THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

T-stress and its implications for crack growth

Some of the “irregular” crack growth behaviour observed in different specimen geometries may not be unrelated. Discrepancies in fatigue crack growth rate have been observed in different specimen geometries of the same material; crack front “tunnelling” and out-of-plane crack growth have been found in mode I tension at elevated temperature. The results presented in this paper seem to indicate the relevance of a crack tip constraint parameter, the elastic T-stress, to the irregular crack growth behaviour that conventional LEFM fails to explain.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

CORRELATION OF FATIGUE CRACK GROWTH BY CRACK TIP DEFORMATION BEHAVIOUR

Growth of a long mode I crack under variable fatigue loading was experimentally investigated on mild steel specimens. A dynamic elastic-plastic two-dimensional finite element program, purposely developed for the simulation of cyclic crack tip deformation, was utilised to model the transient effects on crack tip advance. The model accommodated crack tip opening displacement and both crack tip and crack edge closure. Fifty one different cycle patterns were analysed to include the application of a single overload, a single underload, a single cycle having a combined overload and underload and finally loading blocks of different sequences. Correlations of experimental fatigue crack growth rates were made from knowledge of crack tip deformation behaviour, including the use of data found in the literature. Specimens of eight materials and different geometries were analysed to determine the validity of the present approach.     

Surface flaws behavior under tension,bending and biaxial cyclic loading

Fatigue surface crack growth and in-plane and out-of-plane constraint effects are studied through experiments and computations for the aluminum alloy D16T. A tension/bending central notched plate and cruciform specimens under different biaxial loadings with external semi-elliptical surface cracks are studied. The variation of the fatigue crack growth rate and surface crack paths is studied under cyclic tension, bending and biaxial tension–compression loading. For the experimental surface crack paths in the tested specimens, the T-stress, out-of-plane T_z factor, local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of the I_n-integral are calculated as a function of the aspect ratio by finite element analysis to characterize the constraint effects along the semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface, as well as at the deepest point of the semi-elliptical surface crack front, of the tested tension/bending plate and cruciform specimens. From the results, characteristics of the fatigue surface crack growth rate as a function of the loading conditions are established.     

Successive 3D FE analysis technique for characterization of fatigue crack growth behavior in composite-repaired aluminum plate

An analytical approach using successive finite element analysis technique was conducted to characterize the fatigue crack growth behavior of pre-cracked aluminum plates reinforced with composite patches. For single-sided repairs, due to the asymmetry and the presence of out-of-plane bending, crack front shape would become skewed curvilinear started from a uniform through-crack profile, as observed from previous studies. As the stress intensity factor (SIF) calculated at the crack tip is much influenced by crack front shape, it is necessary to predict the actual crack front shape evolution and take it into account for the accurate analysis of fatigue behavior. Present procedure performed a three-dimensional geometrically nonlinear finite element analysis to determine the SIF distribution at a set of points along the crack front, and then estimated the crack growth increments at these points by invoking a fatigue crack growth rate relationship (power-law relationship). A new crack front was then established for the next step by using a relevant remeshing scheme. Through conducting this procedure successively, the crack path of the patched plate as well as the fatigue life was evaluated with sufficient accuracy. The analytical predictions of both the crack front shape evolution and the fatigue life were in good agreement with the experimental observations.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

THREE-DIMENSIONAL CONSTRAINT EFFECTS ON STRESS INTENSITY DISTRIBUTIONS IN PLATE GEOMETRIES WITH THROUGH-THICKNESS CRACKS

Three-dimensional finite element analyses of through-thickness cracks in plate geometries are presented. It is shown that the local constraint variation towards the crack tip causes an increase in stress intensity which is neglected in analyses which assume a constant stress state throughout the geometry. This means that stress intensity factors for these types of crack geometries are a factor (1 — v²)^-0.5 higher than generally reported in stress intensity handbooks. Analyses on crack tunnelling situations show that if plane stress dominates the global behaviour, an almost constant stress intensity across the thickness is reached for a relative tunnelling depth of a 2.5% of the plate thickness. For geometries which are not predominantly in plane stress this value will be somewhat larger. Crack front tunnelling does not influence the mean stress intensity across the thickness. Shear lips are shown to reduce the mean equivalent stress intensity (the mode I stress intensity which has the same energy release rate as the actual combined mode I, II and III loading) by a factor equal to the square root of the ratio between plate thickness and projected length of the crack front. This may explain the reduction in crack growth rate caused by shear lips during fatigue crack growth experiments. The reduction of the mode I stress intensity factor is considerably larger, which may cause a further reduction of fatigue crack growth rate for crack growth mechanisms that depend primarily on the mode I crack tip loading. Analyses on CNT and SENB specimens show that the conclusions reached on infinite plate models also hold for real structures. However for an SENB specimen with an uncracked ligament equal to the plate thickness, the overall constraint is larger than that of a pure plane stress situation, and the effect of stress intensity increases due to the constraint transition is less pronounced.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

Deformation behaviour at the tip of a physically short fatigue crack due to a single overload

A two-dimensional elastic–plastic finite element analysis was utilized to investigate the transition behaviour of a physically short fatigue crack following the application of a single overload cycle. The deformation accommodated at the tip of a crack artificially advancing with a fully reversed load was considered. The development of the cyclic crack tip opening displacement was computed and then modelled to include the effects of the stress level of the base cycles, overload pattern and crack length at which the transient cycle was applied. The cyclic crack tip opening displacement was initially of a relatively high value. It decreased and then increased to match the behaviour under the base load cycles. The extent and location of both the minimum and matching points were dependent on the overload crack length and the stress compared with the material’s yield stress. In the case of the yield stress being exceeded by the overload, the minimum and the-return-to-normality points are identical. A previously developed crack tip deformation parameter was invoked to predict relevant experimental fatigue growth rates of short cracks reported in the literature.     

Application of the distributed dislocation technique for calculating cyclic crack tip plasticity effects

This paper describes a method for modelling cyclic crack tip plasticity effects based on the distributed dislocation technique (DDT). A strip‐yield model is utilised to allow for the determination of the crack opening displacement, size of the plastic zones and in the case of a fatigue crack, the wake of plasticity. The DDT can be easily implemented for a wide range of cracked geometries with reliable control over the accuracy and convergence. Thickness effects can also be incorporated through a recently obtained solution for an edge dislocation in an infinite plate of finite thickness. Results for finite length cracks that have had limited growth, such that there is no plastic wake, are presented for a range of applied loads and R‐ratios. Further results are provided for a steady‐state fatigue crack in a plate of finite thickness. The present results are compared with analytical solutions and they show an excellent agreement.     

A numerical analysis of the mechanisms behind plasticity induced crack closure: Application to variable amplitude loadings

The effect of loading parameters on fatigue crack growth has been explained using the concept of crack closure. Plasticity induced crack closure (PICC) is linked to the crack tip plastic deformation, which becomes residual with crack propagation. The objective here is to identify the main mechanisms behind PICC, and for that different loading cases were considered namely overloads and load blocks. An analytical model was used to isolate the effect of residual plastic deformation on PICC, however significant differences were obtained relatively to finite element results. A second mechanism, which is crack tip blunting, was used to explain the transient behaviour observed after overloads and load blocks. For overloads and low–high load sequences there is a sudden increase of crack tip blunting with load increase which explains the sudden decrease of crack opening level. For high–low load sequences there is a sudden decrease of crack tip blunting which enhances the effect of residual plastic wake. Finally, the partial closure concept was tested looking to non-linear crack tip parameters but no evidences of Donald’s effect were found for the material studied.     

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.     

Assessment of small fatigue crack growth driving forces in single crystals with and without slip bands

Strain localization under low amplitude cyclic loading is a manifestation of plastic irreversible deformation associated with early crack growth. However, traditional constitutive models cannot usually reproduce strain localization in smooth single crystals, which can affect crack growth predictions for crystallographic fatigue cracks. This work analyzes the influence of bands of localized plastic shear strain on the cyclic crack tip displacement and on a fatigue indicator parameter by making special provision of a crack along the interface of a deformation band. Furthermore, the quality of local and volume-averaged fatigue indicator parameters are assessed using finite element models of a Cu single crystal cycled to induce plastic deformation under multiple loading conditions.     

Ratchetting strain as a damage parameter in controlling crack growth at elevated temperature

Progressive increase in tensile strains near a crack tip has been observed from finite element studies of stationary and growing cracks (Zhao, 2004, 2008) [1] and [2] under cyclic loading conditions. In this work, the significance of such a phenomenon was further explored. In particular, stress-controlled experiments were carried out to evaluate the uniaxial ratchetting response of a nickel-based superalloy, and the material parameters were re-calibrated using both strain-controlled and stress-controlled experimental data. An additional kinematic hardening term was introduced in the viscoplastic constitutive model and the models were utilised via a user-defined subroutine to study near crack tip ratchetting behaviour of a single edge notch tension (SENT) model geometry at elevated temperature. Loading modes near the crack tip were examined, together with the influence of particular constitutive models on the mechanistic response of the crack tip. The crack tip deformation was found to be predominantly strain-controlled, where the mean ratchetting strain seems to be more relevant to crack growth than the strain range. The former was used as a measure of crack tip damage to correlate crack growth rates at selected loading conditions.     

FATIGUE CRACK GROWTH DUE TO TWO SUCCESSIVE SINGLE OVERLOADS

The behaviour of fatigue growth and cyclic tip deformation of long cracks due to two successive single overloads was investigated both experimentally and numerically. The results show the effect of the ratio of the second and first overloads, and the crack increment between the two overloads. The contributions of both crack tip blunting and residual stress fields were separated and accommodated in a previously developed crack tip deformation parameter, which was utilized to predict the resulting fatigue crack growth behaviour. The following trends were experimentally observed. Should the ratio of the second and first overloads not be less than one, fatigue crack growth rates followed the predictions based on the second overload. Otherwise, either of the following two situations resulted: (1) when the two overloads were closely applied, the second overload caused an initial acceleration in growth rates followed by a behaviour controlled by the first overload; (2) when the second overload was applied after the crack growth had reached its minimum rate due to the first overload, more retardation in growth rate was observed. Based on the model developed in the paper, it is possible to enhance the retardation effect of an overload if this overload is preceded by another overload. This enhancement depends on the ratio of the two overloads and the crack increment between them.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Prediction of shape change of corner crack by fatigue crack growth circles

As a fatigue crack grows, its shape changes. Conventional method for predicting the shape change typically requires the computation of several hundred increments to get accurate results. In this paper, a new finite element simulation technique that uses fatigue crack growth circles is developed. Since the circles are perpendicular to the new crack front as well as to the current crack front, they can represent the real path of the fatigue crack well and yield more accurate results. The new technique is validated by applying it to the case of a quarter-elliptical corner crack in a plate with an open hole subjected to tension loading. The effect of the Paris–Erdogan exponent is also investigated.