A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys

A numerical analysis using cohesive zone model under cyclic loading is proposed to develop a coupled predictive approach of crack growth in single crystal. The process of material damage during fatigue crack growth is described using an irreversible cohesive zone model, which governs the separation of the crack flanks and eventually leads to the formation of free surfaces. The cohesive zone element is modeled to accumulate fatigue damage during loadings and no damage during unloadings. This paper presents the damage model and its application in the study of the crack growth for precracked specimens. The use of cohesive zone approach is validated through a convergence study. Then, a general procedure of parameters calibration is presented in pure fatigue crack growth. In the last section, an extension of the cohesive zone model is presented in the case of creep–fatigue regime at high temperature. The model showed its capability to predict with a good agreement the crack growth in the case of complex loading and complex specimen geometries.     

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.     

Plastic zone size estimation under cyclic loadings using in situ optical microscopy fatigue testing

An in situ optical microscopy fatigue testing is proposed in this paper to investigate the forward and reversed plastic zone size under cyclic loadings for Al‐7075‐T6. This experimental study is used to verify the hypotheses in a recently developed small time scale formulation of fatigue crack growth. During the testing, the entire cyclic loading cycle is divided into a certain number of steps. Images of the crack tip are taken at each step. The full strain field around the crack tip is determined using the digital image correlation (DIC) technique. The plastic zone size is obtained by combining the DIC results and the material constitutive relationship. Experimental measurements from the proposed study are compared with theoretical predictions. It is observed that the crack closure has a large effect on the reversed plastic zone size. The plastic zone size remains almost constant when the unloading path is below a certain stress level, which is one of the hypotheses used in a previous crack growth model. Discussions are given for the modelling of plastic zone size variation under cyclic loadings and several conclusions are drawn based on the current investigation.     

Low‐cycle fatigue delamination initiation and propagation in fibre metal laminates

The aim of this paper is to develop an elastic–plastic‐damage constitutive law and a tool for simulation of delamination initiation and propagation in fibre metal laminates (FMLs) under low‐cycle fatigue loading regime. In the previous studies, the significance of plasticity in delamination growth and modelling of FMLs was not considered. Hence, cohesive zone law that combines the damage evolution with plasticity is developed. The new fatigue damage model is implemented as user‐written subroutines that links with ansys based on the cohesive finite element method. The cohesive zone model constitutive law has been verified by modelling of the delaminated adhesively bonded aluminium joint under normal and shear loadings and compared with the available results in the literature. The developed procedure and tool have been used for the analyses of DCB and ENF specimens under uniform and variable loadings. The obtained results for progressive damage and delamination and stress–strain curves are discussed in this paper.     

An Approach to Estimate Interface Shear Stress of Ceramic Matrix Composites from Hysteresis Loops

An approach to estimate interface shear stress of ceramic matrix composites during fatigue loading has been developed in this paper. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix crack space and interface debonding length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. Based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading, the unloading counter slip length and reloading new slip length are determined by the fracture mechanics method. The hysteresis loops of four different cases have been derived. The hysteresis loss energy for the strain energy lost per volume during corresponding cycle is formulated in terms of interface shear stress. By comparing the experimental hysteresis loss energy with computational values, the interface shear stress corresponding to different cycles can then be derived. The theoretical results have been compared with experimental data of three different ceramic composites.     

Computational modeling of mixed-mode fatigue crack growth using extended finite element methods

The extended finite element method (XFEM) combined with a cyclic cohesive zone model (CCZM) is discussed and implemented for analysis of fatigue crack propagation under mixed-mode loading conditions. Fatigue damage in elastic-plastic materials is described by a damage evolution equation in the cohesive zone model. Both the computational implementation and the CCZM are investigated based on the modified boundary layer formulation under mixed-mode loading conditions. Computational results confirm that the maximum principal stress criterion gives accurate predictions of crack direction in comparison with known experiments. Further popular multi-axial fatigue criteria are compared and discussed. Computations show that the Findley criterion agrees with tensile stress dominant failure and deviates from experiments for shear failure. Furthermore, the crack propagation rate under mixed mode loading has been investigated systematically. It is confirmed that the CCZM can agree with experiments.     

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.     

A two-dimensional in situ fatigue cohesive zone model for crack propagation in composites under cyclic loading

In this paper a two-dimensional fatigue cohesive zone model (CZM) for crack propagation in composites under cyclic loading has been formulated and validated through successful predictions of fatigue crack growth under pure and mixed mode conditions for several different composites. The proposed fatigue CZM assumes simple power-law functions for fatigue damage accumulation of which the damage parameters can be calibrated from simple fatigue tests under pure mode I and mode II conditions. The model relies solely on the in situ cohesive responses for fatigue damage rate calculation, enabling the differentiation of the local elemental load history from the global load history. An effective cycle jump strategy for high-cycle fatigue has also been proposed. It has been demonstrated that once calibrated, the fatigue CZM can predict the Paris laws for the pure modes. Furthermore, it can predict the Paris laws of any mixed-mode conditions without the need of additional empirical parameters. This is of significant practical importance because it leads to greatly reduced experimental needs for mixed mode crack propagation widely observed in composites under cyclic loads.     

Fatigue crack growth simulation in adhesively bonded composite joints

A numerical model has been developed for simulating fatigue crack growth (debonding) in adhesively bonded composite joints subjected to mode‐I, mode‐II, and mixed‐mode I + II loading conditions. The model employs a cohesive zone model described by a modified bilinear traction‐separation law. Fatigue damage in the composite adherends is not considered in the model. To account for crack divergence and reduce sensitivity of numerical results on mesh density, a crack front detection algorithm based on the effective element's length was employed. The model is implemented as a user‐defined subroutine (UMAT) in the commercial FE code LS‐DYNA. The model's input parameters, in the form of a modified Paris law, and the validation data were obtained from experimental tests conducted by the authors. It was found that the model is able to successfully simulate crack growth in the regime of the experimental data.     

A procedure for the simulation of fatigue crack growth in adhesively bonded joints based on the cohesive zone model and different mixed-mode propagation criteria

This work deals with the simulation of the fatigue crack growth (FCG) in bonded joints. In particular a cohesive damage model is implemented in the commercial software Abaqus, in order to take into account for the damage produced by fatigue loading. The crack growth rate is evaluated with different Paris-like power laws expressed in terms of strain energy release rate. The crack growth rate is then translated into a variation of the damage distribution over the cohesive zone setting an equivalence between the increment of crack length and the increment of damage. The model takes also into account mixed mode I/II conditions. In this work the validity of the model is tested by comparison with theoretical trends for conditions of pure mode I, pure mode II and mixed mode loading. In the case of mixed mode conditions, different models are implemented for the crack growth rate computation. The results of the model are in very good agreement with the expected trends, therefore the model is adequate to simulate the fatigue crack growth behaviour of bonded joint.     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

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 Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

Investigation of sub-critical fatigue crack growth in FRP/concrete cohesive interface using digital image analysis

The cohesive stress transfer during the sub-critical crack growth associated with the debonding of FRP from concrete under fatigue loading is experimentally investigated using the direct shear test set-up. The study focused on high-amplitude/low-cycle fatigue. The fatigue sub-critical crack growth occurs at a load that is smaller than the static bond capacity of the interface, obtained from monotonic quasi-static loading, and is also associated with a smaller value of the interfacial fracture energy. The strain distribution during debonding is obtained using digital image correlation. The results indicate that the strain distribution along the FRP during fatigue is similar to the strain distribution during debonding under monotonic quasi-static loading. The cohesive crack model and the shape of the strain distribution adopted for quasi-static monotonic loading is indirectly proven to be adequate to describe the stress transfer during fatigue loading. The length of the stress transfer zone during fatigue is observed to be smaller than the cohesive zone of the interfacial crack under quasi-static monotonic loading. The strain distribution across the width of the FRP sheet is not altered during and by fatigue loading. A new formulation to predict the debonding crack growth during fatigue is proposed.     

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

Effect of LCF on HCF crack growth of Ti-17

An improved understanding of fatigue crack growth phenomena applicable to titanium engine disks was developed through complimentary experimental and analytical investigations of Ti-17. The effect of low cycle fatigue (LCF) on the high cycle fatigue (HCF) threshold and rate of crack propagation was studied. A simplified variable-amplitude spectrum, consisting of high-R cycles, corresponding to HCF loading, and periodic R=0.1 cycles, corresponding to LCF loading, was used to demonstrate a load-interaction effect. When the ratio of HCF to LCF cycles was 100 or more the fatigue crack growth lifetimes were significantly lower than predicted using linear damage summation methods assuming no load-interaction effect. Thus, it was concluded that the LCF cycle accelerated the fatigue crack growth rate of subsequent HCF cycles, even when closure was concluded to be negligible. A phenomenological model was formulated based on hypothesized changes in the propagation resistance, K_PR, and fit to the test data. The model confirmed that the periodic LCF cycles increased fatigue crack growth rates of subsequent HCF cycles.     

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.