Microstructure-based multistage fatigue modeling of aluminum alloy 7075-T651

The multistage fatigue model for high cycle fatigue of a cast aluminum alloy developed by McDowell et al. is modified to consider the structure-property relations for cyclic damage and fatigue life of a high strength aluminum alloy 7075-T651 for aircraft structural applications. The multistage model was developed as a physically-based framework to evaluate sensitivity of fatigue response to various microstructural features to support materials process design and component-specific tailoring of fatigue resistant materials. In this work, the model is first generalized to evaluate both the high cycle fatigue (HCF) and low cycle fatigue (LCF) regimes for multiaxial loading conditions, with appropriate modifications introduced for wrought materials. The particular microstructural features of relevance to fatigue in aluminum alloy 7075-T651 include micron-scale Fe-rich intermetallic particles and rolling textures. The model specifically addresses the role of local constrained cyclic microplasticity at fractured inclusions in fatigue crack incubation and microstructurally small crack growth, including the effect of crystallographic orientation on crack tip displacement as the driving force. The model is able to predict lower and upper bounds of the fatigue life based on measured inclusion sizes.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

Probabilistic high cycle fatigue behaviour of nodular cast iron containing casting defects

Theoretical and experimental investigations were combined to characterize the influence of surface casting defects (shrinkages) on the high cycle fatigue (HCF) reliability. On fracture surfaces of fatigue samples, the defect is located at the surface. The shape used for the calculation is a spherical void with variable radius. Finite-element simulations were then performed to determine stress distribution around defects for different sizes and different loadings. Correlated expressions of the maximum hydrostatic stress and the amplitude of the shear stress were obtained by using the response surface technique. The loading representative point in the HCF criterion was then transformed into a scattering surface, which has been obtained by a random sampling of the defect sizes. The HCF reliability has been computed by using the Monte Carlo simulation method. Tension and torsion fatigue tests were conducted on nodular cast iron with quantification of defect size on the fracture surface. The S – N curves show a large fatigue life scattering; shrinkages are at the origin of the fatal crack leading to the final failure. The comparison of the computed HCF reliability to the experimental results shows a good agreement. The capability of the proposed model to take into account the influence of the range of the defect sizes and the type of its statistical distribution has been demonstrated. It is shown that the stress distribution at the fatigue limit is log-normal, which can be explained by the log-normal defect distribution in the nodular cast iron tested.     

High- and low-cycle fatigue influence of silicon,copper, strontium and iron on hypo-eutectic Al–Si–Cu and Al–Si–Mg cast alloys used in cylinder heads

In this publication, ambient condition fatigue investigations with different types of Al–Si–Cu and Al–Si–Mg cast alloys in rotating-bending high-cycle fatigue (HCF) and push–pull low-cycle fatigue (LCF) regimes have been performed with varying Si, Cu, Fe and Sr contents. The cast alloys investigated here are common used in cylinder heads for automotive application. Because the cylinder head is one of the most fatigued parts in combustion chamber engines, the microstructural knowledge of the damage process provides a tool of construction and its material selection. The investigations were also supported with an in-situ microstructural crack observation in high plasticity rotating-bending regimes. The specimens were directly processed out of serial produced T79 heat-treated cylinder heads to provide the equal microstructure for testing as under operational conditions.The observations clearly identified the effects of the individual alloying elements both under low- and high-cycle fatigue. The crack propagation speed and the crack paths were majorly influenced by the eutectic silicon. Additional, the precipitation hardening due to copper affected significantly the fatigue endurance, too. In high plasticities the silicon’s influence got almost lost and only the matrix strength was crucial. Thus, increased fatigue strength in high loaded LCF regimes was observed for alloys with less copper content, thus higher ductility. By contrast, improved HCF and low loaded LCF endurance was only achieved when the matrix strength was increased by copper’s precipitation hardening. Crack branching and deflections strongly influenced the microstructural damage of the ductile AlSi7Mg(Sr) and hence, gained its fatigue strength. Iron phases could not identified as harmful inclusions, since the phases were similar in size of other hard phase elements like the other primary intermetallic phases like ${\text{Al}}_2\text{Cu}$ and β-$\text{Si}$ phases under notch stress aspects, by the well defined solidification process in the test section. Because the crack nucleation mainly occurred on Si particles, strontium as a refinement agent influenced the early crack onset and accordingly the fatigue in total. Thus, the AlSi6Cu4(Sr) had increased lifetimes compared to AlSi6Cu4 both in HCF and LCF. Further, the presented results provide a modification of the Manson–Coffin approach to describe the relationship between plastic strain and lifetime, valid for all proposed alloys with only one set of parameters. Thus, it was possible to perform the fatigue calculation with a reduced range of scatter.     

Influence of foreign object damage on fatigue crack growth of gas turbine aerofoils under complex loading conditions

Foreign object damage (FOD) has been identified as one of the main life limiting factors for aeroengine blades, with the leading edge of aerofoils particularly susceptible. In this work, a generic edge ‘aerofoil’ geometry was utilized in a study of early fatigue crack growth behaviour due to FOD under low cycle fatigue (LCF), high cycle fatigue (HCF) and combined LCF and HCF loading conditions. Residual stresses due to FOD were analyzed using the finite element method. The longitudinal residual stress component along the crack path was introduced as a nodal temperature distribution, and used in the correction of the stress intensity factor range. The crack growth was monitored using a nanodirect current potential drop (DCPD) system and crack growth rates were correlated with the corrected stress intensity factor considering the residual stresses. The results were discussed with regard to the role of residual stresses in the characterization of fatigue crack growth. Small crack growth behaviour in FODed specimens was revealed only after the residual stresses were taken into account in the calculation of the stress intensity factor, a feature common to LCF, HCF and combined LCF + HCF loading conditions.     

On the life-controlling microstructural fatigue mechanisms in ductile metals and alloys in the gigacycle regime

The high-cycle fatigue (HCF) behaviour of ductile metals and alloys, and the life-controlling microstructural fatigue mechanisms known from HCF are reviewed critically with respect to their possible role in the gigacycle or ultra-high-cycle fatigue (UHCF) regime. Arguments are presented to support the hypothesis that, at the very low amplitudes of the UHCF regime, fatigue crack initiation, resulting from cyclic strain localization, and slow early Stage I fatigue crack propagation are the life-controlling mechanisms and that these processes can essentially be described in terms of the microstructurally irreversible portion of the cumulative cyclic plastic strain. Emphasis is placed on the important role of the so-called slip irreversibility which decreases as the amplitude becomes lower and lower. Finally, the Manson–Coffin law is reformulated for very low amplitudes in terms of microstructurally relevant parameters, and a fatigue life diagram is developed, based on these preceding microstructural considerations. Important features of this diagram are: (i) the plastic strain fatigue limit in the HCF regime which is related to the threshold for cyclic strain localization in persistent slip bands; and (ii) the transition from this plastic strain fatigue limit to a threshold of negligible slip irreversibility at still lower amplitudes in the UHCF regime.     

An engineering approach to fatigue analysis based on elastic‐plastic fracture mechanics

Nowadays cast iron components are widely used in highly stressed structures. Component lifetime is strongly influenced by inhomogeneities caused by the material's microstructure and the manufacturing process (graphite particles, (micro‐)shrinkage pores, inclusions). Inhomogeneities often act as a fatigue crack starter. Lifetime until failure may be divided into stages for crack initiation, short and long crack growth. Initiation of a crack of technical size (a ≈ 1mm) is often dominated by the growth of short cracks. The paper presents an approach to analyse the mechanically short fatigue crack growth based on elastic‐plastic fracture mechanics considering the closure behaviour of short cracks. The effective J‐integral range is used as a crack driving force. Finite element analysis results as well as analytical solutions to approximate the crack driving force are presented. The application of the approach is successfully demonstrated for cast iron material EN‐GJS‐400‐18‐LT using data from fatigue tests, microstructure and fracture surface analyses to assess the fatigue life.     

Prediction of Fatigue Lives of MAR‐M247 LC Based on the Crack Closure Concept

Low cycle fatigue (LCF), high cycle fatigue (HCF), and combined LCF and HCF tests are carried out on MAR‐M247 LC at 650 °C in air environment. Under combined LCF and HCF loading, block striations form on the fracture surface which are used to complete an effective crack growth curve by using the linear summation model. Crack growth lives starting from equivalent initial flaw sizes are calculated by the crack closure code FASTRAN and compared with experimental fatigue lives. Under HCF loading, predicted and experimental fatigue lives agree well for lifetimes above 10⁵ cycles. Lower lifetimes are overestimated indicating that the linear summation model is not valid for MAR‐M247 LC in this loading range. Interactions between the non‐crystallographic HCF crack growth and striated crack growth that is caused by the LCF loading are probably responsible for this behavior.     

Fatigue life assessment of nodular cast iron containing casting defects

The fatigue behaviour of a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical elastic–plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10⁶ cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10⁶ cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (>10⁶ cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.     

A MODEL FOR SMALL FATIGUE CRACK GROWTH

Abstract— Based on the assumption that normalized Kitagawa-Takahashi diagrams for different materials are the same, a unified model for microstructurally small fatigue crack and physically small fatigue crack growth rates was developed to describe their behaviour under different fatigue stress ranges. The stress-sensitive blocking effect of microstructural barriers to small fatigue crack growth is satisfactorily simulated by the model. Incorporated with the materials fatigue limit and microstructural barrier spacing, this model can be easily used in the prediction of small fatigue crack lifetime. Small fatigue crack growth rates of previous experimental studies in 7075-T6 Aluminium alloy and HT60 steel under different stress ranges are in an envelope between two boundary prediction curves corresponding to the largest and smallest stress ranges applied in the experiments. Problems concerning model accuracy and model application are also discussed in the present paper.     

Einfluss von Gussfehlern auf die Dauerfestigkeit von Aluminium‐ und Magnesiumgusslegierungen

Influence of casting defects on the endurance limit of aluminium and magnesium cast alloys The influence of porosity (voids and shrinkage) on the fatigue properties at very high numbers of cycles is shown for the alloys AZ91 hp, AM60 hp, AE42 hp, AS21 hp and AlSi9Cu3 produced by high pressure die casting. Fatigue tests performed with ultrasonic equipment up to 10⁹ cycles show that these alloys exhibit a fatigue limit. The mean endurance limits (50% failure probability) of the magnesium alloys are 8–50 MPa and of the aluminium alloy 75 MPa. Fatigue cracks initiate at porosity, and whether a specimen fractures or not depends on the stress amplitude and the area and the site of the defect. Regarding the cast defect as an initial crack, a critical stress intensity value (K_cr) may be found to propagate a crack until final failure. K_cr of the magnesium alloys is 0,80–1,05 MPa√m, and 1,80 MPa√m was found for AlSi9Cu3. Using K_cr it is possible to correlate the probability of different defect sizes and the failure probability at different stress amplitudes. Additionally, predictions of the influence of rare large casting defects on the endurance limit are possible.     

High and low cycle fatigue behavior of linear friction welded Ti–6Al–4V

Linear friction welded Ti–6Al–4V was investigated in fatigue at various stress amplitudes ranging from the high cycle fatigue (HCF) to the low cycle fatigue (LCF) regime. The base material was composed of hot-rolled Ti–6Al–4V plate that presented a strong crystallographic texture. The welds were characterized in terms of microstructure using electron backscatter diffraction and hardness measurements. The microstructural gradients across the weld zone and thermomechanically affected zone of the linear friction welds are discussed in terms of the crystallographic texture, grain shape and hardness levels, relative to the parent material. The location of crack nucleation under fatigue loading was analyzed relative to the local microstructural features and hardness gradients. Though crack nucleation was not observed within the weld or thermomechanically affected zones, its occurrence within the base material in LCF appears to be affected by the welding process. In particular, by performing high resolution digital image correlation during LCF, the crack nucleation site was related to the local accumulation of plastic deformation in the vicinity of the linear friction weld.     

Corrosion fatigue behaviour and microstructural characterisation of G20Mn5QT cast steel in 3.5‐wt% NaCl solution

Corrosion fatigue behaviour and microstructural characterisation of G20Mn5QT cast steel are investigated in simulated seawater. Fractography is performed by using scanning electron microscopy (SEM). The macroscale fracture surface and microstructure of the failed specimen are acquired including the crack initiation, crack propagation, and pitting evolution. The maximum cyclic stress (S) versus number of cycles to failure (N) curves is derived by three‐parameter fatigue curve method. Fatigue life is predominantly controlled by the corrosion pitting‐induced crack initiation when tested in simulated seawater at lower stress levels. As the maximum cyclic stress is less than 185 MPa, the chloride ion erosion is the main influence factor, which affects the fatigue failure of the G20Mn5QT cast steel in simulated seawater.     

A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept – I. Model development

An integrated analytical and experimental approach was taken to develop a fracture mechanics-based methodology for predicting the limiting threshold stress of high-cycle fretting fatigue in structural alloys. The contact stress field for two flat surfaces under fretting was analyzed via an integral equation technique. The local fretting stress field of the uncracked body was then utilized to obtain the stress intensity factor of an arbitrarily oriented fatigue crack using a continuum dislocation formulation. The limiting threshold stress ranges for the nonpropagation of fretting fatigue cracks were predicted on the basis that the fretting fatigue cracks are small cracks that exhibit a size-dependent growth threshold and propagate at stress intensity ranges below the large-crack threshold. In part I, the development of the worst-case fret (WCF) model is described. The influence of the limiting high-cycle fatigue (HCF) threshold stress on a variety of fretting fatigue parameters such as bearing pressure, pad geometry, shear stress, mode mixity, and coefficient of friction are elucidated by parametric calculations. In part II, the WCF model is applied to treating HCF of Ti-6Al-4V where model predictions are compared against critical experiments performed on a kilohertz fretting-fatigue rig.     

Manifestations of dynamic strain aging under low and high cycle fatigue in a type 316LN stainless steel

Influence of Dynamic strain aging (DSA) under low cycle fatigue (LCF) and high cycle fatigue (HCF) loading was investigated by conducting LCF and HCF tests on specimens over a wide range of temperature from 573 to 973 K. DSA was found to be highly pronounced in the temperature range of 823–873 K. DSA was seen to have contrasting implications under LCF and HCF deformation. The cyclic hardening owing to DSA caused an increase in the cyclic stress response under LCF, leading to decrease in cyclic life. On the other hand, the DSA-induced strengthening suppressed the crack initiation phase under HCF where the applied stress remains fixed, leading to an increase in the cyclic life.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Application of a combined high and low cycle fatigue life model on life prediction of SC blade

A combined high and low cycle fatigue life prediction model for nickel-base single crystal (SC) has been presented to analyze the low cycle fatigue (LCF) and high cycle fatigue (HCF) life of SC blade. In the paper, a power law function of life model based on crystallographic theory is adopted to predict the LCF life. A power law function based on elastic analysis is adopted to predict the HCF life. Furthermore, the LCF and HCF experiments at different temperature are carried out to obtain the model parameters. The predicted results show that the model is reasonable for LCF and HCF. The linear life model introduced in the paper satisfies the combined high and low cycle fatigue life prediction of nickel-base single crystal superalloy. Special attention is put on the combined high and low cycle fatigue life of SC turbine blade. The resolved shear stress and first-order vibration stress are analyzed by the crystallographic rate dependent finite element analysis (FEA) and orthotropic elastic FEA, respectively. It is shown that the prediction model can be well used in the fatigue life prediction of SC blade.     

A MICRO-MECHANICS MODEL OF CORROSION-FATIGUE CRACK GROWTH IN STEELS

Principles of Microstructural Fracture Mechanics (MFM) are used to develop a model for the characterization of environment-assisted short fatigue crack growth. Fatigue cracks are invariably initiated at corrosion pits formed at inclusions, hence the analysis includes stress concentration effects at pits that lead to the propagation of fatigue cracks the rates of which are considered to be proportional to the crack tip plastic displacement. This plasticity is constrained by microstructural barriers which are overcome in a non-aggressive environment at critical crack lengths only when the applied stress is higher than the fatigue limit. However, the superposition of an aggressive environment assists fatigue damage via crack tip dissolution, enhancement of crack tip plastic deformation, the introduction of stress concentrations at pits and a reduction of the strength of the microstructural barrier. These environment effects are manifested in a drastic reduction of the fatigue limit and higher crack propagation rates. The model is compared with fatigue crack propagation data of a BS251A58 steel tested in reversed torsion when submerged in a 0.6M NaCl solution.     

A probabilistic model for the high cycle fatigue behaviour of cast aluminium alloys subject to complex loads

This article is dedicated to the high cycle fatigue behaviour of cast hypo-eutectic Al–Si alloys and in particular the AlSi7Cu05Mg03 alloy. In a vast experimental campaign undertaken to investigate the fatigue damage mechanisms operating in this alloy, subject to complex loading conditions, it was shown that two different coexisting fatigue damage mechanisms occur in this materials, depending on the presence of different microstructural heterogeneities (i.e. micro-shrinkage pores, Si particles, Fe-rich intermetallic phases, DAS of the Al-matrix, etc.). In order to take into account both of these damage mechanisms, a probabilistic approach using the weakest link concept is introduced to model the competition between the two mechanisms. This approach leads naturally to a probabilistic Kitagawa type diagram, which explains the relationship between the fatigue behaviour of the material and the different casting processes or post-treatments (e.g. gravity casting and HIP).It is shown that the sensitivity to the different loading modes (i.e. uniaxial with and without mean stress, torsion and equibiaxial tension) depends on the microstructural heterogeneities responsible for crack initiation. For a porosity-free alloy, the predictions are very good for combined tension–torsion loading modes. When pores are present and control the fatigue strength, the predictions are very satisfactory for the uniaxial loads with different R-ratios and slightly conservative for multiaxial loads (i.e. torsion and equibiaxial tension). Never-the-less, they are much better than the predictions of the Dang Van criterion [1].     

AlSi10Mg(Cu)铸铝合金的热疲劳裂纹萌生及早期扩展行为

微观观察AlSi10Mg(Cu)铸铝合金在热疲劳裂纹的萌生和早期扩展过程,重点研究共晶硅粒子对热疲劳裂纹行为的影响。结果表明:热疲劳裂纹萌生于脱粘共晶硅粒子与铝基体间的开裂界面,原因是共晶硅粒子与铝基体的热膨胀系数不同,引起热循环过程中两相热应变不协调,从而在两相界面处产生循环应力而引起疲劳破坏。热疲劳裂纹的扩展在长度和宽度上同时进行,具有良好塑性的铝枝晶对疲劳裂纹的扩展起阻碍作用。对热疲劳过程中共晶硅粒子周围应力场的模拟分析进一步解释了实验现象。