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.     

Plane strain crack closure and cyclic hardening

This study is focused on the understanding of the mechanical effects of cyclic hardening on crack tip plasticity and on plasticity-induced crack closure. Various finite element analyses were conducted using abaqus. Cyclic hardening is found to affect both crack closure and the shape of the plastic zone at the crack tip. Crack growth modelling in plane strain conditions in a cyclically hardening material is discussed. An empirical formula is provided which allows the calculation of the crack tip plastic zone size under plane strain conditions in a cyclically hardening material. The effects of overloads are also examined.     

Overload effects in fatigue crack growth by crack-tip blunting

A basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In the present paper, the effect of an overload in one of the cycles is studied based on this mechanism. In a standard numerical analysis accounting for finite strain, it is not possible to follow the blunting/re-sharpening process during many cycles, as severe mesh distortion at the crack-tip results from the huge geometry changes developing during the cyclic plastic straining. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using remeshing at several stages of the plastic deformation. Crack growth results for purely cyclic loading are compared with predictions for cases where an overload is applied, and it is shown how crack growth slows down after the overload. Different load amplitudes, and an overload at different cycle numbers are considered.     

A numerical study of fatigue crack closure induced by plasticity

Crack closure delays the intrinsic mechanisms responsible for crack growth, therefore, it must be considered in fatigue crack growth modelling. The objective of this work is to develop a numerical procedure to predict crack closure induced by plasticity. First the crack closure was experimentally measured on M(T) 6082‐T6 aluminium alloy specimens of 3 mm thickness. A pin microgauge was used with the compliance technique. Then different parameters of the numerical procedure were analysed, namely the finite element mesh and the crack propagation scheme. The size of crack‐tip elements has an important influence and it is recommended to be of the same order of cyclic plastic zone. Crack‐opening levels only 10% lower than experimental results were obtained considering kinematic hardening and two load cycles in each increment.     

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.     

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 crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

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.     

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。     

Modelling and measurement of crack closure and crack growth following overloads and underloads

Ignoring crack growth retardation following overloads can result in overly conservative life predictions in structures subjected to variable amplitude fatigue loading. Crack closure is believed to contribute to the crack growth retardation, although the specific closure mechanism is debatable. The delay period and corresponding crack growth rate transients following overload and overload/underload cycles were systematically measured as a function of load ratio (R) and overload magnitude. These responses are correlated in terms of the local “driving force” for crack growth, i.e. the effective stress intensity factor range (ΔK_eff). Experimental results are compared with the predictions of a Dugdale-type crack closure model and improvements in the model are suggested.     

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.     

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.     

ELECTRICAL RESISTANCE VARIATIONS ACROSS A GROWING FATIGUE CRACK AS A FUNCTION OF THE LOAD CYCLE

Greater understanding of fatigue crack growth requires detailed measurements of crack tip plastic flow. A high resolution crack length measurement system based on the electrical potential method has been used to measure the variations in electrical resistance of specimens containing growing fatigue cracks. Crack growth increments caused by individual load cycles could be resolved down to a size of 0.1 μm. The electrical resistance has been found to vary cyclically as a function of the applied load. These variations are consistent with Bowles' observations that the crack initially grows with a very sharp crack tip followed by plastic blunting which is resharpened during unloading. Crack closure effects could be observed in the results generated from tests conducted with stress ratios of 0 and 0.1, but not for a test with a stress ratio of 0.5.     

Delamination and fatigue crack growth behavior in Fiber Metal Laminates (Glare) under single overloads

Delamination extension and fatigue crack growth behaviors under single overloads were investigated for GLARE 2-2/1-0.3 with fiber direction of 00/00. The results indicate that the stress intensity factor at the crack tip in metal layer while overload applied, K_tip,ol is a key controlling variable which influences fatigue crack growth and delamination behaviors. When K_tip,ol becomes bigger and exceeds a critical value, an obvious kink in the delamination shape is observed nearby the location of overload applied. Crack growth rate after application of overload could not return to its original level even the crack grows beyond the overload plastic zone. The reduction magnitude of the crack growth rate becomes bigger with the overload ratio (intrinsically K_tip,ol) increasing. These new results for the crack growth behavior have never been reported before, which can be well explained by the delamination extension behavior observed after overload applied.     

Experimental and numerical investigations on the influence of the loading direction on the fatigue crack growth

During a service loading fatigue cracks can be subjected to a mixed mode loading if, due to the alteration of the loading direction, the basic crack modes (Modes I, II and III) are combined. An alteration of the loading direction, e.g. can occur either occasionally paired with an overload (mixed mode overload) or permanently in terms of a mixed mode block loading as a combination of normal and shear stresses.Within the scope of this paper, experimental investigations on both mixed mode overloads, which are interspersed into a Mode I baseline level loading, and mixed mode block loadings are presented. The experimental investigations show that the retardation effect decreases with an increasing amount of Mode II of the overload. Due to the block loading, the fatigue crack growth rate is retarded as well, and the crack is also deflected. The kinking angle depends on the fraction of shear stresses. Furthermore, a detailed elastic–plastic finite element analysis of the fatigue crack growth after mixed mode overloads is presented in order to understand the mechanism of the load interaction effects. By such numerical simulations, it can be shown that, due to mixed mode overloads, plastic deformations occur, which on the one hand reduce the near-tip closure and on the other hand cause a far-field closure. Also the stress distribution before and after the crack tip changes. A mixed mode overload causes lower closure and the crack tip deformations become asymmetrical, which is a reason for the smaller retardation effect of a mixed mode overload.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

Fatigue crack closure after overload

The fatigue crack closure after overload was measured by small foil strain gages. The effect of overload on crack closure stress and crack propagation rate was observed to extend over a range several times larger than the overload plastic zone. Analysis of experimental data showed that the extra amount of plastic deformation introduced by the overload was the controlling factor. A relationshp between crack closure stress and crack length in the affected zone was found, and the amount of plastic deformation by the overload was estimated. This estimate was further confirmed by analysis of the crack closure pictures.     

FGH95粉末高温合金裂纹闭合效应及裂纹扩展特性研究

采用有限元方法研究FGH95粉末高温合金标准紧凑拉伸(CT)试样的塑性诱发裂纹闭合效应,分析裂纹面上的应力分布,并考察本构模型,网格密度及应力比对裂纹闭合效应的影响,进而建立考虑裂纹闭合效应下CT试样裂纹扩展寿命分析模型,并进行寿命预测。结果表明:理想弹塑性模型下的裂纹闭合效应对网格单元的敏感性比多线性随动强化模型高;裂纹尖端塑性区内网格数达到20时,裂纹闭合趋于稳定;应力比增加裂纹闭合效应减小,当应力比达到0.5时裂纹闭合效应消失。修正的寿命预测模型对CT试样的预测精度比传统模型更高。     

Large crack tip deformations and plastic crack advance during fatigue

Finite-deformation elastoplastic analysis of a crack subjected to mode I cyclic loading under small scale yielding was performed. The influence of the load range, load ratio and overload on the crack tip deformations is presented. Cyclic crack tip opening displacements agreed with predictions of simpler models, where available. Crack closure was not detected. Plastic crack advance was evidenced. Its rate per cycle reproduced common trends of the fatigue cracking dependence on loading range and overload.