Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

Fatigue crack growth retardation assessment of 2024-T3 and 6061-T6 aluminium specimens

A fatigue crack growth retardation model is developed. It considers a strip plastic zone with material hardening effect which is taken as one of the basic mechanisms controlling fatigue crack growth. Crack growth is treated incrementally and corresponds to the failure of material elements ahead of an existing crack after a certain critical number of low cycle fatigue. Computed curves are correlated to test data obtained from the 2024-T3 and 6061-T6 aluminium specimens. Deviations from test data increase with increasing crack length.     

Fatigue striation spacing and equivalent initial flaw size in Al 2024-T3 riveted specimens

One of the main concerns of aeronautical structures is structural damage due to fatigue. This phenomenon is accentuated in areas of stress concentration, namely the connection of components. The fuselage is one of the most important structural elements where the connection of the fuselage panels is often done by riveting. Specimens with several geometric configurations are used to study these structures. This work is concerned with the study of one of these specimens, i.e., the lap splice with three rows of rivets and one rivet column. It is part of the IDMEC-Porto contribution to the European project ADMIRE. Stress versus number of cycles results and measurements of fatigue striation spacing along two perpendicular directions using scanning electron microscopy (SEM) are presented. The fractographic reconstitution of fatigue crack growth was carried out. The value of equivalent initial flaw size (EIFS) is calculated using the back extrapolation technique and two models of fatigue crack growth. They consist of a model using the Paris law and another the strain energy density factor concept. The EIFS is used to predict the fatigue behaviour of this structural detail. It is intended to verify the applicability of empirical models based in experimental evidences.     

A micromechanical explanation of the mean stress effect in high cycle fatigue

A micro–macro approach of multiaxial fatigue in unlimited endurance is presented in this study, as an extension of a previous model recently proposed by the authors [Monchiet, V., Charkaluk, E., Kondo, D., 2006. A plasticity–damage based micromechanical modelling in high cycle fatigue. C.R. Mécanique 334 (2), 129–136]. It allows to take into account coupling between polycrystalline plasticity and damage mechanisms which occur at the scale of persistent slip bands (PSB) during cyclic deformation. The plasticity–damage coupled model is obtained by adapting the Gurson [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I – yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15] limit analysis to polycrystalline materials to take into account microvoids growth along PSBs. The macroscopic fatigue criterion corresponds to microcracks nucleation at the PSB–matrix interface. It is shown that this criterion accounts for the effect of the mean stress and of the hydrostatic pressure in high cycle fatigue. Such features of HCF are related to the damage micro-mechanisms. Finally, some illustrations concerning the particular case of cyclic affine loadings are presented and comparisons of the predictions of the fatigue criterion with experimental data show the relevance of this new approach.     

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).     

Fatigue and damage tolerance behaviour of corroded 2024 T351 aircraft aluminum alloy

The fatigue and damage tolerance behaviour of pre-corroded 2024 T351 aluminum alloy specimens has been investigated and compared to the behaviour of the uncorroded material. The experimental investigation was performed on specimens pre-corroded in exfoliation corrosion environment and included the derivation of S–N and fatigue crack growth curves as well as measurements of fracture toughness. The fatigue crack growth tests were performed for different stress ratios R. To obtain reference material behaviour all mechanical tests were repeated under the same conditions for uncorroded specimens. For the corroded material an appreciable decrease in fatigue resistance and damage tolerance was obtained. The results of the experimental investigation were discussed under the viewpoint of corrosion and corrosion-induced hydrogen embrittlement of the 2024 aluminum alloy. The need to account for the influence of pre-existing corrosion on the material’s properties in fatigue and damage tolerance analyses of components involving corroded areas was demonstrated.     

Dislocation pile-up model of fatigue thresholds for 2024- and 7075-alike aluminium alloys

Two parameters, K_max^* and δK_th^*, are presented to describe fatigue threshold behaviour and damage under any load ratio without invoking crack closure. Modelled are two fatigue thresholds that are coherently related to fatigue limit δσ_FL; they predict the fundamental threshold curves for aluminium alloys. By using a continuous configuration of dislocations in pile-up, fatigue limit behaviour is simulated as pile-up of dislocations against grain boundaries. A fatigue limit is determined in terms of a critical condition at which a fictitious microcrack associated with the pile-up corresponds to the onset of propagation. These two fatigue thresholds are attainable as the local stresses at the crack front approaching the fatigue limit. Microstructure is incorporated in the model to account for the effect on threshold behaviour. As a result, two fatigue threshold criteria are required. Quantitative assessment of the two criteria requires only knowledge of the conventional material properties in conjunction with microstructure. The micromechanical modelling exhibits a strong dependence of fatigue thresholds upon local microstructure.     

Mesomechanics of fatigue fracture for polycrystals with macroconcentrators

Fatigue fracture of aluminum alloys is analyzed from analysis of time-spatial mesoscale substructures. The behavior involves many stages at the mesoscale and translational–rotational movement of the bulk structure element in addition to fragmentation. Mesofragments on a trajectory of the fatigue crack were also studied.     

Mechanical characterisation of aluminium alloy 7449-T7651 at high strain rates and elevated temperatures using split hopkinson bar testing

Experimental Techniques - The mechanical behaviour of a 7 series high-strength aluminium alloy that is mainly used by the aerospace industry is under investigation. Aluminium alloy AA7449-T7651 is...     

Hysteresis loops predicted by isoenergy density theory for polycrystals. Part II: cyclic heating and cooling effects predicted from non-equilibrium theory for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium cylindrical bars

Mathematical tools and physical models should fit like hand and glove. Traditionally, such an understanding has worked surprisingly well in mechanics and physics. Differential calculus enabled the determination of motion of celestial bodies. Heisenberg's use of Hilbert space applied to calculations in quantum mechanics. These foot steps, however, failed to continue in the field of material science when attempting to address the evolution of material damage. On one hand, the mathematical formulation of the Riemann–Hilbert problem achieved great success for solving macrocrack problems but whether the same tool could be used for lower scale defects seems to be of less concern. This is a surprise because it is not obvious by any means whether microcracks can be distinguished from macrocrack by size difference alone, particularly when they are both treated in a single formulation.There are several issues of the fatigue problem that must be addressed. To begin with, local failure initiating near a surface should be distinguished from global failure that correspond to separation of a specimen into two or more pieces. The interim stages of initiation and termination would depend on the ductility and brittleness of the material in addition to the history of cyclic loading. Three different materials 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium will therefore be analyzed to show how their uniaxial properties would compare with the dissipation energy density functions and oscillation in temperature. Hysteresis loops for the local material points are determined. Their averages for the ASTM standard hour-glass specimen are then found. They give the global hysteresis loops corresponding to measurements from the uniaxial tests. The local dissipative energy density loops represent the irreversible nature of the materials are also taken into consideration. They are calculated for the soft aluminum and the hard titanium with steel being in between.Obtained also are the cyclic cooling and heating characteristics of the material under fatigue; they fluctuate about the ambient temperature. The -function designating the order and disorder of the fatigue process is also found to be oscillatory in character. Unlike entropy, it is not non-increasing or non-decreasing. It can change sign in a given process. This implies that the order of a system can be enhanced and then impeded or vice versa. Such a behavior is shown to prevail during the initial stage of the fatigue.     

Revised damage evolution equation for high cycle fatigue life prediction of aluminum alloy LC4 under uniaxial loading

The fatigue life prediction for components is a difficult task since many factors can affect the final fatigue life. Based on the damage evolution equation of Lemaitre and Desmorat, a revised two-scale damage evolution equation for high cycle fatigue is presented according to the experimental data, in which factors such as the stress amplitude and mean stress are taken into account. Then, a method is proposed to obtain the material parameters of the revised equation from the present fatigue experimental data. Finally, with the utilization of the ANSYS parametric design language (APDL) on the ANSYS platform, the coupling effect between the fatigue damage of materials and the stress distribution in structures is taken into account, and the fatigue life of specimens is predicted. The outcome shows that the numerical prediction is in accord with the experimental results, indicating that the revised two-scale damage evolution model can be well applied for the high cycle fatigue life prediction under uniaxial loading.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Correlation of crack growth rate and stress ratio for fatigue damage containing very high cycle fatigue regime

A model is proposed to correlate the crack growth rate and stress ratio containing very high cycle fatigue regime. The model is verified by the experimental data in literature. Then a formula is derived for the effect of mean stress on fatigue strength, and it is used to estimate the fatigue strength of a bearing steel in very high cycle fatigue regime at different stress ratios. The estimated results are also compared with those by Goodman formula.     

Very high cycle fatigue for GCr15 steel with smooth and hole-defect specimens

Very high cycle fatigue (VHCF) properties of a low temperature tempering bearing steel GCr15 with smooth and hole-defect specimens are studied by employing a rotary bending test machine with frequency of 52.5 Hz. Both smooth and hole-defect specimens break in VHCF regime with some difference in fatigue crack initiation. For smooth specimens, a fine granular area (FGA) is observed near the grain boundary in the fracture surface of the specimens broken after 10⁷ cycles. But no FGA is observed in the hole-defect specimens broken in VHCF regime, and the VHCF crack does not initiate from the small hole at the surface as it does at low or high cycle fatigue regime. Internal stress is employed to explain the VHCF behavior of these two types of specimens. At last, an advanced dislocation model based on Tanaka and Mura model is proposed to illustrate the internal stress process and to predict fatigue crack initiation life with FGA observed in the fracture region.     

Assessment of High Speed Imaging Systems for 2D and 3D Deformation Measurements: Methodology Development and Validation

Ultra high-speed and moderate speed image acquisition platforms have been characterized, with special emphasis on the variability and accuracy of the measurements obtained when employed in either 2D or 3D computer vision systems for deformation and shape measurements. Specifically, the type of image distortions present in both single channel cameras (HS-CMOS) and multi-channel image intensified cameras (UHS-ICCD) are quantified as part of the overall study, and their effect on the accuracy of experimental measurements obtained using digital image correlation have been determined. Results indicate that established methods for noise suppression and recently developed models for distortion correction can be used effectively in situations where the primary intensity noise components are characterized by minimal cross-talk and stationary spatial distortions. Baseline uniaxial tension experiments demonstrate that image correlation measurements using high speed imaging systems are unbiased and consistent with independent deformation measurements over the same length scale, with point-to-point strain variations that are similar to results obtained from translation experiments. In this study, the point-to-point variability in strain using the image intensified system is on the order of 0.001, whereas the non-intensified system had variability of 0.0001. Results confirm that high speed imaging systems can be utilized for full field two and three-dimensional measurements using digital image correlation methods.

Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100

To quantify the effects of interactions between various microstructure attributes on fatigue life in the high cycle fatigue (HCF) regime, we have proposed a new microstructure-sensitive extreme value statistical framework. This framework couples the extreme value distributions of certain fatigue indicator parameters (FIPs) or response functions to the correlated microstructure attributes that exist at the extreme value locations of these FIPs. We demonstrate the application of this statistical framework to investigate the microstructure-sensitive fatigue response of the PM Ni-base superalloy IN100 at 650 °C. To accomplish this task, we construct statistical volume elements (SVEs) used to compute the local response for 200 instantiations of IN100. These SVEs are constructed and simulated via the finite element method with crystal plasticity constitutive relations. The results of the simulations are used to explore extreme value statistics of the FIPs for these microstructures. The extreme value distributions of the Fatemi–Socie FIP are fit with high confidence by the Gumbel distribution and are defined in a representative nature with as few as 25 simulated microstructure instantiations (i.e., SVEs). The extreme value marked correlation functions of the apparent Schmid factor based on the geometry of the slip systems relative to the loading direction indicate that cube slip may be important to fatigue crack formation in this material system. This supports previous experimental observations of fatigue crack formation and microstructurally small fatigue crack growth along cube planes in IN100 in grains that are unfavorably oriented for octahedral slip at elevated temperatures.     

Probabilistic multiscale models and measurements of self-heating under multiaxial high cycle fatigue

Different approaches have been proposed to link high cycle fatigue properties to thermal measurements under cyclic loadings, usually referred to as “self-heating tests.” This paper focuses on two models whose parameters are tuned by resorting to self-heating tests and then used to predict high cycle fatigue properties. The first model is based upon a yield surface approach to account for stress multiaxiality at a microscopic scale, whereas the second one relies on a probabilistic modelling of microplasticity at the scale of slip-planes.Both model identifications are cost effective, relying mainly on quickly obtained temperature data in self-heating tests. They both describe the influence of the stress heterogeneity, the volume effect and the hydrostatic stress on fatigue limits. The thermal effects and mean fatigue limit predictions are in good agreement with experimental results for in and out-of phase tension-torsion loadings. In the case of fatigue under non-proportional loading paths, the mean fatigue limit prediction error of the critical shear stress approach is three times less than with the yield surface approach.     

Fourier and wavelet analyses for fatigue assessment of concrete beams

We investigate damage detection in a simply-supported pre-stressed beam. A crack was propagated by fatigue loads, which were applied up to two million cycles. Both fast Fourier transform (FFT) and continuous wavelet transform (CWT) are used in the analysis of the structural response to impulse loads. The acceleration response of the full-scale beam was measured each time a certain number of cycles of fatigue loads were applied. The results of this study show that both methods can clearly identify the crack growth induced by fatigue loads. The natural frequencies found by FFT are sensitive to the crack progression. The results from the CWT analysis show a clear difference in structural responses between the initial and damaged states of the structure. The response accelerations are de-noised by a soft-thresholding method before they are analyzed by CWT. In addition to the frequency components, the CWT shows the moment in time when particular frequencies occur. Therefore, wavelet analysis has the potential of becoming an effective tool for damage detection and health monitoring of structures for which the natural frequencies are irregularly changing. As the crack grows, the magnitude of ridges obtained by CWT analysis decreases significantly, which indicates the reduction in structural stiffness.     

Fatigue behaviour of FSW and MIG weldments for two aluminium alloys

The increasing use of aluminium alloys in transportation, such as railways, shipbuilding and aeronautics, calls for more efficient and reliable welding processes that would require more in depth understanding of fatigue failure. The objective of this work focuses on the contrasting difference of fatigue behaviour of joints made from the traditional process of metal inert gas (MIG) welding, and the emerging process of friction stir welding (FSW). Effort is made to relate the macroscopic mechanical behaviour to the microstructural feature of the weldments.     

Critère de fatigue polycyclique pour des matériaux anisotropes : application aux monocristauxA high cycle fatigue criterion for anisotropic materials: application to single crystals

The high-cycle fatigue criteria based on a macroscopic–mesoscopic scale interpretation, initiated by Dang Van, were used essentially for polycrystalline materials. In the existing criteria the material isotropy at both mesoscopic and macroscopic scales plays a key role. The purpose of this paper is to revisit the macroscopic to mesoscopic fatigue approach taking into account the material anisotropy and some results obtained by Bui. The possible applications are some anisotropic steels or monocrystalline structures such as stitanium turbine blades. To cite this article: F. Cano et al., C. R. Mecanique 332 (2004).