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.     

A BOUNDARY ELEMENT MODEL OF PLASTICITY-INDUCED FATIGUE CRACK CLOSURE

This paper describes a plane stress boundary element model of plasticity-induced fatigue crack closure. A simple Dugdale-type strip yield zone is used and quadratic programming techniques are employed to establish crack shape, stress and plastic deformation. The technique is extremely effective and the model can be readily implemented on a personal computer. Predictions of crack closure behaviour are produced for cracks growing under constant amplitude loading, and also following an overload or overload/underload cycle. These results are compared with an empirical R-ratio correction due to Walker and with experimental measurements taken from the literature. The model is found to give good predictions of crack behaviour under constant amplitude loading. Predictions for crack closure levels following an overload cycle give qualitative agreement with experimental results; the differences observed may well be due to the different definition of crack closure in the experiments.     

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 history and in-situ loading studies of the overload effect using high resolution X-ray strain profiling

High-energy synchrotron X-ray diffraction experiments are used to perform local crack plane strain profiling of 4140 steel compact tension specimens fatigued at constant amplitude, subjected to a single overload cycle, then fatigued some more at constant amplitude. X-ray strain profiling results on a series of samples employing in-situ load cycling are correlated with the crack growth rate (da/dN) providing insight into the da/dN retardation known as the “overload effect”. Immediately after the overload, the strain under maximum load is greatly reduced but the range of strain, between zero and maximum load, remains unchanged compared to the pre-overload values. At the point of maximum retardation, it is the strain range that is greatly reduced while the maximum-load strain has begun to recover to the pre-overload value. For a sample that has recovered to approximately half of the original da/dN value following the overload, the strain at maximum load is fully recovered while the strain range, though partially recovered, is still substantially reduced. The dominance of the strain range in the overload effect is clearly indicated. Subject to some assumptions, strong quantitative support for a crack growth rate driving force of the suggested form [(K_max)^1−p(ΔK)^p]^γ is found. A dramatic nonlinear load dependence in the spatial distribution of the strain at maximum retardation is also demonstrated: at low load the response is dominantly at the overload position; whereas at high loads it is dominantly at the crack tip position. This transfer of load response away from the crack tip to the overload position appears fundamental to the overload effect for high R-ratio fatigue as studied here.     

Effects of an overload event on crack closure in 3-D small-scale yielding: finite element studies

This paper describes the effects of a single overload event, within otherwise constant amplitude cycles, on the plasticity‐induced closure process for mode I fatigue crack growth in the small‐scale yielding (SSY) regime. The 3‐D finite element (FE) analyses extend the initially straight, through‐thickness crack front by a fixed amount in each load cycle, using a node release procedure. Crack closure during reversed loading occurs when nodes behind the growing crack impinge on a frictionless, rigid plane. A bilinear, purely kinematic hardening model describes the constitutive response of the elastic–plastic material. Extensive crack growth in the analyses, both before and after the overload, allows the crack to grow out of the initial and the post‐overload transient phases, respectively. The work presented here shows that the large plastic deformation in the overload cycle reduces the crack driving force through enhanced closure. Further, the residual plastic deformations due to the overload cause a disconnected pattern of closure in the wake long after the crack front passes through the overload plastic zone. The computational studies demonstrate that the 3‐D scaling relationship for crack opening loads established in our earlier work for constant amplitude cycling (with and without a T‐stress) also holds before, during and after the overload event. For a specified ratio of overload‐to‐constant amplitude loading (R_OL=K^OL_max/K_max) , the normalized opening load (K_op/K_max) at each location along the crack front remains unchanged when the constant amplitude peak load (K_max) , thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of . The paper concludes with a comparison of the post‐overload response predicted by the 3‐D analyses and by the conventional Wheeler model.     

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.     

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.     

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.     

Overload effect on the fatigue crack propagation in large‐scale tubular joints

This paper examines the overloading effect on the fatigue crack propagations monitored in a large‐scale tubular X‐joint specimen under two separate cyclic tests. The first cyclic test applies a constant‐amplitude brace in‐plane bending to the joint, with a single cycle of 150% overload before the crack depth reaches the mid‐thickness of the chord. The second fatigue test applies two batches of cyclic loads, with the amplitude of the second batch at 66% of the former. The X‐joint specimen experiences a 150% overload cycle during the first batch of loading, followed by the second batch after it has recovered from the overload effect. The experimental results reveal that deep surface cracks experience more significant overload retardation than does a shallow fatigue crack. The Paris law estimation indicates that the single overload cycle applied in the first specimen leads to a 7% increase in the fatigue life of the X‐joint.     

Crack closure - is it just a surface phenomenon?

The fatigue crack closure response in the plane strain regions of a BS4360 50B steel specimen is evaluated. Compliance measurements using a new type of closure gauge, crack-mouth clip gauge and back face strain gauge show that the fatigue crack is closed for a significant portion (20%) of the load cycle. A sectioning technique is used to confirm that the fatigue crack is closed along the whole crack front, at zero load.     

Fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading

ABSTRACT Fatigue crack growth of fibre reinforced metal laminates (FRMLs) under constant and variable amplitude loading was studied through analysis and experiments. The distribution of the bridging stress along the crackline in centre‐cracked tension (CCT) specimen of FRMLs was modelled numerically, and the main factors affecting the bridging stress were identified. A test method for determining the delamination growth rates in a modified double cracked lap shear (DCLS) specimen was presented. Two models, one being fatigue‐mechanism‐based and the other phenomenological, were developed for predicting the fatigue life under constant amplitude loading. The fatigue behaviour, including crack growth and delamination growth, of glass fibre reinforced aluminium laminates (GLARE) under constant amplitude loading following a single overload was investigated experimentally, and the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. An equivalent closure model for predicting crack‐growth in FRMLs under variable amplitude loading and spectrum loading was presented. All the models presented in this paper were verified by applying to GLARE under constant amplitude loading and Mini‐transport aircraft wing structures (TWIST) load sequence. The predicted crack growth rates are in good agreement with test results.     

Elastic-plastic analysis of a stationary crack under cyclic loading and effect of overload

A recently proposed elastoplastic constitutive model has been implemented in a finite element code to study crack front behaviour under variable loading. The importance of proper modelling of a material's behaviour becomes evident when a variable loading condition is considered. We present stress, strain and displacement distribution along a stationary crack front for constant amplitude cyclic loading with an overload cycle. The analysis predicts a decreased tensile stress and damage accumulation following an overload.     

An investigation of crack closure and the propagation of semi-elliptical fatigue cracks in Q1N (HY80) pressure vessel steel

The results of an experimental investigation of the effect of crack closure on the propagation of semi-elliptical fatigue cracks are presented. Load-shedding fatigue threshold tests were carried out at stress ratios of 0.2, 0.35, 0.5 and 0.7. Crack closure was measured at the surface and depth positions using backface strain gauges, near-tip gauges, and a clip gauge. Differences between the surface and depth growth behaviour are explained by considerations of the effects of the transition from plane stress conditions at the surface to plane strain conditions at the depth. The effects of stress ratios are attributed largely to differences in the crack opening displacement, which result in asperities coming into contact to induce roughness-induced crack closure.     

变幅载荷下纤维金属层板的疲劳与寿命预测

文章建立了纤维金属层板等幅疲劳载荷下的疲劳裂纹扩展速率与寿命预测模型。在此基础上对玻璃纤维-铝合金层板（GLARE）的疲劳裂纹扩展与分层扩展行为进行了试验研究,探讨了层板过载疲劳行为的机理,提出了纤维金属层板变幅载荷下疲劳寿命预测的等效裂纹闭合模型,并在GLARE层板上得到了验证。     

FATIGUE CRACK GROWTH AND CLOSURE AT HIGH STRESS RATIOS

Abstract— Fatigue crack growth tests have been carried out on a medium carbon structural steel over a wide range of stress ratios, i.e. from 0 to 0.7. All tests were conducted under constant amplitude loading conditions corresponding to growth rates in the Paris regime. Crack closure behaviour was observed experimentally by a surface strain gauge technique, and numerically by a finite element analysis under plane stress condition. While the crack closure could not be detected by experimental measurements at stress ratios equal to or greater than 0.5, the numerical results showed that closure occurred even at high stress ratios up to 0.7. The differences between experimentally and numerically determined crack opening levels were found for each stress ratio. A cause for these differences is discussed. In addition, two new types of crack tip parameters which have been proposed recently are evaluated by finite element analysis and their relevance to fatigue crack growth are discussed. It is concluded that fatigue crack growth rates are substantially determined by the effective stress intensity factor range which is based on the crack closure concept.     

Measurement of crack closure after the application of an overload cycle, using moiré interferometry

The crack closure behaviour on the application of a single overload cycle was studied in a Ti-6Al-4V specimen. Moiré interferometry with photoresist gratings was used to measure crack displacements. During the overload cycle a large crack opening displacement was observed at the maximum load. This was similar to predictions from a Dugdale-type crack closure model. When the load was taken back to zero, the crack was open at the crack tip due to the high levels of plastic deformation during the overload cycle. As the crack was grown there was some evidence of the deformed material on the crack faces.Moiré interferometry provided displacement data close to the crack faces, even when the crack had grown to over two-and-a-half times the overload crack length. When the overload was applied the crack bifurcated, and the Dugdale-type model under-predicted the crack opening.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Fatigue life and crack closure in specimens subjected to variable amplitude loads under plane strain conditions

The propagation of fatigue cracks in specimens subjected to variable amplitude loading under plane strain conditions was investigated experimentally and numerically, to find the influence of the variable amplitude loading on the stabilised crack closure level. Experiments on four-point-bend specimens with a Gurney block load scheme, showed that the crack closure level depends on the crack length but not on the stress range of the fluctuations. Numerical simulations performed in the fatigue crack growth program FASTRAN-II showed good agreement with the experimental results. In addition, statistical uncertainty analyses performed on the fatigue life show that, for technical applications, the uncertainties in initial crack length and load levels have a greater influence on the uncertainty in fatigue life, than the fluctuation level of the load.     

Fatigue crack growth of filled rubber under constant and variable amplitude loading conditions

Service conditions experienced by rubber components often involve cyclic loads which are more complex than a constant amplitude loading history. Consequently, a model is needed for relating the results of constant amplitude characterization of fatigue behaviour to the effects of variable amplitude loading signals. The issue is explored here via fatigue crack growth experiments on pure shear specimens conducted in order to evaluate the applicability of a linear crack growth model equivalent to Miner's linear damage rule. This model equates the crack growth rate for a variable amplitude signal to the sum of the constant amplitude crack growth rates associated with each individual cycle. The variable amplitude signals were selected to show the effects of R-ratio (ratio of minimum to maximum energy release rate), load level, load sequence, and dwell periods on crack growth rates. In order to distinguish the effects of strain crystallization on crack growth behaviour, two filled rubber compounds were included: one that strain crystallizes, natural rubber, and one that does not, styrene-butadiene rubber. The linear crack growth model was found to be applicable in most cases, but a dwell effect was observed that is not accounted for by the model.     

Prediction of fatigue crack growth and residual life using an exponential model: Part II (mode-I overload induced retardation)

Almost all load bearing components usually experience variable amplitude loading (VAL) rather than constant amplitude loading (CAL) during their service lives. A single overload cycle introduced in a constant amplitude fatigue loading retards fatigue crack growth and increases residual fatigue life. Although many models have been proposed on this subject, but life prediction under these complex situations is still under constant improvement. The present study aims at evaluating retardation in fatigue life due to application of a single tensile overload spike by adopting an exponential model. The proposed model calculates not only parameters related with overload induced retardation in fatigue crack growth, but also residual life in case of 7020-T7 and 2024-T3 aluminum alloys with reasonable accuracy without integration of rate equation. The model also covers stage-II and stage-III of post-overload period.