Applications of crack analogy to fretting fatigue

In literature the most common approach to investigate fretting fatigue is based on contact mechanics. Crack initiation parameters of fretting fatigue are developed using elastic solution of two contacting bodies. Even though contact based parameters has been used extensively, they could not fully capture crack initiation mechanism due to the complexities of the fretting fatigue damage process, which depends on pad geometries, surface properties, material properties, and mechanical loading conditions. This has instigated fretting fatigue researcher to investigate other approaches. Recently, taking advantage of the similarities between contact mechanics and fracture mechanics lead to the development of crack analogy methodology (CAM), which defines the stress intensity factor as a fretting fatigue crack initiation parameter. CAM has shown a great potential investigating fretting fatigue. However, it has not been applied to wide range of fretting fatigue scenarios. The scope of this paper is not to focus on analytical development of CAM as much as validating its ability to analyze various fretting fatigue scenarios. Based on CAM, the present study introduces the crack analogy fretting parameter (CAF-parameter) to investigate crack initiation of fretting fatigue, which is equivalent to the change of mode II stress intensity factor at the contact surface, since the change in the stress intensity factor reflects the cyclic mechanism of fatigue. Further, a modification to the CAM is adopted to include various indenter-substrate geometries. Also, CAF-parameter-life curve, similar to the stress-life S-N curve, will be developed as a prediction tool to crack initiation for various geometric configurations using experimental data. This is consistent with presenting fatigue data. The results show similar pattern to plain fatigue with lower damage tolerance. It also shows scatter and dependency on the pad configuration as expected. Finally, the CAF-parameter shows potentials in effectively analyzing/predicting the complex mechanism of fretting fatigue.     

Multiaxial fretting fatigue testing and prediction for splined couplings

This paper presents a combined experimental and computational methodology for fretting fatigue life prediction of aeroengine splined couplings under combined loading cycles involving cyclic torque and axial load, as well as rotating bending and fluctuating torque. The experimental method is based on the concept of a simplified representative test, which mimics the multiaxial fretting conditions between spline teeth via biaxial loading of specially-designed bridge pads and a fatigue specimen. The numerical method is based on a three-dimensional finite element model of the test rig assembly, including frictional contact effects, along with a multiaxial, critical-plane fatigue parameter for crack nucleation followed by crack growth prediction in the Paris regime using El Haddad small crack correction. The prediction methodology is shown to successfully capture the effect of the key fretting fatigue stress, which mimics the spline rotating bending moment, on total fatigue life.     

Fracture mechanics based fretting fatigue life predictions in Ti-6Al-4V

A fracture mechanics based crack propagation analysis is developed to work directly with the output of a contact mechanics stress analysis for fretting fatigue. A series of remote load fatigue tests were conducted on specimens that had previously been subjected to fretting fatigue loading conditions. The growth of these prior fretting induced cracks were monitored and compared to results from the crack propagation analysis. A combined fatigue crack formation and propagation analysis was then applied to other fretting fatigue experiments with good success. The creation of fretting fatigue stress-life curves is also demonstrated.     

Fretting fatigue limit as a short crack problem at the edge of contact

This paper proposes a local stress concept to evaluate the fretting fatigue limit for contact edge cracks. A unique S–N curve based on the local stress could be obtained for a contact edge crack irrespective of mechanical factors such as contact pressure, relative slip, contact length, specimen size and loading type. The analytical background for the local stress concept was studied using FEM analysis. It was shown that the local stress uniquely determined the ΔK change due to crack growth as well as the stress distribution near the contact edge. The condition that determined the fretting fatigue limit was predicted by combining the ΔK change due to crack growth and the ΔK_th for a short crack. The formation of a non‐propagating crack at the fatigue limit was predicted by the model and it was experimentally confirmed by a long‐life fretting fatigue test.     

Similarities of stress concentrations in contact at round punches and fatigue at notches: implications to fretting fatigue crack initiation

A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P , the ensuing contact is of width 2 b which includes an initial flat part of width 2 a . The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q , is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q /(√( b − a )√ π b ). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a 'notch analogue' by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.     

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.     

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.     

Fatigue crack initiation and propagation under cyclic contact loading

A computational model for contact fatigue damage analysis of gear teeth flanks is presented in this paper. The model considers the conditions required for the surface fatigue crack initiation and then allows for proper simulation of the fatigue crack propagation that leads to the appearance of small pits on the contact surface. The fatigue process leading to pitting is divided into crack initiation and a crack propagation period.The model for prediction of identification of critical material areas and the number of loading cycles, required for the initial fatigue crack to appear, is based on Coffin-Manson relations between deformations and loading cycles, and comprises characteristic material fatigue parameters. The computational approach is based on continuum mechanics, where a homogenous and elastic material model is assumed and results of cyclic loading conditions are obtained using the finite element method analysis.The short crack theory together with the finite element method is then used for simulation of the fatigue crack growth. The virtual crack extension (VCE) method, implemented in the finite element method, is used for simulating the fatigue crack growth from the initial crack up to the formation of the surface pit. The relationship between the stress intensity factor K and crack length a, which is needed for determination of the required number of loading cycles N_p for a crack propagation from the initial to the critical length, is shown.     

Fatigue fracture in plates in tension and out-of-plane shear

Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out-of-plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analyses using shell elements are used to compute the energy release rate and stress intensity factors associated with the loading. Three fatigue crack growth rate experiments were carried out on sheets of 2024-T3 aluminium alloy loaded in tension and torsion. The first set of experiments is constant amplitude fatigue crack growth tests. The second consists of experiments where crack closure is artificially eliminated to determine the rate of crack growth in the absence of crack face contact. The third is a set of constant stress intensity factor amplitude tests. The results all show that as the crack grows extensive crack face contact occurs, retarding crack growth. In the absence of crack face contact, however, the addition of out-of-plane shear loading increases the crack growth rate substantially.     

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.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

Prediction of fretting crack propagation based on a short crack methodology

Fretting tests have been conducted to determine the maximum crack extension under partial slip conditions, as a function of the applied tangential force amplitude. An analytical elastic model representing a fretting-induced slant crack has been implemented and combined with the Kitagawa-Takahashi short crack methodology. This approach provides reasonable qualitative agreement between experimental and predicted maximum fretting crack lengths as long as the global response of the interface remains elastic. It confirms the stability of the crack arrest approach to predict the fretting fatigue endurance. It is, however, observed that the model is systematically conservative when significant plastic deformations are generated in the interface. A discussion of the appropriate fundamental parameters when dealing with steep stress gradients such as those present in fretting, and which are difficult to interpret in the context of the Kitagawa-Takahashi method, is presented. It is also shown that the maximum crack length evolution under plain fretting wear test conditions can be used to calibrate fretting fatigue predictions.     

60Si_2Mn钢的低周拉扭复合微动疲劳特性

测量60Si_2Mn钢在拉扭复合载荷作用下的低周微动疲劳特性,研究了不同轴向循环拉伸应力幅值对微动疲劳寿命、循环软化特性以及摩擦磨损表面和断口形貌的影响.结果表明,随着循环拉伸应力幅值的提高,60Si_2Mn钢的微动疲劳寿命降低幅度不同,发生循环软化的时期不断提前,完成循环软化的疲劳周期也不断缩短。同时,微动摩擦副产生的氧化物磨屑对微动磨损性能有重要影响,在疲劳前期加剧摩擦磨损,在疲劳后期减轻摩擦磨损。微动疲劳裂纹源形成于试样发生微动摩擦磨损的表面,并出现疲劳台阶。在扭矩产生的切向剪切应力作用下,疲劳裂纹沿着与轴向45°角的方向扩展,最终在断口上留下显著的舌状凸起,拉应力的幅值越大舌状凸起越明显。     

FATIGUE CRACK GROWTH BEHAVIOUR OF SM45C STEEL UNDER CYCLIC MODE I WITH SUPERIMPOSED STATIC MODE II LOADINGS

Abstract— The practical applications of studies related to constant amplitude mode I loading are somewhat limited, since mode I crack growth is often influenced by mode II (sliding mode) or mode III (tearing mode) in industrial situations. For these cases, criteria, rules, and laws have to be worked out and verified by experiments. However, it is very difficult to evaluate mixed-mode fatigue cracking due to crack surface interference, crack closure, crack branching, etc. This paper, which defines the length of a branched crack as an effective slant crack with a length equal to the distance between the two crack tips, explains the influences of crack surface interference by introducing concepts of adhesive wear and scrutinizes some related researches on mixed-mode crack growth behaviour. Additionally an effective stress intensity factor range is described which considers crack closure and crack surface interference and is verified with crack growth tests under mode I fatigue loading and cyclic mode I with a superimposed static mode II loading.     

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.     

A TEST METHOD FOR MODE II FATIGUE CRACK GROWTH RELATING TO A MODEL FOR ROLLING CONTACT FATIGUE

Abstract— From fractographic observations of specimens that have failed due to rolling contact fatigue, it has been concluded that the first stage of damage is the formation of mode II fatigue cracks parallel to the contact surface due to the cyclic shear stress component of the contact stress. Although these initial subsurface cracks, in both metals and ceramics, are produced in a direction parallel to the cyclic shear stress, cracks eventually grow in a direction close to the plane of the maximum tensile stress if we apply a simple mode II loading to them. The difference between crack growth in simple mode II loading and crack growth due to rolling contact fatigue is, we suppose, whether or not there is a superimposed compressive stress. Based on this hypothesis, we developed an apparatus to obtain the intrinsic characteristics of mode II fatigue crack growth, and developed a simplified model of subsurface crack growth due to rolling contact fatigue.
Some results in terms of da/dN versus ΔK_II relations have been obtained using this apparatus on specimens of steel and aluminum alloys. Fractographs of the mode II fatigue fracture surfaces of the various materials are also provided.     

Fretting fatigue failure mechanism of automotive shock absorber valve

Fretting fatigue is a complex mechanical failure phenomenon, in which two contact surfaces undergo a small relative oscillatory motion due to cyclic loading. This study proposes a methodology to analyze the fretting fatigue failure mechanism of automotive shock absorber valve by means of experimental and numerical approaches. A servo hydraulic test set-up is used to simulate fretting fatigue under real working conditions. Moreover, a 3-D finite element model is developed to analyze the contact status and stress distribution at contact interface between connected components, i.e. washer-disc contact. The experimental test results depict that fretting damage appears at contact interface between washer and disc, which causes the initial crack nucleation and advancing the crack up to the final fracture of valve disc. Stress field, obtained by numerical simulation, is used to monitor some fretting fatigue features such as the distribution of relative slip amplitude, contact pressure and different stress fields at contact interfaces. Eventually, the crack initiation site is estimated by monitoring variation of equivalent multiaxial damage stress at contact interface.     

Fretting fatigue crack initiation mechanism in Ti–6Al–4V

Fretting fatigue crack initiation in titanium alloy, Ti?6Al?4V, was investigated experimentally and analytically by using finite element analysis (FEA). Various types of fretting pads were used in order to determine the effects of contact geometries. Crack initiation location and crack angle orientation along the contact surface were determined by using microscopy. Finite element analysis was used in order to obtain stress state for the experimental conditions used during fretting fatigue tests. These were then used in order to investigate several critical plane based multiaxial fatigue parameters. These parameters were evaluated based on their ability to predict crack initiation location, crack orientation angle along the contact surface and the number of cycles to fretting fatigue crack initiation independent of geometry of fretting pad. These predictions were compared with their experimental counterparts in order to characterize the role of normal and shear stresses on fretting fatigue crack initiation. From these comparisons, fretting fatigue crack initiation mechanism in the tested titanium alloy appears to be governed by shear stress on the critical plane. However, normal stress on the critical plane also seems to play a role in fretting fatigue life. At present, the individual contributions/importance of shear and normal stresses in the crack initiation appears to be unclear; however, it is clear that any critical plane describing fretting fatigue crack initiation behaviour independent of geometry needs to include components of both shear and normal stresses.     

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.     

Prediction of the crack extension under fretting wear loading conditions

Fretting is associated with small amplitude oscillatory movements between two surfaces in contact. One possible consequence of fretting is the formation and subsequent growth of cracks at the edges of the contact. This paper presents an experimental investigation of the cracking behaviour under fretting loading of two different aluminium alloys: 2024-T351 and 7075-T651. Systematic and controlled experiments with a cylinder-flat contact under partial slip fretting conditions were carried out. A model which combines both crack nucleation and propagation processes is used to predict the crack extension throughout the life of the component. The direction of crack propagation experimentally observed was taken into account by the model. Furthermore, an analytical prediction of crack nucleation based on the process volume approach is made. The predictions of both crack extension and nucleation are compared with the experimental results, and show good agreement.