Surface crack growth of silicon nitride bearings under rolling contact fatigue

Surface crack growth of silicone nitride ceramic bearings under rolling contact fatigue has been investigated from the viewpoints of contact stresses (ring crack model) and fluid pressure (wedge effect model). The mechanisms of these two models have been investigated independently; however, it was impossible to separate the effects of contact stresses and fluid pressure on surface crack growth. In this paper the effects of contact stresses (ring crack model) on surface crack growth are investigated. In the ring crack model the crack growth is caused by contact stresses around the circumference of the contact circle. The growth of surface cracks located inside and outside the contact track was observed in order to obtain data from which we could reexamine the ring crack model. The outside cracks under rolling contact fatigue were propagated by contact stresses alone and also the inside cracks grew as slowly as the outside cracks. We concluded that the cracks are propagated by the single effect of contact stresses. Preliminary observations of surface crack growth showed that the cracks were unaffected by wear and residual stresses.     

A numerical approach to subsurface crack propagation assessment in rolling contact

Subsurface crack mode II propagation parallel to the contact surface is a damage mechanism leading to dramatic failure in many components subjected to cyclic loading. A weight function (WF) was elaborated for calculating the applied mode II stress intensity factor (SIF) of a crack in a two‐dimensional half‐space in plane strain condition, for crack completely closed and frictionless contact between the crack faces. With respect to other methods, the WF allows faster SIF calculation, thus being suitable for simulation of many repeated load cycles and fatigue crack propagation. The WF was applied for simulating a case of rolling contact experiments found in the literature, and good agreement between experimental and numerical results was obtained, showing the effectiveness of the WF method in damage tolerant design.     

Investigation of rolling contact crack initiation in bainitic and pearlitic rail steels

The stress–strain history and the crack initiation lives of bainitic and head‐hardened pearlitic rail steels were determined under rolling contact loading by implementing the semi‐analytical Jiang–Sehitoglu rolling contact model that incorporates both ratchetting and multiaxial fatigue damage. The calculations revealed that the bainitic steel withstands higher loads than the pearlitic steel at low shear tractions, however; both materials behave in an increasingly similar manner as the shear tractions increase. Furthermore, maximum damage occurs in both steels when ratchetting and fatigue damage coincide on the surface. In addition to shedding light on the rolling contact fatigue (RCF) performance of bainitic and pearlitic rail steels, the current work also establishes a methodology for the realistic prediction of crack initiation under RCF.     

Life prediction for rolling contact fatigue crack initiation of kiln wheels

This paper investigates the rolling contact fatigue life of kiln wheels with respect to the axis line deflection related with the applied supporting loads on wheels. Fatigue crack initiation criterions for elastic shakedown, plastic shakedown, and ratcheting material responses are applied to assess wheels responses with two sets of axial line deflection, one is measured in field and the other is optimal adjustment for the measured axial line deflection. The finite element simulations are performed by using the Bilinear material mode for nonlinear and kinematic hardening within ANSYS 11.0. By comparing life prediction from different criterions, it is showned that the low-cycle fatigue is the predominated failure. Results from different axial line deflection indicate that the optimum adjustment can greatly enhance the whole life of the supporting structure, that is useful for kiln adjustment and maintenance.     

Theory of hydrogen-assisted crack growth

A model for hydrogen-induced cracking is proposed and developed on the assumption that hydrogen enters the embrittling process zone (EPZ) ahead of the crack-tip and promotes localized plastic flow which is proportional to its concentration. The formulae of the criterion for crack propagation,K _IH, and the crack growth rate dl/dt, are derived and applied to the experimental data of AISI4340 superhigh-strength steels.     

A rolling contact fatigue crack driven by squeeze fluid film

ABSTRACT A new model of surface breaking rolling contact fatigue (RCF) crack driven by a coupled action of a squeeze oil film built up in the crack interior and a pressure exerted at the external contact interface was developed. The model can be applied to the ‘nominally dry’ contact couples with an occasional presence of liquid in the crack interior (wheel/rail contact) as well as to the elastohydrodynamic lubrication (EHL) conditions. In the first case, the contact load is a result of solid/solid interaction and can be determined by solving the FE contact problem, but the liquid contained in the crack interior forms a thin film between the crack faces changing their interaction into the type of liquid/solid. This liquid is being periodically squeezed under contact load and acts as a ‘squeeze film’ known from the lubrication theory. In the second case, the liquid (lubricating oil) is permanently present in the contact area and consequently in the vicinity of the crack mouth. This creates conditions for filling the crack with oil. Similarly as in the first case, the ‘squeeze oil film’ is built between the crack faces. The contact load in this case results from a liquid/solid interaction and can be approximated by the pressure and traction distributions obtained from the numerical solution of the elastohydrodynamic contact problem. In both cases the model can be used to determine the Linear Elastic Fracture Mechanics (LEFM) crack tip stress intensity histories during cyclic loading and consequently to predict the crack growth rate and direction. An example of applying the model to the EHL case is given to explain the mechanisms and phenomena leading to the crack front loading. The cycle of rolling a roller over the crack was numerically simulated to obtain the mixed mode (I and II) SIF histories. In the analysis, the EHD pressure and traction were determined through the full solution of the EHD line contact problem accounting for the presence of a crack, whilst the pressure in the crack was found with the use of the wedge shaped squeeze oil film (SOF) model. Possible effects of the mode I and mode II stress intensity cycles on crack growth rate and direction are discussed. The solution indicates high pressure in the neighbourhood of the crack tip, exerted on the crack faces by the squeeze oil film. This leads to the ranges of the mode I and mode II SIF variations, which are larger than for the ‘dry’ and ‘fluid entrapment’ models, and can be an explanation for the crack growth rate observed in practice     

Influential microstructural changes on rolling contact fatigue crack initiation in pearlitic rail steels

Abstract

Rail life is controlled by the balance between wear and fatigue damage due to in service loading. To model and optimise rail life, knowledge of the fatigue crack initiation mechanism is required. This paper reports the effect of in service loading on microstructural changes in the subsurface layer of pearlitic rail steels and observations of early stage (10–50 μm length) fatigue crack formation. Micro and nanohardness measurements are reported, along with microstructural observations, showing differential work hardening in the proeutectoid ferrite and pearlite phases. It is proposed that the differential straining results in ductility exhaustion in the proeutectoid ferrite and therefore fatigue crack initiation and initial growth in the proeutectoid ferrite phase. Observations of short (<50 μm) cracks in rails taken out of service containing significant amounts of proeutectoid ferrite (≈20%) confirm the proposed mechanism.     

Experiments under pure shear and rolling contact fatigue conditions: Competition between tensile and shear mode crack growth

In the present paper, the mechanism of shear crack growth under both pure torsion and mixed mode loadings, simulating rolling contact fatigue testing conditions, has been investigated for a bearing steel and the role of the superimposed compressive stress in subsurface RCF has been clarified both numerically and experimentally. In particular a previous data set of fatigue tests on micro-notched specimens subjected to torsion and out-of-phase loads with |σ_min|/τ_max ≅ 3.5 (LP1) has been complemented with the new tests onto micro-notched specimens loads with |σ_min|/τ_max ≅ 0.7 (LP2) and a test under pure compression. The same tests have been also simulated numerically with a non-linear FE analysis of crack advance. The numerical analyses have been conducted with the aim of demonstrating that the compressive stress fully suppresses the tendency to tensile mode growth as the crack extends.Eventually, the competition between tensile and shear mode growth during a fatigue cycle has been investigated theoretically in terms of local branch SIFs. In particular, the conditions for the branch crack growth have been examined on the basis of the effective SIFs: the crack tip shielding effects due to the crack surface interference (both the mode I contribution caused by the asperity mismatch and the shear attenuation produced by the frictional stresses) have been quantified by employing a model for crack sliding interaction under pure mode III and mixed mode I + III loadings.     

Analysis of subsurface crack propagation under rolling contact loading in railroad wheels using FEM

A general subsurface crack propagation analysis methodology for the wheel/rail rolling contact fatigue problem is developed in this paper. A three-dimensional elasto-plastic finite element model is used to calculate stress intensity factors in wheels, in which a sub-modeling technique is used to achieve both computational efficiency and accuracy. Then the fatigue damage in the wheel is calculated using a previously developed mixed-mode fatigue crack propagation model. The advantages of the proposed methodology are that it can accurately represent the contact stress of complex mechanical components and can consider the effect of loading non-proportionality. The effects of wheel diameter, vertical loading amplitude, initial crack size, location and orientation on stress intensity factor range are investigated using the proposed model. The prediction results of the proposed methodology are compared with in-field observations.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

Flaking failure originating from a single surface crack in silicon nitride under rolling contact fatigue

Flaking failure caused by surface cracks of silicon nitride ceramic bearings has been investigated from the viewpoint of the ring crack model. However, the relation between surface and subsurface cracks under rolling contact fatigue is not fully understood. In this investigation subsurface cracks branching from an initial surface crack were observed in detail, and the process of flaking failure was investigated. The specimens were observed prior to the separation of the surface layers and it was found that the initial surface cracks grew vertically to the surfaces and did not curve as predicted by the ring crack model. Subsurface cracks branched from the single surface cracks and grew in a direction parallel to the surface. They grew in both the same and the opposite directions to the ball movement, with small upward and downward branches. These subsurface cracks grew prior to the semi‐circular surface cracks. From these observations it was concluded that the flaking failures are not caused directly by the surface cracks, but by the subsurface cracks that branch from them.     

Elastoplastic modelling of subsurface crack growth in rail/wheel contact problems

Propagation of small subsurface cracks subjected to shear under repeated rolling contact load is studied. An analytical crack model (Dugdale) with plastic strips at the two crack tips is employed. Compressive stresses promoting crack closure and friction between crack faces are considered. The triaxial stress state is used in the yield criterion. A damage criterion is suggested based on experimental LCF data. In a numerical study, critical crack lengths are found below which propagation of an existing crack should be effectively suppressed.     

Theory of stable crack growth in an elastic-perfectly plastic material

A theory of stable crack growth, for generalized plane stress conditions, is presented which is based upon a Dugdale model of plasticity and an energy balance approach to fracture. Several forms for the rate of energy dissipation in the plastic zone are considered. It is shown that the J-integral, when used in conjunction with the Dugdale model, may not be of direct relevance to the rate of stable crack growth. By introducing the well known concept of a fracture process zone, and incorporating it into an expression for the rate of energy dissipation in the plastic zone, a simple stable crack growth law is derived which is very similar to an existing relation based upon a final stretch fracture criterion.The energy balance approach is extended to derive the growth law for cracks propagating in test specimens subjected to point loads. The material may be non-linear elastic-plastic provided that the Dugdale model of yield is appropriate. It is shown how load-displacement records might be used to predict the amount of stable crack growth in linear elastic-perfectly plastic sheets having reasonably general geometries which are subjected to point loads.

---

Résumé On présente une théorie pour la croissance stable d'une fissure dans le cas de conditions d'état plan de déformation généralisé, qui est basée sur le modèle de Dugdale de plasticité et sur une approche d'équilibre d'énergie jusqu'á la rupture. Diverses formes sont envisagées pour le taux de dissipation d'énergie dans la zône plastique. On montre que l'intégrale J, lorsqu' elle est utilisée en conjonction avec le modèle de Dugdale, peut n'être pas directement pertinente pour déterminer la vitesse de croissance stable d'une fissure. En introduisant le concept bien connu de la zône du processus de fracture et en l'incorporant dans l'expression donnant la vitesse de dispersion d'énergie dans la zône plastique, on dérive une loi de croissance stable et simple de la fissure qui est très similaire à la relation existante basée sur un critère de rupture par étirement final.L'approche de l'équilibre d'énergie est étendue afin de dériver la loi de croissance de fissure se propageant dans des éprouvettes d'essai soumises à des charges ponctuelles. Le matériau peut être non linéaire élastique-plastique pourvu que le modèle de Dugdale de l'écoulement plastique soit approprié. On montre comment les enregistrements charge-déplacement peuvent être utilisés pour prédire le taux de croissance stable d'une fissure dans des tôles minces à caractéristiques linéaires élastiques et parfaitement plastiques, et possédant une géométrie raisonnablement générale, et soumises à des charges ponctuelles.

     

Image analysis to reveal crack development using a computer simulation of wear and rolling contact fatigue

Plastic flow of near‐surface rail material under contact loading is a feature of rail–wheel contact, and severe flow typically leads to both wear, and the initiation and development of small surface‐breaking cracks. This paper presents results from a ratcheting based computer simulation, which has been developed to allow the simultaneous investigation of wear, crack initiation and early crack propagation. To identify repeatably small crack‐like flaws, image analysis is applied to the visual representation of the wearing surface generated by the model. This representation shows a good similarity to traditional micrographs taken from sections of worn surfaces. The model clearly reveals the interaction of wear with crack development, processes which are linked because wear truncates surface‐breaking cracks, and can completely remove small surface‐breaking cracks.     

Comparison of virtual crack extension and strain energy density methods applied to contact surface crack growth

The paper is concerned with comparison of two crack propagation methods applied to a two-dimensional computational model of the surface initiated crack growth in the lubricated contact area of meshing gears. The virtual crack extension method and the minimum strain energy density criterion are used for simulation of the crack propagation in the framework of the finite element analysis. The discretised equivalent contact model, with the assumed size and orientation of the initial crack, is subjected to contact loading conditions, accounting for the elasto-hydro-dynamic lubrication effects, tangential loading due to sliding and the influence of lubricating fluid, driven into the crack by hydraulic mechanism. The computational results show that both crack propagation methods give comparable results, although the virtual crack extension method has some clear advantages due to its theoretical superiority in dealing with mixed-mode short crack propagation close to the loading boundary.     

Theory of fatigue crack growth based on a BCS crack theory with work hardening

Our theory of fatigue crack growth, which is based on the Bilby, Cottrell, and Swinden crack theory, is modified to take into account work hardening at fatigue crack tips. In this analysis stress rather than cumulative displacement or cumulative damage is the quantity whose critical value controls the crack growth. The material at the tip of a fatigue crack progressively work hardens until the stress there reaches a critical value. The material then tears apart and the crack advances until it reaches a region in which the stress is smaller than the critical value. An equation which describes the growth of fatigue cracks is derived; it is essentially the same as the crack growth equation found in the earlier analysis. The major change is the replacement of the yield stress term in the older equation with an ultimate stress term in the newer equation. The chief change is the substitution for the average yield stress in the older equation with the ultimate stress in the present equation.

---

Zusammenfassung Unsere Theorie über die Ausbreitung der Müdigkeitsriße, die sich auf die Rißbildungstheorie von Bilby, Cottrell und Swinden begründet, wurde umgeändert um das Härten durch Kaltverformung an der Spitze des Müdigkeitsrisses zu berücksichtigen.In dieser Analyse ist eher die Spannung, als die summierte Fortbewegung oder der summierte Schaden, die Quantität deren kritischen Wert die Ausbreitung des Risses kontrolliert. Die Materie an der Spitze des Müdigkeitsrisses härtet sich nach und nach durch Kaltverformung bis die Spannung dort einen kritischen Wert erreicht. Das Material zerreißt sich dann und der Riß schreitet voran bis er eine Stelle erreicht wo die Spannung niedriger ist als der kritische Wert. Line Gleichung, die die Ausbreitung des Müdigkeitsrisses beschreibt wird abgeleitet und sie hat größtenteils die selbe Form wie die die früher aufgestellt wurde. Der Hauptunterschied liegt darin daß die Elastizitätsgrenze in der älteren Gleichung durch die Bruchspannung in der neuen Gleichung ersetzt wird.

---

Résumé La théorie sur la croissance des fissures de fatigue, développée par l'auteur sur la base de la théorie de la fissuration de Billy, Cottrel et Swinden, a été modifiée pour tenir compte de l'écrouissage à la pointe de la fissure de fatigue. Selon cette analyse, c'est davantage la tension que le déplacement cumulé ou le dommage cumulé qui est la grandeur dont une valeur critique régit la croissance de la fissure.Le matériau à la pointe d'une fissure s'écrouit petit à petit jusqu'à ce que la tension atteigne en cet endroit une valeur critique. Le matériau est alors le siège d'une rupture par séparation et la fissuration progresse jusqu'à atteindre une région où la tension est plus faible que la valeur critique. La croissance des fissures de fatigue a été ainsi décrite par une équation, qui a essentiellement la même forme que celle qui a été établie précédemment. La principale différence réside dans le remplacement du terme limite élastique par un terme charge de rupture dans la nouvelle équation.

---

---

Support by the U.S. Office of Naval Research Contract N00014-67-A-0356-0016.     

Analysis of contact fatigue crack growth using twin-disc tests and numerical evaluations

The contact fatigue damages on the rail surface, such as head check, squats are one of the growing problems. Fracture of rail can be prevented by removing the crack before it reaches the critical length. Therefore, the crack growth rate needs to be estimated precisely according to the conditions of the track and load. In this study, we have investigated the crack growth behavior on rail surface by using the twin-disc tests and the finite element analysis. We have verified the relationship between the crack growth rate and the variety of parameters as cracks grow from the initiation stage.