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.     

S–N curve characteristics and subsurface crack initiation behaviour in ultra-long life fatigue of a high carbon-chromium bearing steel

The S – N curve obtained from cantilever-type rotary bending fatigue tests using hour-glass-shaped specimens of high carbon-chromium bearing steel clearly distinguished the fracture modes into two groups each having a different crack origin. One was governed by crystal slip on the specimen surface, which occurred in the region of short fatigue life and a high stress amplitude level. The other was governed by a non-metallic inclusion at a subsurface level which occurred in the region of long fatigue life and low stress amplitude. The inclusion developed a fish-eye fracture mode that was distributed over a wide range of stress amplitude not only below the fatigue limit defined as the threshold for fracture due to the surface slip mode but also above the fatigue limit. This remarkable shape of the S – N curve was different from the step-wise one reported in previous literature and is characterized as a duplex S – N curve composed of two different S – N curves corresponding to the respective fracture modes. From detailed observations of the fracture surface and the fatigue crack origin, the mechanisms for the internal fracture mode and the characteristics of the S – N curve are discussed.     

Technical note High-cycle fatigue crack initiation and propagation behaviour of high-strength sprin steel wires

An attempt has been made to characterize high-cycle fatigue behaviour of high-strength spring steel wire by means of an ultrasonic fatigue test and analytical techniques. Two kinds of induction-tempered ultra-high-strength spring steel wire of 6.5 mm in diameter with a tensile strength of 1800 MPa were used in this investigation.
The fatigue strength of the steel wires between 10⁶ and 10⁹ cycles was determined at a load ratio R = −1. The experimental results show that fatigue rupture can occur beyond 10⁷ cycles. For Cr–V spring wire, the stress–life ( S – N ) curve becomes horizontal at a maximum stress of 800 MPa after 10⁶ cycles, but the S – N curve of the Cr–Si steel continues to drop at a high number of cycles (>10⁶ cycles) and does not exhibit a fatigue limit, which is more correctly described by a fatigue strength at a given number of cycles. By using scanning electron microscopy (SEM), the crack initiation and propagation behaviour have been examined. Experimental and analytical techniques were developed to better understand and predict high-cycle fatigue life in terms of crack initiation and propagation. The results show that the portion of fatigue life attributed to crack initiation is more than 90% in the high-cycle regime for the steels studied in this investigation.     

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.     

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.     

The role of oxidation damage in fatigue crack initiation of an advanced Ni-based superalloy

The effects of prior oxidation on the room temperature fatigue life of coarse-grained Ni-based superalloy, RR1000, have been investigated. High cycle fatigue tests were conducted, on both machined and pre-oxidised testpieces, at room temperature at an R ratio of 0.1. The oxidation damage was produced by pre-exposures at 700 °C for either 100 or 2000 h. Pre-oxidised testpieces tended to fail with shorter fatigue lives than those obtained from the as-machined testpieces although they were also observed to outperform the as-machined test pieces at peak stress levels around 900 MPa. The chromia scale and intergranular alumina intrusions formed during pre-oxidation are prone to crack under fatigue loading leading to early crack nucleation and an associated reduction in fatigue life. This has been confirmed to be the case both below and above a peak stress level of ∼900 MPa. The better fatigue performance of the pre-oxidised specimens around this stress level is attributed to plastic yielding of the weaker γ′ denuded zone, which effectively eases the stress concentration introduced by the cracking of the chromia scale and intergranular internal oxides. This γ′ denuded zone is also a product of pre-oxidation and develops as a result of the selective oxidation of Al and Ti. Over a limited stress range, its presence confers a beneficial effect of oxidation on fatigue life.     

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.     

On effect of hydrogen on very high cycle fatigue behaviours of high strength steels

Abstract

In order to analyse the effect of hydrogen on very high cycle fatigue properties, hydrogen was precharged into two high strength steels. The applied stress intensity factor range at the periphery of inclusions before and after being precharged is approximately proportional to the cubic root of inclusion size. In addition, the applied stress intensity factor range at the periphery of inclusions after being precharged was lower compared with uncharged specimens. The additional stress intensity factor range generated by hydrogen ΔK_H is raised after the hydrogen was precharged. A simple prediction equation of S–N curve was proposed by introducing the hydrogen influence factor. The proposed prediction equation can reasonably describe the S–N curves for precharged specimens.     

A review about the effects of structural and operational factors on the gigacycle fatigue of steels

It is well‐known that the high cycle fatigue (HCF) strength of steel components is influenced by a lot of factors depending on both material, loading (including environment), specimen or component geometry (design), and manufacturing process. Based on a literature review of a lot of experimental data, a synthesis is proposed in this paper to discuss the effect of the structural and operational factors on the very high cycle fatigue (VHCF) characteristics of steels. HCF and VHCF regimes are distinguished in terms of failure mechanisms and S‐N curve shapes for high and low strength steels. Then, the effect of the microstructural and mechanical features on the VHCF resistance is debated as different parameters (microstructure, inclusion size type and depth, hydrogen, environment, maximum tensile strength, and residual stresses). Next, the influence of the loading conditions is addressed by taking into account both the frequency effect, the highly stressed volume, the loading type, and loading ratio. Finally, the influence of the testing techniques used in VHCF experiments is discussed.     

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 microstructure effect on fretting fatigue crack initiation using crystal plasticity

The onset of fretting fatigue is characterized by material microstructural changes in which the extent of the damage is comparable to grain size, and hence, the microstructure characteristics could have a significant effect on fatigue crack initiation. In this paper, a three‐dimensional finite element crystal plasticity framework is presented for simulation of the fretting fatigue. Controlled Poisson Voronoi tessellation (CPVT) method is employed to generate the polycrystalline region. In the CPVT method, regularity parameter controls the shape of grains. In this study, the impact of grain size and regularity parameter on crack initiation life and initiation site has been investigated. Cumulative plastic slip was used as a parameter of microstructure‐sensitive fatigue indicator. This parameter could effectively predict the location of crack initiation and its life. The results show that regularity parameter has a significant effect on the location of crack initiation. Furthermore, the effect of grain size on the fretting fatigue life of 316L stainless steel was investigated experimentally through testing different specimens with different grain sizes, to validate the simulation results.     

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.     

Prediction of very high cycle fatigue failure for high strength steels, based on the inclusion geometrical properties

This article deals with the experimental and predicted fatigue endurance of the high strength steels, European 100C6 (martensitic and bainitic) and the Japanese SUJ2 in the gigacycle regime. Tests were carried out with stress ratio R = −1 in tension–compression condition at room temperature. To attain the high number of cycles required in a reasonable period of time, an ultrasonic test machine working at 20 KHz was used to obtaining 1.7 × 10⁹ cycles in approximately 24 h. The relationship between the geometrical properties of inclusions associated with fatigue failure and the fatigue life of these steels was studied. Thereafter, with basis on a simplified evaluation of the highest stress in the elliptical inclusion for fatigue Mode I, three models to predict the fatigue life for these high strength steels were proposed adjusting non-linear regression curves to the corresponding experimental results.     

High‐cycle fatigue and fracture behaviours of Cu‐Be alloy with a wide strength range

The high‐cycle fatigue and fracture behaviours of Cu‐Be alloy with tensile strength ranging from 500 to 1300 MPa acquired by different treatments were studied. Fatigue crack initiation, fracture surface morphologies, S‐N curves and fatigue strength show obvious differences due to the change of microstructure. At relatively low‐strength level, some fatigue cracks originated from defects; while at high‐strength level, all the fatigue cracks initiated from cleavage facets. It was found that the fatigue ratio increases linearly and fatigue strength changes quadratically with increasing tensile strength, only considering one strengthening mechanism. Finally, the fatigue strengths of various Cu‐Be alloys were summarized.     

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.     

Determination of lattice level energy efficiency for fatigue crack initiation

Fatigue crack initiation life prediction is a fundamentally challenging problem that is of prime importance as a significant portion of the fatigue life is spent in the initiation phase. In spite of the extensive efforts of research over the past two decades, the concept of crack initiation still remains as an enigma in science. The major challenges in predicting crack initiation life in industry are the evaluation of the crack initiation parameters such as the maximum resolved shear stress range, maximum slip band width and the energy efficiency coefficient. In this paper, we show that the energy efficiency can be successfully estimated with good accuracy by performing lattice level crystal plasticity‐based computational simulations on representative models. The lattice level plasticity‐based finite element computations are reported for the case of single crystal copper in this work, and the results show that this strategy leads to higher accuracy than the existing idea of approximating the efficiency factor. The results show that this strategy could be of great use in improving the reliability in prediction of crack initiation life. The effectiveness of this computational procedure would greatly reduce the financial investments necessary to perform experimental analysis of all structures to determine the crack initiation parameters, as it would require just a single measurement to quantify the measurement of efficiency.     

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.     

On the estimation of fatigue life in notches differentiating the phases of crack initiation and propagation

Over the last three decades, a variety of models have been developed in order to predict the life of components under fatigue. Some of the models are based on the definition of the fatigue process as a combination of the phases of crack initiation and crack propagation, considering component life as the sum of the duration of each phase. Other models consider only one of the phases; some consider only initiation while others only propagation, though in this case, from cracks with lengths in the order of the microstructural dimensions. This article will carry out a comparative analysis of the methods that consider life as the sum of the duration of both phases. In this same line, it proposes yet another method, which simulates crack growth according to damage theories. In analysing the behaviour of each model, this paper will describe various elements: the prediction that each of them produces regarding notched specimens submitted to testing, the advantages and inconveniences of each, and lastly, the possibilities of applying each of the models to more realistic geometries.     

A shear stress-based parameter for fretting fatigue crack initiation

The purpose of this study was to investigate the fretting fatigue crack initiation behaviour of titanium alloy, Ti–6Al–4V. Fretting contact conditions were varied by using different geometries of the fretting pad. Applied forces were also varied to obtain fretting fatigue crack initiation lives in both the low- and high-cycle fatigue regimes. Fretting fatigue specimens were examined to determine the crack location and the crack angle orientation along the contact surface. Salient features of fretting fatigue experiments were modelled and analysed with finite element analysis. Computed results of the finite element analyses were used to formulate a shear stress-based parameter to predict the fretting fatigue crack initiation life, location and orientation. Comparison of the analytical and experimental results showed that fretting fatigue crack initiation was governed by the maximum shear stress, and therefore a parameter involving the maximum shear stress range on the critical plane with the correction factor for the local mean stress or stress ratio effect was found to be effective in characterizing the fretting fatigue crack initiation behaviour in titanium alloy, Ti–6Al–4V.     

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.