Crack Opening Level Research Articles

Fatigue crack closure of a corner crack: A comparison of experimental results with finite element predictions

Plasticity induced corner crack closure has been examined for the case of a middle tension (MT) plate of 14 mm thick 2024-T351 aluminium alloy subjected to cyclic loading. The closure load has been found by comparing the strain just ahead of the crack tip with the far field strain as the specimen was loaded and then unloaded. Special crack detection strain gauges were placed in front of the crack tips on the bore surface and on the free surface to allow measurement of crack opening and closure stress as the crack propagates. The offset observation and slope variation methods were used to determine the crack opening and closure stress levels. A three-dimensional finite element closure model was developed for a corner crack emanating from a hole. Finite element analysis gives the displacement of each node around the crack for which the opening and closure load were evaluated. The fatigue crack closure stress levels from the finite element analysis were compared with the experimental results giving a good agreement.

Finite‐element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

ABSTRACTAn elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.

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.

Numerical analysis for prediction of fatigue crack opening level

Finite element analysis (FEA) is the most popular numerical method to simulate plasticity-induced fatigue crack closure and can predict fatigue crack closure behavior. Finite element analysis under plane stress state using 4-node isoparametric elements is performed to investigate the detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The mesh of constant size elements on the crack surface can not correctly predict the opening level for fatigue crack as shown in the previous works. The crack opening behavior for the size mesh with a linear change shows almost flat stress level after a crack tip has passed by the monotonic plastic zone. The prediction of crack opening level presents a good agreement with published experimental data regardless of stress ratios, which are using the mesh of the elements that are in proportion to the reversed plastic zone size considering the opening stress intensity factors. Numerical interpolation results of finite element analysis can precisely predict the crack opening level. This method shows a good agreement with the experimental data regardless of the stress ratios and kinds of materials.

Effect of Overloads and Underloads on Fatigue Crack Growth and Interaction Effects

Abstract Under constant amplitude loading a single variable (ΔK) is required in crack growth relationships. The transferability of fatigue laws, determined under constant amplitude loading, to variable amplitude fatigue requires at least an additional variable, whose evolution with crack length accounts for the interaction effects between cycles of different types. The crack opening level (Kop) is usually employed for this purpose because it can be determined from the experiments and compared with predictions from models or FEM analyses. This paper presents an analysis of fatigue crack growth on M(T) specimens of medium carbon steel specimens and using FEM analyses. The specimens are subjected to repeated blocks of cycles made up of one or several overloads separated by a variable number of baseline cycles. The experiments are simulated by FEM analyses, taking into account the cyclic plastic behavior of the low carbon steel. The main objective of this study is to better understand the mechanisms at the origin of interactions effects due to the presence of overloads (or underloads) at different locations of the block loading. It is concluded that the interaction effects are closely related to the cyclic plastic behavior of the material and namely to the Bauschinger effect.

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, Smax/σ0. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45 ◦ inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from 'complete slip before opening' to 'opening in mode I before mode II shear offset'. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.

On the Causes of Deviation from the Palmgren-Miner Rule

Abstract Based upon considerations of fatigue crack growth, explanations for the observation that the Palmgren-Miner damage summation often deviates from unity can be established. It is assumed that the fatigue lifetime is taken up entirely in fatigue crack propagation, that is the number of cycles spent in crack initiation is a negligibly small fraction of the total lifetime. This assumption permits the fatigue lifetime to be analyzed in terms of a basic constitutive relation for the rate of fatigue crack growth that is given by: dadN=A(ΔKeff−ΔKeffth)2where a is the crack length, N is the number of cycles, A is a material-environmental constant, ΔKeff is the effective range of the stress intensity factor, i. e., Kmax - Kop, where Kmax is the maximum value of the stress intensity factor in a loading cycle, Kop is the stress intensity factor at the crack opening level, and ΔKeffth is the effective value of the stress intensity factor at the threshold level. Three variable amplitude loading conditions are considered: two-step loading, multiple two-step loading, and overload and underload loading. In each case, the cause for deviation from a Palmgren-Miner damage summation of unity is clarified.

428 Fatigue Crack Growth Rates : A General Method of Analysis

In order to deal with many aspects of fatigue crack growth such as constant amplitude fatigue crack growth, small fatigue crack growth, two-step and multiple two-step loadings, the effects of tensile overloads and compressive underloads, and the effect of mean stress on the fatigue limit, there is a need for a general approach which includes treatment of elastic-plastic behavior, the endurance limit, and the development of crack closure. For this purpose the following constitutive relation has been proposed : [numerical formula] where α is the crack length, N is the number of cycles, A is a material constant of dimensions (MPa)^<1/2>, ΔK_<eff> is the effective range of the stress intensity factor, K, ΔK_<effth> is the effective range of the stress intensity factor at the threshold level, K_c is the cyclic fracture toughness, and K_<max> is the maximum stress intensity factor in a loading cycle. An important feature of the relation is that it is dimensionally correct, a requirement long foreseen by such researchers as Frost and Liu. The expression within the second parentheses is included to deal with the contribution of so-called static modes of separation to the overall fatigue crack growth process, i.e., those modes of separation which are not cyclic in nature but are associated with tensile fracture processes such as cleavage and ductile rupture. These modes of separation become more important as K_<max> approaches K_c. Since K_<max>=ΔK/(1-R), where R is the ratio of the minimum to maximum stress in a loading cycle, the effects of R on the extent of static modes of fracture are included in Eq. 1. The expression within the first parentheses deals with purely cyclic fatigue crack growth, and as such deals with fatigue crack growth in the near-threshold range as a well as in the Paris range when the expression within the second parentheses can be neglected. In such a case Eq.1 becomes [numerical formula] Eq. 2 is deceptively simple. In order to make use of it information is needed about the crack closure level, since ΔK_<eff>=K_<max>-K_<op>, where K_<op> is the crack opening level, which under constant amplitude loading conditions is a function of the crack length and R. In order to deal with the important topic of short fatigue crack growth Eq. 2 must be modified to include consideration of (1) elastic-plastic behavior, since the maximum stress in a loading cycle may be a significant fraction of the yield stress, (2) the development of crack closure in the wake of a newly-formed crack, and (3) the role of the endurance limit (Kitagawa effect) in short fatigue crack growth. Ishihara has shown that even in the high-cycle fatigue range over 90% of the fatigue lifetime is spent in the process of growing fatigue cracks. Therefore the integration of Eq. 2 between the limits of the initial flaw size and the crack length at final fracture can lead to a reasonable estimate of the fatigue lifetime. In this presentation a review of the processes leading to the development of Eq. 1 which have taken place over the last fifty years, and illustrations of its use in dealing with fatigue crack growth, will be given.

Variable amplitude fatigue of spot welds

ABSTRACTA new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.

Experimental study and modelling of short fatigue crack growth in aluminium alloy Al7010-T7451 under random loading

This paper presents work on short crack initiation and growth behaviour under random loading conditions. Newman's crack closure model was extended to include the influence of grain boundary on crack opening level by introducing the concept of constrained crack tip plasticity by grain boundary blocking. A dislocation-based crack growth model (the Navarro–Rios model) was used in conjunction with a crack closure model for lifetime prediction under random loading conditions. Crack growth tests were performed using hourglass shaped specimens of Al7010-T7451 under constant amplitude loading as well as a variety of random loading cases representing the load spectra encountered in various flight missions. A good agreement (within 14% difference) was achieved between the model results and the experimental data. Crack initiation and growth behaviour for constant-amplitude and random loading conditions was also examined by use of plastic replicas and SEM observations.

A study on the determination of closing level for finite element analysis of fatigue crack closure

An elastic-plastic finite element analysis is performed to investigate detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The finite element analysis performed under plane stress using 4-node isoparametric elements can predict fatigue crack closure behavior. The mesh of constant element size along crack surface can not predict the opening level of fatigue crack. The crack opening level for the constant mesh size increases linearly from initial crack growth. The crack opening level for variable mesh size, is almost flat after crack tip has passed the monotonic plastic zone. The prediction of crack opening level using the variable mesh size proportioning the reversed plastic zone size with the opening stress intensity factors presents a good agreement with the experimental data regardless of stress ratios.

Bauschinger effect of alloys and plasticity‐induced crack closure: a finite element analysis

The effect of overloads, underloads and stress ratio on plasticity‐induced crack opening level is examined for different ‘model’ materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results.

Neural network applications in determining the fatigue crack opening load

A neural network approach is developed to determine the crack opening load from differential displacement signal curves. A backpropagation neural network of three layers was employed. In order to examine the measurement accuracy and precision of the neural network method, computer simulation was extensively performed for various combinations of crack opening levels and signal-to-noise (S/N) ratios. For all crack opening levels examined, the method shows good accuracy and precision. The proposed method was applied in practical to constant amplitude loading tests and is found to provide good results.

Crack closure and effect of load variation on small fatigue crack growth behaviour : Jono, M. and Sugeta, A. Fatigue Fract. Eng. Mater. Struct. (1996) 19 (2–3), 165–174

A variable-amplitude block-loading history consisting of high, near-yield-stress, underloads or compression-tension overloads followed by constant-amplitude small cycles was used to examine underload and compression-tension overload induced reductions in crack closure and the subsequent build-up of crack-opening stress to its steady-state level in a 2024-T351 aluminium alloy. Special attention was given to the near-threshold region, where the crack growth rate was less than 10−9 m cycle−1 The crack-opening stress level and the crack growth rate were measured for four different R-ratios of the small cycles following underloads and compression-tension overloads using a 900 power short focal length optical microscope. The crack-opening stress levels were measured at frequent intervals after the underload and compression-tension overload applications until the crack-opening stress returned to a steady-state level. The crack-opening stress build-up was then described by an empirical formula in terms of the ratio of the difference between the instantaneous crack-opening stress of the small cycles (Sop) and the post-underload and compression-tension overload crack-opening stress levels (Sopol), and the difference between the steady-state crack-opening stress of the small cycles (Sopss) and the post-underload and compression-tension overload crack-opening levels, (Sop− Sopol)(Sopss−Sopol). Effective stresses calculated using this formula were used to predict crack growth rates. The formula's predictions showed good agreement with experimentally measured crack growth rates. For simplicity, both underloads and compression-tension overloads will be referred to as overloads in the remainder of this paper.

Prediction uncertainties at variable amplitude fatigue

Predictions of variable amplitude fatigue life suffer from uncertainties originating from different sources. In this paper, important sources are discussed and estimated, by means of a variable amplitude fatigue model, based on level crossing counts and a version of the Palmgren–Miner cumulative damage rule. The influence of random material strength and parameter estimates is treated in certain detail. The use of simple mathematical models in the analysis introduces systematic errors, which are studied here in terms of the uncertainty regarding the crack opening level at variable amplitude. Additional uncertainties occurring in the fatigue design stage, such as load variation and structural component variability, are briefly discussed and exemplified.

Creep Effects on Creep Fatigue Crack Propagation of Center Cracked Plate and Attendant Acceleration/Retardation Phenomena.

A computational analysis addressing to the creep crack propagation problems is conducted. An incremental finite element procedure is developed and applied for investigating the creep effect on a fatigue crack propagation of a center cracked plate. The near crack parameter T, for which the preliminary study showed the validity of its use in the elastoplastic creep regime, is used in the prosent fatigue crack study. The phenomena of crack acceleration and retardation due to loading spectra are discussed in terms of T and the crack opening/closure load level. T as well as crack opening levels indicates the acceleration and retardation. The creep crack propagates faster than that under the non-creep cracks. The creep strain seems to play the role of suppressing acccleration and retardation effects in low to high, high to low and single overload cases.

FATIGUE DAMAGE CALCULATIONS ON BLOCK LOAD SEQUENCES

The problem of fatigue life predictions for variable amplitude loading is considered. A prediction model is proposed that is based on a level crossing count of the effective load, where the effective load is defined according to the crack closure concept. The proposed model is applied to block load sequences presented in the literature and compared to experimental data and other prediction methods. It can be concluded that, provided that the crack opening level can be determined, the model gives reasonable predictions.

Investigation on the J-Integral Range of a Fatigue Crack Emanating from Notches under Biaxial Stresses.

In previous papers, the authors discussed the path integral expression of the J-integral range, ΔJ, for short fatigue cracks emanating from notches under uniaxial stresses and showed that ΔJ evaluated based on the crack-opening level was an appropriate parameter for characterizing the near-tip stress and strain fields. In this paper, finite element simulations of fatigue crack growth at notches under biaxial stresses are conducted. It is found that ΔJ values evaluated by the path integral are almost path independent when the minimum-load level or the crack-opening level was selected as a reference level for the evaluation. The examination of the relationship between ΔJ and the crack-tip-opening displacement leads to the conclusion that ΔJ evaluated by the path integral based on the crack-opening level is the most appropriate parameter for representing the mechanical state near the tip of a crack emanating from notches under biaxial stress conditions. Furthermore, it is shown that ΔJ evaluated by Dowling's simple estimation formula based on the crack-opening level agrees well with ΔJ evaluated by the path integral.

CORRELATION OF FATIGUE CRACK GROWTH BEHAVIOUR WITH CRACK CLOSURE IN PEENED SPECIMENS

Abstract Various residual stress conditions were introduced into the surface of a 7075‐T6 aluminium alloy by shot peening. This resulted in a considerable alteration in subsequent fatigue crack growth behaviour. A systematic investigation into the effects of a variety of conditions on fatigue crack propagation behavior was conducted. The degree of shot peening was established using the Almen scale and calibration strips. Changes occurred in crack re‐initiation lives, crack growth rate and hardness across the thickness profile. Residual stresses were introduced by various peening operations (such as different peening positions and loading specimens prior to and during peening). By measuring the crack opening level of peened specimens, changes in fatigue crack closure effect with respect to the crack extension in CT specimens are reported. The relations of re‐initiation life versus crack opening level and Almen levels, and of the crack closure effect versus Almen scales, were addressed experimentally. It was found that the improvement in re‐initiation life and the retarding effect of crack growth, both influenced by the Almen scales, are associated directly with the elevation of crack opening level, particularly at the stage of crack re‐initiation.

Changes in crack-opening stress after underloads and overloads in 2024-T351 aluminium alloy

A variable-amplitude block-loading history consisting of high, near-yield-stress, underloads or compression-tension overloads followed by constant-amplitude small cycles was used to examine underload and compression-tension overload induced reductions in crack closure and the subsequent build-up of crack-opening stress to its steady-state level in a 2024-T351 aluminium alloy. Special attention was given to the near-threshold region, where the crack growth rate was less than 10 −9 m cycle −1 The crack-opening stress level and the crack growth rate were measured for four different R -ratios of the small cycles following underloads and compression-tension overloads using a 900 power short focal length optical microscope. The crack-opening stress levels were measured at frequent intervals after the underload and compression-tension overload applications until the crack-opening stress returned to a steady-state level. The crack-opening stress build-up was then described by an empirical formula in terms of the ratio of the difference between the instantaneous crack-opening stress of the small cycles ( S op ) and the post-underload and compression-tension overload crack-opening stress levels ( S opol ), and the difference between the steady-state crack-opening stress of the small cycles ( S opss ) and the post-underload and compression-tension overload crack-opening levels, ( S op − S opol ) (S opss −S opol ). Effective stresses calculated using this formula were used to predict crack growth rates. The formula's predictions showed good agreement with experimentally measured crack growth rates. For simplicity, both underloads and compression-tension overloads will be referred to as overloads in the remainder of this paper.