Calculation of KII in crack face contacts using X-FEM. Application to fretting fatigue

In this work, the modeling of LEFM problems that imply crack face closure and contact using the extended finite element method (X-FEM) is presented aiming at its application to fretting fatigue problems. An assessment of the accuracy in the calculation of K_II is performed for two different techniques to model crack face contacts in X-FEM: one is based on the use of additional elements to establish the contact and the other on a segment-to-segment (or mortar) approach. It is concluded that only the segment-to-segment approach can lead to optimal convergence rates of the error in K_II. The crack face contact modeling has also been applied to a fretting fatigue problem, where the estimation of K_II under crack closure conditions plays an important role in the stage I of fatigue crack propagation. The effect of the crack face friction coefficient has been studied and its influence on the range of K_II has been ascertained during loading and unloading cycles.     

Fracture mechanics assessment of stress concentrations in incomplete fretting contacts

Life assessment of fretting fatigue has been studied for decades. Crack-analogy methods have been proposed for analyzing fretting fatigue of flat contact pairs. In the present work we re-consider the stress field near fretting contact pairs and study the feasibility of using known fracture parameters to assess incomplete fretting contact problems. Both analytical and FEM analysis reveal that the stress field near the discontinuous round corner of a friction pad, in which the round surface has been idealized without contacting the workpiece, is the same as that of crack tip. The stress field is described by the known stress intensity factors, K_I and K_II. For sticking contact these two fracture parameters are independent, whereas for the slipping contact K_II is linearly correlated with K_I. Therefore, the stress field around the slipping contact can be characterized only by one fracture parameter, together with friction coefficient. For the continuous contact pairs with finite round contact surface, the local stress concentrations near the contact edge are finite and can be characterized by K_I and K_II, either, in analogy to the blunting crack tip due to finite strains. Detailed computations confirm that using the fracture parameters to characterize the fretting contact failure is affected by both loading condition and friction pad geometry. The dominance zone around the pad corner decreases more significantly with vertical press load than the horizontal friction load. In the bi-material contact friction pair the stress field can be described by K_I and K_II in the same form.     

MIXED-MODE FRACTURE MECHANISMS NEAR THE FATIGUE THRESHOLD OF AISI 316 STAINLESS STEEL

Abstract— Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.     

Analysis of edge crack behaviour influenced by non‐symmetrical contact tractions and bulk tension

This paper analyses a crack growth behaviour, which is initiated from the contact edge between a square punch with rounded edges and a half plane. Investigated are the influences of the contact profile, magnitude of the bulk tension and, crack obliquity, in particular, misalignment between the punch and half plane on the variation of the stress intensity factors K_I and K_II during the crack growth. The misalignment is simulated by a tilting of the punch. A partial slip regime is considered for the contact shear force to accommodate a general fretting fatigue condition. It was found that a crack closure occurs if only the contact forces are applied. The crack grows longer before it is closed if the punch is tilted (clockwise, in this paper) such that it initiates at the opposite site with respect to the direction of tilting. The closure phenomenon disappears when the bulk tension is added and exceeds a certain magnitude, which significantly depends on not only the contact profile but also the degree and direction of tilting. Provided are the lowest values of the bulk tensile stress due to a fatigue load necessary to extend the crack without a closure for each condition of the contact profile and misalignment. This may be used as a design guideline to restrain the contact‐induced failure.     

Two parameter fracture mechanics: Fatigue crack behavior under mixed mode conditions

The fatigue crack path has been studied on a tensile specimen with holes. The experimental crack path trajectories were compared with those calculated numerically. To incorporate the influence of constraint on the crack curving, we predicted the fatigue crack path by using the two-parameter modification of the maximum tensile stress (MTS) criterion. The values of the mixed-mode stress intensity factors K_I, and K_II as well as the corresponding constraint level characterized by T-stress were calculated for the obtained curvilinear and reference crack path trajectories. It is shown that in the studied configuration the effect of T-stress on the crack path is not significant. On the other hand the effect of constraint on the fatigue crack propagation rate is more pronounced.     

Study of the fatigue failure of an anti-return valve of a high pressure machine

This paper presents a study of the fatigue failure of an anti-return valve, designed to work in the high pressure system (500 MPa) of a high pressure processing machine. To do this, the crack propagation has been simulated by means of the linear-elastic fracture mechanics approach under mixed-mode loading conditions. From an initial crack, which size is related with the microstructure and superficial finish, the crack growth has been simulated using the stress intensity factors K_I and K_II of the cracked valve axisymmetric geometry. The crack propagation path has been obtained step by step, applying the criterion of the maximum circumferential stress at the crack tip. The experimental and simulated crack propagation paths have been compared and, as a consequence of the reliable results obtained, the fatigue life of the valve has been calculated using the Paris law of the material with an effective stress intensity factor K_eff. The good agreement with experimental fatigue life allows to perform new improved designs using the methodology presented.     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration

The existing design rules give quite general guidelines to the fatigue assessment of different types of welded joints. The goal of this investigation was to give designers some tools, which would allow more precise assessment of the effect of dimensional variations on the fatigue strength. Therefore the fatigue behaviour of 12 common types of welded joints has been studied parametrically. Two-dimensional (2D) finite element models of the joint were made and evaluated using plane strain linear elastic fracture mechanics (LEFM) calculations. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. A maximum tangential stress criterion with the Paris’ crack growth law was used to predict the growth rate and direction of root and toe cracks under mixed mode K_I-K_II conditions. The effects of weld size and joint dimension ratios on the fatigue strength were systematically studied. In addition to tensile loading, bending and combined tension/bending moment loading in both directions are examined for positive and negative mean stress.     

Fatigue crack propagation under non-proportional mixed mode loading

Under non-proportional mixed I+II loading, two kinds of stable crack propagation may be distinguished. An existing precrack will either kink, mode I controlled (tensile mode), or will propagate, coplanarly mode II controlled (shear mode). Shear mode growth will occur if the effective mode II range exceeds the material-specific threshold ΔK_{II th sm} and in addition to that, the ΔK_II-value on the starter crack is larger than the ΔK¹_I (Δϕ)-range on the infinitesimally short additional crack. Examination under the scanning electron microscope showed that flaws are not the reason for the mode II controlled crack propagation and support the criteria introduced. If the crack opening is large enough, the crack propagation rate is higher for shear-stress controlled crack growth than for normal-stress controlled crack extension, the deviation angle of which is well predictable via the MTS criterion due to Erdogan and Sih [On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963;85:519–25].     

Fatigue cracking in high-cycle- and very-high-cycle-fatigue areas of peened and unpeened Al-based alloys because of fretting damages

In-service fretting damage influenced the fatigue crack origination in materials under the damaged surface for the very-high-cycle fatigue. Specimens of BS L65 Al–Cu alloy with peened and unpeened surfaces tested under cyclic tension and static compression had the crack initiation on the surface because of fretting damage. The static compression was used to reproduce the fretting damage on the specimen surface. The special methodology was applied to the crack growth analysis in the case of the biaxial stress-state with R = ?1.0 for the investigated material. The fretting influence on the fatigue crack propagation was estimated on the basis of the functional correction, F(fr), for the stress intensity factor, K_I. The fretting damage influence on the fatigue crack growth was briefly discussed regarding the kinetic curves reproduced from the fractographic analysis. The bimodal S–N curve was introduced to describe the influence of fretting damages on the behaviour of materials in high- and very-high-cycle-fatigue areas.     

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.     

The condition of fatigue crack growth in mixed mode condition

The condition of the initiation of fatigue crack growth in mixed mode conditions has been investigated by using precracked low carbon steel specimens.It is pointed out that, firstly, the critical condition of crack growth should be defined with regard to the modes of fatigue crack growth, i.e. shear mode and tensile mode. Secondly, it is proposed that the critical condition of fatigue crack growth is given by the local tensile stress and shearing stress at the notch tip determined by stress intensity factors $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$, and that this criterion is generally applicable to in-plane-loading conditions, i.e. Mode $\text{I}$, Mode $\text{II}$ and Mixed Mode conditions.     

Part-circular surface cracks in round bars under tension,bending and twisting

Circular-fronted cracks in round bars subject to tension, bending and twisting are considered. Numerical expressions are given allowing the calculation of stress intensity factors K _I, K _II, K _III at every point on the crack front for a wide range of crack geometries. Comparisons are made with analytical, experimental and numerical results abailable in the literature. Crack shapes satisfying the iso-K _I criterion are also determined, making it possible to investigate the problem of crack growth behaviour under tensile or bending fatigue loads.     

Propagation of fatigue cracks in mixed loading

A model is proposed of propagation of a fatigue crack which makes it possible to determine its growth rate at different ratios of K_I and K_II as well as during the variation of the stress ratio. The model can be used to determine the ratio of the stress intensity factors of the first and second kind corresponding to the threshold growth rate of the fatigue crack. The results of the calculations are compared with experimental data.Translated from Problemy Prochnosti, No. 3, pp. 3–8, March, 1990.     

Progress in the application of notch asymptotics to the understanding of complete contacts subject to fretting fatigue

This paper describes progress in the interpretation of notch fatigue data by re‐working the Williams solution to bring out the effects of mode mixity and the limits of small scale yielding. The results are displayed in K_I versus K_II space. Experimental results from complete fretting fatigue tests using a high strength steel alloy known as “super CMV” are then plotted out on this diagram and it is shown that the fretting damage does not significantly reduce fatigue life, while the stress localisation effects of adhered pad edges does.     

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.     

Finite element analysis of a subsurface crack

The problem of a subsurface crack parallel to the surface of a half space was studied by the finite element method. Without using the interface or gap elements over the crack faces, the crack faces would penetrate into each other for the traction-free boundary condition under shear loading, which is physically impossible. Using the gap elements, this problem was avoided, and a contact zone was observed near one crack tip. The size of the contact zone decreases but the maximum contact pressure at the closed crack tip increases as the crack approaches the surface. For tensile and shear loadings, both K _I (mode I stress intensity factor) and K _II (mode II stress intensity factor) increase as the crack approaches the surface. For shear loading there is no K _I at the closed tip and the K _I and K _II at the open tip are comparable as the crack approaches the surface.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.     

Fatigue crack growth of a railway wheel

Typically, fatigue crack propagation in railway wheels is initiated at some subsurface defect and occurs under mixed mode (I–II) conditions. For a Spanish AVE train wheel, fatigue crack growth characterization of the steel in mode I, mixed mode I–II, and evaluation of crack path starting from an assumed flaw are presented and discussed.Mode I fatigue crack growth rate measurement were performed in compact tension C(T) specimens according to the ASTM E647 standard. Three different load ratios were used, and fatigue crack growth thresholds were determined according to two different procedures. Load shedding and constant maximum stress intensity factor with increasing load ratio R were used for evaluation of fatigue crack growth threshold.To model a crack growth scenario in a railway wheel, mixed mode I–II fatigue crack growth tests were performed using CTS specimens. Fatigue crack growth rates and propagation direction of a crack subjected to mixed mode loading were measured. A finite element analysis was performed in order to obtain the K_I and K_II values for the tested loading angles. The crack propagation direction for the tested mixed mode loading conditions was experimentally measured and numerically calculated, and the obtained results were then compared in order to validate the used numerical techniques.The modelled crack growth, up to final fracture in the wheel, is consistent with the expectation for the type of initial damage considered.     

Influence of initial stress on fracture of a halfspace containing a penny-shaped crack under radial shear

In this study, an axisymmetrical problem for a penny-shaped crack under radial shear is considered. The crack is located parallel to the surface of a halfspace, which is subjected to initial stress parallel to the crack plane. An approach proposed by Guz (1983) in the framework of the three-dimensional linearised solid mechanics is used. Analysis involves reducing the problem to a system of Fredholm integral equations of the second kind, where the solutions are identified with harmonic potential functions. The representations of the stress intensity factors K _I and K _II near the crack edges are obtained. These stress intensity factors are both influenced by the initial stress.