Extended finite element method for fretting fatigue crack propagation

In this paper, the extended finite element method (X-FEM) is considered for the analysis of fretting fatigue problems. A two-dimensional implementation of the X-FEM is carried out within the finite element software ABAQUS? by means of user subroutines, and crack propagation in fretting fatigue problems is investigated. On utilizing the non-linear contact capabilities of this code, the numerical technique is applied to a specimen-indenter model. The use of the X-FEM facilitates very accurate stress intensity factor computations on relatively coarse meshes, and furthermore, no remeshing is required for crack growth simulations. The implementation is applied to complete and incomplete contact fretting problems. A study of crack growth is conducted for several bulk loads applied to the specimen, and the influence of the initial crack angle is ascertained. The numerical simulations reveal the merits of applying the X-FEM to fretting fatigue problems.     

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

Nowadays, numerical simulation of 3D fatigue crack growth is easily handled using the eXtended Finite Element Method coupled with level set techniques. The finite element mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the possible propagation are hence avoided. A 3D two-scale frictional contact fatigue crack model developed within the X-FEM framework is presented in this article. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. A stabilized three-field weak formulation is also proposed to avoid possible oscillations in the local solution linked to the LBB condition when tangential slip is occurring. Two basic three-dimensional numerical examples are presented. They aim at illustrating the capacities and the high level of accuracy of the proposed X-FEM model. Stress intensity factors are computed along the crack front. Finally an experimental 3D ball/plate fretting fatigue test with running conditions inducing crack nucleation and propagation is modeled. 3D crack shapes defined from actual experimental ones and fretting loading cycle are considered. This latter numerical simulation demonstrates the model ability to deal with challenging actual complex problems and the possibility to achieve tribological fatigue prediction at a design stage based on the fatigue crack modeling.     

A fretting fatigue crack detection feasibility study using shear wave non-destructive inspection

A study was conducted to assess the viability of using ultrasonic shear wave non-destructive inspection (NDI) methods to detect fatigue cracks nucleating in the vicinity of a contact regionin situ. Use of this method is hampered by the presence of electronic and acoustic noise in the laboratory environment and by the contact in the experimental configuration. A previously established fretting fatigue test fixture was selected, in which nominally flat pads are held in contact against a thin, flat specimen and gross sliding between the pad and specimen is eliminated. Experiments were performed with Ti-6Al-4V at 300 Hz andR=0.5 for average clamping stresses of 200 and 620 MPa, and applied fatigue stresses of 330 and 250 MPa. The shear wave response was monitored during each test, and the test was interrupted when changes in the waveform were thought to indicate a crack. Also, the effect of the contact load and the sensitivity of the technique under the contact conditions were assessed. For the lower clamping stress, a sizeable portion of life was spent nucleating cracks, and the propagation life was too short to allow interruption of the tests. At the higher clamping stress, cracks with surface lengths of ∼2.5 mm were detected on, 10 mm wide specimens in tests conducted using the shear wave NDI technique. While the presence of the contact produced changes in the ultrasonic waveform, additional changes occurred as the crack propagated that permitted crack detection. A simple waveform correlation was used post-test to quantify the waveform changes, and thereby validate the viability of this NDI method for use in contact regions. In the configuration used for this study, the shear wave NDI technique was insensitive to small cracks. Some refinements that could dramatically improve crack detection capability are discussed. The original color figures found in this article can be seen in the online verson of this article, or can be obtained from A. Hutson.     

A cohesive zone model for fatigue crack growth allowing for crack retardation

A damage-based cohesive model is developed for simulating crack growth due to fatigue loading. The cohesive model follows a linear damage-dependent traction–separation relation coupled with a damage evolution equation. The rate of damage evolution is characterized by three material parameters corresponding to common features of fatigue behavior captured by the model, namely, damage accumulation, crack retardation and stress threshold. Good agreement is obtained between finite element solutions using the model and fatigue test results for an aluminum alloy under different load ratios and for the overload effect on ductile 316 L steel.     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

An asymptotic approach to crack initiation in fretting fatigue of complete contacts

The stress state near the corner of a complete contact subject to fretting action is studied using an asymptotic analysis. The spatial distribution of stress, together with the generalised stress intensity factor defining the severity of the stress state are found, and the implications for experimental determination of crack initiation conditions discussed.     

A new model for fatigue crack propagation in 4340 steel

An investigation on fatigue crack propagation under mode I loading has been performed. Fatigue crack growth data in the case of plane strain mode I have been obtained by performing experiments on compact tension specimens of 4340 steel for increasing ΔK_I, decreasing ΔK_I, and constant ΔK_I loading conditions. Fatigue crack extension predictions have been obtained for Khan's proposed equation [1989], together with the widely used and [1963] and [1967] equations. Khan's equation overcomes the drawbacks associated with the Paris and Forman equations, such as the inclusion of all the three stages of fatigue crack propagation, the nondimensionality of the constant, “C”, and also the accuracy in life prediction. Within the context of Linear Elastic Fracture Mechanics and the types of loading performed at the crack tip, it has been shown that Khan's model can accurately predict the crack growth data from near threshold value to the unstable fracture; these predicted values are much more accurate than those from the Paris and Forman equations.     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

A stochastic Markovian model for fatigue short crack growth across microstructural barriers

A stochastic model for fatigue short crack growth is presented. It takes into account the interaction between the crack-tip plastic zone and grain boundaries. The process is Markovian. It is completely described by the crack length and the size of the plastic zone. The integro-differential equation giving the evolution of the transition probability distribution is derived.     

Stratified model for estimating fatigue crack growth rate of metallic materials

Introduction Thefatiguedestructionisoneofthemaintypesofthemetaldamage.Therelationcurve betweenthefatiguecrackgrowthrateda/dNandthestressstrengthfactoramplitudeΔKisthe importantdatiumoffatiguecapabilityindesigningthemetaldamagetolerantlimitsandpredicting thelifeofmetalcomponentparts.Duetovariabilityofthefatiguecrackgrowthrate,alarge amountoftestsamplesareusuallyrequiredtoderiveahighlyreliableda/dN_ΔKcurve. However,inmostactualengineeringpractice,itishardtofindmultiplespecimenswithvery simil…     

A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

A methodology for thermomechanical fatigue crack growth testing in MMCs

This paper describes the experimental techniques used in an investigation of the crack growth characteristics of a four-ply, unidirectional, silicon carbide fiber reinforced, titanium matrix composite (SCS-6/Ti–6Al–2Sn–4Zr–2Mo) subjected to thermomechanical fatigue. A mechanical test system was assembled which is capable of conducting fully automated, computer-controlled thermomechanical fatigue crack growth tests. The system is able to simultaneously impose operator-defined arbitrary mechanical and thermal histories on the specimen. Crack lengths in single-edge tension [SE(T)] or middle tension [M(T)] specimens are measured by the direct-current electric potential method and optically using a unique telemicroscope system. A series of isothermal, in-phase and out-of-phase crack growth tests was conducted to obtain baseline data for material modeling purposes. The test temperatures ranged from 150°C to 538°C, and the highest thermal frequency was 0.0083 Hz.     

Limitations of the Coulomb friction assumption in fretting fatigue analysis

A significant factor in the fretting process, both experimentally and analytically, is the Coulomb friction. Most analyses of fretting fatigue consider a constant coefficient of friction (CCOF) in modeling a contact geometry. This work reevaluates the constant assumption of the Coulomb friction coefficient, and develops a Coulomb friction model based on a non-classical model allowing the coefficient of friction (COF) to be a function of local contact pressure and local slip magnitude. Here, the Coulomb COF varies locally along the contact surface. Results of computations using this model are applied to fretting fatigue experiments utilizing several specific contact geometries, which have nominally identical fatigue lives experimentally. The analysis shows that certain combinations of parameters in the variable coefficient of friction model can produce nominally identical stress states. Such results cannot be obtained using a CCOF.     

A note on the stress singularity at a non-uniformly moving crack tip

The stress-singularity at a crack tip moving arbitrarily in an elastic plate under plane strain conditions is investigated. By formulating the wave-equations in a polar coordinate system attached to the crack-tip, it is found by an asymptotic analysis that the angle-dependence of the singularity is only dependent on the instantaneous cracktip velocity. This result is used to derive a relation between the dynamic stress-intensity factor and the energyrelease rate.