The effect of vacuum on fatigue crack growth

The paper reviews the modern concepts of the vacuum effect on fatigue crack growth under cyclic loading. It reports and discusses experimental data (obtained by the author and others) on the crack growth rate at separate stages of the process, the size and structural characteristics of the plastic zone and the fracture micromechanisms for different metals and alloys in air and in vacuum. The relationship between the macroscopic and microscopic characteristics of crack growth in both environments is considered. The idea is developed that the vacuum effect on the kinetics of crack propagation is associated with changes in the process of dislocation motion in the plastic zone (in contrast to atmospheric conditions) and the mechanism of the effect is sensitive to the fatigue mechanism of metals and alloys.     

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.     

Mesoscopic mechanisms in fatigue crack initiation in an aluminium alloy

The mechanistic aspects of process of initiation of a mode‐I fatigue crack in an aluminium alloy (AA 2219‐T87) are studied in detail, both computationally as well as experimentally. Simulations are carried out under plane strain conditions with fatigue process zone modelled as stress‐state–dependent cohesive elements along the expected mode‐I failure path. An irreversible damage parameter that accounts for the progressive microstructural damage due to fatigue is employed to degrade cohesive properties. The simulations predict the location of initiation of the fatigue crack to be subsurface where the triaxiality and the opening tensile stresses are higher in comparison with that at the notch surface. Examination of the fracture surface profile of fracture test specimens near notch tip reveals a few types of regions and existence of a mesoscopic length scale that is the distance of the location of highest roughness from the notch root. A discussion is developed on the physical significance of the experimentally observed length scale.     

The relationship between fatigue fracture parameters during selfsimilar fatigue crack growth

The relationship between cyclic fracture toughness and the parameter n during selfsimilar fatigue crack growth has been investigated for SS41 and SM41A steels. The conditions under which selfsimilar growth is realized are also analysed.     

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.     

Prediction of fatigue crack growth based on low cycle fatigue properties

Theoretical models of the fatigue crack growth without artificial adjustable parameters were proposed by considering the plastic strain energy and the linear damage accumulation, respectively. The crack was regarded as a sharp notch with a small curvature radius and the process zone was assumed to be the size of cyclic plastic zone. The near crack tip elastic–plastic stress and strain were evaluated in terms of modified Hutchinson, Rice and Rosengren (HRR) formulations. Predicted results from two established models have been soundly compared with open reports for frequently used materials. It is found that experimental results agree well with theoretical solutions.     

A study on spot heating induced fatigue crack growth retardation

The propagation of a growing fatigue crack can be effectively retarded by heating a spot near the crack tip (under zero stress condition). Spot heating to a subcritical temperature and at a precise location modifies the crack growth behaviour in a way, more or less, similar to specimens subjected to an overload spike. It is observed that the magnitude of spot heating induced crack growth retardation increases with increase in spot temperature. It is also observed that the crack growth behaviour is influenced by the position of the heating spot and there exists an optimum position of hot spot that produces maximum retardation in fatigue crack growth rate. The plastic zone length due to spot heating has been estimated using experimental data. It is found that the plastic zone length due to spot heating increases exponentially with increase in spot temperature. The Wheeler model for crack growth retardation has been modified by introducing a plastic zone correction factor λ. The values of λ and the shaping exponent, m, in the Wheeler model have been obtained for different spot heating temperatures.     

Effects of frequency on fatigue crack growth at elevated temperature

The effects of frequency on fatigue crack growth behaviour have been studied in a prealloyed powder material, Udimet 720Li, at 650 °C. Fracture mode and fatigue crack growth behaviour were studied at frequencies ranging from 0.001 to 5 Hz using a balanced triangular waveform. Tests were carried out under constant Δ K control, with load ratio and temperature being held constant. A mechanism map was constructed where predominantly time, mixed and cycle-dependent crack growth behaviour were identified. The results were verified by SEM analyses. Cycle-dependent crack growth data were obtained at room temperature, while fully time-dependent crack growth data were generated under sustained loads at 650 °C.
It was found that mixed time/cycle-dependent behaviour is of most significance for this material at the temperature and frequencies studied. Data for other nickel-based superalloys from various sources in the literature were compiled and compared with those of U720Li alloy at a given stress intensity and temperature in the mixed regime. An analysis was developed to rationalize the observed effect of frequency on fatigue crack growth rate.     

Stage II fatigue crack growth

The linear part of the fatigue crack growth diagram is found to be divided into Stages IIa and IIb by the point O whose coordinates K^* and A are dependent on the physical and structural characteristics of the material. In Stage IIa K_eff remains constant as the microcrack advances in increments corresponding to the dislocation cell structure size, λ, pausing for (dN−1) cycles to accumulate the elastic energy required for the crack opening. During Stage IIb K_op remains constant and the microcrack opens during each cycle and advances irrespective of the substructure but in accordance with an increasing value of K_eff. The effects of temperature and vacuum on K^* are considered; the A values correspond to those of λ and are independent of the above effects.     

Temperature effects on fatigue thresholds and structure sensitive crack growth in a nickel-base superalloy

Fatigue thresholds and slow crack growth rates have been measured in a powder formed nickel-base superalloy from room temperature to 600°C. Two grain sizes were investigated: 5–12 μm and 50 μm. It is shown that the threshold increases with grain size, and the difference is most pronounced at room temperature. Although crack growth rates increase with temperature in both microstructures, the threshold is only temperature dependent in the material with the larger grain size. It is also only in the latter that the room temperature threshold falls when the load ratio is increased from 0.1 to 0.5. At 600°C the higher load ratio causes a 20% reduction in the threshold irrespective of grain size.The results are discussed in terms of surface roughness and oxide-induced crack closure, the former being critically related to the type of crystallographic crack growth, which is in turn shown to be both temperature and stress intensity dependent.     

Multiaxial small fatigue crack growth in metals

Observations related to the formation and growth of small cracks ranging from subgrain dimension up to the order of 1 mm are summarized for amplitudes ranging from low cycle fatigue (LCF) to high cycle fatigue (HCF) conditions for polycrystalline metals. Further efforts to improve the accuracy of life estimation which address LCF, HCF and LCF–HCF interactions must consider various factors that are not presently addressed by conventional elastic–plastic fracture mechanics (EPFM) or linear elastic fracture mechanics (LEFM) approaches based on long, self-similar cracks in homogeneous, isotropic materials, nor by conventional HCF design tools such as the ε–N curve, the S–N curve, modified Goodman diagram and fatigue limit.Development of microstructure-sensitive fatigue crack propagation relations relies on deeper understanding of small crack behavior, including (a) interactions with microstructure and lack of constraint for microstructurally small cracks, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) local mode mixity effects on small crack growth. The basic technology is not yet sufficiently advanced in these areas to implement robust damage tolerant design for HCF. This paper introduces an engineering model which approximates the results of slip transfer calculations related to crack blockage by microstructure barriers; the model is consistent with critical plane concepts for Stage I growth of small cracks, standard cyclic stress–strain and strain–life equations above threshold, and the Kitagawa diagram for HCF threshold behaviors. It is able to correlate the most relevant trends of small crack growth behavior, including crack arrest at the fatigue limit, load sequence effects, and stress state effects.     

Micromechanisms of fatigue crack growth in aluminium alloys

The fatigue crack growth characteristics of high-strength aluminium alloys are discussed in terms of behaviour during mechanical testing and fracture surface appearance. For a wide range of crack growth rates, the crack extends both by the formation of ductile striations and by the coalescence of micro-voids. Dimples are observed at stress intensities very much less than the plane strain fracture toughness, and this is explained in terms of the probability of inclusions lying close to the crack tip. The striation formation process is described as a combination of environmentally-enhanced cleavage processes and plastic blunting of the crack tip.     

Cycle counting for fatigue crack growth analysis

Fatigue crack propagation tests were carried out on an Al-Cu alloy under specially designed complex load sequences. Electron fractography of the fatigue fracture surfaces suggests that rainflow cycle counting is applicable to the analysis of fatigue crack growth under complex load sequences.     

Vacuum effects on fatigue crack growth in submicrometre‐thick freestanding copper films

To clarify vacuum effects on fatigue crack growth in freestanding metallic thin films, experiments were conducted on approximately 500‐nm‐thick copper films inside a field emission scanning electron microscope. Fatigue crack growth accompanied by intrusion/extrusion formation occurred in vacuum, and da/dN was smaller than in air in the middle‐ΔK region (ΔK ≈ 1.7‐3.1 MPam^1/2). Conversely, in the low‐ΔK region (ΔK ? 1.7 MPam^1/2), da/dN was larger in vacuum than in air. Further, fatigue crack growth in vacuum occurred below the fatigue threshold in air (ΔK_th,air). A nonpropagating crack after reaching ΔK_th,air continued to propagate in vacuum when the environment changed from air to vacuum. This indicates that fatigue crack growth resistance is smaller in vacuum than in air under the same effective driving force. The fatigue damage area near the crack paths in vacuum in the low‐ΔK region became wider, suggesting that the nucleation of fatigue damage was enhanced in vacuum.     

Numerical simulation of fatigue crack growth

A numerical simulation of fatigue crack growth which uses currently available crack tip stress and strain fields is described. The essential features of the numerical model are the concepts of damage accumulation cycle by cycle and repeated re-initiation at the tip of the growing crack. The failure criteria employed are a combination of a failure condition and a critical distance over which this condition must be achieved. This critical distance, the material size parameter, has a magnitude which depends on the failure mechanism.

The use of the model to illustrate the effects of stress ratio and environmental effects is described and the ability of the model to predict the onset of bursts of crack growth due to static failure mechanisms is demonstrated. The phenomenon of self-arresting cracks is also displayed.

Material characteristics are included in the model and comparisons with experimental data are presented for a C-Mn steel used in the fabrication of offshore structures.     

Effect on fatigue crack growth of interactions between overloads

ABSTRACT Various types of interactions between overloads were studied in a 0.38% C low carbon steel. The retarding effect due to consecutive overloads is found to increase with the number of overloads, until it reaches a maximum. Similarly, it is found that a critical distance between overloads ensures the highest retarding effect, while shorter or longer spacing are less efficient for retarding crack growth. These effects are successfully explained using FEM calculations of the effective stress intensity factor. The kinematic hardening of the alloy, which is very efficient in ferritic–pearlitic steels, is shown to be mostly responsible for those effects. Taking into account the amplitude of kinematic hardening allows qualitative explanation of the observed effects. The order of application of the cycles during variable amplitude fatigue is thus important and should be taken into account for predicting fatigue lives.     

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.     

On some criterial problems of fatigue crack initiation and growth in polycrystals

We address a relationship between mechanisms and direction of a fatigue crack growth at stages I and II. The criteria for the fatigue crack growth direction at those stages are substantiated based on a study of physical and mechanical features of the fatigue crack propagation in polycrystals. We discuss the conditions under which microcracks may initiate brittle fracture. __________ Translated from Problemy Prochnosti, No. 4, pp. 5–24, July–August, 2008.     

The fatigue crack growth of a ship steel in seawater under spectrum loading

Fatigue crack growth of ABS EH36 steel under spectrum loading intended to simulate sea loading of offshore structures in the North Sea was studied using fracture mechanics. A digital simulation technique was used to generate samples of load/time histories from a power spectrum characteristic of the North Sea environment. In constant load-amplitude tests, the effects of specimen orientation and stress ratio on fatigue crack growth rates were found to be negligible in the range 2 × 10^?5 to 10^?3 mm/cycle. Fatigue crack growth rates in a 3.5% NaCl solution were two to five times faster than those observed in air in the stress intensity range 25 to 60 MPa √m. The average fatigue crack growth rates under spectrum loading and constant-amplitude loading were in excellent agreement when the fatigue crack growth rate was plotted as a function of the appropriately defined equivalent stress intensity range. This procedure is equivalent to applying Miner's summation rule in fatigue life calculations.