Micromechanical modeling of short fatigue cracks

This paper gives an overview over the micromechanical modeling approaches of short fatigue cracks. Until now many approaches have been presented in the literature, which differ significantly in their degree of complexity ranging from simple empirical or analytical models to complex models based on numerical solutions. In recent years different trends were observed: On the one hand detailed models are presented, which describe the propagation of a microstructurally short fatigue crack in a physically sound way based on discrete dislocations. However, their application is somewhat limited due to their complexity regarding the application in real microstructures. Thus, another trend is to develop models closely related to experimental research work to identify and focus on the main aspects of short fatigue crack growth.     

Description of behavior of short fatigue cracks

The Article was received in the German language. Authorized translation by S. Ya.     

Interaction and evolution of short fatigue cracks

Distinguishing the different contributions to fatigue damage of short cracks having different sizes and locations on the specimen surface, three new concepts, referred to as effective short fatigue cracks (ESFCs), dominant effective short fatigue cracks (DESFC), and density of ESFCs, respectively, are introduced to facilitate an understanding of the mechanism of interaction and evolution of short cracks. These concepts are interrelated and in conjunction produce an 'effective short fatigue crack criterion'. Replica observations of 19 smooth axial specimens of 1Cr19Ni9Ti stainless steel weld metal during low-cycle fatigue tests reveal that the short cracks contribute to the fatigue damage of specimens due to the formation of a critical density of ESFCs. The density reflects the local microstructural growth conditions ahead of the DESFC tips. The DESFC behaviour is a result of interactive short cracks, and this behaviour is deemed suitable to describe the collective behaviour of short cracks. In the microstructural short-crack stage, the DESFC are located in the weakest zone. Due to an irregular microstructural barrier effect, the crack density is higher in this zone and increases with fatigue cycling to reach a maximum value at the transition point into the physical short-crack stage. Then, due to the effects of accelerating coalescence and the DESFC size shielding the formation of new cracks, the density decreases rapidly and tends gradually to a saturation value. This is why the short-crack growth rate is high initially and tends gradually to that of long-crack behaviour. The difference and change in local microstructural growth conditions ahead of DESFC tips are the intrinsic cause of the statistical behaviour of short cracks and the scatter of fatigue lives.     

Critical review of the fatigue growth of short cracks

Retirement for cause (RFC) has become a popular design/analysis philosophy because it facilitates continued use of components which would otherwise be retired based on a safe life philosophy. RFC permits this continued service on the basis that service-induced damage tracked by periodic inspections will not develop to a critical size within a future operating interval. Successful implementation of RFC requires fracture mechanics technology to predict in-service growth behavior. Recent observations suggest that nonconservative estimates of crack growth rate (and therefore inspection interval) and critical flaw size arise when conventional linear elastic fracture mechanics (LEFM) is applied to predict the growth of physically small cracks. This paper summarizes the results of an extensive limited-circulation critical review of the phenomenology and mechanics of short crack growth with a view to identifying when this anomalous growth makes RFC analyses untenable in terms of LEFM. Factors which control the growth of short cracks are enumerated. It is shown for unnotched samples that the apparent effect may be traced to microcrack closure and the metallurgical, mechanical, and environmental transients which develop in the transition from initiation to steady-state growth. For notch samples the anomalous growth of cracks is traced to the inelastic action that develops a displacement-controlled notch field, which, contrary to LEFM analysis, dominates crack extension. Mechanics analyses relevant to characterizing the growth of short cracks are discussed. A crack tip opening displacement criterion is indicated to be appropriate.     

Propagation behaviour of microstructural short fatigue cracks in the high-cycle fatigue regime

In the high-cycle fatigue regime, it is assumed that crack initiation mechanisms and short fatigue crack propagation processes govern fatigue life of a component. Moreover, it is now becoming accepted that the conventional fatigue limit does not imply complete reversibility of plastic strain and is connected to crack initiation. However, interaction of the crack tip with microstructural barriers, such as, e.g. grain boundaries or second phases, leads to a decrease and eventually to a stop in the crack propagation. In the present contribution, examples for propagating and non-propagating conditions of short fatigue cracks in the microstructure of a duplex steel are given, quantified by means of automated EBSD. To classify the results within the scope of predicting the service life for HCF- and VHCF-loading conditions, a numerical model based on the boundary element method has been developed, describing crack propagation by means of partially irreversible dislocation glide on crystallographic slip planes in a polycrystalline model microstructure (Voronoi cells). This concept is capable to account for the strong scattering in fatigue life for very small strain amplitudes and to contribute to the concept of tailored microstructures for improved cyclic-loading behaviour.     

A stress intensity factor approach to the fatigue growth of transverse ply cracks

A model has been developed for the stiffness reduction due to transverse ply crack growth during the fatigue of a (0/90)_s glass-fibre reinforced plastic laminate. A stress intensity factor is derived for a transverse ply crack and related to the stiffness reduction rate by the Paris law. The model gives good agreement with experimental data and can be used to maintain a constant stiffness reduction rate by incremental load-adding. The effect of frequency is considered.     

On propagation of short rolling contact fatigue cracks

Recent accidents involving railway rails have aroused demand for improved and more efficient rail maintenance strategies to reduce the risk of unexpected rail fracture. Numerical tools can aid in generating maintenance strategies: this investigation deals with the numerical modelling and analysis of short crack growth in rails. Factors that influence the fatigue propagation of short surface‐breaking cracks (head checks) in rails are assessed. A proposed numerical procedure incorporates finite element (FE) calculations to predict short crack growth conditions for rolling contact fatigue (RCF) loading. A parameterised FE model for the rolling‐sliding contact of a cylinder on a semi‐infinite half space, with a short surface breaking crack, presented here, is used in linear‐elastic and elastic–plastic FE calculations of short crack propagation, together with fracture mechanics theory. The crack length and orientation, crack face friction, and coefficient of surface friction near the contact load are varied. The FE model is verified for five examples in the literature. Comparison of results from linear‐elastic and elastic–plastic FE calculations, shows that the former cannot describe short RCF crack behaviour properly, in particular 0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is required instead.     

Naked eye observations of microstructurally short fatigue cracks

An experimental methodology is described whereby interactions between cracks and microstructural barriers, and the consequent non-uniform propagation rates are observed without the assistance of any microscopy technique. This experimental procedure consists in increasing the grain size of Al1050 and Al1100 aluminum alloys specimens until the centimeter scale by applying a series of mechanical and heat treatments. By properly adjusting the strains, temperatures and furnace times of both stages a very precise control of the microstructural size is achieved. Once the thermomechanical treatment is completed and the sought microstructural size is obtained, a small circular notch is machined on each specimen in order to initiate the cracks at the desired location, and the samples are subjected to mode I fatigue loading. The fluctuating crack growth rate, the twist and tilt angles of the crack-plane at grain boundaries and crack arrest and branching can be easily observed with the naked eye. Production of secondary crack branches caused by roughness induced closure has also been observed. Tests were performed varying grain size and notch diameter and it was observed that the distance between successive minima in crack growth rate correlates well with the grain size of the specimens. .     

Cyclic fatigue of long and short cracks in alumina

The cyclic fatigue behaviour of long and microstructurally short cracks in a 10 μm grain-size alumina has been investigated. This material was found to be stress sensitive, a modest drop in applied stress resulting in a considerable lifetime enhancement. The growth of long cracks was studied using the circular compact tension geometry and was found to follow a Paris law behaviour. The crack path was entirely intergranular in this material with long fatigue crack growth governed by the degradation of crack-wake bridging. Short-crack growth was investigated using indented discs in a biaxial flexure geometry. Short cracks were observed to grow at lower values of applied ΔK than long cracks, increasing with crack length as bridging of the crack wake increased. The fatigue crack growth of AD90 alumina was also investigated by in situ testing within the specimen chamber of an SEM. The long-crack behaviour was found to be similar to the 10 μm grain-size alumina and other data reported in the literature. However, the crack path followed a mixture of transgranular and intergranular fracture and discontinuous in nature with frequent arrests. The crack-advancement mechanisms in these two alumina materials are different and affect the short-crack behaviour. However, in both cases the long-crack behaviour is dominated by crack-wake effects. This revised version was published online in November 2006 with corrections to the Cover Date.     

A Bayesian evaluation of simulation models of multiple-site fatigue cracks

The rivet holes along the longitudinal top row of the outer skin of the fuselage over a two-bay length are considered as the independent structural unit for the simulated multiple-site fatigue cracks. Models of multiple-site fatigue cracks are proposed. The models are divided into several phases with some uncertain parameters. These phases are incorporated sequentially into a computer code with the Monte Carlo simulation method. The Bayesian estimation of uncertain parameters in the model can be identified on visual inspections by the Bayesian procedure from in-service inspection data measuring crack lengths of each rivet hole. In summary, this study evaluates effects of differences in the simulation models for the crack coalescence and failure phase for the distribution of inspection data measuring crack lengths with the Bayesian estimation of uncertain parameters from simulated in-service inspection data.     

A synergistic fracture mechanics approach to fatigue life evaluation

A technique for modeling synergistic effects in fatigue crack propagation (FCP) is presented. First, a mission (load/temperature history) is segregated into elemental damage events. A simple three parameter model is then used to describe these events. The model coefficients are seen to be interrelated linear functions of FCP rate controlling variables such as frequency, temperature, stress ratio (σ_min/σ_max), dwell, overload ratio ($\text{P}{}_{\mathrm{overload}}$/$\text{P}{}_{\max }$) and cycles between overload. Finally, integrating event-by-event crack advance gives the expected component crack propagation life under mission cycling. Results of this procedure applied to gas turbine disk materials IN100 and Waspaloy are discussed to examine the accuracy of the model.     

J integral applications for short fatigue cracks at notches

Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, l ₀ is introduced into the solutions for both the linear elastic stress intensity factor and the J integral. Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The modified J integral solutions are extended to plastically strained notches, and the solutions obtained are tested in the correlation of data for growth of sort cracks near notches of varying severity with data for long crack under elastic loading. Although constant stress amplitude tests of these notches gave crack growth rate versus crack length curves which varied from monotonically increasing for blunt notches, to an initial decrease followed by an increase of sharp notches, all the data fell within the long crack data when correlated by the J integral solutions. Conversely, these solutions can be used to predict elastic and inelastic short crack growth curves for notches of various severities.

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Résumé On a modifié les solutions de mécanique de rupture élastique et élastoplastique afin de prédire le comportement de fissures courtes. On a introduit une longueur effective de fissure l ₀ dans les solutions donuant le facteur d'intensité de contrainte linéaire élastique et l'intégrale J. Les résultats de croissance de fissure dans le cas de fissures courtes dans des éprouvettes non entaillées soumises à des champs de déformation élastique ou plastique, font état d'un excellent accord avec les données afférant à des fissures longues en condition élastique, lorsqu'ils sont interprétés sous forme de solutions modifiées. Les solutions des intégrales J sont extrapolées aux cas des entailles sollicitées dans le domaine plastique, et les solutions obtenues sont éprouvées dans une corrélation des données de croissance de fissures courtes au voisinage d'une entaille de sévérités diverses, avec les données de croissance de fissures longues sous mise en charge élastique.Les essais à amplitude de contrainte constante sur ces entailles conduisent à une vitesse de croissance qui, en fonction de la longuer de fissure, varie d'un accroissement régulier dans le cas d'entailles arrondies, à une diminution suivie d'un accroissement, dans le cas d'entailles aiguës. Ce nonobstant, toutes les données se sont révélées similaires aux données pour de longues fissures, lorsque l'on établit la corrélation des solutions des intégrales J.Complémentairement, ces solutions peuvent être utilisées pour prédire les courbes de croissance des fissures courtes élastique et inélastique, dans le cas d'entailles de sévérités différentes.

     

Initiation and early growth of short fatigue cracks at inclusions

In this study, the initiation and early growth behaviour of short fatigue cracks in En 7A steel with a high content of elongated MnS inclusions was investigated, by generating and evaluating data on the growth of short fatigue cracks under various stress levels and stress ratios for the six principal specimen orientations. Short cracks usually initiated at the debonded interfaces between the matrix and the inclusions. If there was no debonding, cracking sometimes occurred in the inclusions. In the early stages, short cracks propagated by a mechanism of inclusion influenced growth. Under low stress levels, usually one short crack was initiated which dominated most of the fatigue life, while under high stress levels there was multicrack interaction.

MST/3249A     

Three-dimensional measurement of short fatigue cracks using scanning acoustic microscopy

Abstract

The three-dimensional crack growth of short fatigue cracks in Al–Li 8090 alloy has been examined using time resolved acoustic microscopy. Two sets of specimens were machined having different orientations of the elongated grains. Depending on the orientation of the pancake shaped grains with respect to the propagation direction of the cracks different growth rates were obtained. Furthermore, the influence of the microstructure (e.g. grain boundaries) on the crack path in the two sets of specimens could be determined.

MST/1838     

Initiation of fatigue cracks in commercial aluminium alloys and the subsequent propagation of very short cracks

Experiments have been made on two commercial aluminium alloys (BS L65, Al-Cu-Mg-Si-Mn; DTD 5050, Al-Zn-Mg-Cu-Cr) to observe the initiation of fatigue cracks at a plane polished surface and the subsequent growth of very short cracks [0.006 mm (0.00025 in.)-0.5 mm (0.02 in.) deep]. It was found that cracks initiated at surface inclusions, either from the interface between an inclusion and the matrix or from a crack in an inclusion. In both cases the crack ran into the material in directions approximately perpendicular to the applied tensile stress. The growth rates of the short surface were compared, using linear elastic fracture mechanics, with the rates far long [>0.25 mm (0.01 in.)] through-section cracks. The growth rate for the short cracks tended towards that predicted from long cracks for creek depths greater than about 0.127 mm (0.005 in.) but the average crack rate in the early stages of growth was about 1.27 × 10^?6 mm/cycle (5 ×10^?8in./cycle) which is much faster than would be predicted from the long crack data. For cracks about 0.025 mm (0.001 in.) deep the rate varied approximately as the square root of the crack depth. The effect of stress on the proportion of the total life occupied by initiation and by propagation of the crack is discussed.     

A new approach to detect and size closed cracks by ultrasonics

The effect of a crack on time-of-flight of shear waves (4.5 MHz) polarized in perpendicular (t ) and parallel (t ) directions to the crack surface, propagating parallel to the direction of crack growth is investigated. The first and second back-wall echoes are used instead of the weak crack-tip echo for the measurement of time-of-flight. The measurement is made for fatigue cracks grown by different loading histories in ferritic steel (pressure vessel steel A533B-1) under the condition of no loading. The normalized time-of-flight (t –t )/t at the crack position is found to change proportionally as the ratio of crack depth to specimen width increases. The change is mainly due to the effect of plastic deformation occurring around the crack ont . It is shown that the depth of tightly closed fatigue crack in austenitic stainless steel (AISI 304) also can be evaluated under the condition of no loading by using this relationship.