Fatigue crack growth and damage tolerance

The problems arising as a result of aging aircraft, rail and civil infrastructure have focused attention on tools for predicting the growth of cracks from small naturally occurring material discontinuities. To this end, the present paper discusses on the difference between the analysis tools needed for ab initio design and sustainment, modelling of cracks that grow from small naturally occurring material discontinuities and ways to determine the short crack da/dN versus ΔK data from long crack American Society for Testing and Materials (ASTM) tests. It also discusses how existing equations can be used to predict short crack growth and how to account for the variations seen in crack growth histories. Attention is also focused on the recent Federal Aviation Administration limit of validity ruling and the effect of the environment on widespread fatigue damage in civil transport aircraft.     

Calculating crack growth from small discontinuities in 7050-T7451 under combat aircraft spectra

This paper supplements previous work which showed that the crack growth rate in a large range of metallic materials fitted a variant of the Hartman–Schijve equation where da/dN is a function of (ΔK − ΔK_thr)^α, where ΔK_thr is a parameter that reflects the apparent fatigue stress intensity threshold of the material, and α is approximately 2. For the case of 7050-T7451 aluminium alloy the same equation is shown to fit both long and short crack growth data once the appropriate ΔK_thr is chosen for each specific data set. This equation is used here to produce accurate predictions of the fatigue crack growth in 7050-T7451 aluminium alloy specimens with both a low and high stress concentration subjected to two combat aircraft loading spectra. Thus, it is postulated that if long crack data are fitted to the variant of the Hartman–Schijve equation then accurate predictions can be made in the short crack regime for a wide range of materials.     

The growth of short fatigue cracks ahead of a notch in high strength steel

This paper is concerned with the short crack growth behaviour in notched specimens of high strength steels mainly used for automotive parts. Attention is focused on the appropriate estimation of the stress intensity range ΔK, when the short cracks grow in the stress field of a notch and attempts are made to investigate whether this is appropriate or whether further allowance may have to be made for short crack effects at low ΔK.The stress distribution for the notch in bending was taken into account for the estimation of ΔK. This enabled us to produce a more precise evaluation of short crack growth in the stress field of the notch. Our findings are that the short cracks, which propagate in the notch field, grow faster at low ΔK when their lengths are extremely short compared with the notch root radius. The short crack effect at low ΔK in the notch stress field is analysed by expressing the crack growth data in terms of the parameter, ΔK_s, in which stress gradient ahead of the notch is taken into account.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

Crack growth behavior and fatigue-life prediction based on worst-case near-threshold data of a large crack for 9310 steel

ABSTRACT Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks, near‐threshold growth behavior of large cracks at constant R‐ratio/decreasing ΔK and constant K_max/decreasing ΔK, respectively, for 9310 steel. The results showed that a pronounced small‐crack effect was not observed even at R = ?1, small cracks initiated by a slip mechanism at strong slip sites. Worst‐case near‐threshold testing results for large cracks under several K_max values showed that an effect of K_max on the near‐threshold behavior does not exist in the present investigation. A worst‐case near‐threshold test for a large crack, i.e. constant K_max/decreasing ΔK test, can give a conservative prediction of growth behavior of naturally initiated small cracks. Using the worst‐case near‐threshold data for a large crack and crack‐tip constraint factor equations defined in the paper, Newman's total fatigue‐life prediction method was improved. The fatigue lives predicted by the improved method were in reasonable agreement with the experiments. A three‐dimensional (3D) weight function method was used to calculate stress‐intensity factors for a surface crack at a notch of the present SENT specimen (with r/w = 1/8) by using a finite‐element reference solution. The results were verified by limited finite‐element solutions, and agreed well with those calculated by Newman's stress‐intensity factor equations when the stress concentration factor of the present specimen was used in the equations.     

SMALL CRACK GROWTH IN THE ALUMINIUM–LITHIUM ALLOYS 8090 AND 8091

The relationship between microstructure and the fatigue behaviour of small cracks has been examined for the aluminium–lithium alloys 8090 and 8091 after peak ageing at 170°C. Duplex ageing and pre-stretching were used to vary the distribution of S'precipitates and thus the distribution of slip. No effect of S'distribution an small crack growth was observed in either alloy. This is thought to be due to a combination of the lack of closure and lower overall slip reversibility in small cracks. Small cracks in 8091 were found to grow slower than in 8090 due to differences in grain shape rather than texture. Small cracks in both alloys were observed to grow much faster than long cracks for equivalent ΔKs. This difference was reduced when small crack data were compared with long crack data generated at R= 0.7 due to the reduced closure. The use of ΔJ made long and small crack growth rates still more comparable.     

SMALL FATIGUE CRACK GROWTH BEHAVIOUR UNDER TWO STRESS LEVEL MULTIPLE LOADING

Small fatigue crack growth behaviour in a low alloy steel was investigated under two stress step multiple loading in which the secondary stress was below the fatigue limit. Crack growth rates were presented in terms of a stress intensity factor and compared with data obtained under constant amplitude loading. In the higher ΔK region, crack growth rates increased monotonously with increasing ΔK even though the stress level was below the fatigue limit, and tended to be lower than those for constant amplitude loading. In the lower ΔK region, cracks showed a complicated behaviour, that is, an initial high growth rate was observed followed by an arrest or a drop to a minimum value and then a gradual increase. The average crack growth rates per cycle at both primary and secondary stresses in each block were approximately consistent with the da/dn-ΔK relation for constant amplitude loading. A suggestion for the prediction of crack growth life is given.     

The influence of cyclic stress intensity threshold on fatigue life scatter

Understanding factors that contribute to scatter in fatigue lives of metallic structures (particularly airframes) subjected to identical spectrum is critical to maintaining safety and optimising designs. This paper first briefly discusses the sources of scatter, and then concentrates on the effect of variations in the “cyclic stress intensity threshold” (ΔK_thr) on fatigue crack growth. It shows that a version of the NASGRO equation can be used to account for the crack growth scatter seen in a number of classical fatigue experiments by accounting for variations in ΔK_thr. This is an important outcome for safety and is particularly useful when considering lead cracks for which ΔK_thr is small (approaching zero) as these cracks appear to commence growing soon after introduction into service.     

Influence of interfacial stress transfer on fatigue crack growth in SiC-fibre reinforced titanium alloys

An important damage mechanism during fatigue of unidirectional SiC-fibre reinforced titanium alloys is the formation of matrix cracks transverse to the fibre direction. Due to the relatively low fibre/matrix bond strength these matrix cracks initially do not break the fibres, so that matrix cracks bridged by fibres develop. It is shown experimentally, that the strong drop in fatigue strength is caused by the formation of a bridged crack of a critical size and the crack propagation rate (da/dN) for a single load level has been determined. A prediction of da/dN on the basis of finite element calculation of the stress intensity factor range of the bridged matrix crack ΔK_m and the ΔK_m–da/dN relationship of the used titanium alloy (Timetal 834) has been performed. Calculation of ΔK_m assuming a negligible fibre/matrix bond strength and considering shear load transfer at the fibre/matrix interface due to Coulomb friction (coefficient of friction μ=0.5 and μ=0.9) led to a large discrepancy between the measured and predicted crack growth rate. It can be concluded, that the assumed conditions of stress transfer at the fibre/matrix interface neglecting bonding is the reason for this discrepancy.     

Acceleration of FCP in toughened PMMA following a step increase in load amplitude

Fatigue crack growth measurements on rubber-toughened poly(methyl methacrylate) show that the relationship between crack growth rate da/dn and stress intensity range ΔK can be represented by two intersecting Paris curves of different slope. Sudden increases in load amplitude cause an acceleration in crack growth rate which is much greater than that predicted by the Paris law, but the rate falls sharply over the first 10 cycles at high stress amplitude, tending asymptotically to the ‘Paris values’ for mature crack growth. Results for crack extension during the first high load cycle indicate that accelerated growth occurs even when the increase in load amplitude is relatively small (there is no observable threshold) and that crack growth rates are dependent only on K_max for ΔK_high/ΔK_low above about 1.5.     

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     

Crack growth in a naturally corroded bridge steel

This paper summarises the findings of an international collaborative programme that focuses on the problem of the growth of cracks that arise from natural corrosion in bridge steels. The experimental data presented in this paper confirm that the bridge steel da/dN versus ΔK relationship is similar to that seen by the high‐strength aerospace steels D6ac and 4340. It is then shown that the methodology developed to predict the growth of small naturally occurring cracks in aerospace materials can also be used to compute the growth of cracks that arise because of natural corrosion in bridge steels.     

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial K _II /K _I mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small K _II /K _I ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.     

Threshold and growth mechanism of fatigue cracks under mode II and III loadings

ABSTRACT The fatigue crack growth behaviour of 0.47% carbon steel was studied under mode II and III loadings. Mode II fatigue crack growth tests were carried out using specially designed double cantilever (DC) type specimens in order to measure the mode II threshold stress intensity factor range, ΔK_IIth. The relationship ΔK_IIth > ΔK_Ith caused crack branching from mode II to I after a crack reached the mode II threshold. Torsion fatigue tests on circumferentially cracked specimens were carried out to study the mechanisms of both mode III crack growth and of the formation of the factory‐roof crack surface morphology. A change in microstructure occurred at a crack tip during crack growth in both mode II and mode III shear cracks. It is presumed that the crack growth mechanisms in mode II and in mode III are essentially the same. Detailed fractographic investigation showed that factory‐roofs were formed by crack branching into mode I. Crack branching started from small semi‐elliptical cracks nucleated by shear at the tip of the original circumferential crack.     

A unified method of design for fatigue crack growth resistance in structural materials

It is well established that there are two fatigue crack tip driving forces – the cyclic, ΔK, and the static, K_max. In this study, the effects of each crack tip driving force on crack growth were evaluated for various structural materials. A unified method of design that allows for predicting the response of long and physically small fatigue cracks at positive stress ratios is introduced. Good agreement between predicted and experimental long and physically small fatigue crack growth data was obtained. The importance of this method in material and component design is discussed as part of a contemporary design philosophy.     

On the dominant role of crack closure on fatigue crack growth modeling

Crack closure is the most used mechanism to model thickness and load interaction effects on fatigue crack propagation. But assuming it is the only mechanism is equivalent to suppose that the rate of fatigue crack growth da/dN is primarily dependent on ΔK_eff=K_max−K_op, not on ΔK. But this assumption would imply that the normal practice of using da/dN×ΔK curves measured under plane-stress conditions (without considering crack closure) to predict the fatigue life of components working under plane-strain could lead to highly non-conservative errors, because the expected fatigue life of “thin” (plane-stress dominated) structures could be much higher than the life of “thick” (plane-strain dominated) ones, when both work under the same stress intensity range and load ratio. However, crack closure cannot be used to explain the overload-induced retardation effects found in this work under plane-strain, where both crack arrest and delays were associated to an increase in ΔK_eff. These results indicate that the dominant role of crack closure in the modeling of fatigue crack growth should be reviewed.     

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range ΔK. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and “Unified Approach” models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model.     

Acoustic emission study of fatigue crack closure of physical short and long cracks for aluminum alloy LY12CZ

Crack closure of physical short and long cracks of LY12CZ aluminum alloy during fatigue process was investigated using acoustic emission (AE) technique. Results showed that the effective fatigue crack growth curve (da/dN vs. ΔK_eff) of physical short and long cracks obtained by the AE technique was consistent with the effective fatigue crack growth curve at high stress ratio (R = 0.8), which implied that the AE technique could measure the crack closure level, especially for physical short crack. The growth rate of physical short crack was much higher than that of long crack at the same ΔK, and the lower crack closure level of short crack was the main reason.     

A simple method based for computing crack shapes

The growth of cracks from small naturally occurring material discontinuities plays a major role in the operational lifespan of aircraft structures. Calculating the life of an airframe structure requires the determination of the crack path(s) which for complex real life geometries can often be highly complex. This paper presents a simple method based on finite element analysis for estimating the crack growth path. The analysis is based on an element removal approach and uses the major principal stress as the failure criteria. Evolution strategies are derived from the biological process of evolution. Three examples are presented demonstrating the utility of the proposed technique.