Examination of the fatigue crack growth equations

Most of the crack growth equations proposed so far correlate the crack growth rate (da/dN or da/dt) with crack tip parameters such as the stress intensity factor (SIF) or energy release rate (ERR). In our previous works, an experimental setup was designed to examine the applicability and the boundary of the functional relationship between da/dN and the crack tip parameters, particularly, ERR. In the present paper, the variation of the ERR along the experimentally observed curvilinear crack trajectories is obtained by means of the finite element method. The analysis shows that the Paris-Erdogan type of laws are applicable until the crack tip is located outside the strong crack-defect interaction region (SI region). A functional relationship between da/dN and ERR breaks down within this region. This suggests the existence of additional crack tip parameters that are not accounted for within conventional fracture mechanics. An approach to modeling the observed phenomenon is discussed following the concept of the Crack Layer theory.     

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.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

A model for evaluating the effect of fatigue crack repair by the infiltration method

Infiltration of foreign materials into a fatigue crack has previously been shown to be able to retard the crack and extend fatigue life. Most of the related studies were empirical and phenomenological in nature. To aid engineering decisions, it would be advantageous if the possible outcome of a repair can be evaluated beforehand. To this end, a crack closure model taking into account the additional closure effect of the infiltrant has been developed and verified against experimental results. With this model, the sensitivity of the repair effect to various parameters such as mechanical properties of the infiltrant, depth of penetration and infiltration load level can be assessed.     

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.     

Sigmoidal crack growth rate curve: statistical modelling and applications

The present paper proposes a statistical model for describing sigmoidal crack growth rate curves. Major novelties are: a) exploitation of the maximum likelihood principle for obtaining material estimates by pooling together experimental data belonging to the different crack propagation regions; b) a general formulation which allows to adopt different sigmoidal models and any kind of statistical distribution for the model variables; c) fatigue life predictions through numerical integration of analytical functions with no need of Monte Carlo simulations. Experimental data taken from NASGRO database are used to check the validity of the statistical model in estimating material parameters included in the crack growth NASGRO algorithm. Illustrative plots of number of cycles to failure and crack length after a given number of cycles are presented, showing good agreement between the proposed statistical model and NASGRO results.     

Limited weld residual stress measurements in fatigue crack propagation: Part II. FEM-based fatigue crack propagation with complete residual stress fields

Using a limited set of residual stress measurements acquired by neutron diffraction and an equilibrium‐based, weighted least square algorithm to reconstruct the complete residual stress tensor field from the measured residual stress data, the effect of weld residual stress on fatigue crack propagation is investigated for 2024‐T351 aluminium alloy plate joined by friction stir welding. Through incorporation of the least squares, complete equilibrated residual stress field into a finite element model of the Friction Stir Weld (FSW) region, progressive crack growth along a direction perpendicular to the welding line is simulated as part of the analysis. Both the residual stress redistribution and the stress intensity factor due to the residual stress field, K_res, are calculated during the crack extension process. Results show that (a) incorporation of the complete, self‐equilibrated residual stress field into a finite element (FE) model of the specimen provides a robust, hybrid approach for assessing the importance of residual stress on fatigue crack propagation, (b) the calculated stress‐intensity factor due to the residual stress field, K_res, has the same trend as measured experimentally by the ‘cut‐compliance method’ and (c) the da/dN results are readily explained with reference to the effect of the residual stress field on the applied stress intensity factor.     

A fatigue crack nucleation model for anisotropic materials

Based on Tanaka‐Mura's dislocation‐dipole pile‐up configuration, a formulation of mixed mode fatigue crack nucleation is derived using the Stroh formalism for generally anisotropic materials. The fatigue life is explicitly expressed as inversely proportional to the stored plastic energy, depending on the material's anisotropic elastic matrix F ^?1, surface energy, Burgers vector, and lattice resistance. The model has been shown to agree with experimental observation on critical slip planes in PWA 1493 single crystal Ni‐base superalloy.     

Multiscale fatigue crack growth modelling for welded stiffened panels

The influence of welding residual stresses in stiffened panels on effective stress intensity factor (SIF) values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics simulations as well as a Tanaka–Mura approach for the analysis of the problem. Mode I SIFs, K_I, were calculated by the finite element method using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K_tot, is derived by a part due to the applied load, K_appl, and by a part due to welding residual stresses, K_res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.     

Influence of residual thermal stresses on fatigue crack growth life of discontinuous reinforcements in metal matrix composites

The fatigue life prediction model based on crack propagation from micro-structural features is derived and presented for planar and randomly oriented Discontinuous Reinforced Metal Matrix Composites (DRMMCs). The model contains the influence of micro-structural properties such as aspect ratio, volume fraction of particle/fibre and constraint between particle and the matrix. The effect of residual thermal stresses generated within the matrix during development of composite is considered. The particle/fibre plays a dominant role in the development of the cyclic plastic zone size ahead of the crack tip; moreover, it enhances the cyclic plastic deformation characteristics of DRMMC. The theoretical model-based evaluations for low cycle fatigue in DRMMCs are within the proximity of the experimental results.     

A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

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 physics-based model for evaluating hot compressive dwell effects on fatigue crack growth in 319 cast aluminum alloys

Fatigue crack growth under hot compressive dwell (HCD) conditions, a case of creep–fatigue occurring under compressive loading, is an important failure mode in high temperature environments. Creep-induced tensile residual stresses gradually built up in the vicinity of the crack are considered to be a key factor contributing to crack growth under HCD conditions. To understand and quantify this effect, a simple physics-based model has been developed, in which the residual stress contributions associated with creep and plasticity are added to the elastic response of the material to predict crack growth under HCD conditions using Linear Elastic Fracture Mechanics (LEFM). Test of a cast 319 Al alloy has been conducted both for material characterization and under baseline and HCD conditions to evaluate the model. With HCD, the crack growth rate was increased on average by a factor of about 6, which is consistent with model predictions.     

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.     

Modelling fatigue crack growth in shot-peened components of Al 2024-T351

Microstructural fracture mechanics concepts are used to develop a model to incorporate shot-peening effects into crack propagation laws and fatigue life predictions. Shot peening produces a residual stress which resists opening of the crack and also produces a work-hardened layer within which the flow stress is raised. The model takes account of these effects to give an accurate prediction of the increase in fatigue life. The model was also used to derive the conditions for crack arrest, and the results are presented in the form of a fatigue damage map (FDM). The FDM can be used for the determination of safe loads in durability and maintainability analyses.     

A cohesive XFEM model for simulating fatigue crack growth under mixed-mode loading and overloading

Structures are subjected to cyclic loads that can vary in direction and magnitude, causing constant amplitude mode I simulations to be too simplistic. This study presents a new approach for fatigue crack propagation in ductile materials that can capture mixed-mode loading and overloading. The extended finite element method is used to deal with arbitrary crack paths. Furthermore, adaptive meshing is applied to minimize computation time. A fracture process zone ahead of the physical crack tip is represented by means of cohesive tractions from which the energy release rate, and thus the stress intensity factor can be extracted for an elastic-plastic material. The approach is therefore compatible with the Paris equation, which is an empirical relation to compute the fatigue crack growth rate. Two different models to compute the cohesive tractions are compared. First, a cohesive zone model with a static cohesive law is used. The second model is based on the interfacial thick level set method in which tractions follow from a given damage profile. Both models show good agreement with a mode I analytical relation and a mixed-mode experiment. Furthermore, it is shown that the presented models can capture crack growth retardation as a result of an overload.