Effects of grain size on cyclic plasticity and fatigue crack initiation in nickel

Fatigue experiments were conducted on polycrystalline nickel of two grain sizes, 24 and 290 μm, to evaluate the effects of grain size on cyclic plasticity and fatigue crack initiation. Specimens were cycled at room temperature at plastic strain amplitudes ranging from 2.5×10⁻⁵ to 2.5×10⁻³. Analyses of the cyclic stress–strain response and evolution of hysteresis loop shape indicate that the back stress component of the cyclic stress is significantly affected by grain size and plastic strain amplitude, whereas these parameters have little effect on friction stress. A nonlinear kinematic hardening framework was used to study the evolution of back stress parameters with cumulative plastic strain. These are related to substructural evolution features. In particular, long range back stress components are related to persistent slip bands. The difference in cyclic plasticity behavior between the two grain sizes is related to the effect of grain size on persistent slip band (PSB) morphology, and the effect this has on long range back stress. Fine grain specimens had a much longer fatigue life, especially at low plastic strain amplitude, as a result of the influence of grain size on fatigue crack initiation characteristics. At low plastic strain amplitude (2.5×10⁻⁴), coarse grain specimens initiated cracks where PSBs impinged on grain boundaries. Fine grain specimens formed cracks along PSBs. At high plastic strain amplitude (2.5×10⁻³), both grain sizes initiated cracks at grain boundaries.     

Short crack growth and fatigue life in austenitic-ferritic duplex stainless steel

The kinetics of short crack growth has been studied in austenitic‐ferritic 2205 duplex stainless steel. Smooth cylindrical specimens and specimens with shallow notch were subjected to constant plastic strain amplitude loading. The crack growth was studied in notched specimens. The notch area has been mechanically and electrolytically polished to facilitate the observation of crack initiation and growth. The initiated cracks were observed in an SEM (scanning electron microscope). The crack growth was studied using long distance QUESTAR optical microscope equipped with high‐resolution camera. In constant plastic strain amplitude loading the microcracks were initiated and their growth kinetics has been studied. The characteristic features of the crack growth at different plastic strain amplitudes were recorded. Two approaches to analyse the crack growth rates were adopted. The comparison of the prediction of the fatigue life using the plastic‐strain‐dependent crack growth rate was compared with Manson–Coffin law and the relation between parameters of this law and parameters of the short crack growth law were established.     

High resolution digital image correlation measurements of strain accumulation in fatigue crack growth

Microstructure plays a key role in fatigue crack initiation and growth. Consequently, measurements of strain at the microstructural level are crucial to understanding fatigue crack behavior. The few studies that provide such measurements have relatively limited resolution or areas of observation. This paper provides quantitative, full-field measurements of plastic strain near a growing fatigue crack in Hastelloy X, a nickel-based superalloy. Unprecedented spatial resolution for the area covered was obtained through a novel experimental technique based on digital image correlation (DIC). These high resolution strain measurements were linked to electron backscatter diffraction (EBSD) measurements of grain structure (both grain shape and orientation).Accumulated plastic strain fields associated with fatigue crack growth exhibited inhomogeneities at two length scales. At the macroscale, the plastic wake contained high strain regions in the form of asymmetric lobes associated with past crack tip plastic zones. At high magnification, high resolution DIC measurements revealed inhomogeneities at, and below, the grain scale. Effective strain not only varied from grain to grain, but also within individual grains. Furthermore, strain localizations were observed in slip bands within grains and on twin and grain boundaries. A better understanding of these multiscale heterogeneities could help explain variations in fatigue crack growth rate and crack path and could improve the understanding of fatigue crack closure and fracture in ductile metals.     

Microstructural influences on the growth of small cracks in Ti-6Al-4 V

ABSTRACT The effects of microstructure on the growth of small cracks in Ti-6Al-4 V under fatigue loading are presented. The small crack growth is compared with large crack growth. Two large crack tests were performed at a stress ratio of 0.4 and a frequency of 15 Hz. For small crack growth tests, double edge notch specimens were loaded under constant amplitude at four maximum stresses with a stress ratio of 0.4 and a frequency of 15 Hz. A plastic replication technique was used to monitor the small fatigue crack growth rate. The microstructure consists of bands of α and β phases. The present study indicates that the crack growth direction and shape are dependent upon the grain size and grain orientations, and that the crack growth rate seems to be affected by the spacing of α-rich and β-rich bands. Small cracks are propagated at stress intensity factors well below the large crack threshold stress intensity factor.     

Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands

Strain localization under low amplitude cyclic loading is a manifestation of plastic irreversible deformation associated with early crack growth. However, traditional constitutive models cannot usually reproduce strain localization in smooth single crystals, which can affect crack growth predictions for crystallographic fatigue cracks. This work analyzes the influence of bands of localized plastic shear strain on the cyclic crack tip displacement and on a fatigue indicator parameter by making special provision of a crack along the interface of a deformation band. Furthermore, the quality of local and volume-averaged fatigue indicator parameters are assessed using finite element models of a Cu single crystal cycled to induce plastic deformation under multiple loading conditions.     

STATISTICAL INVESTIGATION OF THE BEHAVIOUR OF SMALL CRACKS AND FATIGUE LIFE IN CARBON STEELS WITH DIFFERENT FERRITE GRAIN SIZES

Abstract— In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.     

A MODEL FOR SHORT FATIGUE CRACK PROPAGATION WITH AN INTERPRETATION OF THE SHORT-LONG CRACK TRANSITION

The behaviour of short cracks approaching growth barriers (e.g. grain boundaries) is considered. The crack model of Bilby, Cottrell and Swinden is applied to simulate the blocking of the plastic zone at the grain boundary and to obtain the stress concentration ahead of the crack as it approaches the barrier. The idea of the Hall-Petch type relationship that the transmission of slip across grain boundaries needs the previous achievement of a critical stress has been used. By making the crack growth rate proportional to the plastic displacement at the root of the crack the deceleration behaviour of short cracks and the existence of non-propagating cracks may be explained. The fatigue limit is related to the stress below which a crack growing in a single grain is unable to promote slip in the neighbouring grain. The different behaviour in the so-called long crack period has been rationalized in terms of the plastic zone exceeding the grain size. For this case, and in the grain completely included within the plastic zone, the Hall-Petch analysis must be applied. Hence the maximum back-stress sustained by this grain cannot exceed the yield stress. After this point the Bilby et al. model is used with uy as a friction stress (i.e. the Dugdale model). Finally use is made of Fracture Mechanics to correlate the results in the long crack phase.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique

The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries.     

On the interactions between strain accumulation, microstructure, and fatigue crack behavior

Fatigue crack growth is a complex process that involves interactions between many elements ranging across several length scales. This work provides an in-depth, experimental study of fatigue crack growth and the relationships between four of these elements: strain field, microstructure, crack path, and crack growth rate. Multiple data sets were acquired for fatigue crack growth in a nickel-based superalloy, Hastelloy X. Electron backscatter diffraction was used to acquire microstructural information, scanning electron microscopy was used to identify locations of slip bands and crack path, and optical microscopy was used to measure crack growth rates and to acquire images for multiscale digital image correlation (DIC). Plastic strain accumulation associated with fatigue crack growth was measured at the grain level using DIC. An ex situ technique provided sub-grain level resolution to measure strain variations within individual grains while an in situ technique over the same regions showed the evolution of strain with crack propagation. All of these data sets were spatially aligned to allow direct, full-field comparisons among the variables. This in-depth analysis of fatigue crack behavior elucidates several relationships among the four elements mentioned above. Near the crack tip, lobes of elevated strain propagated with the crack tip plastic zone. Behind the crack tip, in the plastic wake, significant inhomogeneities were observed and related to grain geometry and orientation. Grain structure was shown to affect the crack path and the crack growth rate locally, although the global crack growth rate was relatively constant as predicted by the Paris law for loading with a constant stress intensity factor. Some dependency of crack growth rate on local strain and crack path was also found. The experimental comparisons of grain structure, strain field, and crack growth behavior shown in this work provide insight into the fatigue crack growth process at the sub-grain and multi-grain scale.     

Model of fatigue crack propagation by damage accumulation at the crack tip

Modelling fatigue crack propagation by damage accumulation at the crack tip originally proposed by McClintock is reworked out using metallurgical considerations. On a physical basis it is shown that the validity of such models is actually confined to the low crack growth rate range corresponding to stage I growth such as along crystallographic planes. At higher crack growth rates there is a transition to plastic stretching mechanisms which could be described by crack opening displacement models. An evaluation of two models has been carried out on a ³³Co Ni alloy where extensive information was available: both are based on the strain singularity as computed by Tracey from a finite element analysis of plane strain small scale yielding and as adapted to cyclic loading under Rice's hypothesis and taking the grain as the critical element below which size continuum mechanics do no longer apply. It is pointed out that the use of this strain singularity which is not able to account for crack closure, renders models unable to predict experimental crack growth rates curves but only intrinsic curves relating the growth rate to the effective stress intensity amplitude as defined by Elber. The first model which assumes fatal cracking of a grain with an average uniform cyclic equivalent strain, underestimates the crack growth rates and in addition it yields results very sensitive to the shape and size of the grain. The second model which assumes progressive cracking in a grain with a cyclic equivalent strain gradient is able to predict the intrinsic crack growth rate curve in the ³³Co Ni alloy and to yield predictions consistent with other experimental data.     

Plastic deformation and fracture in coarse-grained aluminum

Plastic deformation and fracture in aluminum polycrystalline aggregate were investigated experimentally. A series of tensile specimens with a single edge crack were made of coarse-grained aluminum plates. The in-plane moiré technique was used to quantitatively obtain the deformation field around the crack tip. The strain field ahead of the crack tip prior to crack growth, as well as grain rotations during the course of plastic deformation, were evaluated from the corresponding moiré fringe patterns. The results of this study show that for small plastic deformation, grain rotation starts to take place at the very beginning of the plastic deformation and increases proportionally with plastic strain. The plastic strain ahead of the crack tip prior to crack growth drops significantly with decreasing average grain size of the specimen. Grain boundary sliding was also observed at some of the grain boundaries where the resolved shear stress had reached a critical value. The results also show that the crack propagated with maximum velocity at the center of a grain and assumed much slower velocity near grain boundaries or grain boundary junctions. The influence of the deformation rate is also discussed in terms of the stress relaxation.     

Fatigue damage in nickel and copper single crystals at nanoscale

Nanoscale fatigue damage simulations using molecular dynamics were performed in nickel and copper single crystals. Cyclic stress–strain curves and fatigue crack growth were investigated using a middle-tension (MT) specimen with the lateral sides allowing periodic boundary conditions to simulate a small region of material as a part of a larger component. The specimen dimensions were in the range of nanometers, and the fatigue loading was strain controlled under constant and variable amplitude. Four crystal orientations, [111], [100], [110] and [101] were analyzed, and the results indicated that the plastic deformation and fatigue crack growth rates vary widely from one orientation to another. Under increasing strain amplitude loading, nickel nanocrystals experienced a large amount of plastic deformation causing at least in one orientation, [101], out-of-plane crack deviation in a mixed mode I+ II growth. Under constant amplitude loading, the fatigue cracks were a planar mode I type. Double slip is observed for some orientations, while for others, many more slip systems were activated causing a more evenly distributed plastic region around the crack tip. A comparative analysis revealed that small cracks grow more rapidly in copper than in nickel single crystals.     

Characteristics of hydrogen-assisted intergranular fatigue crack growth in interstitial-free steel: role of plastic strain localization

The behavior of intergranular fatigue crack growth in an interstitial-free (IF) steel in a hydrogen environment was investigated at different frequencies. Focusing on the plastic strain localization, we observed details of the striation-like feature on the intergranular fracture surface, slip behavior around microvoids, and crystallographic orientation gradient underneath the fracture surface. It was determined that the intergranular fatigue crack growth mechanism in the IF steel is microvoid formation at the crack tip and subsequent coalescence with the crack. Moreover, it was found that the grain boundaries, acting as propagation paths, suffer from pre-damage arising from plastic strain localization near the grain boundaries even before the main crack propagates to a certain location. Therefore, fatigue cracks in a hydrogen environment easily propagate to the grain boundaries. The frequency dependence of fatigue crack growth in the hydrogen environment is significantly smaller than that in a low carbon steel, probably because of the frequency dependence of the pre-damage evolution behavior.     

Plastic strain-controlled short crack growth and fatigue life

Constant plastic strain-controlled and constant stress-controlled tests were performed on smooth and lightly notched specimens machined from a massive forging of 42CrMo4 steel. Comparison of the fatigue life curves plotted as function of the plastic strain amplitude and stress amplitude shows a decisive role of plastic strain amplitude. Crack initiation and the kinetics of short crack growth were studied in constant plastic strain amplitude loading and the relation between the crack growth coefficient and plastic strain amplitude was established. This is equivalent to the Coffin–Manson law and shows that the Coffin–Manson law can be interpreted in terms of short crack growth.     

A new mechanism in hydrogen-enhanced fatigue crack growth behavior of a 1900-MPa-class high-strength steel

This paper presents a new mechanism controlling the acceleration of fatigue crack growth of a hydrogen-charged high-strength steel (bearing steel SAE52100, ?? _ult?>?1, 900MPa, HV =?569). Three- dimensionally complicated shape of a primary crack and secondary cracks were observed in hydrogen- charged specimens. Marked acceleration of fatigue crack growth in the presence of hydrogen was observed particularly at low test frequency, and was attributed to the initiation and successive coalescence of secondary cracks formed ahead of primary crack. These secondary cracks were produced along prior-austenite grain boundaries and carbide boundaries, or by direct cracking of carbides. Surprisingly, secondary cracks were observed outside the ordinary plastic zone ahead of the crack tip. TEM observation elucidated that the secondary cracks outside the crack tip plastic zone were produced by hydrogen-induced deformation twins impinging on grain boundaries and carbides. These results suggest a new mechanism of the acceleration of fatigue crack growth rates in high-strength steels caused by hydrogen-induced deformation twins, rather than due to hydrogen- enhanced localized plasticity. The phenomena associated with time dependent fatigue crack growth are presumed to be correlated with the initiation and coalescence of secondary cracks in the presence of hydrogen.     

Cyclic crystal plasticity analyses of stationary, microstructurally small surface cracks in ductile single phase polycrystals

ABSTRACT This paper explores the effects of microstructural heterogeneity on the cyclic crack tip opening and sliding displacements for stationary, microstructurally small transgranular surface cracks in a single phase metallic polycrystal using planar double slip crystal plasticity computations. Crack tip displacements are examined under plane strain conditions for stationary cracks of different lengths relative to grain size as a function of the applied nominal strain amplitude for tension-compression and cyclic shear. Nominal strain amplitudes range from well below to slightly above the nominal cyclic yield strength for each type of loading condition. Results indicate the complex nature of the crack tip sliding and opening displacements as functions of nominal strain amplitude and orientation of the nearest neighbour grains, the influence of the free surface in promoting the cyclic opening displacement even for cracks in the first surface grain, the rather restricted limits of applicability of linear elastic fracture mechanics, and very interesting crack tip plasticity effects which include crack tip displacement ratcheting or progressive accumulation, even for completely reversed, proportional applied loading. Results are compared for cases with and without crack face friction.     

THE EFFECT OF GRAIN SIZE ON FATIGUE CRACK GROWTH IN AN ALUMINIUM MAGNESIUM ALLOY

Abstract Fully reversed uniaxial fatigue tests were performed on aluminium magnesium alloy Al 5754 with four different grain sizes in order that the effect of grain size on fatigue crack growth could be examined. Surface cracks were monitored by a plastic replication technique. Fatigue strength was shown to improve with a decrease in grain size. The endurance stress is a function of the inverse square root of the grain size and is described empiricdty by a Hall-Petch type relation. The effect of grain size on fatigue crack growth is most significant when the crack length is of the order of the microstructure. Fluctuations in the growth rate of microstructurally short cracks are most marked in a fine grained microstructure and may be related to the need to transfer slip to adjacent grains. Crack path deviation is greatest in the coarsest grained microstructure and SEM fractography reveals a more pronounced crack surface roughness in the coarser grained alloy than in the finer grained alloy.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.