Effect of frequency on high-temperature fatigue crack growth in a silicon carbide reinforced silicon nitride composite

A detailed study on a silicon nitride reinforced with silicon carbide whiskers, Si₃N₄SiC_W, has been undertaken at elevated temperature during static and dynamic loading at increasing K and ΔK respectively. It is shown that cyclic sub-critical crack growth rates are lower than static crack growth rates. The increased crack growth rate during static far field loading is attributed to the stress relaxation of the inter-granular glass phase which allows time-dependent processes to occur ahead of the crack tip which lead to enhanced sub-critical crack growth rates. During cyclic fatigue the glass phase has insufficient time to relax and glassy ligaments are able to bridge the crack wake thereby shielding the crack tip from the full force of the applied load. Also, at particular temperatures, bridging between the surfaces of the crack wake by the inter-granular glass phase results in increased strength and fatigue retardation. The extent of ‘crack wake healing’ is shown to be time and temperature dependent. The viscosity of the glass phase is directly related to the temperature and the bonding force associated with glass phase bridging is observed to reduce with increasing temperature. The results from a previous study at room temperature are compared to those found during this investigation.     

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J-integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account.More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out.In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters (J-integral, T-stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α_g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α_g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.     

Cyclic fatigue of ceramics

The fatigue behaviour of alumina, zirconia-toughened alumina (ZTA) and tetragonal zirconia (TZP) have been investigated using three different techniques. Direct push-pull testing has been used to generate both static and cyclic fatigue data. The results clearly show that all the materials studied are susceptible to both static and cyclic fatigue, and that the times to failure under cyclic loading are considerably shorter than under static loads. The fatigue failure origins have been identified and the influence of surface condition on fatigue life has been assessed. The slow propagation of cracks subject to cyclic tensile and compressive loads has been studied using compact tension specimens and tapered double cantilever beam specimens. These investigations have confirmed the existence of cyclic fatigue effects in coarse-grained alumina and have shown the crack increment per cycle (da/dN) to have a power-law dependence on the peak stress intensity factor. A technique, based on repeated indentation, has been used to investigate the propagation of sub-surface cracks subjected to cyclic loading in both fine-grained alumina and ZTA. The results of the investigation suggest that compressive or closure loads on the crack faces are factors which affect the cyclic fatigue crack growth in ceramics. Based on those observations, an explanation is proposed for the mechanical cyclic fatigue effects in the ceramics investigated.     

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.     

Cyclic fatigue of a sintered Al2O3/ZrO2 ceramic

A systematic experimental and theoretical study on the crack growth behaviour of a sintered Al₂O₃/ZrO₂ ceramic under cyclic loading is presented. It is found that in the cyclic fatigue experiments conducted on the single-edge-notched beam (SENB) geometry, for similar testing conditions, the crack growth rates are significantly faster than those under static fatigue. Al₂O₃/ZrO₂ therefore suffers genuine mechanical fatigue. Further experiments with the compact tension (CT) geometry show that the mechanical fatigue effect arises mainly from the degradation of the bridging mechanism. A theoretical analysis based on the compliance technique and a power law relationship between the crack-wake bridging stress and the crack-face separation is developed to evaluate quantitatively the degradation of the bridging stress due to cyclic fatigue.     

Elevated-temperature crack growth in polycrystalline alumina under static and cyclic loads

An experimental investigation has been conducted to study the crack growth characteristics of a 90% pure aluminium oxide in 1050 °C air under static and cyclic loads. It is shown that the application of both sustained and fluctuating tensile loads to the ceramic, tested in a precracked four-point bend specimen configuration, results in appreciable subcritical crack growth. The crack velocities under cyclic loading conditions are up to two orders of magnitude slower than those measured in static loading under the same maximum stress intensity factor. Cyclic crack growth rates are markedly affected by the loading frequency, with a decrease in test frequency causing an increase in the rate of crack advance. Detailed optical and electron microscopy observations have been made in an attempt to study the mechanisms of stable crack growth and the mechanistic differences between static fatigue fracture. Under both static and cyclic loads, the predominant mode of fracture is intergranular separation. The presence of a glass phase along the grain boundaries appears to have a strong effect on the mechanisms of crack growth. Apparent differences in the crack velocities between static and cyclic fatigue in alumina arise from crack-wake contact effects as well as from the rate-sensitivity of deformation of the glass phase. Our results also indicate that the cyclic fatigue crack growth rates cannot be predicted solely on the basis of sustained load fracture data. White stable crack growth occurs in the 90% pure alumina over a range of stress intensity factor spanning 1.5 to 5 MPa m^1/2, such subcritical fracture is essentially suppressed in a 99.9% pure alumina, ostensibly due to the paucity of a critical amount of glass phase. Both static and cyclic fracture characteristics of the 90% pure alumina are qualitatively similar to those found in an Al₂O₃-SiC composite wherein situ formation of glass phases, due to the oxidation of SiC in high-temperature air, is known to be an important factor in the fracture process.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

Mechanical fatigue of Sn-rich Pb-free solder alloys

Recent fatigue studies of Sn-rich Pb-free solder alloys are reviewed to provide an overview of the current understanding of cyclic deformation, cyclic softening, fatigue crack initiation, fatigue crack growth, and fatigue life behavior in these alloys. Because of their low melting temperatures, these alloys demonstrated extensive cyclic creep deformation at room temperature. Limited amount of data have shown that the cyclic creep rate is strongly dependent on stress amplitude, peak stress, stress ratio and cyclic frequency. At constant cyclic strain amplitudes, most Sn-rich alloys exhibit cycle-dependent and cyclic softening. The softening is more pronounced at larger strain amplitudes and higher temperatures, and in fine grain structures. Characteristic of these alloys, fatigue cracks tend to initiate at grain and phase boundaries very early in the fatigue life, involving considerable amount of grain boundary cavitation and sliding. The growth of fatigue cracks in these alloys may follow both transgranular and intergranular paths, depending on the stress ratio and frequency of the cyclic loading. At low stress ratios and high frequencies, fatigue crack growth rate correlates well with the range of stress intensities or J-integrals but the time-dependent C* integral provides a better correlation with the crack velocity at high stress ratios and low frequencies. The fatigue life of the alloys is a strong function of the strain amplitude, cyclic frequency, temperature, and microstructure. While a few sets of fatigue life data are available, these data, when analyzed in terms of the Coffin–Mason equation, showed large variations, with the fatigue ductility exponent ranging from −0.43 to −1.14 and the fatigue ductility from 0.04 to 20.9. Several approaches have been suggested to explain the differences in the fatigue life behavior, including revision of the Coffin–Mason analysis and use of alternative fatigue life models.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

High temperature fatigue crack growth in Inconel 718

Abstract

The nickel base superalloys are extensively used in high temperature applications, so it is important to know their behaviour under conditions of high-temperature fatigue. This paper studies the influence of ΔK, loading frequency, stress ratio and temperature on the high temperature fatigue crack growth rate of nickel base superalloys. This study is based on fatigue tests carried out in corner crack specimens of Inconel 718 at 600°C and at room temperature. Three stress ratios (R = 0.05, 0.5 and 0.8) and loading frequencies ranging from 0.0017 to 15 Hz were considered in the tests. For frequencies below 0.25 Hz, the load wave shape was trapezoidal with different dwell times at maximum load. At relatively high frequencies the propagation is cycle dependent, while for lower frequencies it is time dependent. At intermediate frequencies a mixed crack growth occurs. The transition frequencies from cycle dependent to mixed regime and from mixed to time dependent regime were obtained for each R. The increase of R increases the transition frequencies, i.e., extends the time dependent crack growth to higher frequencies. The increase of R also produces an increase of cyclic crack growth rate for all regimes of crack growth. In the time dependent regime, a higher variation is observed, that can be explained by an acceleration of oxidation damage promoted by the increase of maximum stress. An approach for modelling the high-temperature fatigue crack growth in nickel base superalloys is presented. A good agreement was observed between time dependent fatigue results and mathematical models based on static load results.     

Fracture toughness and fatigue crack growth behaviour of an Al2O3-SiC composite

The fracture toughness and fatigue crack growth characteristics of an Al₂O₃-SiC whisker composite were investigated. Quasi static fracture experiments were conducted on double edge-notched tension specimens and on four-point bend specimens containing a through-thickness Mode I crack which was introduced under uniaxial cyclic compression. The toughness results obtained using this procedure are more reproducible than those derived from the indentation technique and the notched bend bar method. The fracture toughness of the composite is about 60% higher than that of the unreinforced matrix material. Crack growth characteristics at room temperature were also investigated in notched plates of Al₂O₃-SiC subjected to fully compressive far-field cyclic loads. In the presence of a stress concentrator, this composite is found to be highly susceptible to fatigue crack growth under cyclic compressive loads.     

Multiple mechanisms controlling fatigue crack growth

Recognizing that fatigue is a two‐parameter problem requiring two load parameters to define cyclic loads unambiguously, a unified approach has been developed to account for crack growth behaviour in terms of ΔK and K_max . Since both driving forces govern the crack growth rate, any analysis based on either ΔK or K_max will provide only partial information about the fatigue behavior of materials. It is shown that ΔK–K_max plots and the associated crack growth trajectory maps reflect the basic mechanisms that contribute to crack growth in a material. These plots also provide a convenient basis to recognize the changes in the micromechanisms that can occur as a function of load ratio or crack growth rate, or both. Taking examples from the literature, crack growth trajectory maps are provided showing such changes in the governing mechanisms of crack growth. It is shown that the ΔK–K_max approach is not an alternative to crack closure models, but it reflects the intrinsic material behaviour that must be understood before reliable crack prediction models can be developed.     

High-temperature cracking resistance in cast steel in reforming oven tubes

Summary Results are given from high-temperature tests (770, 870, 920, and 960°C) to estimate the short-time and cyclic cracking resistance for cast NK-40 steel tubes from reforming ovens in the initial state and after use for 75,400 h. The crack growth resistance in static loading has been determined from the crack resistance limit, and in cyclic loading from the kinetic diagrams for the fatigue failure in terms of the crack growth ratev against the scale of the nominal stress intensity coefficient K. Metallography shows that there are differences in structure in the various states, and material that has been used has pores and microcracks, whose numbers are largest in the inner wall layers. Cyclic tests with constant K show substantial increase in the crack growth rate in the defective material.The cracking stability limit falls as the test temperature rises, while the fatigue crack growth rate increases, particularly above 920°C. Increased asymmetry in the loading cycle (R=–1; –0.5; 0; 0.4) is accompanied by deterioration in the cyclic cracking resistance. There are two opposite trends in the effects of loading frequency (f=0.001–10 Hz) on the failure kinetics: in the high-amplitude loading range, reduction inf increases the crack growth rate, while in the low-amplitude range, there is a decrease. The results are explained in terms of creep and fatigue crack opening.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 2, pp. 68–74, March–April, 1990.     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

Fatigue crack growth behaviour of gamma base titanium aluminides under different loading conditions

Static and cyclic fatigue crack growth behaviour of gamma base titanium aluminides with three different microstructures were investigated. Influence of cyclic test frequency on fatigue crack growth behaviour was also studied at room temperature under a controlled humidity condition. The crack growth behaviour both under static and cyclic loading was strongly influenced by the microstructure. The threshold stress intensity and crack growth behaviour under cyclic loading were much inferior than that under static loading indicating the ‘true-cyclic fatigue’ effect exhibited in gamma base titanium aluminides. No significant effect of test frequency on the crack growth behaviour was observed for the equiaxed and duplex microstructure materials.     

Crack propagation and fatigue in zirconia-based composites

This paper reviews existing published studies on crack propagation behavior of zirconia-based composites. The first part of the paper is concerned with slow crack growth (SCG) under static loading. SCG in zirconia ceramics is shown to be a consequence of stress corrosion by water molecules at the crack tip. The influence of transformation toughening on SCG is discussed in terms of a stress intensity factor acting to reduce the net driving force for propagation. This proposition is in agreement with results obtained on 3Y-TZP and Mg-PSZ ceramics. A master curve is proposed which could be applied roughly to all zirconia ceramics. The influence of zirconia addition to alumina ceramics (ZTA ceramics) is also discussed. The second part of the paper deals with SCG under cyclic loading. A mechanical degradation of all zirconia-based composites is observed by a decrease of crack shielding. This degradation of zirconia-based composites under cyclic loading leads to increased velocities as compared to the static fatigue case. A master curve is also obtained, as in the case of static fatigue. Cyclic fatigue results are interpreted in terms of stress corrosion at the crack tip assisted by a decrease of the reinforcement.     

Modelling the effect of creep–fatigue interaction on crack growth

Time-dependent creep–fatigue crack growth (CFCG) is a major consideration in estimating the remaining life of elevated temperature components. Fracture mechanics approaches have proven useful in providing a framework for characterizing crack growth under service conditions, and in defining safe operating conditions and selecting inspection criteria and intervals. Experimental and analytical approaches have been developed to characterize crack growth under combined creep and fatigue loading conditions using (C_t )_avg as the crack tip parameter. The analytical approaches that have been proposed to characterize CFCG are limited in their application because they do not completely account for the effect of creep–fatigue interactions in modelling crack tip deformation, and thus, accurately estimating the (C_t )_avg value. A new creep-reversal parameter, C_R , is defined in this study to quantify the extent of creep–fatigue interaction at the crack tip, and is used in an analytical scheme, suitable for components, for calculating (C_t )_avg . This approach does not rely on any simplifying assumptions regarding the extent of reinstatement of C_t , which is dependent on the amount of creep reversal due to cyclic plasticity, during the unloading part of a trapezoidal loading waveform cycle. The (C_t )_avg values calculated by this approach compare well with the experimentally obtained values for compact type (CT) specimens, thus providing an experimental verification of the approach.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

Flexural fatigue of short glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide

Flexural fatigue tests were conducted on injection molded glass fiber reinforced a blend of polyphenylene ether ketone and polyphenylene sulfide composite using four-point bending with different stress ratios and different frequencies. The fatigue behavior of this material was described. The constructed S-N curves shift their trends obviously at the maximum cyclic stress being about 80% of the ultimate flexural strength. Examinations of failure surfaces for various loading conditions show that the fatigue failure mechanisms appear to be matrix yielding at high stresses and crack growth at low stresses. Analyses of the fatigue data at various stress ratios reveal that the data at low stress superimpose to form a single curve which is nearly linear when they are plotted as stress range versus number of cycles to failure in bilogarithmic axes, while the data at high stresses also converge to yield a single curve when they are plotted as (S _max S _range)^1/2 against specimen lifetimes (S _max is the maximum stress andS _range is the stress range). These results show that for the studied material the main factor influencing the lifetime is the stress range at low stresses and the parameter (S _max S _range)^1/2 at high stresses. Comparison of fatigue data in the frequency range of 0.89–7.0 Hz was made, no significant effect of frequency on the fatigue behavior is found.