THE EFFECT OF INTERMEDIATE HEAT TREATMENTS ON OVERLOAD INDUCED RETARDATIONS DURING FATIGUE CRACK GROWTH IN AN Al-ALLOY

Abstract— Crack growth fatigue tests were carried out on 2024-T3 specimens. Constant-amplitude loading was periodically interrupted by 10 overload cycles. Intermediate heat treatments (T4) were applied to remove the residual stress in the crack tip zone and the crack closure wake behind the crack tip. Retardation effects induced by crack closure due to the previous load history were fully erased by the heat treatments. Overload effects were easily introduced again by new overload cycles afterwards. Crack growth rate results and fractographic observations indicate that primary crack tip plastic deformation (in virgin material) is more effective for crack extension than secondary plastic deformation in an existing plastic zone. This conclusion is significant for cycle-by-cycle crack growth prediction models for variable-amplitude loading.     

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.     

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.     

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.     

Overload effects on fatigue crack‐tip fields under plane stress conditions: surface and bulk analysis

The surface crack opening displacements are characterised by digital image correlation for a (thin) plane stress 316 stainless steel compact tension sample subjected to an overload event. This supports a traditional plasticity‐induced closure interpretation showing a knee in the closure response prior to overload, an absence of closure in the accelerated growth regime followed by accentuated closure in the retardation regime. By contrast, measurement of the mid‐thickness elastic strain field behind and ahead of the crack made by synchrotron X‐ray diffraction shows no evidence of significant crack face contact stresses behind the crack tip on approaching minimum loading. Rather the changes during loading and overloading can mostly be explained by a simple elastic plastic analysis using a value of the yield stress intermediate between the initial yield stress and the UTS. This shows very significant compressive reverse plastic strains ahead of the crack that start to form early during unloading. At the moment it is not clear whether this difference is because of the increasing stress intensity applied as the crack grows, or for some other reason, such as prevention of the crack faces closing mid‐thickness due to the reverse plastic zone.     

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.     

A FINITE ELEMENT ANALYSIS OF A CRACK GROWING UNDER CYCLIC LOADING

Abstract— Crack growth under cyclic loading has been studied by the finite element method. The calculation was made for plane stress conditions. The crack tip zone was modelled as a cohesive zone. The displacement of the free crack surface during unloading was found to be governed by the surrounding continuum and was independent of the details in the fracture zone. This means that crack closure upon unloading is directly related to the ultimate separation, of the cohesive zone, which in turn controls the residual plastic deformation left in the wake of the growing crack. If the distance over which closure takes place is rather small, closure may be very difficult to detect by the compliance technique.     

Elastic–plastic material response of fatigue crack surface profiles due to overload interactions

The deformation caused by single and periodic overloads on the crack surface profile is studied using finite element fatigue crack closure simulations in a material with linear kinematic hardening. Differential surface profiles (difference of crack surface displacements before and after overloads), Δu_y, are found useful in understanding the role and the interaction between overloads. Three parameters, ΔK_OL/ΔK, ΔK and R, are found necessary to characterize deformation response of a single overload on the crack surface profile. The simulation procedure and results are discussed based on experimental and numerical studies reported in literature on overload interactions.The deformation occurred on the crack surface due to an applied single overload (hump) inhibits reversed plastic deformations by acting like a spring. Therefore, a second single overload leads to a larger deformation response even if this second overload is applied outside the overload plastic zone of the first single overload. This second deformation response is found equivalent to the response of a single overload with a higher K_min value.     

A537钢疲劳裂纹扩展单次拉伸超载效应及裂尖形变,裂纹闭合行为

研究了恒定ΔＫ条件下，单次拉伸超载对Ａ５３７钢疲劳裂纹扩展速率的影响，并利用激光散斑技术原位研究超载前后的裂尖应变场，裂纹闭合效应。结果表明：超载后裂纹闭合效应呈增强趋势，裂尖应变呈下降趋势。伸超载有阻滞裂纹扩展的作用。     

Fatigue crack growth retardation inconel 600

The effect of single-cycle overloads on the subsequent fatigue crack growth behavior of Inconel 600 is studied. Overloads ranging from 10 to 50% are applied to a sample undergoing baseline fatigue crack growth at constant Δ$\text{K}$. In all cases, the crack growth rate increases slightly immediately after the overload and then decreases rapidly to a minimum value before later returning to the pre-overload value. The plastic zone size, affected crack length and the crack growth increment at minimum crack growth rate, $\text{a}\text{?}$, are measured for each overload.The affected crack length is considerably larger than the overload plastic zone size for overloads greater than 20%. Consequently, although the minimum crack growth rate occurs within the plane stress overload plastic zone, the effect of the overload extends well beyond the overload region.Within the overload plastic zone, contact occurs between the crack faces due to the excessive deformation produced during the overload cycle. The size of the contact region agrees very well with the overload plastic zone size. Beyond the overload region, Δ$\text{K}{}_{\mathrm{eff}}$ remains less than the applied Δ$\text{K}$ for some time due to the wedge action of the plastically deformed overload region, delaying recovery of the pre-overload crack growth rate. The crack growth rate recovers only after the crack grows out of the region of influence of the wedge.     

Four lectures on fatigue crack growth: II. Fatigue cracks,plasticity effects and crack closure

Concepts introduced are residual plastic deformation, residual stress, reversed plastic deformation, plastic deformation in the wake of the crack and crack closure under tensile load. COD measurements as a method to determine the crack closure level are discussed. The significance of crack closure for fatigue crack growth is analysed and illustrated by several examples, including effects of yield stress, stress ratio and delayed crack growth after a peak load. Finally some attention is paid to three dimensional aspects following from thickness effects, shear lips and curved crack fronts.     

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.     

Effect of tensile overloads on fatigue crack growth of high strength steel wires

Fatigue of the tensile armor wires is the main failure mode of flexible risers. Techniques to increase the life of these components are required to improve the processes safety on oil exploration. This work evaluates the crack growth retardation of high strength steel wires used in flexible pipelines. Fracture toughness tests were performed to establish the level of stress intensity factor wherein the wires present significant plastic deformation at the crack tip. The effect of tensile overload on fatigue behavior was assessed by fatigue crack growth testing under constant ΔK control and different overload ratios with two different load ratios. The outcomes show that the application of controlled overloads provides crack retardation and increases the fatigue life of the wires more than 31%. This behavior is also evident at stress ratio of 0.5, in spite of the crack closure effect being minimized by increasing the applied mean stress.     

Effects of a single tensile overload on fatigue crack growth in a 316L steel

The aim of this study was to investigate the effects of a single tensile overload on subsequent fatigue crack growth in a 316L stainless steel. Fatigue tests were conducted under the plane stress condition, and further supplemented with compliance measurements and field emission scanning electron microscopy (FESEM) observations. Effects of a tensile overload, e.g. initial acceleration and subsequent retardation of fatigue crack growth, were explained and quantified by FESEM and compliance measurements. The FESEM observations suggest that the initial crack growth acceleration stems from void and quasi-cleavage fracture within the fatigue damage zone in the vicinity of the crack tip. Systematic compliance measurements taken during fatigue crack growth suggest that the overall crack growth retardation is related to strain hardening and residual compressive stress produced by the plastic deformation associated with the tensile overload.     

CRACK CLOSURE AND PLASTIC ZONE SIZES IN FATIGUE

Abstract— An elastic-plastic finite element simulation of growing fatigue cracks which accounts for plasticity-induced crack closure is used to study the size of the forward and reversed plastic zones at the crack tip. Forward plastic zone widths for fatigue cracks and stationary, monotonically loaded cracks are compared and found to be similar. The width of the forward plastic zone at the tip of a fatigue crack is not significantly influenced by closure. The traditional Irwin-Rice estimate for crack tip plastic zone size in plane stress is found to be generally consistent with the finite element results. The width of the reversed plastic zone at the tip of a growing fatigue crack in plane stress is found to be considerably less than one-fourth the size of the forward plastic zone, the traditional Rice estimate. This decrease appears to be due to fatigue crack closure. A simple model is developed which permits estimation of the reversed plastic zone size for any stress ratio from information about maximum and minimum stresses and the closure stress. The predictions of this model agree closely with plastic zone sizes calculated by the finite element analysis. These observations appear to be consistent with experimental measurements of forward and reversed plastic zones sizes reported in the literature.     

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.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

ON THE OVERLOAD INDUCED FATIGUE CRACK PROPAGATION BEHAVIOR IN ALUMINUM AND STEEL ALLOYS

The overload induced fatigue crack propagation behavior of several aluminum and steel alloys was examined as a function of the baseline stress intensity factor range (δ K _b). In order to gain a clearer understanding of the parameters which influence the cyclic delay phenomenon, under both plane strain and plane stress conditions, tests were conducted at δ K _b values ranging from the near threshold regime to high δ K levels approaching fast fracture. Large amounts of overload induced cyclic delay (˜100,000 cycles) were observed at both high and low δ K levels (provided the plastic zone size/thickness ratio and plastic zone size/grain size ratio approached unity, respectively) with significantly less delay occurring at intermediate δ K values. All alloys examined exhibited this type of delay behavior which can be described by a "U-shaped" plot. The delay phenomenon at high δ K _b levels under plane stress conditions was attributed to increased crack closure associated with large tensile displacements in the wake of the advancing crack. At low δ K _b levels increasing cyclic delay was attributed to an increased effective overload ratio as δ K approached δ K _th.     

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

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

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.