A unified approach to damage accumulation and fatigue crack growth

An approach is proposed to the theory of fatigue cracks propagation based on the following postulate: a growing crack at least once in a cycle becomes a nonequilibrium one (in the Griffith's sense) under the condition that the resistance to crack growth is calculated with an account of damage accumulated at the crack tip during the loading history. The theory is used for nonuniaxial stress states including jumplike growth, stops, kinking and branching phenomena. The general structure of differential equations is discussed for the averaged crack growth rate under nonuniaxial loading.     

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.     

Probabilistic simulation of fatigue crack growth by damage accumulation

A fatigue crack growth simulation model based on probabilistic damage accumulation is presented. The modified weakest-link hypothesis determines the reinitiation of voids ahead of the crack, which in turn determines the crack advance. From a linearly cumulated-damage standpoint, this is shown to be approximated by a statistical Miner's law. The historical damage on the material elements at the crack-tip vicinity, neglected in previous analysis, is quantified, and shown to be significant. The model includes a prediction of the fatigue threshold stress-intensity factor range, and a comparison with published crack growth rate data for three different structural metals.     

Early fatigue crack growth as the damage accumulation process

A probabilistic approach to modeling of the initial stage of fatigue crack growth is suggested based on the concepts of continuum damage mechanics. The material is presented as a set of microstructural elements with randomly distributed properties. Both the grains and intergranular boundaries are considered as the elements of microstructure. The parameters of resistance of each element to damage accumulation are considered as random variables. These parameters are distributed among the elements independently that allows to model the damage process in polycrystalline materials. The damage measure depends on the characteristic normal and tangential stresses in order to take into account the tensile and shear fracture modes for each element of microstructure. It is assumed that a nucleus of a crack is initially present near the body surface as a single completely ruptured element. The final damage of an element is considered as the crack advancement. The crack is modelled as a sequence of ruptured grains for the transgranular fracture, and as a sequence of couples of neighboring ruptured grains when the intergranular rupture is considered. Numerical simulation is performed to illustrate feasibility of the proposed model. In particular, non-planar crack propagation, blunting, kinking and branching of cracks at the early stage is demonstrated. The non-monotonous pattern of the short crack growth process is observed. Statistical scattering of the current crack size and the crack growth rate as functions of the cycle number and the crack depth is studied.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

Cumulative damage model for fatigue crack growth based on reaction rate theory—II

A study is continued of a macro model of fatigue crack growth (FCG) that is based upon a micro result from reaction rate theory. The previously presented deterministic (mean) model is examined further, and a probabilistic model is introduced. Analysis of FCG data for periodic tensile loads reveals that three material parameters are required. The model also explicitly contains the load and the temperature T. It is shown that T and the form of the periodic load are important quantities, of which the former has interesting implications for accelerated testing. The minimum amount of testing required for predictive purposes is also discussed.     

A cumulative model of fatigue crack growth

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 by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.     

A cohesive model of fatigue crack growth

We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.     

The generalised Frost–Dugdale approach to modelling fatigue crack growth

This paper summarises recent developments in the formulation and application of the generalised Frost–Dugdale crack growth law. We first reveal the relationship between the generalised Frost–Dugdale crack growth law, dislocation based crack growth laws, the two parameter crack growth model, and fractal fatigue concepts. We then show that a range of aircraft materials characterisation test data are consistent with this law and how it can be used to predict crack growth in a range of full-scale aircraft fatigue tests, and coupon tests including crack growth in aircraft fuselage lap joints.     

Influence of the crack morphology on the fatigue crack growth rate: A continuously-kinked crack model based on fractals

Threshold condition and rate of fatigue crack growth appear to be significantly affected by the degree of deflection of cracks. In the present paper, the reduction of the fatigue crack growth rate for a so-called ‘periodically-kinked crack’ as compared to that for a straight counterpart is quantified via the Paris–Erdogan law modified according to some simple theoretical arguments. It is shown that such a reduction increases as the value of the kinking angle increases. Then, a so-called ‘continuously-kinked crack’ (the kink length tends to zero) is considered and modelled as a self-similar invasive fractal curve. The sequence of kinking angles in the crack is such that the fatigue crack path is ‘on average’ straight. Using the Richardson’s expression for self-similar fractals, the fractal dimension of the crack is expressed as a function of the kinking angle. It is shown that the fatigue crack growth rate in the Paris range depends not only on the above fractal dimension and in turn on the kinking angle, but also, in an explicit fashion, on the crack length. Some experimental results related to concrete and showing a crack size effect on the fatigue crack growth rate are analysed.     

Proposed fatigue damage measurement parameter for shot-peened carbon steel based on fatigue crack growth behavior

A new technique for evaluating fatigue-damage accumulation in shot-peened (SP) carbon steel based on variations in residual stress is proposed. Using findings from previous studies, a fatigue damage parameter for a material treated with SP based on the change in induced compressive residual stress (CRS) is examined. A plastic replica method with the focused ion beam (FIB) technique is used to assess the relationship between the residual stress state and the fatigue crack growth (FCG) behavior of SP specimens over the fatigue lifespan. It is found that the residual stress relaxation phenomenon can be used as an effective parameter for determining the fatigue damage growth, provided the residual stress relaxation rate of each mechanical load and the critical threshold relaxation boundary of each material is known.     

A model of fatigue crack growth in polymers

Journal of Materials Science - A model of fatigue crack growth is proposed based on a line plastic zone analysis. It is assumed that the effect of cycling is to reduce the craze stress to some...     

Model of fatigue crack propagation by damage accumulation at the crack tip

Modelling fatigue crack propagation by damage accumulation at the crack tip originally proposed by McClintock is reworked out using metallurgical considerations. On a physical basis it is shown that the validity of such models is actually confined to the low crack growth rate range corresponding to stage I growth such as along crystallographic planes. At higher crack growth rates there is a transition to plastic stretching mechanisms which could be described by crack opening displacement models. An evaluation of two models has been carried out on a ³³Co Ni alloy where extensive information was available: both are based on the strain singularity as computed by Tracey from a finite element analysis of plane strain small scale yielding and as adapted to cyclic loading under Rice's hypothesis and taking the grain as the critical element below which size continuum mechanics do no longer apply. It is pointed out that the use of this strain singularity which is not able to account for crack closure, renders models unable to predict experimental crack growth rates curves but only intrinsic curves relating the growth rate to the effective stress intensity amplitude as defined by Elber. The first model which assumes fatal cracking of a grain with an average uniform cyclic equivalent strain, underestimates the crack growth rates and in addition it yields results very sensitive to the shape and size of the grain. The second model which assumes progressive cracking in a grain with a cyclic equivalent strain gradient is able to predict the intrinsic crack growth rate curve in the ³³Co Ni alloy and to yield predictions consistent with other experimental data.     

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.     

A stochastic damage accumulation model for creep crack propagation

Previously a stochastic model for damage accumulation was proposed to obtain an expression for the fatigue crack propagation rate. In this paper, the model is used in order to derive the creep crack propagation law. The theoretical results show a good agreement with the experimental data. This suggests an extensive applicability of the present model. On these theoretical bases, it is concluded that the creep crack propagation rate is proportional to the process region size.     

A damage model for creep crack growth

A model is developed for damage produced by the growth of isolated grain boundary cavities under power law creep. This damage model is combined with the small scale yielding stress and strain fields to predict the damage ahead of a stationary and a steadily propagating crack tip in an elastic-power law creeping material. A failure criterion, based upon the damage ahead of the crack tip attaining a critical value, is invoked. This criterion leads to predictions for the incubation time prior to initiation of crack growth and for the relationship between the remote stress intensity factor and the steady state crack speed. Results are presented for both elastic-primary and -secondary creep crack growth. In either case, there exists a minimum stress intensity factor below which steady state crack growth is not possible. Comparisons of the predictions of this model with others for steady state crack propagation in elastic-secondary creeping materials are also made.

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Résumé On développe un modèle décrivant le dommage produit par la croissance de cavités isolées aux frontières des grains sous l'effet d'un fluage selon une loi parabolique. Ce modèle d'endommagement est combiné aux champs de contrainte et de déformation conduisant à une plastification à petite échelle, en vue de prédire le dommage qui se produit en avant de l'extrémité d'une fissure stationaire et en propagation lente, dans un matériau soumis à fluage selon une loi élastique. On invoque un critère de rupture basé sur la valeur critique atteinte par le dommage en avant de l'extrémité de la fisure. Ce critère conduit à prédire le temps d'incubation avant amorçage de la croissance d'une fissure, ainsi que la relation entre le facteur d'intensité des contraintes appliquées à une certaine distance et la vitesse de croissance stable de la fissure.On présente les résultats dans les cas de croissance d'une fissure de fluage au stade secondaire. Dans les deux cas, il existe un facteur d'intensité de contrainte minimum en dessous duquel une croissance stable de la fissure n'est pas possible. On procède également à des comparaisons des prédictions données par ce modèle avec d'autres, pour la propagation en état stable d'une fissure dans des matériaux soumis à fluage secondaire élastique.

     

A third-order state-space model for fatigue crack growth

A second‐order state‐space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1 - 4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075‐T6 and 2024‐T3 at constant‐amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third‐order state‐space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second‐order state‐space model is treated as the third state variable in this model. Through simulations, it is shown that the third‐order state‐space model gives better predictions than the second‐order state‐space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.     

Probabilistic crack growth by nonlinear damage accumulation

A probabilistic crack growth model based on a nonlinear damage accumulation criterion is presented. The damage criterion takes cognizance of the effect of the loading sequence, and is an energy-based function. The simulation results are shown to compare favourably with experimental data of four different types of steels and an aluminum alloy. The predicted results are also compared with that of the linear damage theory and, in general, are found to be superior.

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Résumé On présente un modèle probabiliste de croissance d'une fissure, basé sur un critère d'accumulation du dommage non linéaire. Le critère d'endommagement prend en compte l'effet de la séquence de mise en charge, et est une fonction de lénergie. On montre que les résultats d'une simulation soutiennent favorablement la comparaison avec des données expérimentales, dans le cas de quatre aciers différents et d'un alliage d'aluminium. Les résultats prédits sont également comparés avec ceux que fournit la théorie du dommage linéaire et, en général, apparaissent leur être supérieurs.

     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.