A generalized Paris’ law for fatigue crack growth

An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wöhler SN curve of the material, suggesting a more general “unified law”. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Δa, the “fracture quantum”. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Δa, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture “quantum” on the applied stress range level such that the correct convergence towards the Wöhler-like regime is obtained. Hence, the final law includes both Wöhler's and Paris’ material constants, and can be seen as either a generalized Wöhler's SN curve law in the presence of a crack or a generalized Paris’ law for cracks of any size.     

Fatigue crack growth simulation in coated materials using X-FEM

In the present work, the eXtended Finite Element Method (XFEM) is used to study the effect of bi-material interfaces on fatigue life in galvanised panels. X-FEM and Paris law are implemented in ABAQUS software using Python code. The XFEM method proved to be an adequate method for stress intensity factor computation, and, furthermore, no remeshing is required for crack growth simulations. A study of fatigue crack growth is conducted for several substrate materials, and the influence of the initial crack angle is ascertained. This study also compares the crack growth rate between three types of bi-materials alloys zinc/steel, zinc/aluminium, and zinc/zinc. The interaction between two cracks and fatigue life, in the presence of bi-material interface, is investigated as well.     

Prediction of fatigue crack growth life under variable-amplitude loading using finite element analysis

This article presents an elastic-plastic study aiming at predicting the fatigue crack growth (FCG) of 2024-T3 aluminum alloys under variable-amplitude loading. The proposed analysis needs the estimation of the residual stress distribution ahead of the crack tip during propagation. An elastic-plastic FE analysis has been implemented for modeling FCG using Chaboche's model. The FE study has been carried out through consideration of the loading history effect using the memory rules. Three different loading spectra have been applied in this work. The obtained results have been compared to the experimental ones and it has been proved that the suggested model has a better prediction of the FCG lives of cracked 2024-T3 aluminum alloy structures subjected to variable-amplitude loading.     

The role of grain boundaries on fatigue crack initiation - An energy approach

In this paper, we construct a model for prediction of fatigue crack initiation based on the material’s microstructure. In order to do so, the energy of a persistent slip band (PSB) is monitored and an energy balance approach is taken, in which cracks initiate and the material fails due to stress concentration from a PSB (with respect to dislocation motion). These PSBs are able to traverse low-angle grain boundaries (GB), thus belonging to clusters of grains. As a consequence of the ongoing cyclic slip process, the PSBs evolve and interact with high-angle GBs, the result of which leads to dislocation pile-ups, static extrusions in the form of ledges/steps at the GB, stress concentration, and ultimately crack initiation. Hence, this fatigue model is driven by the microstructure, i.e. grain orientations, widely distributed grain sizes, precipitates, PSB-GB interactions, as well as the affect of neighboring grains. The results predict that cracks initiate near twin boundaries from PSBs spanning a single large grain with a favorable orientation or multiple grains connected by low-angle GBs. Excellent agreement is shown between model predictions and experimental data.     

Accumulative damage near crack tip for welded bridge members: fatigue life determination

The behavior of crack growth for the fatigue damage accumulation near tip where damage is most severe is analyzed. Fatigue life is assessed for the welded members of bridges under traffic loading. Two parts are considered. They consist of the development of a fatigue damage accumulation model for welded bridge members and a method for calculating the stress intensity factor that is needed for evaluating the fatigue life of welded bridge members with cracks. Based on the concept of continuum damage accumulation and fatigue and fatigue crack growth relations, results are obtained to describe the relationship between the cracking count rate and the effective stress intensity factor. Crack growth and fatigue life are found for two types of welded members assisted by using fatigue experimental results. The stress intensity factors are modified by correcting for the geometric shape of the welded members in order to reflect the influence of the weldment and geometry. This is accomplished via the stress intensity factor. The calculated and measured fatigue lives were generally in good agreement for the initial cracking conditions of two types of welded members widely used in steel bridges.     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.     

Prediction models of fatigue crack closure and growth under random loading

The effects of plastic zones both in front of and behind crack tip on crack closure have been analysed. The total residual deformations of crack surfaces involve two parts, that is, the amount of plastic blunting of crack tip and the residual deformation in the wake of the tip. This paper presents a fatigue crack closure model in which the influences of compressive load on closure stress are discussed. The model is applied to random loading conditions by the assumption of limited memory properties. The fatigue lives are predicted using the proposed crack growth model for CCT plane stress specimen cut from 2219-T851 aluminum alloy under flight spectrum loadings, and the prediction values agree with the test results.The project was supported by the natural science foundation of China.     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

A stochastic theory of cumulative fatigue damage

A stochastic theory for the cumulative fatigue damage of structural components with random fatigue strength under random loading is proposed on the basis of Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components with constant fatigue strength subject to a narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to both metallic and non-metallic materials, narrow band and wide band stress process, and adapted to a sequence ofn, stationary stress processes or quasi-stationary stress process. The scatter and degradation of fatigue strength and the inspection maintenance can also be incorporated into the theory.     

One, no one, and one hundred thousand crack propagation laws: A generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth

Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m=2-5 in metals and m=10-50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review.     

Predicting the fatigue life and crack aspect ratio evolution in complex structures

This paper discusses a computationally efficient method for determining the behaviour of complex structures containing three-dimensional cracks. A simple method is presented for calculating the mode I stress intensities for semi-elliptical cracks emanating from the saddle point of two intersecting tubular members. This method, which gives results in good agreement with published values, uses the finite element technique, but does not require the crack to be modelled explicitly. The technique is then used, in conjunction with FASTRAN II, to study fatigue crack growth and the results are compared to experimental data. Good agreement is achieved between both the predicted and measured fatigue crack growth and the evolution of the crack aspect ratios.     

An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.     

On the formation of crack networks in high cycle fatigue

A probabilistic model based on an initial distribution of sites is proposed to describe different aspects of the formation, propagation and coalescence of crack networks in thermomechanical fatigue. The interaction between cracks is modeled by considering shielding effects. To cite this article: N. Malésys et al., C. R. Mecanique 334 (2006).     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

An asymptotic approach to crack initiation in fretting fatigue of complete contacts

The stress state near the corner of a complete contact subject to fretting action is studied using an asymptotic analysis. The spatial distribution of stress, together with the generalised stress intensity factor defining the severity of the stress state are found, and the implications for experimental determination of crack initiation conditions discussed.     

Surface finish of open holes on fatigue life

In this paper, the effect of surface finish of open holes on the fatigue life has been studied. Four defects of the surface finish are simulated. They are scratch, void, inclusion and roundness. Firstly, the effect of the four defects on the stress distributions around the holes has been studied by the finite element method (FEM). The fatigue lives are determined based on the stress distributions by the method of nominal stress approach. The results show that the fatigue lives are dependent on the quantity of the surface finished. There are the critical defect values of scratch, void and inclusion, smaller than which there is no effect of the surface finish on the fatigue life. For these three defects, the fatigue lives decrease with the increasing of the values of the defects. It is the same to the defect of roundness, e.g. the bigger roundness tolerance is, the shorter the life is. Further, an approximate quadratic curve has been found for the relationship between the roundness tolerances and their logarithmic fatigue lives.     

Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach

A hybrid weight function approach (HWFM) is presented for the fatigue life prediction of infinite body and welded joint structure containing elliptical cracks. A self-containing computer code has been developed for this purpose. Numerical computations were first conducted on cracked infinite body showing a physical fact, that the elliptical shape of the crack becomes circular during its evolution. The prediction of the fatigue crack growth shows that the present results are in perfect concordance with those reported in the literature. Then, numerical tests were carried out on two types of specimens of welded joint structure. The present results were compared to the experimental and predicted ones of other authors, demonstrating that the hybridization method is a powerful numerical technique, and that the SEDF approach (using the Sih’s law) is more valid for the critical cases of welded joints than the SIF approach (using the Paris law). A parametric study has been conducted on the stress ratio “R” showing that the fatigue life to failure decreases with the increase of “R”.     

Micro-macro investigations about the fatigue behavior of pre-hardened 304L steel

In this work, the effect of cyclic pre-hardening (CPH) and monotonic pre-hardening (MPH), on the Cyclic Stress-Strain Curve (CSSC) and fatigue are considered. New tension-compression tests on two types of 304L alloys used in nuclear power plants are carried out under the following conditions: (i) strain or stress control near endurance limit; (ii) zero or positive mean stress; (iii) virgin, CPH or MPH specimens. Macroscopic results show a detrimental effect of pre-hardening in strain control and a beneficial one in stress control. Some macroscopic considerations are given to explain this result and the effects of an applied mean stress which differ under stress and strain control. Relations between macroscopic results and microstructures at failure are investigated using SEM and TEM. SEM is used for analysis of fatigue striation space.TEM analyses suggest that cyclic pre-hardening mainly promotes wavy slip during subsequent fatigue testing, while monotonous pre-loading favors planar slip. For CPH case it seems that primary cells which are preserved and refined for the most part during fatigue testing, constitute the hard stable structure. After MPH and subsequent fatigue testing, a hard structure is constituted by embedding of three kinds of microstructures, small twins, small cells, crossing twin systems. The formation of a hard structure creates an important internal stress. Observation shows that in pre-hardened specimens, softening arrays as veins and PSBs are frequent under strain control and rather scarce under stress control. It can be so deduced that the increase of fatigue life by pre-hardening in stress control is related to reduced mean free path of mobile dislocations due to internal stress.The obtained results may help to understand some aspects about linear versus non linear fatigue damage accumulation.