A statistical fatigue model covering the tension and compression Wöhler fields

A statistical fatigue model to predict the Wöhler field for any combination of _σmin${\sigma }_{min}$, _σmax${\sigma }_{max}$ or R=_σmin/_σmax$R={\sigma }_{min}/{\sigma }_{max}$ is presented. The model extends an existing model to the case of _σmax${\sigma }_{max}$ being tension and _σmin${\sigma }_{min}$ being tension or compression, and is derived based on physical, statistical and compatibility conditions, thus, eliminating the selection of arbitrary functions. The main tool to derive the model is a functional equation, which allows obtaining the most general model satisfying all the stated conditions. In particular, the regression formula for the _σmax${\sigma }_{max}$–logN$logN$ field for fixed R$R$ values is analyzed. A particular and powerful model is selected and its main properties are derived. This model is applied to some real data to illustrate its applicability to practical problems. The results seem to be very promising, especially because the model, due to its physical and statistical constraints, appears to be very robust and with a high capacity to detect outliers.     

New quantized failure criteria: application to nanotubes and nanowires

In this paper new quantized failure criteria are proposed, also for nanoscale applications. The main theories in the context of the strength of solids, i.e., of brittle fracture, dynamic fracture, fatigue and Weibull Statistics are reconsidered according to the proposed “quantization rules”. The “corresponding principle” is verified and thus the classical theories are found to be the limit cases of the quantized counterparts. As an example, our treatment is applied to very recent experimental results on carbon or WS₂ nanotubes and to futurist ultra-nanocrystalline diamond nanowires, for which the tensile, bending and ideal strength are estimated.     

Influence of woven ply degradation on fatigue crack growth in thin notched composites under tensile loading

This paper deals with the fatigue of the through-the-thickness crack propagation in thin notched composite laminates made of two glass woven plies. It highlights the different crack growths between warp and weft directions of the woven ply. Experimental results show a decrease of the crack growth rate per cycle with the increase of the crack initiation time. Moreover, it has been shown that it is necessary to take into account the fatigue damage of the woven plies in term of loss of rigidity in the initiation phase. The fatigue crack growth rates are then quantified using Paris law type equations and linear elastic fracture mechanics (LEFM).     

Influence of defects on fatigue crack propagation in laser hybrid welded eccentric fillet joint

Fatigue cracking of laser hybrid welded eccentric fillet joints has been studied for stainless steel. Two-dimensional linear elastic fracture mechanics analysis was carried out for this joint geometry for four point bending load. The numerical simulations explain for the experimental observations why the crack propagates from the lower weld toe and why the crack gradually bends towards the root. Lack of fusion turned out to be uncritical for the initiation of cracks due to its compressive stress conditions. The linear elastic fracture mechanics analysis has demonstrated in good qualitative agreement with fatigue test results that lack of fusion slightly (<10%) reduces the fatigue life by accelerating the crack propagation. For the geometrical conditions studied here improved understanding of the crack propagation was obtained and in turn illustrated. The elaborated design curves turned out to be above the standard recommendations.     

From a local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints

This paper investigates the possibility of unifying different criteria concerned with the fatigue strength of welded joints. In particular, it compares estimates based on local stress fields due to geometry (evaluated without any crack-like defect) and residual life predictions in the presence of a crack, according to LEFM. Fatigue strength results already reported in the literature for transverse non-load-carrying fillet welds are used as an experimental database. Nominal stress ranges were largely scattered, due to large variations of joint geometrical parameters. The scatter band greatly reduces as soon as a 0.3-mm virtual crack is introduced at the weld toe, and the behaviour of the joints is given in terms of Δ K _I versus total life fatigue. Such calculations, not different from residual life predictions, are easily performed by using the local stress distributions determined near the weld toes in the absence of crack-like defects. More precisely, the analytical expressions for K _I are based on a simple combination of the notch stress intensity factors K ₁^N and K ₂^N for opening and sliding modes. Then, fatigue strength predictions, as accurate as those based on fracture mechanics, are performed by the local stress analysis in a simpler way.     

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part I: Experiments

The effect of bondline thickness, from 130 μm to 790 μm, on the fatigue and quasi-static fracture behavior of aluminum joints bonded using a toughened epoxy adhesive was studied experimentally under mode-I (DCB) and mixed-mode (ADCB) loading. Under mode-I loading, it was found that the fatigue threshold energy release rate, G_th, decreased for very thin bondlines, while under mixed-mode loading, the G_th changed very little with bondline thickness. In both cases, the effect of bondline thickness was more pronounced at higher crack growth rates. For quasi-static fracture, the effect of adhesive thickness on the energy release rate for the onset of fracture from the fatigue threshold, G_c0, was similar to that found for the fatigue threshold; however, the steady-state energy release rate, , increased linearly with increasing bondline thickness.     

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered.     

Fracture mechanics in fatigue calculations as the assistance in structural design. Case study

A case study originated from a request to perform fatigue calculations on a partial penetration weld in a steel casting on a new heavy lift ship. The ship has a special lifting system for lifting and transporting topsides of offshore oil/gas platforms. There are many sizes of offshore platforms so the lift system is designed to move along the vessel on rails, which are part of the main deck of the ship hull. The loads passing into the rails during lift operations are large, and massive steel castings of complex shapes are used to distribute these loads into the hull. The castings are very thick so it is difficult to achieve full penetration welds, and therefore the initial design proposed partial penetration welds. In order to decide if the partial penetration welds were adequate, a fatigue assessment was carried out using a fracture mechanics approach based on BS7910. Different possibilities of the bevelling of castings edges in preparation for welding were considered in the stress analysis and in the crack growth estimations. In the areas of the ship hull which experienced high dynamic stress ranges none of the different possibilities showed acceptable fatigue life, and would demand re-design. The stress intensity factors obtained through the extensive finite element analysis were compared with the analytical solutions available in literature. Both results showed good correspondence.     

The mixed-mode investigation of the fatigue crack in CTS metallic specimen

The experiments of a fatigue crack under mixed-mode loading are performed with CTS (Compact-Tension-Shear) specimens associated to a mixed mode loading device. The effect of loading angle on crack growth rate and on crack bifurcation angle is analyzed. Also, the welded specimens are introduced in the experiments in order to investigate the influence of the filled weld. In the fatigue tests, three loading angles, two loading levels and two materials are selected in the experiments. Furthermore, on the basis of the experimental data, a mixed-mode crack growth model is proposed in order to evaluate numerically a fatigue crack growth rate, in which the effects of the loading mode and of the residual stresses due to weld are considered. The validation of the model is carried out on CTS specimens under mixed mode loading.     

Fatigue in fibre metal laminates: The interplay between fatigue in metals and fatigue in composites

With the introduction of fibre metal laminates (FMLs) as a (fatigue) damage tolerant material concept in aeronautics, an interesting field emerged where fatigue damage interaction plays a dominant role. The hybrid concept effectively demands evaluating fatigue damage growth based on fracture phenomena typical for both metals and fibre‐reinforced composites that continuously interact with each other. This paper explains current understanding of the fatigue fracture phenomena in FMLs, and it demonstrates how this interaction limits the criticality of both the metallic and composite fracture phenomena. In addition, it explains how the laminated hybrid configuration can be further exploited scientifically to unravel the physics of the individual fatigue fracture phenomena.     

A multiparameter approach to the prediction of fatigue crack growth in metallic materials

A multiparameter approach is proposed for the characterization of fatigue crack growth in metallic materials. The model assesses the combined effects of identifiable multiple variables that can contribute to fatigue crack growth. Mathematical expressions are presented for the determination of fatigue crack growth rates, d a /d N , as functions of multiple variables, including stress intensity factor range, Δ K , stress ratio, R , crack closure stress intensity factor, K _cl , the maximum stress intensity factor K _max , nominal specimen thickness, t , frequency, Ω , and temperature, T . A generalized empirical methodology is proposed for the estimation of fatigue crack growth rates as a function of these variables. The validity of the methodology is then verified by making appropriate comparisons between predicted and measured fatigue crack growth data obtained from experiments on Ti–6Al–4V. The effects of stress ratio and specimen thickness on fatigue crack growth rates are then rationalized by crack closure considerations. The multiparameter model is also shown to provide a good fit to experimental data obtained for HY-80 steel, Inconel 718 polycrystal and Inconel 718 single crystal. Finally, the implications of the results are discussed for the prediction of fatigue crack growth and fatigue life.     

Monitoring quasi-static and cyclic fatigue damage in fibre-reinforced plastics by Poisson’s ratio evolution

Even if the extent of fatigue damage in fibre-reinforced plastics is limited, it can already affect the elastic properties. Therefore, the damage initiation and propagation in composite structures is monitored very carefully. Beside the use of nondestructive testing methods (ultrasonic inspection, optical fibre sensing), the follow-up of the degradation of engineering properties such as the stiffness is a common approach.In this paper, it is proved that the Poisson’s ratio can be used as a sensitive indicator of fatigue damage in fibre-reinforced plastics. Static tests, quasi-static cyclic tests and fatigue tests were performed on [0°/90°]_2s glass/epoxy laminates, and longitudinal and transverse strain were measured continuously. The evolution of the Poisson’s ratio ν_xy versus time and longitudinal strain ε_xx is studied. As the transverse strain measurement is crucial to monitor the degradation of the Poisson’s ratio, three techniques were applied to measure the transverse strain (strain gauges, mechanical extensometer and external optical fibre sensor).Finally, the technique has been applied to a totally different material: a carbon fabric thermoplastic composite. The results show a very similar degradation of the Poisson’s ratio, although no stiffness degradation can be observed during fatigue loading of this material.It is concluded that the degradation of the Poisson’s ratio can be a valuable indicator of fatigue damage, in combination with the stiffness degradation.     

Scaling and fractality in fatigue resistance: Specimen‐size effects on Wöhler's curve and fatigue limit

The present contribution investigates size effects on Wöhler's curve in accordance with dimensional analysis and intermediate asymptotics theory. These approaches provide a generalised equation able to interpret the specimen‐size effects on Wöhler's curve. Subsequently, using a different approach based on lacunar fractality concepts, analogous scaling laws are found for the coordinates of the limit‐points of Wöhler's curve, so that a theoretical explanation is provided to the decrement in fatigue resistance by increasing the specimen size. Eventually, the proposed models are compared with experimental data available in the Literature, which seem to confirm the advantage of applying fractal geometry to the problem.     

Improvement in the fatigue strength of chromium electroplated AISI 4340 steel by shot peening

In landing gear, an important mechanical component for high responsible applications, wear and corrosion control is currently accomplished by chrome plating or hard anodising. However, some problems are associated with these operations. Experimental results have also shown that chrome‐plated specimens have fatigue strength lower than those of uncoated parts, attributed to high residual tensile stress and microcracks density contained into the coating. Under fatigue conditions these microcracks propagate and will cross the interface coating‐substrate and penetrate base metal without impediment. Shot peening is a surface process used to improve fatigue strength of metal components due to compressive residual stresses induced in the surface layers of the material, making the nucleation and propagation of fatigue cracks difficult. This investigation is concerned with analysis of the shot peening influence on the rotating bending fatigue strength of hard chromium electroplated AISI 4340 steel. Specimens were submitted to shot peening treatment with steel and ceramic shots and, in both cases, experimental results show increase in the fatigue life of AISI 4340 steel hard chromium electroplated, up to level of base metal without chromium. Peening using ceramic shot resulted in lower scatter in rotating bending fatigue data than steel shots.     

Influence of microstructure on fatigue crack propagation under bending in the alloy Ti–6Al–4V after heat treatment

The paper presents the test results obtained for fatigue crack growth in Ti–6Al–4V titanium alloy subjected to bending. The tests were performed in plane specimens with the stress concentrators being a one‐sided sharp notch. The tested specimens were made of the oxygenated Ti–6Al–4V subjected to various variants of heat treatment. The tests were carried out at the fatigue test stand MZGS‐100 under loading frequency 28.4 Hz. From the obtained results of fatigue and structural tests it appears that schemes of crack propagation and fatigue lives of the considered alloy are different depending on a structure obtained as a result of a given heat treatment.     

Numerical simulation of the coupling between thermal dissipation and fish‐eye crack growth in very high cycle fatigue regime

In this paper, we study the temperature field associated with the propagation of a fatigue crack in a very high cycle fatigue regime during ultrasonic fatigue testing. We use a Paris–Hertzberg crack growth law to compute the evolution of the crack and a perfectly elastic–plastic constitutive law to compute the plastic dissipation per cycle at the tip of the crack. A thermomechanical finite element model is proposed to estimate the evolution of the temperature field during the crack propagation. Numerical results obtained agree fairly well with experimental results.     

Micro- and macro-approach to the fatigue crack growth in progressively drawn pearlitic steels at different R-ratios

This paper deals with the role of microstructure on the fatigue behaviour of pearlitic steels with different degrees of cold drawing. The analysis is focussed on the region II (Paris) of the fatigue behaviour, measuring the constants (C and m) for the different degrees of drawing. From the engineering point of view, the manufacturing process by cold drawing improves the fatigue behaviour of the steels, since the fatigue crack growth rate decreases as the strain hardening level in the material increases. In particular, the coefficient m (slope of the Paris laws) remains almost constant and independent of the drawing degree, whereas the constant C decreases as the drawing degree rises. The paper focuses on the relationship between the pearlitic microstructure of the steels (progressively oriented as a consequence of the manufacturing process by cold drawing) and the macroscopic fatigue behaviour. To this end, a detailed metallographic analysis was performed on the fatigue crack propagation path after cutting and polishing on a plane perpendicular to the crack front (fracto-metallographic analysis). It is seen that the fatigue crack growth path presents certain roughness at the microscopic level, such a roughness being related to the pearlitic colony boundaries more than to the ferrite/cementite lamellae interfaces. Fatigue cracks are transcollonial and exhibit a preference for fracturing pearlitic lamellae, with non-uniform crack opening displacement values, micro-discontinuities, branchings, bifurcations and frequent local deflections that create microstructural roughness. The net fatigue surface increases with cold drawing due to the higher angle of crack deflections. With regard to the influence of the R-ratio, an increase of such a stress ratio produces microcracking with a higher number of branchings for the same stress intensity range.