A numerical analysis of the mechanisms behind plasticity induced crack closure: Application to variable amplitude loadings

The effect of loading parameters on fatigue crack growth has been explained using the concept of crack closure. Plasticity induced crack closure (PICC) is linked to the crack tip plastic deformation, which becomes residual with crack propagation. The objective here is to identify the main mechanisms behind PICC, and for that different loading cases were considered namely overloads and load blocks. An analytical model was used to isolate the effect of residual plastic deformation on PICC, however significant differences were obtained relatively to finite element results. A second mechanism, which is crack tip blunting, was used to explain the transient behaviour observed after overloads and load blocks. For overloads and low–high load sequences there is a sudden increase of crack tip blunting with load increase which explains the sudden decrease of crack opening level. For high–low load sequences there is a sudden decrease of crack tip blunting which enhances the effect of residual plastic wake. Finally, the partial closure concept was tested looking to non-linear crack tip parameters but no evidences of Donald’s effect were found for the material studied.     

Plastic mismatch effect on plasticity induced crack closure: Fatigue crack propagation perpendicularly across a plastically mismatched interface

In the present work, comprehensive investigation of both theoretical analysis and numerical simulation was carried out to investigate the plastic mismatch effect on plasticity induced crack closure (PICC) behavior and effective fatigue crack tip driving force. During the process of crack tip approaching interface, crack tip load and crack tip load ratio will change, resulting in the change of PICC degree. When the crack propagates towards higher strength side, K_op/K_max increases; when the crack propagates towards lower strength side, K_op/K_max decreases firstly and then increases. The two mechanisms of “interface plastic mismatch effect on nominal fatigue crack tip driving force” and “interface plastic mismatch effect on PICC degree” were compared. The second mechanism must be considered when building crack tip driving force model for describing fatigue crack crossing plastically mismatched interface, because it is more physically factual and maybe more important than the first mechanism.     

Fatigue crack closure: A myth or a misconception?

In this paper, we have extended our previous study on fatigue crack closure to examine the phenomenon of crack opening displacement (COD) and its impact on the crack tip fields in both 2D and 3D specimen geometries using full‐field experimental measurements and integrated finite element modelling. Digital image correlation (DIC) and digital volume correlation (DVC) were used to measure the near‐tip material responses on the surfaces (DIC) and the interior (DVC) of the specimens. Materials with elastic‐plastic and large plastic characteristics were chosen for the study, where plasticity‐induced premature contact between the crack flanks is known to occur. Displacement maps around the cracks were obtained using DIC and DVC at selected load increments and were introduced as boundary conditions into the finite element (FE) models to obtain the “effective” crack driving force in terms of J‐integral, and the results were compared with those “nominal” from the standard FE analysis. Both visual observation and compliance curves were used to determine the “crack opening” levels; whilst the impacts of the crack opening on the crack driving force J and the normal strains ahead of the crack tip were evaluated in 2D and 3D. The results from the study indicate that, crack closure, although clearly identifiable in the compliance curves, does not appear to impact on global crack driving force, such as J‐integral, or strains ahead of the crack tip; hence, it may well be a misconception.     

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.     

疲劳裂纹扩展中裂纹尖端应变变化的详细考察

传统的ASTM2%偏差法和卸载弹性法是以柔度轨迹的线性区段确定开闭口载荷(Pop和Pcl),往往因人工误差导致结果相差很大.本文注重裂纹尖端塑性变形带给柔度变化的物理意义,描述了一个载荷循环下柔度变化与裂纹开闭口以及弹塑性行为的关系.采用自行开发的高精度局部柔度测量法,针对结构钢进行了疲劳试验,记录了裂纹尖端应变与载荷关系的系列迟滞回线,并以微分法定量求出迟滞回线上的特征载荷.根据试验考察结果,分析了文献中几种疲劳裂纹扩展参量的关系.结果表明,ΔKRPG比ΔKcl和ΔKop更适合作为裂纹扩展驱动力参量.     

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.     

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

The mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of K_max. A new empirical model is therefore proposed here, dependent on K_max and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔK_eff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.     

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

The influence of cross-sectional thickness on fatigue crack growth

For thin structures, fatigue crack growth rates may vary with the structure's thickness for a given stress intensity factor range. This effect is mainly due to the change in the nature of the plastic deformation when the plastic zone size becomes comparable with, or greater than, the cross-sectional thickness. Variations in the constraint affect both the crack tip plastic blunting behaviour as well as the fatigue crack closure level. Approximate expressions are constructed for the constraint factor based on asymptotic values and numerical results, which are shown to correlate well with finite element results. It is demonstrated that the present results not only permit predictions of the specimen thickness effects on fatigue crack propagation under spectrum loading, but also eliminate the need to determine the constraint factor by curve-fitting crack growth data.     

A numerical study of plasticity induced crack closure under plane strain conditions

The level of plasticity induced crack closure (PICC) is greatly affected by stress state. Under plane strain conditions, however, the level and even the existence of PICC still are controversial. The objective here is to study the influence of the main numerical parameters on plane strain PICC, namely the total crack propagation, the number of load cycles between crack increments, the finite element mesh and the parameter used to quantify PICC. The PICC predictions were included in a parallel numerical study of crack propagation, in order to quantify the impact of plane strain values on fatigue life. The results indicate that literature may be overestimating plane strain PICC due to incorrect numerical parameters. The number of load cycles usually considered is unrealistically small, and its increase was found to vanish crack closure, particularly for kinematic hardening. This effect was linked to the ratcheting effect observed at the crack tip. The total crack increment, Δa, must be large enough to obtain stabilized PICC values, but this may imply a huge numerical effort particularly for 3D models. The size of crack tip plastic zone may be overestimated in literature, which means that the meshes used may be too large. Additionally, the crack propagation study showed that the plane strain PICC has usually a dominant effect on fatigue life, and plane stress PICC is only relevant for relatively thin geometries.     

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.     

Methods for crack opening load and crack tip shielding determination: a review

In this paper a review of the literature on crack closure/opening load and crack tip shielding effects determination methods is presented. Commonly used ‘subjective’ (visual) and ‘non‐subjective’ approaches have been included. Procedures associated with the determination of an effective crack driving force for both Elber type and that of partial (or incremental) crack closure models have been covered. Comparison among different methods of analyses based on compliance and fatigue crack growth rate measurements is discussed together with their implications and difficulties in fatigue crack growth correlations.     

A cumulative model of fatigue crack growth and the crack closure effect

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated using the local stress/strain at the crack tip by assuming that a small highly strained area $\text{x}{}^1$, existing at the crack tip, is responsible for the fatigue crack growth, and that the fatigue crack growth may be regarded as the cumulation of successive crack re-initiations over a distance $\text{x}{}^1$. It is shown that crack closure can be modelled using the effective contact zone g behind the crack tip. The model allows the fatigue crack growth rate over the near threshold and linear ranges of the general da/dN versus ΔK curve to be calculated. The fatigue crack growth retardation due to overload and fatigue crack arrest can also be analysed in terms of g and $\text{x}{}^1$.Calculated fatigue crack growth rates are compared with experimental ones for low and high strength steel.     

Determination of displacements around fatigue cracks using image analysis of in‐situ scanning electron microscope images

A technique to in‐situ measure the displacements in the vicinity of the crack tip during fatigue crack propagation has been developed. High‐resolution images of the crack tip were taken continuously throughout the fatigue load cycles with a scanning electron microscope (SEM), and an image analysis program was used to determine the displacements at different positions with respect to the crack tip. The displacements were then used to determine crack shapes and compliance curves. The measured crack shapes show a general √r dependence versus the distance to the crack tip. However, close to the crack tip the crack shape is clearly affected by plastic deformation, even in cases when small scale yielding prevails. The compliance curve measurements close to the crack tip can be used to determine the global stress level when the crack surfaces are separated, so that the exact opening and closure stresses can be determined.     

Influence of through-thickness crack shape on plasticity induced crack closure

In most of the previous three‐dimensional (3D) numerical studies of plasticity induced crack closure (PICC), ideal shapes have been assumed for the cracks. The aim of present paper is to study the effect of crack shape on PICC. With this objective a 3D numerical model was developed to predict PICC in middle‐tension (MT) specimens with different thicknesses and crack shapes. The radial size of crack tip elements and the stabilization of closure level were studied to ensure the quality of numerical predictions. Simultaneously, an independent numerical model was developed to predict crack shape evolution, stable crack shapes and corresponding K distributions. Crack closure was found to produce a significant tunnelling effect, with maximum values of ΔK and K_max at the surface. The curved crack presented significant plastic deformation near the free surface which has a high impact on the computation time, compared to the straight crack. The modification of ΔK and K_max with crack shape produced a variation of 38% in opening values at the interior positions, but relatively small variations at the surface. Considering the great influence of crack shape on PICC, it is fundamental to model realistic crack shapes.     

Local crack plasticity and its influences on the global elastic stress field

This paper presents the background and development of a novel ‘plastic inclusion’ approach for dealing with the local plasticity which occurs at the tip of a growing fatigue crack. Localised plasticity arises from crack growth mechanisms and essentially blunts the crack, creates a reversed cyclic plastic zone, and induces shear along the crack flanks, along with the possible generation of wake contact stresses which act on the applied elastic stress field at the boundary of the elastic–plastic enclave surrounding the crack. The paper outlines the development of a meso-scale model of the elastic stress field around a growing crack that explicitly incorporates these interaction effects. The outcome is a modified crack tip stress intensity factor that includes some aspects of the magnitude of plastic wake-induced crack tip shielding and which the authors propose has the potential to help resolve some long-standing controversies associated with plasticity-induced closure. A full-field approach is developed for stress using photoelasticity and also for displacement using digital image correlation.     

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.     

Investigation of fatigue crack closure using multiscale image correlation experiments

Two full-field macroscale methods are introduced for estimating fatigue crack opening levels based on digital image correlation (DIC) displacement measurements near the crack tip. Crack opening levels from these two full-field methods are compared to results from a third (microscale) method that directly measures opening of the crack flanks immediately behind the crack tip using two-point DIC displacement gages. Of the two full-field methods, the first one measures effective stress intensity factors through the displacement field (over a wide region behind and ahead of the crack tip). This method reveals crack opening levels comparable to the limiting values (crack opening levels far from the crack tip) from the third method (microscale). The second full-field method involves a compliance offset measurement based on displacements obtained near the crack tip. This method delivers results comparable to crack tip opening levels from the microscale two-point method. The results of these experiments point to a normalized crack tip opening level of 0.35 for R ∼ 0 loading in grade 2 titanium. This opening level was found at low and intermediate ΔK levels. It is shown that the second full-field macroscale method indicates crack opening levels comparable to surface crack tip opening levels (corresponding to unzipping of the entire crack). This indicates that effective stress intensity factors determined from full-field displacements could be used to predict crack opening levels.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.