical features. Under spectrum loading and for each spectrum peak stress level, a minimum of five specimens were tested. Based on the analysis of the measured spectrum crack growth data using linear elastic fracture mechanics, it was found that the concept of geometry factors formulated in the stress intensity factor could not collapse the crack growth rate data derived from each stress concentration feature, particularly near the small crack growth region. In order to investigate the possible reasons for this, three-dimensional elastic-plastic finite element analysis was used to determine notch plastic zone sizes for each stress concentration geometry. As a consequence, an alternative crack growth driving force by considering both notch elastic-plastic stress field and gross net-section stress field was proposed and used to interpret the fatigue crack growth data under spectrum loading. It was found that the predictions of crack growth under spectrum loading for different stress concentration factors at different peak load levels agree reasonably well with the experimental results.     

The effect of hole shape on the extent of fatigue life improvement by cold expansions

The cold expansion of circular holes is known to improve resistance to fatigue. In this study the effect of the cold expansion of a circular hole on fatigue life by means of a quasi-elliptical pin was investigated. Additional evaluations were conducted, including determinations of the effects of crack propagation from the hole. The major life extension was obtained through slower crack growth in the short-crack stage. The decrease in fatigue crack growth in cold-expanded specimens was related to higher crack-opening stresses which are a consequence of the presence of compressive residual stresses arising from cold expansion. In this study, an experimental investigation was carried out to quantify the effect of the cold expansion on the initiation and the propagation of the fatigue crack and was discussed. Fatigue life improvement of the cold-worked hole specimen was explained by determining the hardness results around the cold-worked hole. The results indicate that significant life improvements can be obtained through cold expansion applied with a quasi-elliptical pin in this work with the optimum results being obtained when the pin diameter is 4% larger than the diameter of the specimen hole. Also, a brief examination of the effect of the rivet shape on the fatigue life of a riveted specimen was carried out. To lengthen the fatigue life of a riveted plate which uses countersunk head rivets, the shape of the countersink and the rivet head were improved. The experimental results showed that the fatigue life of the riveted plate was improved where the improved rivet was used.     

RELAXATION OF RESIDUAL STRESSES AT COLD-WORKED FASTENER HOLES DUE TO FATIGUE LOADING

Abstract— Cold-expansion of fastener holes is now commonly used within the aerospace industry to increase the fatigue endurance of airframes. Although a number of methods of cold expansion are possible, the split-sleeve cold-expansion process is the most widely accepted and is frequently used in the repair and manufacture stages of both military and civil aircraft. In the present work, the redistribution of residual hoop stresses due to the application of constant amplitude fatigue loading at 4% cold-expanded holes has been studied. A modified Sachs method was adopted to evaluate the residual stress profiles and a replication technique was used to quantify crack growth. It was found that the decay of the residual hoop stress profile near the bore of the hole was due to the initiation and growth of small fatigue cracks. Cracks were found to initiate both near and below the fatigue limit, but subsequently arrested so stabilising the overall residual stress profile.     

Accelerated testing for long-term durability of GFRP laminates for marine use

Our proposed accelerated testing methodology for the long term durability of polymer composites is based on the time–temperature superposition principle to be held for the viscoelasticity of polymer matrix. The long term flexural fatigue life of plain woven glass fiber/vinyl-ester (GFRP) laminates for conventional marine use was predicted based on the proposed methodology. As results, the flexural fatigue strengths of GFRP laminates decreases strongly with increasing time and temperature as well as the number of cycles to failure. The long term fatigue strength at any time, temperature and number of cycles to failure can be predicted using the master curves of fatigue strength obtained based on our proposed accelerated testing methodology.     

EXPERIMENTAL INVESTIGATION ON THE EFFECTS OF COLD EXPANSION OF FASTENER HOLES

A series of experimental investigations concerning the residual stress fields at cold-expanded fastener holes and of the behavior of fatigue cracks at such holes has been conducted. These studies have included measurement of the initial, cold-work-induced residual stress fields at both uncracked and cracked holes and the performance of both constant amplitude and spectrum fatigue crack growth tests.