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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Evaluation of overload-induced fatigue crack growth retardation parameters using an exponential model

In this study, fatigue crack growth rate in mixed-mode overload (modes I and II) induced retardation zone has been predicted by using an “Exponential model”. The important parameter of this model is the specific growth rate. This has been correlated with various crack driving parameters such as stress intensity factor range, maximum stress intensity factor, equivalent stress intensity factor, and mode mixity, as well as material properties such as modulus of elasticity and yield stress. An equation has been formulated for specific growth rate which has been used to calculate crack growth rate under mixed-mode loading conditions. It has been observed that the crack growth rate predicted by the model is in good agreement with experimental results.     

Evaluation of the overload effect on fatigue crack growth with the help of synchrotron XRD strain mapping

The overload retardation effect on fatigue crack growth rate (FCGR) in titanium alloy Ti-6Al-4V is studied. Synchrotron X-ray diffraction strain mapping of near-crack tip regions of pre-cracked fatigued samples is used to determine the effective stress intensity factors experienced by the crack tip. The effective stress intensity factor values are computed by finding the best match between the experimental strain maps and linear elastic fracture mechanics (LEFM) predictions. The dependence of the effective stress intensity factor, K, on the applied load is plotted, and an interpretation of the overload retardation effect is proposed. The present approach permits to reconcile the traditional LEFM fatigue crack propagation prediction and the experimental measurement of strain fields.     

Singular and non-singular approaches for predicting fatigue crack growth behavior

In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed: mechanisms acting before, at or after the crack tip. After reviewing the crack closure idea, which is based on what happens behind the crack tip, quantitative models are proposed to predict the effects at the crack tip due to crack bifurcation. To predict the behavior ahead of the crack tip, a damage accumulation model is proposed. In this model, fatigue cracking is assumed caused by the sequential failure of volume elements or tiny εN specimens in front of the crack tip, calculated by damage accumulation concepts. The crack is treated as a sharp notch with a small, but not zero radius, avoiding the physically unrealistic singularity at its tip. The crack stress concentration factor and a strain concentration rule are used to calculate the notch root strain and to shift the origin of a modified HRR field, resulting in a non-singular model of the strain distribution ahead of the crack tip. In this way, the damage caused by each load cycle, including the effects of residual stresses, can be calculated at each element ahead of the crack tip using the correct hysteresis loops caused by the loading. The proposed approach is experimentally validated and extended to predict fatigue crack growth under variable amplitude loading, assuming that the width of the volume element broken at each cycle is equal to the region ahead of the crack tip that suffers damage beyond its critical value. The reasonable predictions of the measured fatigue crack growth behavior in steel specimens under service loads corroborate this simple and clear way to correlate da/dN and εN properties.     

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.     

3D modelling of plasticity induced fatigue crack closure-effect of material constitutive relations

3D finite element method is utilized to analyze the plasticity-induced crack closure (PICC) phenomenon in a cracked plate under constant-amplitude cyclic loading. To accurately capture the PICC process the choice of material model employed is of significant importance. This paper considers a relatively new model, the Ellyin-Xia elastic-plastic constitutive relations, and the more widely used kinematic hardening model. The study shows considerable difference in the results obtained while employing the two material models. Experimental results support the predictions by the Ellyin-Xia material model.     

Discussions of three-dimensional models for mixed-mode fatigue crack growth

This technical note discusses several three-dimensional models for mixed-mode fatigue crack growth that were developed recently by Bian and coauthors [1], [2], [3], [4] and [5]. However, these models are found being formulated from a generally incorrect three-dimensional crack-front stress field for embedded elastic elliptical cracks. The corresponding correct crack-front stress field for the elliptical cracks is thus presented, and then the three-dimensional fatigue crack growth models are corrected and expressed in much simpler functions.     

Effect of underloads or overloads in fatigue crack growth by crack-tip blunting

Crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading is one of the basic mechanisms for fatigue crack growth in ductile metals. Here, based on an elastic-perfectly plastic material model, crack growth computations are continued up to 700 full cycles by using re-meshing at several stages of the plastic deformation. A compressive underload in one of the cycles tends to increase the rate of cyclic crack growth, and this effect is studied in detail for a single underload, based on the blunting re-sharpening mechanism. Subsequently, the increased rate of crack growth due to periodically occurring underloads is analysed. A single overload has the opposite effect of giving a significant delay in the subsequent fatigue crack growth. An analysis is carried out to compare the effect of a small overload to that of a larger overload.     

Extension of the Tanaka-Mura model for fatigue crack initiation in thermally cut martensitic steels

A multi scale numerical approach for evaluation of crack initiation and propagation in thermally cut structural elements made of martensitic steel is presented. A numerical simulation of micro-crack initiation is based on the Tanaka-Mura micro-crack nucleation model, where individual grains of synthetic microstructure are simulated using the Voronoi tessellation. Three improvements are added to this model (multiple slip bands, micro-crack coalescence and segmented micro-crack generation). Crack propagation is then solved on a macro scale model using linear elastic fracture mechanics approach. Some experimental tests have also been performed to check the accuracy of the numerical model. The results of the proposed computational model show a reasonable correlation with the experimental results.