TIME-DEPENDENT FATIGUE CRACK GROWTH IN TITANIUM METAL MATRIX COMPOSITES

Abstract The interaction of fatigue and creep in a titanium metal matrix composite was studied by employing loading frequencies of 10 Hz (in both air and vacuum environment) and 0.1 Hz with and without hold times (in air) at 500°C. It was shown that, for the same loading frequency, the crack growth rate is lower in vacuum than in air. In an air environment, however, where the influence of load-related creep and environmental effects exist, it was shown that a decrease in the loading frequency leads to a decrease in the crack growth rate. This behavior is interpreted in terms of the redistribution of fiber and matrix stresses occurring in response to the creep-related relaxation of matrix stresses. The result of this stress redistribution is the generation of a compressive axial residual stress in the matrix phase in the region of the composite ahead of the crack tip. As the crack bridges the fibers in this region, the release of the matrix residual compressive stress leads to the closure of the matrix fractured surfaces at the crack tip, thus leading to a decrease in the crack tip driving force. To support this concept, experimental measurements of the crack opening displacement at different loading frequencies are presented. In addition, a simple model is proposed to describe the nature of the residual stresses developed in the matrix phase during cyclic loading. Results of this model have been examined using finite element analysis. The influence of time-dependent effects during a fatigue cycle was, furthermore, investigated by carrying out high frequency fatigue tests on specimens which have been previously subjected to creep deformation. Results of these tests in terms of the crack growth rate and associated crack closure, support the conclusion that a predeformed matrix produces a decrease in the crack growth rate of the corresponding composite.     

FATIGUE CRACK GROWTH IN NICKEL-BASED SUPERALLOYS AT 500-700°C. I: WASPALOY

Abstract— The effects of cyclic frequency, hold time, and stress-intensity-factor range (δ K ) on rates of fatigue crack growth in air at 500-700°C have been studied for Waspaloy—a nickel-based superalloy used for gas-turbine engine discs. The main effects observed were: (i) higher rates of crack growth for lower cyclic frequencies at high δ K at 600 and 700°C. and (ii) lower rates of crack growth at low δ K (and higher δ K thresholds) for longer hold times at 700°C, compared with those at a baseline frequency of 2 Hz. Metallographic and fractographic observations suggested that the effects of cyclic frequency and hold time could be rationalised in terms of the competing effects of enhancement of cracking due to creep and inhibition of cracking caused by oxide-induced crack closure, fracture-surface-roughness induced crack closure, and crack-branching/deflection. Possible mechanisms for promoting intergranular and transgranular cracking at low cyclic frequencies or long hold times are discussed.     

Effect of strain rate on stepwise fatigue and creep slow crack growth in high density polyethylene

The effects of frequency and R-ratio (the ratio of minimum to maximum stress in the fatigue loading cycle) on the kinetics of step-wise crack propagation in fatigue and creep of high density polyethylene (HDPE) was characterized. Stepwise crack growth was observed over the entire range of frequency and R-ratio examined. A model relating crack growth rate to stress intensity factor parameters and applied strain rate was proposed by considering the total crack growth rate to consist of contributions from creep and fatigue loading components. The creep contribution in a fatigue test was calculated from the sinusoidal loading curve and the known dependence of creep crack growth on stress intensity factor in polyethylene. At a very low frequency of 0.01 Hz, fatigue crack growth rate was found to be completely controlled by creep processes. Comparison of the frequency and R-ratio tests revealed that the fatigue loading component depended on strain rate. Therefore, crack growth rate could be modeled with a creep contribution that depended only on the stress intensity factor parameters and a fatigue contribution that depended on strain rate.     

A fatigue-to-creep correlation in air for application to environmental stress cracking of polyethylene

The present study was undertaken to determine whether the correlation between fatigue and creep established for polyethylene in air could be extended to environmental liquids. Fatigue and creep tests under various conditions of stress, R-ratio (defined as the ratio of minimum to maximum load in the fatigue loading cycle), and frequency were performed in air and in Igepal solutions. The load–displacement curves indicated that stepwise fatigue crack growth in air was preserved in Igepal solutions at 50 °C, the temperature specified for the ASTM standard. In air, systematically decreasing the dynamic component of fatigue loading by increasing the R-ratio to R = 1 (creep) steadily increased the lifetime. In contrast, the lifetime in Igepal was affected to a much smaller extent. The fatigue to creep correlation in air was previously established primarily for tests at 21 °C. Before testing the correlation in Igepal, it was necessary to establish the correlation in air at 50 °C. Microscopic methods were used to verify stepwise crack growth by the sequential formation and breakdown of a craze zone, and to confirm the fatigue to creep correlation. The crack growth rate under various loading conditions was related to the maximum stress and R-ratio by a power law relationship. Alternatively, a strain rate approach, which considered a creep contribution and a fatigue acceleration factor that depended only on strain rate, reliably correlated fatigue and creep in air at 50 °C under most loading conditions of stress, R-ratio and frequency. The exceptions were fatigue loading under conditions of R = 0.1 and frequency less than 1 Hz. It was speculated that compression and bending of highly extended craze fibrils were responsible for unexpectedly high crack speeds.     

Modes of failure under creep/fatigue loading of a nickel-based superalloy

Crack growth experiments have been carried out under combined creep and fatigue loading at 700° C on a hot isostatically pressed powder nickel alloy. A fractographic investigation has been undertaken of the modes of failure over a frequency range of 0.001 to 10 Hz. The observations indicate that under static loading and at low frequencies failure is intergranular and controlled by creep processes, whereas at high frequencies a transgranular fatigue fracture is obtained. The transition from creep to fatigue behaviour is found to be progressive, and to begin at a lower frequency the higher the ratio of cyclic to mean load. In the transition region a mixed intergranular and transgranular fracture surface is observed, which correlates well with the recorded proportion of creep to fatigue crack growth.     

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.     

Crack growth in discontinuous glass fibre reinforced polypropylene under dynamic and static loading conditions

Crack propagation in single edge notched tensile specimens of isotactic polypropylene reinforced with short E-glass fibres has been investigated under both fatigue and creep loading conditions. Fatigue crack propagation (FCP) experiments have been performed at three different frequencies (0.1, 1, 10 Hz) and at a mean applied tensile load of 1200 N. Isothermal creep crack propagation (CCP) tests have been conducted under a constant tensile applied load of 1200 N at various temperatures in the range from 32 to 60 °C. Analysis of FCP data allowed an estimation of the pure fatigue and pure creep components of the crack velocity under the adopted cyclic loading conditions. Crack growth at low frequencies (0.1 and 1 Hz) is mainly associated with a non-isothermal creep process. At higher frequency (10 Hz), the pure fatigue contribution appeared more pronounced. Finally, the comparison of FCP and CCP as a function of the mean applied stress intensity factor confirmed the major contribution of creep crack growth during FCP process at low frequencies.     

Cyclic fatigue in monolithic alumina: mechanisms for crack advance promoted by frictional wear of grain bridges

The microstructural basis of cyclic fatigue-crack propagation in monolithic alumina has been investigated experimentally and theoretically. A true cyclic fatigue effect has been verified, distinct from environmentally assisted slow crack growth (static fatigue). Microstructures with smaller grain sizes were found to promote faster crack-growth rates; growth rates were also increased at higher load ratios (i.e. ratio of minimum to maximum applied loads). Using in situ crack-path analysis performed on a tensile loading stage mounted in the scanning electron microscope, grain bridging was observed to be the primary source of toughening by crack-tip shielding. In fact, crack advance under cyclic fatigue appeared to result from a decrease in the shielding capacity of these bridges commensurate with oscillatory loading. It is proposed that the primary source of this degradation is frictional wear at the boundaries of the bridging grains, consistent with recently proposed bridging/degradation models, and as seen via fractographic and in situ analyses; specifically, load versus crack-openingdisplacement hysteresis loops can be measured and related to the irreversible energy losses corresponding to this phenomenon.     

Fatigue crack growth of UDIMET 720 Li superalloy at elevated temperature

The fatigue crack growth rate and fracture behaviour of a nickel–base superalloy UDIMET 720 Li was investigated at 700°C in vacuum and air environments using corner crack specimens. The effects of load ratio at a frequency of 0.25 Hz were examined while the effects of loading frequency from 5 Hz to 0.008 Hz were also examined for a constant load ratio. The mode of fracture was intergranular at all load ratios at a frequency of 0.25 Hz in an air environment. Two-parameter models were proposed to describe separately the effects of load ratio and frequency. The model prediction was combined with data from vacuum tests to form a fracture mechanism map showing limited contribution of creep, while oxidation controls the fatigue crack growth rate as the frequency decreases.     

Numerical simulation of fatigue crack growth behavior by crack-tip blunting

In ductile metals one of basic mechanisms for fatigue crack growth is that based on crack-tip blunting under the maximum load and re-sharpening of the crack-tip under minimum load. In this paper, simulations of fatigue crack growth by crack-tip blunting using ANSYS finite element code are presented. This investigation focuses solely on simulation of fatigue crack growth due to crack-tip plasticity only. As such, any material damage and its fracture is not considered. Due to high plastic deformation the present simulations utilize a remeshing technique which allows applying a number of load cycles without terminating the simulation due to the error caused by excessive mesh distortion. The simulations were conducted using a center cracked specimen under various loading conditions including different load ranges and load ratios R = −1, 0 and 0.333. It is shown that fatigue crack growth (FCG) slows down with number of cycles towards a steady state value. The simulated FCG data for constant amplitude loading follow the Paris power law relationship and also indicate a typical R-ratio dependence. It can be noted that for all load cases with load ratios R > 0 no crack closure in the vicinity of the crack-tip wake was observed.     

Influence of prior cyclic hardening on high temperature deformation and crack growth in type 316L (N) stainless steel

For power generating equipment subjected to cyclic loading at high temperature, crack growth could arise from the combinations of fatigue and creep processes. There is potential for the material to undergo hardening (or more generally changes of material state) as a consequence of cyclic loading. Results of an experimental study to examine the influence of prior cyclic hardening on subsequent creep deformation are presented for type 316L(N) stainless steel at 600°C. Experiments were also carried out to explore creep crack growth at constant load, and crack growth for intermittent cyclic loading. For the as-received material there is substantial primary creep (hardening) at constant load, while for the cyclically hardened material at constant load the creep curves show recovery, and increasing creep rate with increasing time. Specimens subjected to prior cyclic hardening were also used for a series of creep and creep-fatigue crack growth tests. These tests demonstrated that there was accelerated crack growth compared to crack growth in as-received material.     

Correlation of stepwise fatigue and creep slow crack growth in high density polyethylene

The kinetics and mechanism of slow crack growth in fatigue and creep of high density polyethylene were studied. The relationship between fatigue and creep was examined by varying the R-ratio (the minimum/maximum loads in the fatigue loading cycle) in the tensile mode such that loading ranged from mainly dynamic (R = 0.1) to static (R = 1.0, creep test). The stepwise crack propagation mechanism characteristic of long-term failures in polyethylene was observed for all loading conditions studied. Fatigue fracture kinetics allowed for extrapolation to the case of creep failure, which suggested that short-term fatigue testing can be used to predict long-term creep fracture properties. The size of the craze damage zone ahead of the arrested crack tip was controlled only by the mean stress, however the lifetime of the zone was determined by both the maximum stress and the mean stress. Crack growth rate was related to the maximum stress and the mean stress by a power law relationship, which described crack growth over the entire range of loading conditions studied.     

Creep-fatigue crack propagation in lead-free solder under cyclic loading with various waveforms

Crack propagation tests of lead-free solder were conducted using center-notched plate specimens under cyclic tension-compression of three load waveforms: pp waveform having fast loading and unloading, cp-h waveform having a hold time under tension, and cc-h waveform having a hold time under tension and compression. In the case of fatigue loading, i.e. pp waveform, the path of crack propagation was macroscopically straight and perpendicular to the maximum principal stress direction, showing tensile-mode crack propagation. The introduction of the creep components by hold time in cc-h and cp-h waveforms promoted shear-mode crack propagation. For fatigue loading of pp wave, the crack propagation rate was expressed as a power function of the fatigue J integral and the relation was identical for load-controlled and displacement-controlled conditions. The creep component due to the hold time greatly accelerates the crack propagation rate when compared at the same values of the fatigue J integral or the total J integral (the sum of fatigue J and creep J integrals). The creep crack propagation rate was expressed as a power function of the creep J integral for each case of cp-h and cc-h waveforms. The crack propagation rate for cp-h waveform is higher than that for cc-h waveform. The predominant feature of fracture surfaces was striations for pp waveform and grain boundary fracture for cp-h waveform. Grain fragmentation was abundantly observed on the fracture surface made under cc-h waveform.     

Plasticity induced crack closure in adhesively bonded joints under fatigue loading

The mean load of a cyclic loading has a large effect on fatigue crack growth rates in metallic materials and bonded joints. In metallic structures, this effect has been attributed to plasticity-induced crack closure, but little is known about the mechanism responsible for this mean load effect on fatigue crack growth in adhesively bonded joints. This paper presents a computational investigation of the plasticity-induced crack closure mechanism affecting disbond growth in adhesively bonded joints under fatigue loading. The results show that the ratios of crack-opening and crack-closure are approximately independent of the level of plastic constraint, indicated by the ratio between the plastic zone size and the adhesive thickness. An effective strain-energy release rate parameter, which accounts for the crack closure behaviour, has been developed as a new correlating parameter for disbond growth. Comparisons with the experimental results pertinent to four different adhesive bonded joints reveal that this new correlating parameter is capable of unifying the fatigue growth rates by eliminating the effect of mean loads.     

Time dependent effects in fatigue of titanium and nickel alloys

The paper explores fatigue at both low and high temperature where creep and environmental damage interact with the normal cyclic processes of crack development. This is achieved by studying two contrasting material systems: the titanium alloys (Ti685, Ti834, Ti6246) and the nickel alloys (Udimet 720Li). Particular attention is given to both load and strain control fatigue response and crack development at stress concentration features. In each case there is an interesting balance between the beneficial effects of stress relaxation and the damaging effects of creep and environmental factors. On the crack growth side, the relative contributions of creep and environment are highlighted through measurements made in air and vacuum and by varying R value and dwell time. At the same time, any complications due to closure are removed by careful measurement of closure levels for each condition. The inadequacy of linear damage models for combining cyclic and time dependent effects is highlighted.     

FATIGUE UNDER CYCLIC COMPRESSIVE LOAD

For ultra-high strength steels and aluminium alloys, a fatigue crack could initiate from a notch tip under cyclic compressive load. The threshold value for fatigue crack initiation under compressive load can be as great as four times that under tensile load. The crack grew at a decreasing rate until eventually it stopped growing altogether under cyclic compressive load with a maximum length of 0.2-0.5 mm. If the minimum compressive load was near zero, i.e. compression to zero load cycling, the threshold value was near that under tensile loading and the compressive fatigue crack could continue to grow; however, the crack growth rate under compression to zero load fatigue was 10–100 times less than that under the tensile fatigue loading.     

Overload effects in fatigue crack growth by crack-tip blunting

A basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In the present paper, the effect of an overload in one of the cycles is studied based on this mechanism. In a standard numerical analysis accounting for finite strain, it is not possible to follow the blunting/re-sharpening process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using remeshing at several stages of the plastic deformation. Crack growth results for purely cyclic loading are compared with predictions for cases where an overload is applied, and it is shown how crack growth slows down after the overload. Different load amplitudes, and an overload at different cycle numbers are considered.     

A numerical analysis of the mechanisms behind plasticity induced crack closure: Application to variable amplitude loadings

The effect of loading parameters on fatigue crack growth has been explained using the concept of crack closure. Plasticity induced crack closure (PICC) is linked to the crack tip plastic deformation, which becomes residual with crack propagation. The objective here is to identify the main mechanisms behind PICC, and for that different loading cases were considered namely overloads and load blocks. An analytical model was used to isolate the effect of residual plastic deformation on PICC, however significant differences were obtained relatively to finite element results. A second mechanism, which is crack tip blunting, was used to explain the transient behaviour observed after overloads and load blocks. For overloads and low–high load sequences there is a sudden increase of crack tip blunting with load increase which explains the sudden decrease of crack opening level. For high–low load sequences there is a sudden decrease of crack tip blunting which enhances the effect of residual plastic wake. Finally, the partial closure concept was tested looking to non-linear crack tip parameters but no evidences of Donald’s effect were found for the material studied.     

CRACK CLOSURE AND THE FATIGUE-CRACK PROPAGATION THRESHOLD AS A FUNCTION OF LOAD RATIO

The phenomenon of crack closure, which involves the premature closing of fatigue cracks during the unloading portion of a fatigue cycle resulting in the development of crack-tip shielding due to crack wedging, has become widely accepted as a critical mechanism influencing many aspects of the behaviour of fatigue cracks in metallic materials; these include effects of load ratio, variable-amplitude loading, crack size, microstructure, environment and the magnitude of the fatigue threshold. Recently, however, the significance of crack closure has been questioned and alternative suggestions made for many of these phenomena, e.g. the effect of the load ratio (i.e. the ratio R of the minimum to maximum loads) on threshold behaviour. In the light of this, the present paper provides evidence to rebut the assertion that crack closure is an insignificant process. Particular attention is given to the effect of crack closure on the threshold level as a function of load ratio.