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.     

Effects of shot-peening intensity on fretting fatigue crack-initiation behaviour of Ti–6Al–4V

The effects of shot‐peening intensity on fretting fatigue crack‐initiation behaviour of titanium alloy, Ti–6Al–4V, were investigated. Three intensities, 4A, 7A and 10A with 100% surface coverage, were employed. The contact geometry involved a cylinder‐on‐flat configuration. Residual stress and improvement in fretting fatigue life were directly related to shot‐peening intensity. The magnitude of compensatory tensile stress and its location away from the contact surface increased with increasing intensity. The relaxation of residual stress occurred during fretting fatigue which increased with increasing the number of cycles. An analysis using a critical plane‐based fatigue crack‐initiation model showed that stress relaxation during the fretting fatigue affects life and location of crack initiation. Greater relaxation of the residual stress caused greater reduction of fatigue life and shifted the location of crack initiation from inside towards the contact surface. Modified shear stress range (MSSR) parameter was able to predict fretting fatigue crack‐initiation location, which agreed with the experimental counterparts. Also, the computed parameter showed an appropriate trend with the experimental observations of the measured fretting fatigue life based on the shot‐peening intensity.     

Fretting fatigue behaviour of shot-peened Ti-6Al-4V at room and elevated temperatures

Fretting fatigue behaviour of shot‐peened titanium alloy, Ti‐6Al‐4V was investigated at room and elevated temperatures. Constant amplitude fretting fatigue tests were conducted over a wide range of maximum stresses, σ_max= 333 to 666 MPa with a stress ratio of R= 0.1 . Two infrared heaters, placed at the front and back of specimen, were used to heat and maintain temperature of the gage section of specimen at 260 °C. Residual stress measurements by X‐ray diffraction method before and after fretting test showed that residual compressive stress was relaxed during fretting fatigue. Elevated temperature induced more residual stress relaxation, which, in turn, decreased fretting fatigue life significantly at 260 °C. Finite element analysis (FEA) showed that the longitudinal tensile stress, σ_xx varied with the depth inside the specimen from contact surface during fretting fatigue and the largest σ_xx could exist away from the contact surface in a certain situation. A critical plane based fatigue crack initiation model, modified shear stress range parameter (MSSR), was computed from FEA results to characterize fretting fatigue crack initiation behaviour. It showed that stress relaxation during test affected fretting fatigue life and location of crack initiation significantly. MSSR parameter also predicted crack initiation location, which matched with experimental observations and the number of cycles for crack initiation, which showed the appropriate trend with the experimental observations at both temperatures.     

The Effect of Surface Pit Treatment on Fretting Fatigue Crack Initiation

This paper analyses the effect of surface treatment on fretting fatigue specimen by numerical simulations using Finite Element Analysis. The processed specimen refers to artificially adding a cylindrical pit to its contact surface. Then, the contact radius between the pad and the specimen is controlled by adjusting the radius of the pit. The stress distribution and slip amplitude of the contact surface under different contact geometries are compared. The critical plane approach is used to predict the crack initiation life and to evaluate the effect of processed specimen on its fretting fatigue performance. Both crack initiation life and angle can be predicted by the critical plane approach. Ruiz parameter is used to consider the effect of contact slip. It is shown that the crack initial position is dependent on the tensile stress. For same type of model, three kinds of critical plane parameters and Ruiz method provide very similar position of crack initiation. Moreover, the improved sample is much safer than the flat-specimen.     

Experimental and numerical investigation on crack initiation of fretting fatigue of dovetail

The present study investigated the fretting fatigue crack initiation of dovetail structure based on experimental observation and multiple axial criteria. Two typical critical plane approaches of the Smith‐Watson‐Topper (SWT) and the Fatemi and Socie (FS) model were used to predict the crack initiation location, orientation angle, and fatigue life. The results indicate that both SWT and FS models predict consistent results with the experiment in crack initiation location. Regarding the crack initiation angle, FS model shows good agreement with the experimental observation, but SWT model exhibits a large difference. The two models give conservative results in fretting fatigue life. In view of this, the theory of critical distance (TCD) was incorporated into the SWT and the FS models. It shows that both the TCD‐SWT and the TCD‐FS predict fatigue lives within a scatter band of 2. It suggests that introducing the TCD into the critical plane model can greatly reduce the conservatism of the prediction. Furthermore, the prediction has less dependence on specific models.     

Effects of Shot‐Peening on Fretting Fatigue Crack Growth Behavior in Ti‐6Al‐4V

Abstract: The effects of shot‐peening on fretting fatigue crack growth behaviour in titanium alloy, Ti‐6A1‐4V were investigated. Three shot‐peening intensities: 4A, 7A and 10A were considered. The analysis involved the fracture mechanics and finite element sub‐modelling technique to estimate crack propagation lives. These computations were supplemented with the experimentally measured total fretting fatigue lives of laboratory specimens to assess the crack initiation lives. Shot‐peening has significant effect on the initiation/propagation phases of fretting fatigue cracks; however this effect depends upon the shot‐peening intensity. The ratio of crack initiation and total life increased while the ratio of the crack propagation and total life decreased with an increase of shot‐peening intensity. Effects of residual compressive stress from shot‐peening on the crack growth behaviour were also investigated. The fretting fatigue crack propagation component of the total life with relaxation increased in comparison to its counterpart without relaxation in each shot‐peened intensity case while the initiation component decreased. Improvement in the fretting fatigue life from the shot‐peening and also with an increase in the shot‐peening intensity appears to be not always due to increase in the crack initiation resistance from shot‐peened induced residual compressive stress.     

Stress gradient effect on the crack nucleation process of a Ti–6Al–4V titanium alloy under fretting loading: Comparison between non-local fatigue approaches

This study focuses on the stress gradient effect regarding the crack nucleation of a cylinder/plane Ti–6Al–4V titanium alloy contact under low cycle fatigue (LCF) fretting loading. Several local and non-local analytical approaches were compared to predict experimental results. The first part of the study presents fretting nucleation boundaries for three different cylinder radii in the partial slip regime. In the next part, the Crossland and Papadopoulos multi-axial fatigue criteria are computed and compared. Finally, local and non-local fatigue approaches are compared. Square constant volume, critical distance and weighted function approaches have been compared.The methodology used covers a large range of stress gradients. The impact of varying the stress gradients is that the larger the stress gradient, the larger the difference between experiments and local stress fatigue predictions. A Crossland local form was applied to confirm that a local stress fatigue analysis cannot predict the fretting cracking risk. Three non-local approaches were carried out, and the results allowed the proper prediction of the empirical thresholds with a 3–5% margin of error. The positive results obtained helped to select a multi-axial fatigue criterion and a non-local approach which take into account the gradient effect of contact fretting behavior.     

A procedure for estimating the total life in fretting fatigue

ABSTRACT This paper proposes a procedure for estimating the total fatigue life in fretting fatigue. It separately analyses the fatigue crack initiation and propagation lives. The correlation between crack initiation and propagation is made considering a non‐arbitrary crack initiation length provided by the model. The number of cycles to initiate a crack is obtained from the stress distribution beneath the contact zone and a multiaxial fatigue crack initiation criterion. The propagation of the crack is considered using different fatigue crack propagation laws, including some modifications in order to take the short crack growth into account. The results obtained by this method are compared with the fatigue lives obtained in various fretting fatigue tests under spherical contact with 7075‐T6 aluminium alloy.     

TWO-PARAMETER MODEL OF FRETTING FATIGUE CRACK GROWTH

Abstract— A fretting fatigue crack growth model is proposed accounting for the effects of tribological parameters of the contacting materials and the biaxiality of contact together with bulk stresses, upon fretting fatigue crack growth rate and direction of growth in the fretting-zone subsurface layers. Based on this model a new technique is developed to determine fatigue life and predict the fatigue limit in an aluminium alloy, AMg6N, and a titanium alloy, VT9, under fretting conditions. For the above cases, fretting fatigue crack growth behaviour predicted by the proposed model is in good agreement with the experimental results.     

Finite element analysis of fretting fatigue behavior of steel wires and crack initiation characteristics

The effects of fretting parameters on stress distributions of contacting wires during the initial stage of fretting–fatigue of steel wires were investigated using the finite element method. The roles of fretting parameters on crack initiation characteristics were discussed employing the multiaxial fatigue criteria of Fatemi–Socie and Smith–Watson–Topper, and three-dimensional coordinate transformation. Non-uniform stress distributions on contact surfaces and ring-shaped stress distributions near the contact zone on the symmetric plane are observed. Different fretting parameters induce distinct fretting regimes, stress distributions and abrupt changes of stress near the trailing edge. Crack initiation becomes more difficult with increasing contact load as compared to the increased possibility of crack initiation with increasing relative displacement.     

The use of multiaxial fatigue models to predict fretting fatigue life of components subjected to different contact stress fields

This work describes the application of multiaxial fatigue criteria based on critical plane and mesoscopic (Dang Van, 1973, Sciences et Techniques de lÁrmement, 47 , 647—722) approaches to predict the fatigue initiation life of fretted components. To validate the analysis, several tests under closely controlled laboratory conditions are carried out in a Ti‐6Al‐4V alloy. These classical Hertzian tests reveal a size effect where fretting fatigue lives vary with contact size. Experimentally available data for fretting fatigue of an Al‐4Cu alloy are also used to assess the models. Neither the critical plane models nor the mesoscopic criterion considered can account for the effects of different contact stress fields on the initiation life, if the calculation is based only on highly stressed points on the surface. It is shown, however, that satisfactory results can be achieved if high values of the fatigue parameters are sustained over a critical volume.     

A finite element analysis of fretting fatigue crack growth behavior in Ti-6Al-4V

There is a need for methodology(ies) to analyze the crack growth behavior under fretting fatigue condition since its experimental determination is a challenging task. A finite element sub-modeling method was used to estimate the crack propagation life in titanium alloy, Ti-6Al-4V specimens. Two contact geometries, cylinder-on-flat and flat-on-flat, were analyzed. The computed crack propagation lives were combined with the results of an experimental study where total fatigue lives were measured. The combined numerical-experimental approach provided the crack initiation lives. The crack propagation life increased with increasing applied cyclic bulk stress in similar manner for both contact geometries. Almost 90% of the fretting fatigue life was spent during the crack nucleation and initiation phases in the high cycle fatigue regime. A parametric study was also conducted to investigate the effects of contact load, coefficient of friction and tangential force on the crack growth behavior. The crack propagation life decreased with increase of these three parameters. This decrease was similar for the contact load and the tangential force in both contact geometries, however, the decrease in the case of coefficient of friction was relatively more in the cylindrical pad than in the flat pad.     

Initiation criteria in fretting fatigue with spherical contact

This paper analyses different methods used to estimate fatigue life adding initiation with propagation in fretting fatigue tests with spherical contact. In particular, the discussion will be centred on the initiation phase. Some of the methods presented define a crack length in advance, after which crack propagation is considered and calculated. Stresses close to the surface are then used to estimate initiation. The initiation life is estimated by using either the stresses averaged up to a certain depth or the stresses at a certain depth. Yet another method combines initiation with propagation, although in this case the initiation length is not a fixed quantity, it is obtained as a result of analysing each specific case. These methods are applied to a series of fretting fatigue tests with spherical contact, performed with 7075-T6 aluminium alloy and the results are discussed.     

Effect of build direction on the fracture toughness and fatigue crack growth in selective laser melted Ti‐6Al‐4 V

Experimental investigation was conducted to evaluate the fracture toughness and fatigue crack growth characteristics in selective laser‐melted titanium 6Al‐4 V materials as a follow‐on to a previous study on high cycle fatigue. For both the fracture toughness and crack growth evaluation, the compact tension specimen geometry was used. It was found that the fracture toughness was lower than what would be expected from wrought or cast product forms in the same alloy. This was attributed to the rapidly cooled, martensitic microstructure, developed in the parts. At low stress ratios, the crack growth rates were faster than in wrought titanium but became comparable at higher ratios. The fracture toughness appears to be higher when the crack is oriented perpendicular to the build layers. The difference in the average threshold and critical stress intensity values for the crack growth results for the three orientations was within the scatter of the data, so there was essentially no difference. The same was true for the empirically derived Paris Law constants. Residual stresses were likely to have overshadowed any variation in crack growth because of microstructural directionalities associated with build orientation.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

Application of fracture mechanics to estimate fretting fatigue endurance curves

This paper presents approximations to fatigue curves in fretting conditions with spherical contact in the alloy Al 7075. The curves are defined for a specific contact geometry and loads applied in the tests (axial load on the specimen, the normal and tangential contact forces). In order to obtain a curve of this type it is necessary to fix all parameters except for one and analyse its influence on life. The method used to estimate life in fretting fatigue combines initiation with propagation. Different approaches to the growth of short cracks are employed and in some cases a fretting fatigue limit is predicted. Various groups of fretting tests have been analysed, evaluating the suitability of each approximation.     

A novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.     

Influence of residual stresses from shot peening on fretting fatigue crack growth

One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental fretting life results from specimens in a Titanium alloy with and without shot peened surfaces were evaluated numerically. The residual stresses were measured at different depths below the fretting scar and compared to the corresponding residual stress profile of an unfretted surface. Thus, the amount of stress relaxation during fretting tests was estimated. Elastic–plastic finite element computations showed that stress relaxation was locally more significant than that captured in the measurements. Three different numerical fatigue crack growth models were compared. The best agreement between experimental and numerical fatigue lives for both peened and unpeened specimens was achieved with a parametric fatigue growth procedure that took into consideration the growth behaviour along the whole front of a semi‐elliptical surface crack. Furthermore, the improved fretting fatigue life from shot peening was explained by slower crack growth rates in the shallow surface layer with compressive residual stresses from shot peening. The successful life analyses hinged on three important issues: an accurate residual stress profile, a sufficiently small start crack and a valid crack growth model.