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.     

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.     

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.     

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.     

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.     

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.     

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.     

Mixed-mode separation in dynamic fracture mechanics: New path independent integrals

This paper presents a theoretical and numerical analysis of mixed-mode separation in fracture dynamics, based on new path independent integrals. The M-integral method proposed by Chen and Shield is generalized for dynamic fracture applications. Strain energy density is expressed as a function of the actual displacement field and of an auxiliary kinematically admissible field. On the other hand, the concept of the G-integral developed by Destuynder using the Rice J-integral is extended to dynamic problems. Introducing the same concept in the M-integral formulation leads to the new path-independent integral M in elastodynamics. Numerical tests give us accurate results of separated mode.     

Application of the Hartman-Schijve equation to represent Mode I and Mode II fatigue delamination growth in composites

This paper discusses the potential of a variant of the Hartman-Schijve equation to represent both Modes I and II constant amplitude delamination growth in composites. To this end we show that the delamination growth rate da/dN can often be related to (Δ√G − Δ√G_th)^α, where α is approximately 2. As such the exponent in this relationship is considerably lower than the exponent in “Paris like” power law representations. We also show that this particular representation of delamination growth in composites is similar to that seen for crack growth in metals.     

A fracture mechanics approach to estimate the fatigue endurance of welded t-joints including residual stress effects

Residual stresses and weld defects play a major role in the fatigue behaviour of welded structures, so these effects need to be accounted for in a theoretical analysis. A simplified engineering procedure based on linear‐elastic fracture mechanics is applied to estimate the fatigue behaviour, particularly the limit of endurance. Local geometrical irregularities and pre‐existing flaws, which are typical for this kind of weld, are covered by an overall notch intensity factor instead of a specific stress intensity factor, so the initial flaw size is not needed explicitly in the analysis. The effect of residual stresses can be easily included. The cut‐compliance method was applied to measure the residual stress distribution on the cross‐section of the weld. A welded T‐joint was used as a benchmark. Unexpectedly, compressive residual stresses were found to prevail in the root region. According to the analysis, they contribute to the endurance limit of the considered joint by about 50%. This result was confirmed by fatigue tests where a significant decrease in the fatigue strength after a post‐weld stress relieving heat treatment was observed.     

Understanding fatigue crack propagation in AISI 316 (N) weld using Elber’s crack closure concept: Experimental results from GCMOD and acoustic emission techniques

An experimental study of fatigue crack propagation and crack closure behaviour, in compact tension specimens of AISI 316 (N) weld has been conducted. The crack closure load was determined from the changes in the slope of the load–displacement curves using global crack mouth opening displacement (GCMOD) type gauge. The results were compared with those measured by acoustic emission technique which showed good agreement with each other. The experimental data bear clear evidence of fatigue crack closure. The crack opening force was found to increase moderately with crack length and increasing R-ratio, under a constant P_max of 5 kN. Above a critical R-ratio of 0.45 (approximately), the crack closure load is smaller than the minimum applied load. A good correlation was obtained for ΔK_eff/ΔK = 0.6684 – 2.4135R + 7.0077R² in the range 0 R  0.5. The magnitude of crack closure is used to interpret observed crack growth behaviour at different R-ratios.     

An example of the use of neural computing techniques in materials science—the modelling of fatigue thresholds in Ni-base superalloys

Two adaptive numerical modelling techniques have been applied to prediction of fatigue thresholds in Ni-base superalloys. A Bayesian neural network and a neurofuzzy network have been compared, both of which have the ability to automatically adjust the network’s complexity to the current dataset. In both cases, despite inevitable data restrictions, threshold values have been modelled with some degree of success. However, it is argued in this paper that the neurofuzzy modelling approach offers real benefits over the use of a classical neural network as the mathematical complexity of the relationships can be restricted to allow for the paucity of data, and the linguistic fuzzy rules produced allow assessment of the model without extensive interrogation and examination using a hypothetical dataset. The additive neurofuzzy network structure means that redundant inputs can be excluded from the model and simple sub-networks produced which represent global output trends. Both of these aspects are important for final verification and validation of the information extracted from the numerical data. In some situations neurofuzzy networks may require less data to produce a stable solution, and may be easier to verify in the light of existing physical understanding because of the production of transparent linguistic rules.     

Three-dimensional effects on fatigue crack closure in the small-scale yielding regime – a finite element study

Plasticity induced closure often strongly influences the behaviour of fatigue cracks at engineering scales in metallic materials. Current predictive models generally adopt the effective stress‐intensity factor (ΔΚ_eff = Κ_max–Κ_op) in a Paris law type relationship to quantify crack growth rates. This work describes a 3D finite element study of mode I fatigue crack growth in the small‐scale yielding (SSY) regime under a constant amplitude cyclic loading with zero T‐stress and a ratio Κ_min/Κ_max = 0 . The material behaviour follows a purely kinematic hardening constitutive model with constant hardening modulus. Dimensional analysis suggests, and the computational results confirm, that the normalized remote opening load value, Κ_op/Κ_max, at each location along the crack front remains unchanged when the peak load (Κ_max), thickness (B) and material flow stress (σ₀) all vary to maintain a fixed value of . Through parametric computations at various K levels, the results illustrate the effects of normalized peak loads on the through‐thickness opening–closing behaviour and the effects of σ₀/E, where E denotes material elastic modulus. The examination of deformation fields along the fatigue crack front provides additional insight into the 3D closure process.     

Stress enhancement at inclusion particles in aluminum matrix composites: computational modeling and implications to fatigue damage

The evolution of stresses inside the native inclusion particles in silicon carbide (SiC) particulate reinforced aluminum (Al) matrix composites is studied computationally by recourse to the finite element method. It is motivated by the experimental findings that inclusion fracture serves as the fatigue crack initiation in such types of composite materials. The analyses were performed for a simplistic model, with the inclusion embedded within a homogeneous material bearing the properties of Al/SiC mixture, and a refined model, with the inclusion, Al matrix and SiC particles specifically included. The simplistic model was found to be able to predict the stress enhancement in the inclusion that is consistent with the measured propensity of fatigue crack initiation when elasticity dominates. When plastic yielding occurs, the simplistic model failed to predict the experimental trend due to its inability to capture the highly non-uniform plastic flow field within the Al matrix. The refined three-phase model is needed for the plastic analysis. Implications of the present findings to general numerical modeling of composite materials are discussed.