Utilization of partial crack closure for fatigue crack growth modeling

Load ratio effects are of prime concern when modeling of fatigue crack growth (FCG) rate is required as a prerequisite for a reliable life prediction. The majority of research efforts regarding the load ratio effects are based on Elber's ΔK_eff approach. However, there are intrinsic difficulties encountered with its consistent application to FCG prediction. In this paper two popular crack-growth-life prediction codes FASTRAN and AFGROW are modified utilizing the enhanced partial crack closure model. The proposed utilization aggregates apparent closure mechanisms involved and demonstrates a better correlation and a significant scatter reduction of FCG data taken from literature, especially in the near-threshold region.     

Growth of surface cracks under constant and variable amplitude loading

Fatigue crack growth experiments were performed on surface cracked tensile specimens of Inconel 718 at 400 °C. The loading was carried out at constant as well as at variable amplitude. The experimental results for the mean growth rate were compared with predictions based on data obtained from testing of compact tension specimens. Both nominal data as well as data corrected from measured crack closure were used in the predictions. The corrected data provided much better predictions than the nominal ones indicating that the level of crack closure during the testing of the surface cracked specimens was much lower than in compact tension specimens.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

CRACK GROWTH AND CLOSURE BEHAVIOUR OF SURFACE CRACKS UNDER AXIAL LOADING

Abstract— Crack growth and closure behaviour of surface cracks in 7075-T6 aluminium alloy are investigated under axial loading, noting the difference in fatigue growth behaviour at the maximum crack depth point and at the surface intersection point and also with through-thickness crack growth behaviour. The plane strain closure response at the point of maximum depth of a surface crack is monitored using an extensometer spanning the surface crack at the midpoint of its length. The plane stress closure at the surface intersection point is observed by multiple strain gauges placed at appropriate intervals ahead of the crack tip and continuously monitored without interrupting the fatigue test. The crack opening ratio is found to be about 10% greater at the maximum depth point than at the surface intersection point. Under axial loading, the difference in plane strain crack closure behaviour between the surface crack and the through-thickness crack is relatively small. Growth rates of surface cracks can be well described by the effective stress intensity factor range based on the closure measurements made in this study. The growth rates in terms of the effective stress intensity factor range seem to be slightly slower in surface cracks than in through-thickness cracks.     

EXAMINATION OF SHORT-CRACK MEASUREMENT AND MODELLING UNDER CYCLIC INELASTIC CONDITIONS

The opening and closure behaviour of short fatigue cracks is seen as one of the important phenomena which control fatigue life of components where a major part of life consists of the growth of short cracks. Therefore attempts are undertaken to experimentally assess and to model the behaviour of short cracks with respect to opening and closure. In this paper crack opening results obtained by Sunder et al. through SEM evaluation of striation patterns of 2000 series aluminium alloys are examined and compared to predictions using a model recently developed for fatigue life prediction based on fracture mechanics of short cracks. Sunder's technique for crack opening measurements involves particular load sequences with increasing and decreasing load ranges applied to notched specimens with naturally nucleated surface cracks where crack opening levels are identified by steady-state striation widths for increasing load ranges. A detailed review of Sunder's results, however, indicates a number of inconsistencies and contradictions which are discussed. Opening and closure behaviour of short fatigue cracks, in particular for inelastic conditions, is compared to predictions obtained with the above-mentioned model which incorporates a constant strain opening and closure assumption. For inelastic conditions that may develop at notches this assumption means that cracks would close at considerably lower stress levels as compared to the opening stress which becomes important when effective (local) stress-strain ranges are to be determined for fatigue life prediction under spectrum loading. The constant strain assumption is supported by a number of experimental observations from the literature as discussed in the paper. The approximative nature of this assumption and further details of the model are pointed out which show a need for further developments.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials under cyclic compression

For prediction of the fatigue crack growth (FCG) behavior under cyclic compression, a plasticity-corrected stress intensity factor (PC-SIF) range ΔK_pc is proposed on the basis of plastic zone toughening theory. The FCG behaviors in cyclic compression, and the effects of load ratio, preloading and mean load, are well predicted by this new mechanical driving force parameter. Comparisons with experimental data showed that the proposed PC-SIF range ΔK_pc is an effective single mechanical parameter capable of describing the FCG behavior under different cyclic compressive loading conditions.     

14MnNbq焊接桥梁钢的疲劳裂纹扩展行为研究

该文系统地研究了14MnNbq桥梁钢焊接热影响区的疲劳裂纹扩展行为。首先,由中心穿透裂纹(MT)试样疲劳裂纹扩展试验,获得了不同应力比R下的疲劳裂纹扩展速率和门槛值;然后考察了应力比R的影响,给出了适于不同应力比的疲劳裂纹扩展速率和门槛值的一般表达式;最后提出了一种由疲劳裂纹扩展门槛值▽Kth确定闭合参数U的新方法,将控制疲劳裂纹扩展的有效应力强度因子幅度写为▽Keff=▽K-▽Kth,由此讨论闭合参数U的确定方法。研究结果表明:对于14MnNbq焊接桥梁钢,该文给出的疲劳裂纹扩展速率表达式与试验结果符合得相当好。     

An analysis of fracture under biaxial loading using the non-singular T-stress

Finite element analysis using a two-dimensional modified-boundary-layer approach was used to model the effects of biaxial loading on crack tip stress fields. Loadings were applied corresponding to an elastic KI field, non-singular T-stress and a biaxial stress. For through-thickness cracks the T-stress inherent in the specimen geometry is augmented by the external biaxial stress. For surface-notched specimens the biaxial stress acts out of the crack plane. This effect was modelled with generalized plane strain elements. Results were analysed using the Anderson-Dodds approach for cleavage and the Beremin model in the ductile regime. Biaxial loading is predicted to have a large effect on the toughness of a through-thickness crack but little effect on a surface crack. Experimental results from a previous series of large-scale biaxial fracture tests are generally consistent with these predictions.     

Fatigue crack growth prediction in nuclear piping using Markov chain Monte Carlo simulation

In this paper, we present and demonstrate a methodology to improve probabilistic fatigue crack growth (FCG) predictions by using the concept of Bayesian updating using Markov chain Monte Carlo simulations. The methodology is demonstrated on a cracked pipe undergoing fatigue loading. Initial estimates of the FCG rate are made using the Paris law. The prior probability distributions of the Paris law parameters are taken from the tests on specimen made of the same material as that of pipe. Measured data on crack depth over number of loading cycles are used to update the prior distribution using the Markov chain Monte Carlo. The confidence interval on the predicted FCG rate is also estimated. In actual piping placed in a plant, the measured data can be considered equivalent to the data received from in-service inspection. It is shown that the proposed methodology improves the fatigue life prediction. The number of observations used for updating is found to leave a significant effect on the accuracy of the updated prediction.     

Determination of the opening load for a growing fatigue crack: evaluation of experimental data reduction techniques and analytical models

In metallic materials, growing cracks will remain closed or partially closed for a portion of the applied cyclic load as a consequence of plastically deformed material left in the wake of a growing crack, surface roughness along the crack surfaces, or corrosion debris. Proper characterization of this crack closure and the subsequent opening load is required for accurate prediction of crack growth. In the laboratory, global load–displacement data are commonly used in conjunction with a data reduction technique to estimate the opening load for a growing crack. Different data reduction techniques will be compared, and the influence of data smoothing will be demonstrated, using AA 7075-T651 specimens tested under constant amplitude cyclic loading with load ratios R = 0.1, 0.2, and 0.3. The ratio of maximum stress intensity factor to plane strain fracture toughness was approximately K _max / K _Ic = 0.5. The measured crack opening loads are also compared with predictions obtained from two different strip-yield models and three-dimensional elastic–plastic finite element analyses. Results show the necessity of using smoothed data, and the poor behaviour of the compliance offset data reduction technique, when analysing high load ratio data. A modification to this technique is proposed which improves crack opening load estimates. Overall, the analytical model predictions compare well with the experimental results; especially those results generated using the modified compliance offset technique.     

Numerical simulation of fatigue crack growth behavior by crack-tip blunting

In ductile metals one of basic mechanisms for fatigue crack growth is that based on crack-tip blunting under the maximum load and re-sharpening of the crack-tip under minimum load. In this paper, simulations of fatigue crack growth by crack-tip blunting using ANSYS finite element code are presented. This investigation focuses solely on simulation of fatigue crack growth due to crack-tip plasticity only. As such, any material damage and its fracture is not considered. Due to high plastic deformation the present simulations utilize a remeshing technique which allows applying a number of load cycles without terminating the simulation due to the error caused by excessive mesh distortion. The simulations were conducted using a center cracked specimen under various loading conditions including different load ranges and load ratios R = −1, 0 and 0.333. It is shown that fatigue crack growth (FCG) slows down with number of cycles towards a steady state value. The simulated FCG data for constant amplitude loading follow the Paris power law relationship and also indicate a typical R-ratio dependence. It can be noted that for all load cases with load ratios R > 0 no crack closure in the vicinity of the crack-tip wake was observed.     

Numerical and experimental evaluation of SIF for threaded connectors

This paper presents a methodology for fatigue crack growth analysis in tubular threaded connectors. A solution for stress intensity factor for semi-elliptical surface cracks emanating from a thread root in a screw connector is also discussed in the paper. The solution is based on a mixed approach incorporating weight function and finite element methods. The weight functions used are the universal functions for cracks in mode I and these are linked with a thread through-thickness stress distribution obtained from finite element analysis to produce a stress intensity factor for a crack at the critical tooth of a thread. The resulting crack growth data are then validated experimentally.     

The effect of overload on the fatigue crack growth behaviour of 304 stainless steel in hydrogen

Fatigue crack growth (FCG) behaviour and its characteristics following tensile overloads were investigated for AISI 304 stainless steel in three different atmospheres; namely dry argon, moist air and hydrogen. The FCG tests were performed by MTS 810 servohydraulic machine. CT specimens were used for the tests and crack closure measurements were made using an extensometer. FCG rates of 304 stainless steel at both dry argon and moist air atmospheres have shown almost the same behaviour. In other words, the effect of moisture on FCG of this material is very small. However, in a hydrogen atmosphere, the material showed considerably higher crack growth rate in all regimes. In general, for all environments, the initial effect of overloads was to accelerate the FCG rate for a short distance (less than a mm) after which retardation occurred for a considerable amount of time. The main causes for retardation were found as crack blunting and a long reinitiation period for the fatigue crack. Regarding the environmental effect, the overload retardation was lowest in a hydrogen atmosphere. This low degree of retardation was explained by a hydrogen embrittlement mechanism. In a general sense, hydrogen may cause a different crack closure mechanism and hydrogen induced crack closure has come in to the picture. Scanning electron microscope and light microscope examinations agreed well with the above results.     

AN ANALYSIS OF CRACK TIP SHIELDING IN ALUMINUM ALLOY 2124: A COMPARISON OF LARGE, SMALL, THROUGH-THICKNESS AND SURFACE FATIGUE CRACKS

Abstract— The development of crack closure during the plane strain extension of large and small fatigue cracks has been investigated in a 2124 aluminum alloy using both experimental and numerical procedures. Specifically, the growth rate and crack closure behavior of long (∼17–38 mm) cracks, through-thickness physically-short (50–400 μm) cracks, and naturally-occurring microstructurally-small (2–400 μm) surface cracks have been examined experimentally from threshold levels to instability (over the range 10–^12–10–⁶m/cycle). Results are compared with those predicted numerically using an elastic-plastic finite element analysis of fatigue crack advance and closure under both plane stress and plane strain conditions. It is shown that both the short through-thickness and small surface cracks propagate below the long crack threshold at rates considerably in excess of long cracks, consistent with the reduced levels of closure developed in their limited wake. Numerical analysis, however, is found consistently to underpredict the magnitude of crack closure for both large and small cracks, particularly at near-threshold levels; an observation attributed to the fact that the numerical procedures can only model contributions from cyclic plasticity, whereas in reality significant additional closure arises from the wedging action of fracture surface asperities and corrosion debris. Although such shielding mechanisms are considered to provide a prominent mechanism for differences in the growth rate behavior of large and small cracks, other factors such as the nature of the stress and strain singularity and the extent of local plasticity are shown to play an important role.     

Numerical simulation of plasticity induced crack closure: Identification and discussion of parameters

Numerical studies play a major role in the understanding and prediction of plasticity induced crack closure (PICC). However, the available numerical models can be considered simplifications of reality as they consider discrete crack propagations, relatively high fatigue crack growth rates (FCGR), sharp cracks, and propagation occurring at well-defined loads. Besides, there are a great number of numerical and physical parameters affecting the predictions of PICC. The aim of this paper is to discuss the numerical study of PICC. The numerical parameters affecting the accuracy of the numerical simulations, and the dependent parameters used to characterise the plastic wake and the closure level, are identified. The influence of the radial size of crack front elements and crack propagation is analysed. An extrapolation model is proposed, with excellent results. An intrinsic uncertainty is associated with the number of load cycles between crack increments and the definition of crack closure level. Finally, the effect of the stress ratio (R) on crack closure level is analysed.     

Improved structural reliability assessment using non-linear regression techniques to process raw fatigue crack growth test data

A new method is proposed to process raw fatigue crack growth (FCG) test data for estimating the parameters of any crack propagation (FCG) model. This method is based on iterative minimization techniques for non-linear regression, extensively available in the literature. The method presented here permits a significantly reduced contribution of the variability inherent in the usual raw FCG data processing techniques to the predictions of the crack length distributions derived by any analytical FCG model and, consequently, improved structural reliability assessment is achieved.     

Application of the substructured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures

The substructured finite element/extended finite element (S-FE/XFE) approach is used to compute stress intensity factors in large aircraft thin walled structures containing cracks. The structure is decomposed into a ‘safe’ domain modeled with classical shell elements and a ‘cracked’ domain modeled using three-dimensional extended finite elements. Two applications are presented and discussed, supported by validation test cases. First a section of stiffened panel containing a through-thickness crack is investigated. Second, small surface cracks are simulated in the case of a generic ‘pressure membrane’ with realistic crack configurations. These two semi-industrial benchmarks demonstrate the accuracy, robustness and computational efficiency of the substructured finite element/extended finite element approach to address complex three-dimensional crack problems within thin walled structures.     

Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Fatigue thresholds and fatigue crack growth (FCG) rates in corner notched specimens of a forged Ti–6Al–4V aero-engine disk material were investigated at room temperature and 350 °C. The threshold stress intensity range, ΔK_th, was determined by a method involving a step change in stress ratio (the ‘jump in’ method). It was found that for three high stress ratios (R=0.7–0.9), where crack closure effects are widely accepted to be negligible, there were similar ΔK_th values at room temperature and 350 °C under the same R. For a given temperature, ΔK_th was observed to decrease from 3.1 to 2.1 MPam with R increasing from 0.7 to 0.9. The fatigue crack growth rate was influenced by increasing temperature. For high stress ratios, FCG rate at 350 °C was higher than that at room temperature under the same ΔK. For a low stress ratio (R=0.01), higher temperature led to higher FCG rates in the near-threshold regime, but showed almost no effect at higher ΔK. The influence of stress ratio and temperature on threshold and FCG rates was analysed in terms of a K_max effect and the implication of this effect, or related mechanisms, are discussed. In light of this, an equation incorporating the effects of the K_max and fatigue threshold, is proposed to describe FCG rates in the near-threshold and Paris regimes for both temperatures. The predictions compare favourably with experimental data.     

Corrosion fatigue of BS 4360:50D structural steel in seawater

Research on through-thickness defects is reported for BS 4360:50D structural steel in air and in seawater; the results of experiments on the propagation of surface-breaking, semi-elliptic flaws under three-point bend loading are also presented. The mechanisms of corrosion fatigue crack growth of through-thickness and semi-elliptic cracks in seawater are considered, and the application of crack growth data to endurance tests on welded cruciform and tubular joints is discussed.