On the development of crack closure at high R levels after an overload

ABSTRACT In a 1999 paper it was asserted that crack closure cannot be of major importance in the mechanism of crack retardation following an overload, particularly since the authors found no evidence for crack closure at high R‐values, although crack retardation was observed. In the present work, overload experiments were carried out at R = 0.5 and crack closure was observed. In addition, the rate of fatigue crack growth in both constant amplitude and overload tests was found to be a function of ΔK_eff. It is concluded that crack closure is an important part of the retardation mechanism.     

Fatigue crack growth retardation after single-cycle peak overload in Ti-6Al-4V titanium alloy

Fatigue crack growth after single-cycle peak overload was investigated in Ti-6Al-4V sheet. Strain hardening was determined not to be the major controlling mechanism retarding crack growth after peak over-load, but instead, strain hardening slightly accelerated crack growth for the case when strain hardening was induced prior to crack initiation. Crack growth after peak overload was characterized by: (1) no effect after 20 per cent overload: (2) crack arrest immediately following 70 and 100 per cent overloads; (3) subsequent retarded crack growth rates after 70 and 100 per cent overloads; and (4) retardation but no arrest following 50 per cent overload. The Wheeler model of crack growth retardation was investigated. The physical appearance of post-test fracture surfaces were as hypothesized by the Elber concept of crack closure after overload. The The recovery of an overloaded crack was linear with respect to the constant load amplitude cyclic stress intensity.     

Effects of tensile overloads on crack closure and crack propagation rates in 7050 aluminum

It has been suggested that the crack closure concept can account for the retardation in crack growth rate following removal of tensile overloads. To test this possibility measurements of effective stress were made on center notched cracked specimens during tests in which tensile overloads were applied. A comparison of the changes in crack growth rate and in effective stress following removal of the overload indicates that the crack growth rate reaches a minimum value before the effective stress does indicating that the closure concept cannot account for the decrease in crack growth rate. Additional evidence for the inability of crack closure to account for the retardation in crack growth rate is provided by specimens run at a high mean stress and then overloaded. No crack closure is observed when there is a high mean stress present, yet the crack growth rate does decrease by an amount about the same as that observed at low mean stresses where crack closure is present. Measurements of closure stress and effective stress were obtained from load-displacement curves recorded using an extensometer mounted across the crack on the specimen centerline. This procedure also enabled us to measure the distance over which the crack faces were in contact when the stress was at its minimum value in the stress cycle. The length of crack closed reached a minimum value later than did either the crack growth rate or the effective stress. It occurred when the crack tip had propagated nearly across the plastic zone created by the application of the overload.     

Micromechanisms of fatigue crack growth retardation following overloads

New mechanistic interpretations to rationalize fatigue crack growth retardation due to load excursions are presented. It is reasoned that crack closure arising from residual tensile displacements is not the primary mechanism for growth attenuation following a peak tensile overload. A new mechanism for retardation is discussed in terms of a “micro-roughness” model. Quantitative analyses are provided to estimate the extent of reductions in effective driving force in the retarded growth region due to possible crack branching and fracture face micro-roughness. It is argued that the retarded crack advance is effectively governed by the micromechanisms of Stage I growth although nominally Stage II conditions exist in the post-overload zone. The implications of the present arguments are shown to be consistent with a number of typical post-overload phenomena cited in the literature.     

Estimation of fatigue crack growth retardation due to crack branching

Quantitative analysis is provided to estimate the reduction of fatigue crack growth rate due to overload crack branching. A recent mixed-mode fatigue crack growth model based on the dilatational component of the accumulated strain energy density near the crack tip is modified to quantify the retardation factor of crack growth rate following an overload. It is found that crack branching due to an overload results in considerable reduction of fatigue crack growth rate. The retardation factor estimated by the proposed methodology is correlated with test results for the 2090-T8E41 aluminum–lithium alloy indicating encouraging agreement.     

Prediction of crack growth following a single overload in aluminum alloy with sheet and plate microstructure

The fatigue crack growth behavior under constant amplitude and under single overload of 2024 aluminum alloy in sheet and plate product form has been investigated. Constant amplitude fatigue crack growth tests showed superior crack growth resistance of the plate attributed to a pronounced roughness induced crack closure as a result of the coarse and elongated grain structure. Crack growth tests with single overload showed that the retardation effect caused by the overload is not primarily influenced by roughness crack closure at the crack path. In this case, the sheet material with lower yield strength revealed a higher retardation effect than the plate material. The observed crack growth behavior has been simulated with the LTSM-F model, which accounts for retardation of crack growth after an overload due to material strain hardening at the crack front. Dissimilar strain hardening at the crack tip due to different yield strength for the sheet and plate has been considered by means of strength gradients inside the overload plastic zone. The analytical results confirmed the observed material crack growth trends.     

The effects of overloads in fatigue crack growth

Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.     

Fatigue life prediction of engineering structures subjected to variable amplitude loading using the improved crack growth rate model

It is a difficult task to predict fatigue crack growth in engineering structures, because they are mostly subjected to variable amplitude loading histories in service. Many prediction models have been proposed, but no agreed model on fatigue life prediction adequately considering loading sequence effects exists. In our previous research, an improved crack growth rate model has been proposed under constant amplitude loading and its good applicability has been demonstrated in comparison with various experimental data. In this paper, the applicability of the improved crack growth rate model will be extended to variable amplitude loading by modifying crack closure level based on the concept of partial crack closure due to crack‐tip plasticity. It is assumed in this model that the crack closure level can instantly go to the peak/valley due to a larger compression/tensile plastic zone resulted from the overload/underload effect, and gradually recovers to the level of constant amplitude loading with crack propagation. To denote the variation in the affected zone of overload/underload, a modified coefficient based on Wheeler model is introduced. The improved crack growth rate model can explain the phenomena of the retardation due to overload and the tiny acceleration due to underload, even the minor retardation due to overload followed by underload. The quantitative analysis will be executed to show the capability of the model, and the comparison between the prediction results and the experimental data under different types of loading history will be used to validate the model. The good agreement indicates that the proposed model is able to explain the load interaction effect under variable amplitude loading.     

A mechanistic model for the influence of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—I. Crack-ductile materials

Concentrating on local behavior of a highly stressed zone ahead of the crack tip, a recent mechanistic approach to analyse LEFM fatigue crack growth behavior in three stages at stress ratio R = 0 is extended here to include the effect of a positive stress ratio. This paper is limited to analysing primarily the stages I and II of “crack-ductile” materials, characterised by a purely “reversed shear” (or ductile “striation”) growth mechanism in stage II. It is shown that in these materials stage I is R-sensitive and stage II is insensitive, and these can, without invoking crack closure arguments, be rationalised alternatively by considering the dominance of a K_max-controlled “Submicroscopic Cleavage” and a ΔK-controlled “ reversed shear ” fracture mechanism, respectively. Assuming Paris type power relations to hold, a predictive model is developed that contains separate growth equations with R-effect for stages I and II and shows the existence of a characteristic “master shear-curve” and a “moving pivot-point” on this curve for a class of materials. Good agreement was found between quantitatively predicted growth curves at selected R-values and a relatively large volume of available experimental data for low strength steels, aluminum alloys and titanium alloys. Besides providing more physical explanations for the observed growth behavior, the model may also be useful as a convenient alternative to crack closure for obtaining fairly accurate and conservative estimates of fatigue life for design applications.     

A new model for fatigue crack growth retardation following an overload

This paper details the theoretical development of a new model for fatigue crack growth retardation resulting from an applied overload. The model is based upon the concept that residual stresses due to plastic deformation reduce the value of the stress intensity range that drives fatigue crack propagation. A calculation is presented showing the variation of plastic zone size as the crack tip advances through the overload plastic zone. This information is used to define an effective stress intensity range that applies during the retardation period. A strip-yield representation of crack tip plasticity is employed in the analysis, and the effect of crack closure is included by means of a previously developed analytic function method. The fracture mechanics based model predicts the delayed retardation effect and other experimentally observed features of overload-influenced fatigue crack growth.     

Effect of overload on crack closure in thick and thin specimens via digital image correlation

The displacement field of compact tension (CT) specimens have been mapped by digital image correlation (DIC) local to growing fatigue cracks to study overload effects for plane stress and plane strain. We have extracted crack opening displacement (ΔCOD) and stress intensity (K) determined by a Muskhelishvili fit to the crack tip displacement field to infer the closure load. In both cases a classical knee was observed upon unloading consistent with closure which disappeared during the accelerated growth following OL, before increasing during retardation. In both cases following OL the crack growth rate is perturbed for a distance similar to the plastic zone.     

FEM analysis of crack closure and delay effect in fatigue crack growth under variable amplitude loading

An analysis of fatigue crack closure under variable amplitude loading was made by using the finite element technique. Two basic types of variable amplitude loading were selected for the analysis; constant amplitude loading with a single overload and block loading. A characteristic variation of a crack closure level was found to exist for both types of loading: the trace of the crack closure level vs crack length rose to a maximum value and then decreased asymptotically. The characteristic behavior was explained in terms of the residual stress which had been induced by an overload or a load preceding to the variation. The predicted fatigue crack growth behavior which was obtained analytically was consistent with the experimental results, and it was concluded that the retardation and acceleration phenomena are closely correlated with the crack closure.     

The retardation phenomenon of fatigue crack growth in HT80 steel

The fatigue crack growth behavior resulting from single and multiple applications of overload was investigated for HT80 steel. A peak load was found to cause retardation of the crack growth rate, which becomes stronger with increasing the peak/baseline stress ratio or with decreasing baseline stress intensity. Multiple overloads resulted in additional retardation. These experimental data were explained according to a new model based on crack closure conception, being correlated with the residual plastic zone size ahead of crack tip induced by the peak overload(s). The proposed formulation of retardation was expressed simply as a function of peak/baseline stress ratio, $\text{r}$, and two material parameters, $\text{m}$ and β. $\text{m}$ the exponent parameter in Paris equation and β is the ratio of crack distance at the maximum retardation to the residual plastic zone size. The retardation was predicted to increase with increasing $\text{r}$ and $\text{m}$ and with decreasing β. It was suggested that the parameter, β, reflects the change in the morphology of crack tip resulted from the application of overload, which determines the shape of the curve for retarded crack growth rate vs crack distance.     

Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

Fatigue crack growth and crack closure in an AlMgSi alloy

This study reports an experimental investigation of fatigue crack propagation in AlMgSi1-T6 aluminium alloy using both constant and variable load amplitudes. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. For the constant amplitude tests four different stress ratios were analysed. The crack closure parameter U was calculated and related with Δ K and the stress ratio, R . The threshold of the stress intensity factor range, Δ K _th , was also obtained. Fatigue crack propagation tests with single tensile peak overloads have been performed at constant load amplitude conditions. The observed transient post overload behaviour is discussed in terms of the overload ratio, Δ K baseline level and R . The crack closure parameter U trends are compared with the crack growth transients. Experimental support is given for the hypothesis that crack closure is the main factor determining the transient crack growth behaviour following overloads on AlMgSi1-T6 alloy for plane stress conditions.     

Fatigue crack growth retardation in plane stress and plane strain

The fatigue crack growth retardation phenomenon following a single peak overload applied tothick andthin SEN bend specimens has been studied for a low carbon structural steel. Fatigue tests were performed under a constant load ratio of 0.6, constant stress intensity range of 10 MPam^1/2 and a constant overload ratio of 2.5. An immediate increase followed by a transient retardation in the fatigue crack growth rate, due to the applied overload, was observed for thethick specimen but complete crack arrest was obtained for thethin specimen. The immediate increase in the fatigue crack growth rate following the single peak overload in thethick specimen was attributed to the coincidence of monotonic fracture modes.     

Evaluation of overload effects on fatigue crack growth and closure

Fatigue crack propagation tests with single tensile peak overloads have been performed in 6082-T6 aluminium alloy at several baseline ΔK levels and stress ratios of 0.05 and 0.25. The tests were carried out at constant ΔK conditions. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. The observed transient post-overload behaviour is discussed in terms of overload ratio, baseline ΔK level and stress ratio. The crack closure parameter U was obtained and compared with the crack growth transients. Experimental support is given for the hypothesis that plasticity-induced closure is the main cause of overload retardation for plane stress conditions. Predictions based on crack closure measurements show good correlation with the observed crack growth rates for all the post-overload transients when discontinuous closure is properly taken into account.     

Predicting fatigue crack growth under irregular loading

We describe a model for predicting fatigue crack growth (FCG) with the presence in the loading spectrum of peak and block tensile overloads. The model is based on account for the following factors influencing crack growth retardation: change of the quantity K_op as a consequence of the induction of a system of residual compressive stresses at the crack tip and increase of the degree of crack closure that is due to plastic deformation of the material in the wake of the tip of the growing crack; plastic blunting of the crack tip. We propose a technique for quantitative prediction of the residual crack tip opening (radius of the blunted tip) after a peak tensile overload. Experimental verification of the proposed FCG model with differing applied load irregularity showed that the model may serve as the basis of a method for predicting the service life of cracked structural members operating in irregular loading regimes.Translated from Problemy Prochnosti, No. 8, pp. 3–16, August, 1994.     

Load and temperature interaction modeling of fatigue crack growth in a Ni-base superalloy

An approach was developed to predict the thermo-mechanical fatigue crack growth rates under typical gas turbine engine spectrum loading conditions. The material studied in the development of this model was a polycrystalline superalloy, Inconel 100. Load interaction effects were determined to have a major effect on the crack growth life. A yield zone load interaction life prediction model was modified to include temperature dependent properties. Multiple overload effects were included in the model to incorporate enhanced retardation compared to single overload retardation behavior. Temperature interaction effects were included and proved to be very important because of the wide temperature ranges to which turbine engine components are subjected. The effects of oxidation and temperature changes were accounted for in the model by accelerating crack growth in regions that had been previously affected by elevated temperatures. Experimental data of isolated, first order effects were used to calibrate and verify the model. Temperature dependent mechanical properties were determined and were essential in the model’s development. Parametric studies were performed using this model to assess the sensitivity of specific crack growth variables on life predictions.