An irreversible cohesive zone model for interface fatigue crack growth simulation

Fatigue crack growth (FCG) along an interface is studied. Instead of using the Paris equation, the actual process of material separation during FCG is described by the use of an irreversible constitutive equation for the cyclic interface traction-separation behavior within the cohesive zone model (CZM) approach. In contrast to past development of CZMs, the traction-separation behavior does not follows a predefined path. The model definition, its predicted cyclic material separation behavior and application to a numerical study of interface FCG in double-cantilever beam, end-loaded split and mixed-mode beam specimens are reported.     

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.     

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.     

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.     

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.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

Crack closure and fatigue crack growth near threshold of a metastable austenitic stainless steel

In this paper R-ratio effects on fatigue crack growth near threshold region of a metastable austenitic stainless steel (MASS) in two different conditions, i.e. annealed and cold rolled, is investigated. The authors present two approaches to correlate FCGR data for R = 0.1, 0.3, 0.5, 0.7 and K_max = 23 MPa√m using a two-parameters approach (ΔK, K_max and α in Kujawski’s model) and crack closure model (using Elber’s K_op and in Donald’s ACRn2 approaches). The K_op and ACRn2 were experimentally measured on a single edge tension specimens. The K_op measurements were performed using a modified method and based on ASTM standards. While the two driving force approaches correlate data well in the Paris region, they fail to correlate them in the threshold region. However, this correlation can be improved in the threshold region when a different α value from the Paris region is used. The authors indicated that two different mechanisms operate; one in the Paris region and another in the near threshold. Hence, they proposed to combine the two-parameter and crack closure approaches where ΔK is replaced by ΔK_eff (estimated by a new method proposed in this paper), which is shown to correlate the FCGR data for different stress ratios for annealed steel. The correlation for cold rolled condition shows improvement with the new approach but is not as good as for the annealed one. The author further suggests to modify K_max in the two-parameter approach.     

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.     

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.     

A numerical analysis of constraint effects in fatigue crack growth by use of an irreversible cohesive zone model

The analysis of constraint effects in fatigue crack growth in multi-layer structures is discussed. The process of material separation under cyclic loading is described by a cohesive zone model (CZM) with an irreversible constitutive relationship. The traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. A modified boundary layer model is used in simulations of fatigue crack growth along the centerline crack of the metal layer sandwiched between two elastic substrates. Fatigue crack growth is computed for a series of values of metal layer thickness under constant and variable amplitude loading conditions. The results of the computations demonstrate that certain combinations of load magnitude, layer thickness and material properties results in significant constrain effects in fatigue crack growth. The influence of these constraint effects on fatigue crack growth rates and on crack closure processes is determined. The evolutions of the traction–separation law, the accumulated and current plastic zones, as well as the stress fields during the crack propagation are discussed.     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

Mode I fatigue crack growth reduction mechanisms after a single Mode II load cycle

A single Mode II load cycle, large enough to create residual displacements, decreases the subsequent Mode I crack growth rate. The distance for Mode I crack growth rate to fully recover, i.e., revert to the same da/dN as before Mode II load, is much longer than Mode II plastic zone size. The higher Mode II load, the larger is the reduction in growth rate and the longer the recovery distance. Higher Mode I R-ratio means smaller reduction in growth rate. Above a certain R-ratio, no reduction occurs at all. In the present study it is found that the reduction in growth rate is solely caused by crack closure due to tangential displacement of crack-surface irregularities that induce a surface mismatch between the upper and lower crack faces. The mechanism is called Mode II-induced crack closure. A model based on both analytical and experimental results is developed in order to estimate the degree of Mode II-induced crack closure after a Mode II load.     

基于小波内聚力模型的界面裂纹扩展

利用区间B样条小波良好的局部化性能,将内聚力模型（CZM）引入小波有限元法（WFEM）数值分析中,以区间B样条小波尺度函数作为插值函数,构造小波内聚力界面单元,推导了小波内聚力界面单元刚度矩阵,基于虚拟裂纹闭合技术（VCCT）计算界面裂纹应变能释放率（SERR）,采用β-Κ断裂准则,实现界面裂纹扩展准静态分析。将WFEM和传统有限元法（CFEM） 的SERR数值分析结果与理论解进行比较,结果表明:采用WFEM和CFEM计算的SERR分别为96.60 J/m2 和 101.43 J/m2,2种方法的SERR数值解与理论解相对误差分别为1.85%和3.06%,这明确表明WFEM在计算界面裂纹扩展方面能用较少单元和节点数获得较高的计算精度和效率。在此基础上,探讨了界面裂纹初始长度和双材料弹性模量比对界面裂纹扩展的影响,分析结果表明:界面裂纹尖端等效应力随界面裂纹初始长度的增加而增加;双材料弹性模量比相差越大,界面裂纹越易于扩展,且裂纹扩展长度也越大,因此可通过调节双材料弹性模量比来延缓界面裂纹扩展。      

Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

Fatigue crack propagation in a ductile superalloy at room temperature and extensive cyclic plastic flow

Fatigue crack propagation experiments under both force and displacement control have been performed on the wrought superalloy Haynes 230 at room temperature, using a single edge notched specimen. The force controlled tests are nominally elastic, and the displacement controlled tests have nominally large plastic hysteresis at the beginning of the tests, but saturates towards linear elastic conditions as the crack grows. As some tests are in the large scale yielding regime, a non-linear fracture mechanics approach is used to correlate crack growth rates versus the fracture parameter $\mathrm{\Delta }$J. It is shown that crack closure must be accounted for, to correctly model the crack growth seen in all the tests in a unified manner. For the force controlled small scale yielding tests the Newman crack closure model was used. The Newman equation is however not valid for large nominal cyclic plasticity, instead the crack closure in the displacement controlled tests is extracted from the test data. A good agreement between all tests is shown, when closure is accounted for and effective values of $\mathrm{\Delta }$J are used.     

A multifractal analysis of fatigue crack growth and its application to concrete

As is well-known, strength of materials is influenced by the specimen or structure size. In particular, several experimental campaigns have shown a decrease of the material strength under static or fatigue loading with increasing structure size, and some theoretical arguments have been proposed to interpret such a phenomenon. As far as fatigue crack growth is concerned, limited information on size effect is available in the literature, particularly for so-called quasi-brittle materials like concrete. In the present paper, by exploiting concepts of fractal geometry, some definitions of fracture energy and stress intensity factor based on physical dimensions different from the classical ones are discussed. A multifractal size-dependent fatigue crack growth law (expressing crack growth rate against stress intensity factor range) is proposed and used to interpret relevant experimental data related to concrete.     

Texture effect on fatigue crack propagation in aluminium alloys: an overview

Texture or grain orientation was of crucial importance to fatigue crack propagation (FCP) in aluminium alloys due to boundary character between neighbouring grains and crack closure effect. The current understanding of the relationship among texture, grain size, slipping and crack propagation at fatigue stage I to III was reviewed and discussed. The recommendations for improving FCP resistance were proposed. Intensifying Goss, P and Q textures and moderating these grains were an effective method to improve FCP resistance in Paris regime. However, in stage I, due to the predominated crack closure effect, large grain is beneficial for improving the threshold value of crack propagation. Principally, excellent FCP resistance could be obtained at a balance of crack deflection and crack closure.     

Fatigue crack growth of a metastable austenitic stainless steel

The fatigue crack growth behavior of an austenitic metastable stainless steel AISI 301LN in the Paris region is investigated in this work. The fatigue crack growth rate curves are evaluated in terms of different parameters such as the range of stress intensity factor ΔK, the effective stress intensity factor ΔK_eff, and the two driving force parameter proposed by Kujawski K¹.The finite element method is used to calculate the stress intensity factor of the specimens used in this investigation. The new stress intensity factor solution has been proved to be an alternative to explain contradictory results found in the literature.Fatigue crack propagation tests have been carried out on thin sheets with two different microstructural conditions and different load ratios. The influence of microstructural and mechanical variables has been analyzed using different mechanisms proposed in the literature. The influence of the compressive residual stress induced by the martensitic transformation is determined by using a model based on the proposal of McMeeking et al. The analyses demonstrate the necessity of including K_max as a true driving force for the fatigue crack growth. A combined parameter is proposed to explain the effects of different variables on the fatigue crack growth rate curves. It is found that along with residual stresses, the microcracks and microvoids are other factor affecting the fatigue crack growth rate in the steel studied.     

Microstructure dependent fatigue crack growth in aged hardened aluminium alloys

Fatigue crack propagation tests in constant amplitude loading, as well as with single peak overloads, have been performed in AlMgSi1-T6 aluminium alloys with different Mn and Cr contents. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. A moderate stress ratio and a strong material dependence effects on the fatigue crack growth were observed. These effects are discussed in terms of the different dominant closure mechanism (plasticity-induced closure or roughness-induced closure). Roughness-induced closure dominates crack closure in the alloys with higher contents of Mn and Cr elements. In the alloy with a lower content of these elements, plasticity-induced closure is dominant. When roughness-induced closure is the prime pre-overload closure mechanism, the retardation effect is decreased in comparison to when plasticity-induced closure is dominant.     

Mode I fatigue crack growth under biaxial loading

This paper is centred on the role of the T-stress during mode I fatigue crack growth. The effect of a T-stress is studied through its effect on plastic blunting at crack tip. As a matter of fact, fatigue crack growth is characterized by the presence of striations on the fracture surface, which implies that the crack grows by a mechanism of plastic blunting and re-sharpening (Laird C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation. In: Fatigue crack propagation, STP 415. Philadelphia: ASTM; 1967. p. 131–68 [8]). In the present study, plastic blunting at crack tip is a global variable ρ, which is calculated using the finite element method. ρ is defined as the average value of the permanent displacement of the crack faces over the whole K-dominance area. The presence of a T-stress modifies significantly the evolution of plastic deformation within the crack tip plastic zone as a consequence of plastic blunting at crack tip. A yield stress intensity factor K_Y is defined for the cracked structure, as the stress intensity factor for which plastic blunting at crack tip exceeds a given value. The variation of the yield stress intensity factor was studied as a function of the T-stress. It is found that the T-stress modifies significantly the yield point of the cracked structure and that the yield surface in a (T, K_I) plane is independent of the crack length. Finally, a yield criterion is proposed for the cracked structure. This criterion is an extent of the Von-Mises yield criterion to the problem of the cracked structure. The proposed criterion matches almost perfectly the results obtained from the FEM. The evolution of the yield surface of the cracked structure in a (T, K_I) plane was also studied for a few loading schemes. These results should develop a plasticity model for the cracked structure taking into account the effect of the T-stress.