Application of the distributed dislocation technique for calculating cyclic crack tip plasticity effects

This paper describes a method for modelling cyclic crack tip plasticity effects based on the distributed dislocation technique (DDT). A strip‐yield model is utilised to allow for the determination of the crack opening displacement, size of the plastic zones and in the case of a fatigue crack, the wake of plasticity. The DDT can be easily implemented for a wide range of cracked geometries with reliable control over the accuracy and convergence. Thickness effects can also be incorporated through a recently obtained solution for an edge dislocation in an infinite plate of finite thickness. Results for finite length cracks that have had limited growth, such that there is no plastic wake, are presented for a range of applied loads and R‐ratios. Further results are provided for a steady‐state fatigue crack in a plate of finite thickness. The present results are compared with analytical solutions and they show an excellent agreement.     

Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure

The understanding of fatigue crack closure has been proved to be a challenging and controversial topic among the fatigue community over the last three decades. The effect of the specimen (or component) thickness has been shown to have a significant effect on closure behaviour and this seems to be related to the relative size of the plastic zone. Real cracks are inherently three-dimensional; plane stress-like behaviour is found close to the region where the crack front intersects the free surface, whereas most of the crack front will experience something close to plane strain. The aim of the present work is to investigate the influence of specimen thickness on closure behaviour (both close to and remote from the surface) and on fatigue crack propagation. The paper will present results from a simple experimental program, which consists of fatigue testing CT specimens with different thicknesses. Fatigue crack propagation is measured optically. Crack closure is assessed using traditional compliance techniques (clip gauge and back face strain gauge) and Digital Image Correlation methods. Experimental results are compared with two and three-dimensional simulations of plasticity-induced fatigue crack closure. The implications of thickness effects for predicting the propagation of three-dimensional fatigue cracks are discussed.     

Simulation of plasticity-induced fatigue crack closure in part-through cracked geometries using finite element analysis

The part-through semi-elliptical surface flaw is commonly encountered in engineering practice. Proper characterization of plasticity-induced crack closure is necessary to predict both flaw growth and flaw shape evolution under cyclic loading. Three-dimensional elastic-plastic finite element analyses are used to model the plasticity-induced closure developed along the surface flaw crack front, and the subsequent crack opening behavior under constant amplitude loading. Resulting crack opening stresses are compared with results from a strip-yield model and with experimentally measured values reported in the literature. It was found that the computed values were larger than those measured.     

Bauschinger effect of alloys and plasticity-induced crack closure: a finite element analysis

The effect of overloads, underloads and stress ratio on plasticity-induced crack opening level is examined for different 'model' materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results.     

Numerical modelling of plasticity-induced crack closure for interfacial cracks in bi-material specimens

This paper reports the results of a fairly detailed finite element study which modelled the plasticity-induced crack closure (PICC) behaviour of interfacial cracks in various bi-material specimens. In particular, the fatigue crack-opening stress (S_op) level and the crack-tip deformation fields (Modes I and II) have been assessed for a number of different material combinations, chosen so as to throw some light on the effects of modulus of rigidity and strength level of the alloy on PICC. The material combinations included specimens based on aluminium alloy steel, medium strength-high strength steel, and aluminium or steel specimens coated with a rigid ceramic. Results obtained indicate that stabilised values of closure, S_op, can be interpreted as supporting the hypothesis that it is the elastic constraint on, and deformability of, the plastic zone surrounding a crack that are the major contributors to PICC, rather than any permanent ‘stretch’ associated with crack growth. Positive Mode II slip of the upper crack face over the lower face (i.e. the upper surface moving over the lower surface towards the crack-tip) can elevate S_op level, while a negative slip (i.e. the upper surface moving over the lower surface away from the crack-tip) causes a reduction in its value.     

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.     

Utilization of partial crack closure for fatigue crack growth modeling

Load ratio effects are of prime concern when modeling of fatigue crack growth (FCG) rate is required as a prerequisite for a reliable life prediction. The majority of research efforts regarding the load ratio effects are based on Elber's ΔK_eff approach. However, there are intrinsic difficulties encountered with its consistent application to FCG prediction. In this paper two popular crack-growth-life prediction codes FASTRAN and AFGROW are modified utilizing the enhanced partial crack closure model. The proposed utilization aggregates apparent closure mechanisms involved and demonstrates a better correlation and a significant scatter reduction of FCG data taken from literature, especially in the near-threshold region.     

Crack growth retardation following the application of an overload cycle using a strip-yield model

Experiments have shown that the application of an overload cycle can act to retard crack growth and even potentially lead to crack arrest. This paper describes a new method for investigating fatigue crack growth after the application of an overload cycle under plane stress conditions. The developed method is based on the concept of plasticity-induced crack closure and utilises the distributed dislocation technique and a modified strip-yield model. The present results are compared to previous experimental data for several materials. A good agreement is found, with the predictions showing the same trends in the various stages of post-overload crack growth.     

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.     

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.     

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.     

Influence of minimum element size to determine crack closure stress by the finite element method

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results.In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.     

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique

We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, Δ, used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several—seemingly different—suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a Δ-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for Δ-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter ε.     

Finite element analysis of plasticity-induced fatigue crack closure: an overview

Finite element analysis is perhaps the most commonly used numerical method to model plasticity-induced fatigue crack closure. The state-of-the-art is reviewed and a comprehensive overview is presented, summarizing issues which must be considered and emphasizing potential difficulties. These include mesh refinement level, crack advancement schemes, crack shape evolution, geometry effects, and crack opening value assessment techniques.     

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

Fatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.     

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.     

The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and ΔK_eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P_max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation.In this paper, instead of working with the same negative R ratio (R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P_max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied (Ck45-cyclic hardening; Ti6Al4V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC).In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and ΔK_eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like da/dN−ΔK or da/dN−ΔK (K_max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.     

On the number of overload-induced delay cycles as a function of thickness

In this paper, a brief review of the experimental facts associated with the crack growth delay period following a tensile overload is given. In the retardation process, crack closure is considered to play a dominant role. A scenario for the two crack opening processes which develop as a fatigue crack penetrates the overload plastic zone is presented. This scenario deals with the effect of specimen thickness on the crack opening processes. Consideration is given to the delay distance and to the minimum crack growth rate. A method of analysis for the determination of the number of delay cycles following an overload is then developed. Finally the method of analysis is used to compare with recent experimental results.     

基于虚拟裂纹闭合技术的应变能释放率分析

基于虚拟裂纹闭合技术(VCCT),建立了复合材料层合板层间裂纹尖端的应变能释放率(SERR)三维有限元计算模型。该模型考虑了裂纹尖端大转动和离散单元形状变化对应变能释放率计算的影响,修正了裂纹尖端应变能释放率的计算方法。利用该模型计算了裂纹长度为15 mm和35 mm时纯Ⅰ型和纯Ⅱ型的应变能释放率,纯Ⅰ型应变能释放率分别为 207 J/m2和 253 J/m2;纯Ⅱ型应变能释放率分别为 758 J / m 2和 1040 J / m2;计算值与试验值吻合得很好。同时,该模型计算了混合型不同比值 R=(G_Ⅱ/G_Ⅰ+G_Ⅱ)的长裂纹层合板层间断裂过程的应变能释放率,其中Ⅰ型和Ⅱ型应变能释放率计算值与试验平均值的最大误差为 11.4%,最小误差为 0.4%。该模型能有效计算裂纹尖端的应变能释放率。     

Numerical simulation of plasticity induced fatigue crack opening and closure for autofrettaged intersecting holes

The autofrettage of intersecting holes leads to extremely high compressive residual stress fields. These stresses in combination with the plastic deformations decelerate fatigue cracks initiated at the hole intersection notch. Simulations of plasticity induced crack closure of such cracks are presented based on the strip yield and a finite element model. The strip yield model has been extended to allow for an input of residual stresses coming from elsewhere, e.g. from a finite element calculation or measurements. The calculations are applied for constant as well as variable amplitude loading. The numerical expense of the finite element based modelling for variable amplitude loading is still too high if millions of cycles have to be considered. Therefore, a new approximation method is proposed introducing compensatory load sequences. Simulation results are compared to experimentally determined results showing good agreement. However, the accuracy of crack initiation life estimates has turned out to provide a high potential for further improvement.