On fatigue lifetimes and fatigue crack growth behavior of bone cement

Bone cement is used to develop a mechanical bond between an artificial joint and the adjacent bone tissue, and any degradation of this bond is of serious concern since it can lead to loosening and eventually malfunction of the artificial joint. In the present study, the fatigue lives and fatigue crack propagation behavior of two bone cements, CMW Type 3 and Zimmer, were investigated, and it was found that the size and distribution of pores played a major role in influencing both the fatigue crack initiation and propagation processes. The fatigue lifetimes of CMW exceeded those of Zimmer because of a lesser density of large pores. When the fatigue lifetimes were plotted as a function of K _limax, the maximum initial stress intensity factor based upon the initiating pore size, the difference in fatigue lifetimes between CMW and Zimmer bone cements was greatly reduced. The fatigue crack growth behavior of both bone cements were similar. This is a further indication that the noted differences in fatigue lifetimes were related to the size of the pore at the crack initiating site.     

Probabilistic modeling of fatigue related microstructural parameters in aluminum alloys

This paper presents the results of probabilistic modeling of the fatigue related microstructural parameters in unclad 2024-T351 aluminum sheets. The statistical distributions of the constituent particle size, which were obtained from metallographic measurements from polished surfaces, were determined by graphical goodness-of-fit tests. The distributions of the crack-nucleating particle sizes were determined using the data measured from various fatigue fracture surfaces. Initially, an extreme value theory based model was investigated to correlate the overall particle distribution with its fatigue subsets. Furthermore, a new Monte Carlo simulation was developed to determine the fatigue subsets using the microstructural parameters such as particle size, grain size, and grain orientation distributions, in association with qualitative criteria on fatigue crack nucleation and growth mechanisms.     

High cycle fatigue mechanisms in a cast AM60B magnesium alloy

ABSTRACT We examine micromechanisms of fatigue crack initiation and growth in a cast AM60B magnesium alloy by relating dendrite cell size and porosity under different strain amplitudes in high cycle fatigue conditions. Fatigue cracks formed at casting pores within the specimen and near the surface, depending on the relative pore sizes. When the pore that initiated the fatigue crack decreased from approximately 110 µm to 80 µm, the fatigue life increased two times. After initiation, the fatigue cracks grew through two distinct stages before final overload specimen failure. At low maximum crack tip driving forces (K_max < 2.3 MPa√m), the fatigue crack propagated preferentially through the α‐Mg dendrite cells. At high maximum crack tip driving forces (K_max > 2.3 MPa√m), the fatigue crack propagated primarily through the β‐Al₁₂Mg₁₇ particle laden interdendritic regions. Based on these observations, any proposed mechanism‐based fatigue model for cast Mg alloys must incorporate the change in growth mechanisms for different applied maximum stress intensity factors, in addition to the effect of pore size on the propensity to form a fatigue crack.     

Effects of microstructure on mixed-mode, high-cycle fatigue crack-growth thresholds in Ti-6Al-4V alloy

Effect of microstructure on mixed‐mode (mode I + II), high‐cycle fatigue thresholds in a Ti‐6Al‐4V alloy is reported over a range of crack sizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditions were examined—a fine‐grained equiaxed bimodal structure (grain size ～20 µm) and a coarser lamellar structure (colony size ～500 µm). Studies were conducted over a range of mode‐mixities, from pure mode I (ΔK_II/ΔK_I = 0) to nearly pure mode II (ΔK_II/ΔK_I ～ 7.1), at load ratios (minimum load/maximum load) between 0.1 and 0.8, with thresholds characterized in terms of the strain‐energy release rate (ΔG) incorporating both tensile and shear‐loading components. In the presence of through‐thickness cracks—large (> 4 mm) compared to microstructural dimensions—significant effects of mode‐mixity and load ratio were observed for both microstructures, with the lamellar alloy generally displaying the better resistance. However, these effects were substantially reduced if allowance was made for crack‐tip shielding. Additionally, when thresholds were measured in the presence of cracks comparable to microstructural dimensions, specifically short (～200 µm) through‐thickness cracks and microstructurally small (< 50 µm) surface cracks, where the influence of crack‐tip shielding would be minimal, such effects were similarly markedly reduced. Moreover, small‐crack ΔG_TH thresholds were some 50–90 times smaller than corresponding large crack values. Such effects are discussed in terms of the dominant role of mode I behaviour and the effects of microstructure (in relation to crack size) in promoting crack‐tip shielding that arises from significant changes in the crack path in the two structures.     

A review of equivalent pre‐crack sizes in aluminium alloy 7050‐T7451

This paper reviews some analyses of quantitative fractography measurements of the fatigue fracture surfaces of 7050 aluminium alloy specimens along with relevant fatigue crack information including crack initiating discontinuity size and type. These data were used to assess whether surface finish or applied stress level has any effect on the estimated effective crack initiating discontinuity size, namely the equivalent pre‐crack size (EPS). The statistical distributions for the EPSs of the following initiating discontinuity types were examined: chemically etched pits, glass bead peening damage, mechanical damage, inclusions and porosity. The EPSs at various percentile levels for these types were determined on the basis of the samples considered. Finally, the correlation between measured initiating discontinuity depth and EPS was investigated, and good correlation was found in the case of mechanical damage. The purpose of conducting these analyses was to gain a better understanding of the parameters governing the fatigue crack‐like effect of discontinuities to facilitate the better prediction of fatigue lives.     

A RELIABILITY-BASED MODEL TO PREDICT SCATTER IN FATIGUE CRACK NUCLEATION LIFE

This paper investigates the scatter inherent in the early stages of fatigue life. A probabilistic fatigue model is proposed which relates the microstructural heterogeneity to the scatter in crack nucleation life. The crack nucleation life is defined as the number of cycles necessary to develop a crack with a length equal to the grain size. The model assumes homogeneity at the level of the grain size. A fracture mechanics-based microstructural model is used to describe the response of the grains. The primitive random variables which drive crack nucleation are identified and recent developments recorded in the literature are used to describe their statistical characteristics. First order reliability methods are used to predict the statistical distribution of fatigue crack nucleation life. Comparisons are made with trends in experimental observations.     

Long fatigue life critical crack lengths*

A model based on surface strain redistribution and crack closure is presented for prediction of the endurance or fatigue limit stress by determining the threshold stress and critical length of short cracks that develop under microstructural control. The threshold stress first decreases with crack size to a local minimum then increases to a local maximum corresponding to the fatigue limit stress. This occurs at the critical crack length corresponding to about four grain diameters. The model is capable of determining the threshold stress range and depth of propagating and non‐propagating surface cracks as a function of stress ratio, material and grain size. The microstructure is shown to be particularly significant in the very long life regime (N_f ≈ 10⁹ cycles). When the surface cracks become non‐propagating, internally initiated cracks continue growing slowly, eventually reaching the critical crack length with failure occurring after a very high number of cycles (10⁷ < N_f < 10⁹ cycles).     

MODELING THE LONG-LIFE FATIGUE BEHAVIOR OF A CAST ALUMINUM ALLOY

As-cast specimens and smooth specimens of a AA 319 cast aluminum alloy containing casting porosity were fatigue tested with special attention given to the long-life region ( N 1.25 × 10⁸ cycles). Fatigue cracks were observed to initiate from the near-surface casting pores or from discontinuities resulting from the as-cast surface texture. The observed fatigue lives were strongly dependent on the size (√area) of these casting defects.
The effect of casting defects on the fatigue life was modeled assuming the fatigue life to be the sum of the crack nucleation and the crack propagation life (including both the growth of short and long cracks). The crack growth behavior of (mechanically) short cracks was considered in detail by a developed crack-closure-at-a-notch (CCN) model. The CCN model predicted the fatigue lives for both as-cast and machine-notched specimens. Extension of the CCN model to reliability-based design was attempted using the measured size distribution of the fatigue-initiating casting pores.     

Probabilistic modeling of fatigue crack growth in Ti–6Al–4V

This paper proposes an approximate approach to efficient estimation of some variabilities caused by the material microstructural inhomogeneities. The approach is based on the results of a combined experimental and analytical study of the probabilistic nature of fatigue crack growth in Ti–6Al–4V. A simplified experimental fracture mechanics framework is presented for the determination of statistical fatigue crack growth parameters from two fatigue tests. The experimental studies suggest that the variabilities in long fatigue crack growth rate data and the Paris coefficient are well described by the log-normal distributions. The variabilities in the Paris exponent are also shown to be well characterized by a normal distribution. The measured statistical distributions are incorporated into a probabilistic fracture mechanics framework for the estimation of material reliability. The implications of the results are discussed for the probabilistic analysis of fatigue crack growth.     

A probabilistic total fatigue life model incorporating material inhomogeneities,stress level and fracture mechanics

Testing on notched specimens from thin sheet aluminum 2024-T3 was carried out to investigate the formation of fatigue cracks at constituent particles and to quantify the critical distributions and their stress level dependence. The distributions of fatigue lives, nucleation lives, and crack nucleating (CN) particle sizes were determined for each specimen and exhibited a significant stress level dependence. The measured distributions provided the foundation for the total fatigue life model, which uses a probabilistic Monte Carlo method in conjunction with Newman's fastran ii crack closure model. The total life model closely predicted the cumulative distribution function (CDF) of fatigue lives for the three stress levels examined and specifically predicted the shortest fatigue lives, critical from a design for reliability standpoint, and their variability. The total life model accounted for both nucleation and propagation lives; however, the results based on modeling the total life entirely as crack propagation were accurate and slightly conservative. Additionally, a probability of crack nucleation (POCN) concept to relate the distribution of all particles to the distribution of CN particles was developed based on the experimental observations and provides a better representation of the data than traditional threshold approaches.     

Effect of inclusions on fatigue behaviour of hardened spring steel

Abstract

The fatigue lifetimes of hourglass shaped specimens of a hardened spring steel were studied. The failure probability was determined experimentally at one loading level and causes of fatigue failure were identified on fracture surfaces. The depth profile of residual stresses after fatigue testing was determined using X-ray techniques. Cyclic flow data, long crack growth data, and the threshold for crack propagation were determined. Inclusion size distributions of the steel were obtained using different techniques. A model for the probability of fatigue failure of the hourglass specimens was formulated. Microcracks are assumed to exist at all inclusions and specimen failure is controlled by those cracks which can propagate to failure. Two different models based on linear fracture mechanics were used to determine critical inclusion sizes for crack propagation. The models take into account all the above independent experimental data, i.e. residual stresses, cyclic flow data, threshold for crack propagation, inclusion distribution, etc. Experimental failure probabilities were satisfactorily reproduced by the model.

MST/1648     

Analysis of fatigue crack initiation and S-N response of model cast aluminium piston alloys

Fatigue crack initiation and S-N fatigue behaviour of hipped model Al7Si-Sr and Al0.7Si piston alloys have been investigated after overaging at 260 °C for 100 h to provide a practical simulation of in-service conditions. The results show that hipping did not affect the S-N behaviour of Al7Si-Sr. This is attributed to the lack of significant change in porosity distribution in this alloy because of its low porosity levels even in the unhipped state. However, hipping profoundly improved the fatigue performance of alloy Al0.7Si due to the significant reduction in porosity. In this investigation, it was observed that porosity was rendered impotent as a fatigue crack initiator in both hipped alloys. Instead, fatigue cracks were observed to originate mainly from intermetallic particles (particularly the Al₉FeNi phase) in both alloys and sometimes from oxide particles in Al0.7Si alloy. Fatigue cracking was also frequently observed at intermetallic clusters in hipped Al0.7Si. The observed scatter in fatigue life is discussed in terms of the size of fatigue crack initiating particles and the overall particle size distribution which follows a power law distribution function.     

A 'crack-like' notch analogue for a safe-life fretting fatigue design methodology

Various analogies have recently been proposed for comparing the stress fields induced in fretting fatigue contact situations, with those of a crack and a sharp or a rounded notch, resulting in a degree of uncertainty over which model is most appropriate in a given situation. However, a simple recent approach of Atzori–Lazzarin for infinite‐life fatigue design in the presence of a geometrical notch suggests a corresponding unified model also for fretting fatigue (called Crack‐Like Notch Analogue model) considering only two possible behaviours: either ‘crack‐like’ or ‘large blunt notch.’ In a general fretting fatigue situation, the former condition is treated with a single contact problem corresponding to a Crack Analogue model; the latter, with a simple peak stress condition (as in previous Notch Analogue models), simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical situation of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions can be readily stated. Not only is the model asymptotically correct if friction is infinitely high or the contact area is very small, but also remarkably accurate in realistic conditions, as shown by excellent agreement with Hertzian experimental results on Al and Ti alloys. The model is useful for preliminary design or planning of experiments reducing spurious dependences on an otherwise too large number of parameters. In fact, for not too large contact areas (‘crack‐like’ contact) no dependence at all on geometry is predicted, but only on three load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the ‘large blunt notch’ region occurring typically only at very large sizes of contact, does the size‐effect disappear, but the dependence is on all other factors including geometry.     

Prediction of fatigue limit reliability of high strength steel with deep notch under mean stress <Emphasis Type="Italic">σ</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> = 0

Because a fatigue limit of high strength steel with Vickers hardness H _V > 400 is scattered, it is difficult to predict the fatigue limit for S-N curve experimentally. The authors have proposed a nondestructive method for predicting the fatigue limit reliability of plain specimen of the high strength steel by the stress-strength model which consists of “statistical characteristics of hardness of a matrix under a small indentation load” and “statistical characteristics of hardness required for non-propagations of fatigue cracks from microstructural defects in a material”. In this paper, a nondestructive method for predicting the fatigue limit reliability of notched specimen of the high strength steel with microstructural defects such as non-metallic inclusions and pits from characteristics of a stress field near a notch, statistical characteristics of Vickers hardness and defect size is proposed. Especially, the method is applied to a structure with a deep notch under a mean stress σ _m = 0. Then, fatigue tests were carried out on the notched specimens of quenched-tempered 0.5% carbon steels with H _V ≃ 600 changing a notch root radius under a constant notch depth, and the validity of the prediction method is examined by comparing predicted results to experimental ones.     

Microstructure variation effects on room temperature fatigue threshold and crack propagation in Udimet 720Li Ni-base superalloy

An assessment of the effects of microstructure on room temperature fatigue threshold and crack propagation behaviour has been carried out on microstructural variants of U720Li, i.e. as‐received U720Li, U720Li‐LG (large grain variant) and U720Li‐LP (large intragranular coherent γ′ variant). Fatigue tests were carried out at room temperature using a 20 Hz sinusoidal cycling waveform at an R‐ratio = 0.1 on 12.5 mm × 12.5 mm square cross‐section SENB specimens with a 60° starter notch. U720Li‐LG showed the highest threshold ΔK (ΔK_th), whilst U720Li‐LP showed the lowest ΔK_th value. U720Li‐LP also showed higher crack growth rates in the near‐threshold regime and at high ΔK (although at higher ΔK levels the difference was less marked). Crack growth rates of U720Li and U720Li‐LG were relatively similar both in the near‐threshold regime and at high ΔK. The materials showed crystallographic stage I type crack growth in the near‐threshold regime, with U720Li showing distinct crystallographic facets on the fracture surface, while U720Li‐LG and U720Li‐LP showed mostly microfacets and a lower proportion of large facets. At high ΔK, crack growth in the materials becomes flat and featureless indicative of stage II type crack growth. The observed fatigue behaviour, which is an effect of the combined contributions of intrinsic and extrinsic crack growth resistances, is rationalized in terms of the microstructural characteristics of the materials. Enhanced room temperature fatigue threshold and near‐threshold long crack growth resistance are seen for materials with larger grain size and higher degree of planar slip which may be related to increased extrinsic crack growth resistance contributions from crack tip shielding and roughness‐induced crack closure. Differences in the deformation behaviour, either homogeneous or heterogeneous due to microstructural variation in this set of materials may provide approximately equivalent intrinsic crack growth resistance contributions at room temperature.     

Modeling and Simulation of Microstructurally Small Crack Formation and Growth in Notched Nickel-base Superalloy Component

Studies on microstructurally small fatigue cracks have illustrated that heterogeneous microstructural features such as inclusions, pores, grain size distribution as well as precipitate size distribution and volume fraction create stochasticity in their behavior under cyclic loads. Therefore, to enhance safe-life and damage-tolerance approaches, accurate modeling of the influence of these heterogeneous microstructural features on microstructurally small crack formation and growth from stress raisers is necessary. In this work, computational micromechanics was used to predict the high cycle fatigue of microstructurally small crack formation and growth in notched polycrystalline nickel-base superalloys and to quantify the variability in the driving force for formation and growth of microstructurally small crack from notch root in the matrix with non-metallic inclusions. The framework involves computational modeling to obtain three-dimensional perspectives of microstructural features influencing fatigue crack growth in notched nickel-base superalloys, which accounts for the effects of nonlocal notch root plasticity, loading, microstructural variability, and extrinsic defects on local cyclic plasticity at the microstructure-scale level. This approach can be used to explore sensitivity of minimum fatigue lifetime to microstructures. The simulation results obtained from this framework were calibrated to existing experimental results for polycrystalline nickel-base superalloys.     

About inclusion shape effect on the endurance limit of ductile matrix materials

The theory describing fatigue mechanism in elastoplastic material containing pores or inclusions of different shape and size has been developed. The paper is a continuation of the analysis presented in J. Mat. Sc. 31 (1996) 2475 where the effect of only circular inclusion shape was investigated. An attempt at quantitative determination of the effect of endurance limit reduction by plastic zones size formed near the inclusions, and their cracking has been done. The geometrical configuration, consisting of round inclusion, horizontal, vertical and angular elliptical inclusions, from which a nucleating crack emerged, as well as sharp cracks was considered, and the stress intensity factors of such configurations were analysed. Based on threshold value of K below which crack propagation ceases, the critical value of loading stress was determined for different shapes and sizes of pores using an equivalent ellipse concept. Theoretical results were compared with results from experiments, showing quite good agreement. For plastic zones size determination finite elements technique and photo-stress experimental method were applied. Surprisingly it was found that circular shape of the pores is the most dangerous which explains why so many earlier investigations using circular pore shape model are, so well supported by the experiment.     

Cyclic plasticity at pores and inclusions in cast Al-Si alloys

Finite element analyses of micronotches including pores and silicon particles of an A356 aluminum alloy were performed to elucidate microstructure-property relations for fatigue crack incubation. Several important findings resulted. By varying the particle and pore size, spacing, aspect ratio, and clustering, the relative microstructural differences were quantified related to micronotch root cyclic plasticity. Results from realistic two-dimensional microstructures showed that minimal microstructure-scale cyclic plasticity corresponds well to the measured fatigue strength at 10⁷ cycles for low porosity A356 aluminum alloy specimens. “Realistic” and idealized particles/pores simulations were used to formulate a local Coffin-Manson type law for crack incubation.     

NON-DAMAGING NOTCHES IN FATIGUE*

The fact that very small notches (cavities, holes, scratches, etc.) have no effect on the fatigue limit of metallic materials is well known. This paper presents both a qualitative explanation for the existence of non-damaging notches and a quantitative derivation of their critical sizes. The condition for a notch (characterized by the stress concentration factor K_t and the notch root radius ρ) to be non-damaging in a metallic material (characterized by a critical crack size l₀) is (K²_t? 1)ρ≤ 4.5 l₀. The critical crack size can be expressed with good approximation in terms of the threshold stress intensity for fatigue crack growth and the plain fatigue limit. Therefore the above relation can be applied for an engineering evaluation of non-damaging notches. Test results obtained for copper and a pressure vessel steel demonstrate the applicability of the proposed method.     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.