A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Very-high-cycle fatigue crack initiation and propagation behaviours of magnesium alloy ZK60

The aim of this paper is to assess the very-high-cycle fatigue (VHCF) behaviour of a magnesium alloy (ZK60). Results indicate that the fatigue crack initiates from an area consisting of many distributed facets, while the region of early crack propagation is characterised by parallel traces, based on a fractographic analysis. The significant differences in morphology around the crack initiation area result from the interaction between the deformation twinning and the plastic zone at the crack tip. In addition, the fatigue crack propagation rate around the crack initiation site is also estimated based on a modified Murakami model. It is found that the formation stage for the fatigue crack is of great importance to the fatigue failure mechanism in the VHCF regime.     

Investigation of small fatigue crack initiation and growth behaviour of nickel base superalloy GH4169

Surface replication method was utilized to monitor the small fatigue crack initiation and growth process of single‐edge‐notch tension specimens fabricated by nickel base superalloy GH4169. Three different stress levels were selected. Results showed that small fatigue cracks of nickel base superalloy GH4169 initiated from grain boundaries or surface inclusions. The small fatigue crack initiation and growth stages took up about 80–90% of the total fatigue life. Multiple major cracks were observed in the notch root, and specimen with more major cracks seemed to have smaller fatigue life under the same test conditions. At the early growth stage, small crack behaviour might be strongly influenced by microstructures; thus, the crack growth rates had high fluctuations. However, the stress level effect on the small fatigue crack growth rates was not distinguishable for the three different stress levels. And no clear differences were found among the crack initiation lives by using replication technique.     

Modelling fatigue crack initiation life

An accurate formula for the fatigue crack initiation (FCl) life, correlating it with the geometry of notched speciments, the cyclic loading conditions, the behaviour of metals and the tension overloading effect, has been developed based on the hypothesis of the widely used local strain approach, and checked by test results on the FCl life of aluminum alloy notched specimens. In addition, the overloading effect factor z has been defined. It can be used to characterize quantitatively the interaction between larger load and smaller loads in the load spectrum. Taking into account the interaction between loads, Miner's rule can be used to calculate the cumulative damage in the FCl phase. Based on the work mentioned above, a new model has been developed and substantiated for accurate prediction of FCl life under variable amplitude loading. Further work is needed to increase the FCl life prediction accuracy.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

Fatigue crack initiation behaviors throughout friction stir welded joints in AA7075-T6 in ultrasonic fatigue

This paper presents the results of experimental investigation on fatigue behaviors of friction stir welded joints in AA7075-T6 with ultrasonic fatigue test system (20 kHz). Two kinds of particles, Fe-rich intermetallic compounds and Mg₂Si-based particles, governed the fatigue crack initiation. The plastic deformation and recrystallization during welding process led to the changes in particle size and micro crack occurrence between thermo-mechanically affected zone (TMAZ) and nugget zone (NZ). Therefore, the fatigue crack initiation sites leaned to be located at the TMAZ in short fatigue life, or at the NZ in very high cycle fatigue regime.     

Small crack behavior and fracture of nickel-based superalloy under ultrasonic fatigue

Fracture and small crack behavior in the very high cycle domain of 10⁹ cycles were investigated with a nickel-based superalloy under ultrasonic fatigue in ambient air at room temperature. The influence of ultrasonic frequency is examined by comparing the results with those in conventional low frequency fatigue. It is found that fatigue strength increases as frequency is raised up to 19.5 kHz and the most of fatigue life is consumed in nucleating and propagating small cracks up to 100 μm. Transition of fracture mode from transgranular ductile fracture to cleavage-dominated fracture occurs beyond a critical stress intensity factor range of approximately , leading to the catastrophic failure under ultrasonic fatigue.     

Numerical modelling of fatigue crack initiation and growth of martensitic steels

This paper presents a numerical simulation of micro‐crack initiation that is based on Tanaka‐Mura micro‐crack nucleation model. Three improvements were added to this model. First, multiple slip bands where micro‐cracks may occur are used in each grain. Second improvement deals with micro‐crack coalescence by extending existing micro‐cracks along grain boundaries and connecting them into a macro‐crack. The third improvement handles segmented micro‐crack generation, where a micro‐crack is not nucleated in one step like in Tanaka‐Mura model, but is instead generated in multiple steps. High cycle fatigue testing was also performed and showed reasonably good correlation of proposed model to experimental results. Because numerical model was directed at simulating fatigue properties of thermally cut steel, edge properties of test specimens were additionally inspected in terms of surface roughness and micro‐structural properties.     

Thermodynamic entropy generation in the course of the fatigue crack initiation

Evolution of the thermodynamic entropy generation during fatigue crack initiation life of notched specimens is studied. A set of experimental results of AA7075‐T651 is examined to determine applicability of the thermodynamic entropy generation as an index of fatigue crack initiation. Entropy accumulation is calculated from hysteresis energy and temperature rise. An increasing trend of entropy accumulation with the number of cycle to failure is observed on macroscale measurements. Results also determine that the entropy generations from the samples under the same operating conditions are similar as the crack grows. Scanning electron microscope analysis is performed on the fractured surfaces to observe the fatigue striations, and persistent slip bands are observed employing an optical microscope. A discussion is presented regarding the length scales on which crack initiation occurs and entropy calculation is made.     

The effect of random grain distributions on fatigue crack initiation in a notched coarse grained superalloy specimen

Coarse grained superalloys are of large interest in high temperature applications, and can be found in e.g. gas turbine components, where great care must be given with respect to high temperature fatigue. Due to the large grain size, the material behaviour at e.g. sharp notches cannot be considered homogeneous. As a consequence, the fatigue behaviour is likely to expose a large variation. In order to numerically investigate this variation, a Monte Carlo analysis has been carried out by 100 FE-simulations of notched specimens, where placements and orientations of the grains were randomised. Furthermore, each grain was modelled as a unique single-crystal, displaying both anisotropic elastic and plastic behaviour and tension/compression asymmetry. The effect of randomness was investigated by the obtained dispersion in fatigue crack initiation life. It was concluded that the fatigue life behaviour of coarse grained nickel-base superalloys may show a considerable variation, which cannot be captured by one single deterministic analysis based on data for a homogenised material. Furthermore, the dispersion is of such a magnitude that it needs to be taken into account in industrial applications where highly stressed coarse grained materials are used.     

Mesoscopic mechanisms in fatigue crack initiation in an aluminium alloy

The mechanistic aspects of process of initiation of a mode‐I fatigue crack in an aluminium alloy (AA 2219‐T87) are studied in detail, both computationally as well as experimentally. Simulations are carried out under plane strain conditions with fatigue process zone modelled as stress‐state–dependent cohesive elements along the expected mode‐I failure path. An irreversible damage parameter that accounts for the progressive microstructural damage due to fatigue is employed to degrade cohesive properties. The simulations predict the location of initiation of the fatigue crack to be subsurface where the triaxiality and the opening tensile stresses are higher in comparison with that at the notch surface. Examination of the fracture surface profile of fracture test specimens near notch tip reveals a few types of regions and existence of a mesoscopic length scale that is the distance of the location of highest roughness from the notch root. A discussion is developed on the physical significance of the experimentally observed length scale.     

Oxidation assisted fatigue crack growth under complex non-isothermal loading conditions in a nickel base superalloy

This paper deals with the prediction of fatigue crack growth at high temperatures in the N18 nickel base superalloy, which is employed by Snecma for turbine disc applications. This material and other nickel base superalloys were widely studied in the past under isothermal conditions and constant amplitude fatigue. Dwell time effects are observed which are attributed, in this material, to grain boundary oxidation. The main objective of this research is to use this knowledge to model the fatigue crack growth rate in the N18 nickel base superalloy when complex “missions” are encountered. This implies variable amplitude and non-isothermal loading conditions (450–650 °C). For this purpose, an incremental fatigue crack growth model which was originally developed for isothermal variable amplitude loading conditions was extended so as to be applicable to non-isothermal loading conditions. In addition, the incremental form of the fatigue crack growth law in this model is very useful to account for the coupling effect between fatigue and time-dependent phenomena such as creep or oxidation. In the present case, the effect of the environment was modelled as a competition between two phenomena: a detrimental effect of grain boundary oxidation ahead of the crack tip and a beneficial effect of the growth of a passivation layer of oxides on the freshly created crack surfaces. The model was used to simulate fatigue crack growth under complex cycles at high temperature and the comparisons with experimental results are satisfactory.     

Fatigue crack initiation and growth in solder alloys

In modern electronic packaging, especially surface mount technology (SMT), thermal strain is usually induced between components during processing, and in service, by a mismatch in the thermal expansion coefficients. Since solder has a low melting temperature and is softer than other components in electronic packaging, most of the cyclic stresses and strains take place in the solder. Fatigue crack initiation and fatigue crack propagation are likely to occur in the solder even when the cyclic stress is below the yield stress. It is an objective of this research to study the behaviour of fatigue crack initiation and propagation in both lead‐containing solder (63Sn‐37Pb), and lead‐free solders (Sn‐3.5Ag). The effect of alloying (Cu and Bi addition), frequency, tensile hold time and temperature on low cycle fatigue (LCF) behaviour of the solders is discussed. Mechanisms of LCF crack initiation and propagation are proposed and LCF life prediction, based on the various models, is carried out.     

Influence of bulk damage on crack initiation in low‐cycle fatigue of 316 stainless steel

To investigate the effect of bulk damage on fatigue crack initiation, crack initiations due to low‐cycle fatigue of Type 316 stainless steel were observed by electron backscatter diffraction (EBSD) and scanning electron microscopy. The EBSD observations showed that local misorientation developed inhomogeneously due to the cyclic strain, and many cracks were initiated from the slip steps and grain boundaries where the local misorientation was relatively large. The crack initiations could be categorized into two types: enhancement of the driving force by geometrical discontinuity (slip steps and notches), and reduction of material resistance against crack initiation caused by accumulated bulk damage at grain boundaries. In particular, more than half of the cracks were initiated from grain boundaries. However, in spite of the significant bulk damage, the fatigue life was extended by removing the surface cracks under strain of 1 and 2% amplitude. The stress state at the microstructural level was changed by the surface removal, and the damaged portion did not suffer further damage. It was concluded that although bulk damage surely exists, the fatigue life can be restored to that of the untested specimen by removing the surface cracks.     

Effect of microstructure on crack propagation in high-temperature fatigue of directionally solidified Ni-based superalloy

In order to clarify the crack propagation properties of an anisotropic material (Ni‐based directionally solidified superalloy), longitudinally loaded specimens (L‐specimens) and transversely loaded specimens (T‐specimens) with a crack are subjected to high temperature fatigue. The crack propagation rate is reasonably well correlated with the effective stress intensity factor range regardless of the propagation direction (specimens L and T), the stress range and the stress ratio. However, the crack propagation rate shows a notable fluctuation particularly in the T‐specimens. It is at most about five times faster than the average. The fracture surface features can be classified into four types with three transgranular and one intergranular types. In the former, though the crack is along the {100} or {110} planes on a macroscopic scale, it threads through the {111} or {100} planes on a microscopic scale. Crack propagation is notably accelerated in the intergranular region, while deceleration is caused by crack branching.     

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.     

Evaluation of fatigue crack initiation life from a notch

Local strain at the notch-root and its effect on fatigue crack initiation was investigated in four metals by the real-time, fine-grid method. Special attention was focused on local notch-root strain behaviour until crack initiation. From the application of strain hysteresis at the notch root, the maximum strain under loading conditions during each cycle was investigated in detail. One of the main results was that the maximum strain value at the first cycle of the fatigue test coincided with that at crack initiation. Maximum strain defined from the cyclic strain changes at the notch root was proposed as one possible parameter for estimating fatigue crack initiation life. Based on the curvilinear relationship between maximum strain and number of cycles to crack initiation, a new life evaluation method for fatigue crack initiation is proposed. This approach differs fundamentally from the usual fracture mechanics method based on the stress intensity factor.     

Creep, fatigue and oxidation in crack growth in advanced nickel base superalloys

This paper presents some of our recent results from an ongoing collaborative research programme on creep-fatigue behaviour of two advanced nickel base superalloys for turbine disc applications. The role of creep, fatigue and oxidation in crack growth has been investigated at 650°C under typical loading waveforms at selected loading frequencies. Load-line deflections were monitored in selected tests under static and long dwell loading conditions. Scanning electron microscopy was adopted to identify the fracture mode and to facilitate the evaluation of oxidation.

The results show that mixed time and cycle dependent crack growth seems to be the predominant crack growth mode in the two PM nickel alloys studied. Whilst limited creep may be present at the crack tip, particularly under static and long dwell loading conditions, oxidation appears to be the predominant mechanism for crack growth under the test conditions examined.     

Load and temperature interaction modeling of fatigue crack growth in a Ni-base superalloy

An approach was developed to predict the thermo-mechanical fatigue crack growth rates under typical gas turbine engine spectrum loading conditions. The material studied in the development of this model was a polycrystalline superalloy, Inconel 100. Load interaction effects were determined to have a major effect on the crack growth life. A yield zone load interaction life prediction model was modified to include temperature dependent properties. Multiple overload effects were included in the model to incorporate enhanced retardation compared to single overload retardation behavior. Temperature interaction effects were included and proved to be very important because of the wide temperature ranges to which turbine engine components are subjected. The effects of oxidation and temperature changes were accounted for in the model by accelerating crack growth in regions that had been previously affected by elevated temperatures. Experimental data of isolated, first order effects were used to calibrate and verify the model. Temperature dependent mechanical properties were determined and were essential in the model’s development. Parametric studies were performed using this model to assess the sensitivity of specific crack growth variables on life predictions.     

High temperature fatigue of nickel-base superalloys – A review with special emphasis on deformation modes and oxidation

Low cycle fatigue, high cycle fatigue, fatigue crack propagation and thermo-mechanical fatigue in Ni-base superalloys are reviewed in terms of fundamental deformation mechanisms, environmental effects, and interactions between environment and deformation mode. These factors are related to the chemical composition and underlying microstructure for all currently-used product forms (i.e. powder metallurgy, wrought, conventionally cast and single crystal). The basic principles that are developed are used to show how both intrinsic and extrinsic variables can be manipulated to control fatigue behaviour and as a guide for formulation of engineering life prediction models.