CRACK CLOSURE IN SMALL FATIGUE CRACKS—A COMPARISON OF FINITE ELEMENT PREDICTIONS WITH IN-SITU SCANNING ELECTRON MICROSCOPE MEASUREMENTS

Abstract— A three dimensional, elastic-plastic, finite element analysis of fatigue crack growth and plasticity-induced crack closure has been performed for a range of small, semi-circular cracks. Predicted crack opening displacements have been compared with data obtained from in-situ SEM measurements for a coarse-grained aluminium alloy 2024-T351. The magnitude of fatigue crack closure measured from in-situ SEM measurements was consistently higher than that predicted from the finite element analysis. It is deduced that the higher closure stresses obtained from in-situ SEM measurements are due to the contact of asperities on the fatigue crack surfaces. A simple mathematical model is suggested to describe the fatigue crack closure stress caused by the combination of both a plastic wake and asperities on the fatigue crack surfaces. The predicted fatigue crack closure stresses and their dependence on crack size are consistent with experimental measurement.     

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.     

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.     

FINITE ELEMENT ANALYSIS OF CLOSURE BEHAVIOUR OF FATIGUE CRACKS IN RESIDUAL STRESS FIELDS

An elastic-plastic finite element analysis with high order elements is performed to examine closure behaviour of fatigue. cracks in residua1 stress fieids and the numerical results are then compared with experimental results. The finite element analysis, performed under plane stress using 8-node isoparametric elements, can predict fatigue crack closure behaviour through residual stress fields very well. The crack opening and closing behaviour through a compressive residual stress field is found to be complicated and influenced by the applied load magnitude and the location of the crack tip. Three different types of crack opening behaviour, namely, normal, unsymmetric partial and symmetric partial crack opening behaviour are observed through a compressive residual stress field. The partial crack opening stress intensity factor including the partial crack opening effect is recommended for the prediction of fatigue crack growth through a compressive residual stress field.     

加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟

采用不同应力比条件下的16MnR钢紧凑拉伸试样,设计了三种有限元分析模型,即不考虑加载历史效应的静态裂纹扩展模型,同时考虑加载历史和裂纹闭合的动态裂纹扩展模型以及仅考虑加载历史的伪动态裂纹扩展模型,对疲劳裂纹闭合过程、裂纹尖端的应力-应变迟滞环、疲劳损伤和裂纹扩展速率进行了数值模拟与分析,进而着重探讨了加载历史和裂纹闭合影响疲劳裂纹扩展行为的交互作用机制。结果表明:对于同类分析模型,应力比越大越不容易产生裂纹闭合;而在应力比相同的情况下,加载历史引起的残余压应力对裂纹闭合有明显的促进作用。裂纹闭合效应阻碍了平均应力的松弛,减小了裂纹尖端附近的应力-应变场强度、疲劳损伤和裂纹扩展速率,而加载历史引起的残余压应力则加快了平均应力的松弛和抑制了棘轮效应。与实验结果比较发现,只有同时考虑了裂纹闭合效应和加载历史影响的动态裂纹扩展模型,才能对疲劳裂纹扩展行为进行准确、定量的模拟。     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Prediction of fatigue crack growth rates using crack closure finite element analysis

A three-dimensional finite element fatigue crack closure model of a corner crack and of a through thickness crack has been developed to evaluate the range of effective stress intensity factor from the distribution of the range of stress ahead of the crack tip. The corresponding fatigue crack growth rate was evaluated from a Paris law fit to experimental data from high stress ratio tests. The point of origin for the range of stress distribution was adjusted in accordance with Irwin’s plastic zone correction. Encouraging comparisons of finite element predictions of fatigue crack growth rate incorporating closure effects with experimental measurements were obtained.     

Analytical and numerical modelling of plasticity-induced crack closure in cold-expanded holes

The aim of this research was the development of an analytical model for plasticity-induced fatigue crack closure for cold expanded holes. This paper extends Nowell's plane stress model of plasticity-induced crack closure for a plate with a circular hole and two radial symmetric cracks. The possibility of existence of an initial residual stress field is also taken into account. This model has potential to be applied to other cracked geometries and arbitrary residual stress fields, although the paper is focused on the study of cold-expanded holes. Hole cold-expansion is widely used in aircraft industry, for improving the fatigue performance of rivet holes by delaying fatigue crack propagation. This paper shows that the residual stress field due to cold-expansion has a strong influence on the closure behaviour and therefore on fatigue crack propagation. The analytical model developed, was compared with finite element analyses of plasticity-induced crack closure with and without residual stresses. Finally, the model was used to predict fatigue lives for some experiments recently reported in the literature for fatigue crack propagation from cold-expanded holes. Predicted fatigue lives correlate well with experimental data.     

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.     

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.     

Ermüdungsrißwachstum in Kerben

Fatigue Crack Growth in Notches Nowadays it is wellknown that an important part of the fatigue life time, usually differenciated in crack initiation and crack growth, is often controlled by fatigue crack growth of cracks in notches. An elastic-plastic on the J-integral based crack growth model considering the crack opening and closure phenomenon will be described to determine crack growth of cracks in notches between crack initiation and failure. Experimental results and finite element analysis were used to verify the developed model.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

Prediction on fatigue life of U‐notched PMMA plate

In this paper, fatigue life prediction of U‐notched polymethyl methacrylate (PMMA) plate is numerically investigated based on the combination of fatigue damage mechanism and fatigue crack propagation mechanism. First, strength and stiffness degeneration criterions during the fatigue process are established on the basis of nonlinear progressive damage evolution, and the fatigue crack initiation life is estimated. Second, fatigue crack propagation phase is analysed through virtual crack closure technique. The fatigue crack propagation life before totally fracture is also predicted. Finally, finite element models of PMMA plate weakened by lateral symmetric U‐notch are built up using ABAQUS, and the total fatigue life of notched plate is calculated by combining the crack initiation life with the crack propagation life. These results will play an important role for evaluating the fatigue life of U‐notched PMMA plate.     

DETERMINATION OF THE MOST APPROPRIATE MESH SIZE FOR A 2-D FINITE ELEMENT ANALYSIS OF FATIGUE CRACK CLOSURE BEHAVIOUR

Abstract— A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to examine closure behaviour of fatigue cracks, giving special attention to the determination of the most appropriate mesh sizes. It is found that a smaller mesh size does not always give more accurate simulation results in the fatigue crack closure analysis, unlike a conventional structural analysis. A unique, most-appropriate mesh size exists for a given loading condition that will provide numerical results which agree well with experimental data. The most appropriate mesh size can be determined approximately in terms of the theoretical reversed plastic zone size. In particular, the ratio of the most appropriate mesh size to the theoretical reversed plastic zone size is nearly constant for a given stress ratio in the so-called crack-length-fixed method proposed in this study. By using the concept of the most appropriate mesh size, the finite element analysis can predict fatigue crack closure behaviour very well.     

On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems

The accurate calculation of the opening and closing stresses is an important issue in fatigue crack closure problems, since the effective driving force for crack growth is dependent on accurate calculation of the opening stresses. Often numerical methods such as finite element analysis are used to model plasticity-induced fatigue crack closure problems. There are many difficulties associated with this modelling work, since the results may depend on a wide range of parameters such as mesh refinement, node release scheme and modelling of the contact between the crack faces etc. Even after a great deal of modelling work some arbitrariness is evident in the technique used for assessing the opening and closing stresses. A number of techniques have been proposed in the literature and the current work will assess and compare these approaches. The node displacement method, the change in stresses at the crack tip, and the weight function technique will each be applied to a finite element model of a plane stress crack for a range of stress levels. In addition, an analytical model for plasticity-induced crack closure under plane stress conditions will be used to discuss the accuracy of these techniques. The investigation shows that all these techniques are equivalent provided that the displacement and stress at the crack tip are assessed accurately. However, it will be shown that use of the tensile tip stress method, proposed by some authors for assessing the closing stress, is erroneous.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

A study of the relationship between variable level fatigue crack growth and the cyclic constitutive behaviour of steel

Sensitivity of fatigue crack growth to the material behaviour was studied in two previous numerical studies (Pommier S. Plane strain crack closure and cyclic hardening. Eng Fract Mech, in press; Pommier S, Bompard P. Bauschinger effect of alloys and plasticity-induced crack-closure: a finite element analysis. Fatigue Fract Eng Mater Struct 2000;23:129–39). It was shown, in particular, that material hardening induces a rotation of the crack tip plastic zone from the front to the back of the crack, which enhances the effects of crack closure (Pommier S. Plane strain crack closure and cyclic hardening. Eng Fract Mech, in press). The type of hardening is also of key importance: Isotropic hardening is found to lower the effective part of the fatigue cycle, while kinematic hardening (Pommier S, Bompard P. Bauschinger effect of alloys and plasticity-induced crack-closure: a finite element analysis. Fatigue Fract Eng Mater Struct 2000;23:129–39) is found to increase it. This study is devoted to check the validity of those numerical results in a 0.4% C carbon steel, which displays a high Bauschinger effect and a moderate amount of isotropic hardening. The comparison between numerical results and experiments is satisfactory.     

Finite element visualization of fatigue crack closure in plane stress and plane strain

Elastic-plastic finite element simulations of growing fatigue cracks in both plane stress and plane strain are used as an aid to visualization and analysis of the crack closure phenomenon. Residual stress and strain fields near the crack tip are depicted by both color fringe plots and x-y graphs. Development of the residual plastic stretch in the wake of a growing plane stress fatigue crack is shown to be associated with the transfer of material from the thickness direction to the axial direction. Finite element analyses indicate that crack closure does occur under pure plane strain conditions. The development of the residual plastic stretch in plane strain is shown to be associated with the transfer of material from the in-plane transverse direction to the axial direction. This in-plane contraction also leads to the generation of complex residual stress fields. The total length of closed crack at minimum load in plane strain is shown to be a small fraction of the total crack length, especially for positive stress ratios. This suggests that experimental measurement of plane strain closure would be extremely difficult, and may explain why some investigators have concluded that closure does not occur in plane strain.     

On damage accumulations in the cyclic cohesive zone model for XFEM analysis of mixed-mode fatigue crack growth

Predicting mixed-mode fatigue crack propagation is an important and troublesome issue in structure assessment for decades. In the present paper an extended finite element method (XFEM) combined with a new cyclic cohesive zone model (CCZM) is introduced for simulating fatigue crack propagation under mixed-mode loading conditions, which has been implemented in the commercial general purpose software ABAQUS. The algorithm allows introducing a new crack surface at arbitrary locations and directions in a finite element mesh, without re-meshing. The cyclic cohesive zone model is based on the known S–N curves and Goodman diagram for metallic materials and validated by uniaxial tension results. Furthermore, the sensitivity of the model parameter is investigated for mixed-mode fatigue. The virtual crack closure technique has been extended to the cohesive zone model and proposed to calculate the energy release rate for the generalized Paris’ law. Finally, the crack propagation rate and direction under mixed-mode fatigue loading conditions are studied.