For the fatigue life of thin-walled components, not only fatigue crack initiation, but also crack growth is decisive. The phase-field method for fracture is a powerful tool to simulate arbitrary crack phenomena. Recently, it has been applied to fatigue fracture. Those models pose an alternative to classical fracture-mechanical approaches for fatigue life estimation. In the first part of this paper, the parameters of a phase-field fatigue model are calibrated and its predictions are compared to results of fatigue crack growth experiments of aluminium sheet material. In the second part, compressive residual stresses are introduced into the components with the help of laser shock peening. It is shown that those residual stresses influence the crack growth rate by retarding and accelerating the crack. In order to study these fatigue mechanisms numerically, a simple strategy to incorporate residual stresses in the phase-field fatigue model is presented and tested with experiments. The study shows that the approach can reproduce the effects of the residual stresses on the crack growth rate.
Mode II fatigue crack growth under reversed shear and static biaxial compression was investigated in two bearing steels. Many aborted branches, quasi-orthogonal to the main crack, were observed along the crack face. The compressive stress parallel to the main crack hindered the growth of these branches and favored coplanar mode II crack growth. The crack face sliding displacement profiles measured by DIC were used to derive $Δ_{\rm KII,eff}$, at the main crack tip, using elastic-plastic FE simulations with crack face friction, by an inverse method. Friction corrected crack growth kinetics were…
Cast and HIP'ed \textgamma-TiAl 4522XD is being developed for use in jet engine low pressure turbine blades, where temperature variations occur through the flight cycle. The effects of temperature variations on fatigue cracking were therefore examined in this study. It was found that fatigue crack growth rates were higher at 750C than 400C, but that $ΔK_\mathrm{th}$ was also higher. Temperature excursions between 400 and 750C during fatigue crack growth resulted in retardation of the crack growth rate, both on heating and cooling. It was also found that for notches $0.6$~mm in length and small…
A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1<D<2) and the parameters defining the fatigue crack propagation rate. The exponent m of the Paris' law is found to be an increasing function of the fractal dimension of the crack profile, m=2D/(2-D). This trend is confirmed by a quantitative analysis of fractographic images of Titanium alloys with different grain sizes (different roughness of crack profiles), by a new experimental test and by an indirect estimation of D from crack gr…
The deformation and fatigue crack nucleation mechanisms were studied by means of slip trace analysis and secondary electron microscopy in a textured AZ31B-O Mg alloy subjected to fully-reversed cyclic deformation at two different cyclic strain semi-amplitudes. Samples were deformed in two orientations leading to symmetric and non-symmetric cyclic stress-strain curves due to the activation of different deformation mechanisms. They were ascertained in longitudinal sections of the specimens, which included a large number of grains (from 1500 to 4500 for each specimen), to obtain statistically sig…
Nanocrystalline metals typically have high fatigue strengths, but low resistance to crack propagation. Amorphous intergranular films are disordered grain boundary complexions that have been shown to delay crack nucleation and slow crack propagation during monotonic loading by diffusing grain boundary strain concentrations, suggesting they may also be beneficial for fatigue properties. To probe this hypothesis, in situ transmission electron microscopy fatigue cycling is performed on Cu-1 at.% Zr thin films thermally treated to have either only ordered grain boundaries or to contain amorphous in…
The accumulated entropy is used to evaluate the initiation of crack in flat notched specimen made of stainless steel 304. Two notch radii have been studied to capture the thermography of crack initiation and measure accumulated heat dissipation. It has been observed that under pull-push loading with an R-ratio of -1, the accumulated entropy for crack initiation and crack length's growth up to a specific number, Fracture Fatigue Entropy remains nearly constant. Anaclastic deformation dissipation has been taken into account and a mathematical model based on Kelvin-Voigt type element has been dis…
The present work discusses the micro-mechanism of low cycle fatigue (LCF) crack growth in smooth bar specimens of Haynes 282. Two parametric approaches, i.e. crack tip opening angle (CTOA) and maximum tangential stress (θMTS) have been opted to characterize the cracks. CTOA variations along with a propagating crack, exhibit a non-linear decay followed by a stabilized regime. Mixicity of local KI and KII fields is directly proportional to θMTS and that can be assessed by measuring local deflections. Around the crack, the role of grain incompatibility has been addressed through EBSD and slip tra…
Considering the sensitivity of both fatigue strength and corrosion rate to the surface characteristics, apposite surface treatments could address the related challenges for biodegradable magnesium-based materials. Herein, we treated the surface of a biocompatible magnesium alloy by a low cost and versatile severe plastic deformation technique, severe shot peening, to evaluate the potential of surface grain refinement to enhance functionality in biological environment. The evolution of surface grain structure and surface morphology were investigated using optical as well as scanning and transmi…
Crack initiation and propagation under high-cycle fatigue conditions have been investigated for a polycrystalline Ni-based superalloy by in-situ synchrotron assisted diffraction and phase contrast tomography. The cracks nucleated along the longest coherent twin boundaries pre-existing on the specimen surface, that were well oriented for slip and that presented a large elastic incompatibility across them. Moreover, the propagation of microstructurally short cracks was found to be determined by the easy slip transfer paths across the pre-existing grain boundaries. This information can only be ob…
The deformation and crack initiation mechanisms were analyzed in a textured AZ31B-O Mg alloy subjected to fully-reversed, strain-controlled cyclic deformation along the rolling direction after 50 cycles (approximately 33% of the fatigue life). Distinct deformation bands corresponding to pyramidal slip or tensile twins were found in 538 grains out of 2100 grains. Slip trace analysis showed that 72.3% were pyramidal slip bands and 18.4% were twin boundaries. Both pyramidal slip and twinning was only found in 9.1% of the grains with deformation bands. Cracking was widespread after 50 cycles. Grai…
Three-dimensional dislocation dynamics simulations are used to study micro-crack interaction with the first micro-structural barrier in face-centred cubic bi-crystals loaded in high cycle fatigue conditions. In the examined configuration, we assumed that micro-crack transmission occurs due to surface relief growth in the secondary grain ahead of the primary crack. This indirect transmission mechanism is shown to strongly depend on grain-1/grain-2 disorientation. For instance, small grain disorientation induces plastic strain localisation ahead of the crack and faster transmission through the f…
We introduce a class of models based on near crack tip degradation of materials that can account for fracture growth under cyclic loads below the Griffith threshold. We incorporate the gradual degradation due to a cyclic load through a flow equation that decreases spatially varying parameters controlling the fracture toughness in the vicinity of the crack tip, with the phase and displacement fields relaxed to an energy minimum at each time step. Though our approach is phenomenological, it naturally reproduces the Paris law with high exponents that are characteristic of brittle fatigue crack gr…
In the present work, theoretical approaches, based on grain orientation dependent Young's modulus and Schmid factor are used to describe the influence of local grain orientation on crack initiation behaviour of the coarse grained nickel base superalloy René80. Especially for strongly anisotropic crystal structures with large grain size, such as the investigated material, the local elastic properties must be taken into account for assessment of fatigue crack initiation. With an extension of Schmid's law, the resulting shear stress amplitude, which triggers local cyclic plastic deformation, can …
This paper investigates correlation properties of fluctuations in fatigue crack growth of polycrystalline materials, such as ductile alloys, that are commonly encountered in structures and machinery components of complex electromechanical systems. The model of crack damage measure indicates that the fluctuations of fatigue crack growth are characterized by strong correlation patterns within short time scales and are uncorrelated for larger time scales. The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed in this paper, is characterized by a micro-structure which is res…
Aluminum alloy A356-T6 was subjected to fully reversed cyclic loading under tension, torsion and combined loading. Results indicate that endurance limits are governed by maximum principal stress. Fractography demonstrates long shear mode III propagation with multiple initiation sites under torsion. Under other loadings, fracture surfaces show unique initiation sites coincidental to defects and mode I crack propagation. Using the replica technique, it has been shown that the initiation life is negligible for fatigue lives close to 1E6 cycles for combined loading. The natural crack growth rate h…
We investigate the influence of microstructural traps in hydrogen-assisted fatigue crack growth. To this end, a new formulation combining multi-trap stress-assisted diffusion, mechanism-based strain gradient plasticity and a hydrogen- and fatigue-dependent cohesive zone model is presented and numerically implemented. The results show that the ratio of loading frequency to effective diffusivity governs fatigue crack growth behaviour. Increasing the density of \emph{beneficial} traps, not involved in the fracture process, results in lower fatigue crack growth rates. The combinations of loading f…
Electrode particle cracking is one of the main phenomena driving battery capacity degradation. Recent phase field fracture studies have investigated particle cracking behaviour. However, only the beginning of life has been considered and effects such as damage accumulation have been neglected. Here, a multi-physics phase field fatigue model has been developed to study crack propagation in battery electrode particles undergoing hundreds of cycles. In addition, we couple our electrochemo-mechanical formulation with X-ray CT imaging to simulate fatigue cracking of realistic particle microstructur…
Fatigue crack advance induced by the application of cyclic quasistatic loads is investigated both numerically and analytically using a lattice spring model. The system has a quasi-one-dimensional geometry, and consists in two symmetrical chains that are pulled apart, thus breaking springs which connect them, and producing the advance of a crack. Quasistatic crack advance occurs as a consequence of the plasticity included in the springs which form the chains, and that implies a history dependent stress-strain curve for each spring. The continuous limit of the model allows a detailed analytical …
In a recent very interesting and illuminating proposal, Yao et al. (2014) have discussed the use of the strain energy release rate (SERR) as a parameter to characterize fatigue delamination growth in composite materials. They consider fatigue delamination data strongly affected by R-curve behaviour due to fibres bridging and argue that a better approach is to correlate the crack advance with the total work per cycle measured in the testing machine. This seems to work better than estimating the compliance as a linear fit of experimental curves from Modified Compliance Calibration ASTM standards…
The damage mechanisms and load redistribution of high strength TC17 titanium alloy/unidirectional SiC fibre composite (fibre diameter = 100 $μ$m) under high temperature (350 °C) fatigue cycling have been investigated in situ using synchrotron X-ray computed tomography (CT) and X-ray diffraction (XRD) for high cycle fatigue (HCF) under different stress amplitudes. The three-dimensional morphology of the crack and fibre fractures has been mapped by CT. During stable growth, matrix cracking dominates with the crack deflecting (by 50-100 $μ$m in height) when bypassing bridging fibres. A small numb…
We obtain the Paris law of fatigue crack propagation in a disordered solid using a fuse network model where the accumulated damage in each resistor increases with time as a power law of the local current amplitude. When a resistor reaches its fatigue threshold, it burns irreversibly. Over time, this drives cracks to grow until the system is fractured in two parts. We study the relation between the macroscopic exponent of the crack growth rate -- entering the phenomenological Paris law -- and the microscopic damage-accumulation exponent, $γ$, under the influence of disorder. The way the jumps o…
The CrMnFeCoNi high-entropy alloy is highly printable and holds great potential for structural applications. However, no significant discussions on cyclic plasticity and fatigue damage in previous studies. This study provides significant insights into the link between print processes, solidification microstructure, cyclic plasticity and fatigue damage evolution in the alloy fabricated by laser powder bed fusion. Thermodynamics-based predictions (validated by scanning transmission electron microscopy (STEM) energy dispersive X-ray spectroscopy (EDX)) showed that Cr, Co and Fe partition to the c…
This paper describes a two-dimensional (2D) finite element simulation for fracture and fatigue behaviours of pure alumina microstructures such as those found at hip prostheses. Finite element models are developed using actual Al2O3 microstructures and a bilinear cohesive zone law. Simulation conditions are similar to those found at a slip zone in a dry contact between a femoral head and an acetabular cup of hip prosthesis. Contact stresses are imposed to generate cracks in the models. Magnitudes of imposed stresses are higher than those found at the microscopic scale. Effects of microstructure…
A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation function that effectively reduces the fracture toughness as a proper history variable accumulates. This macroscopic approach allows to reproduce the main known features of fatigue crack growth in brittle materials. Numerical experiments show that the Wöhler curve, the crack growth rate curve and the Paris law are naturally recovered, while the approximate Palmgren-…
Many people are aware of the theory of elastic fracture originated by AA Griffith, and although Griffith used the theorem of minimum potential energy most people seem unaware of the broader implications of this theorem. If it is set within its classical mechanics roots, it is clear that it is a restricted form of a Lagrangian. In advanced texts on fracture cracks are treated as dynamic entities, and the role of stress waves is clearly articulated. However, in most non-advanced texts on fracture and fatigue the role of stress waves are either not included or not emphasised, often leading to a p…
Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain pat…
We present a new theoretical and numerical phase field-based formulation for predicting hydrogen-assisted fatigue. The coupled deformation-diffusion-damage model presented enables predicting fatigue crack nucleation and growth for arbitrary loading patterns and specimen geometries. The role of hydrogen in increasing fatigue crack growth rates and decreasing the number of cycles to failure is investigated. Our numerical experiments enable mapping the three loading frequency regimes and naturally recover Paris law behaviour for various hydrogen concentrations. In addition, Virtual S-N curves are…
The distributions of size and chemical composition in the regolith on airless bodies provides clues to the evolution of the solar system. Recently, the regolith on asteroid (25143) Itokawa, visited by the JAXA Hayabusa spacecraft, was observed to contain millimeter to centimeter sized particles. Itokawa boulders commonly display well-rounded profiles and surface textures that appear inconsistent with mechanical fragmentation during meteorite impact; the rounded profiles have been hypothesized to arise from rolling and movement on the surface as a consequence of seismic shaking. We provide a po…
The interaction between cracks, as well as their propagation, in single-crystal aluminum is investigated at the atomic scale using the molecular dynamics method and the modified embedded atom method. The results demonstrated that the crack propagation in aluminum is a quite complex process, which is accompanied by micro-crack growth, merging, stress shielding, dislocation emission, and phase transformation of the crystal structure. The main deformation mechanisms at the front of the fatigue crack are holes, slip bands, and cross-slip bands. During crack propagation, there are interactions betw…
This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic formulation for rate-independent systems, coupling a phase-field description of fatigue fracture to a cyclic plasticity model that includes multi-surface kinematic hardening, gradient-enhanced isotropic hardening/softening and ratcheting. The coupled model embeds two distinctive fatigue effects. The first captures the characteristic features of low-cycle fatigue, d…
The fatigue fracture surfaces of a metallic alloy, and the stress corrosion fracture surfaces of glass are investigated as a function of crack velocity. It is shown that in both cases, there are two fracture regimes, which have a well defined self-affine signature. At high enough length scales, the universal roughness index 0.78 is recovered. At smaller length scales, the roughness exponent is close to 0.50. The crossover length $ξ_c$ separating these two regimes strongly depends on the material, and exhibits a power-law decrease with the measured crack velocity $ξ_c \propto v^{-ϕ}$, with $ϕ\s…
Natural hard composites like human bone possess a combination of strength and toughness that exceeds that of their constituents and of many engineered composites. This augmentation is attributed to their complex hierarchical structure, spanning multiple length scales; in bone, characteristic dimensions range from nanoscale fibrils to microscale lamellae to mesoscale osteons and macroscale organs. The mechanical properties of bone have been studied, with the understanding that the isolated microstructure at micro- and nano-scales gives rise to superior strength compared to that of whole tissue,…
The lifetime of most metals is limited by cyclic loads, ending in fatigue failure. The progressive growth of cracks ends up in catastrophic failure. An advanced method is presented for the determination of cyclic crack growth on the microscale using a nanoindenter, which allows the characterization of > 10,000 loading cycles. It uses focused ion beam fabricated notched microcantilevers. The method has been validated by cyclic bending metallic glass and tungsten microcantilevers. The experiments reveal a stable crack growth during the lifetime of both samples. The metallic glass shows less plas…
Crack initiation governs high cycle fatigue life and is susceptible to microstructural details. While corresponding microstructure-sensitive models are available, their validation is difficult. We propose a validation framework where a fatigue test is mimicked in a sub-modeling simulation by embedding the measured microstructure into the specimen geometry and adopting the experimental boundary conditions. Exemplary, a phenomenological crystal plasticity model was applied to predict deformation in ferritic steel (EN1.4003). Hotspots in commonly used fatigue indicator parameter maps are compared…
The propagation front of a crack generates large strain gradients and it is therefore a strong source of gradient-induced polarization (flexoelectricity). Herein, we demonstrate that, in piezoelectric materials, a consequence of flexoelectricity is that crack propagation will be helped or hindered depending on whether it is parallel or antiparallel to the piezoelectric polar axis. This means that the theory of fracture physics can no longer assume mechanical symmetry in polar materials. The discovery of fracture asymmetry also has practical repercussions for the electromechanical fatigue of fe…
Identification and characterization of three-dimensional crack propagation mechanism in the Aluminium alloy AA2024-T3 using high-resolution Digital Image Correlation
Unravelling the mechanisms underlying crack initiation in additively manufactured steel
University of Michigan（密歇根大学）；ESRF, The European Synchrotron（欧洲同步辐射装置）；Michigan Center for Materials Characterization, University of Michigan（密歇根大学材料表征中心）；ENSCM（法国国家化学工程学院）；Imperial College London（伦敦帝国理工学院）；Mines Paris, PSL University（巴黎矿业学院，PSL大学）
It was shown that a material fatigue fracture diagram can be viewed as a locus of points with $σ$ and $\sqrt l$ coordinates' product equal to $K_{1c}/2$, and $σ$ and $l$ product -- to $G_{1c}/2$, where $K_{1c}$ and $G_{1c}$ are non-linear fracture mechanics force and energy criteria. It was established that the average number of interatomic bonds destroyed within one alternate stress $\nabla_{1cs}$ cycle is directly proportional to $σ$ that is twice as large as a peak value of $σ^a$. It was found that low-cycle fatigue is characterized by $σ>σ_{0.2}$ and $σ_{1cs}> 1$, high-cycle fatigue -- by …
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of quasi-static fracture, fatigue damage and dynamic cracking. The finite element results obtained reveal the robustness of quasi-Newton monolithic schemes, with convergence readily attained under both stable and unstable cracking conditions. Moreover, since the solution method is unconditionally stable, very significant computational gains are observed relative to the …
This work investigated how the structure size affects the quasi-static and fatigue behaviors of graphene polymer nanocomposites, a topic that has been often overlooked. The results showed that both quasi-static and fatigue failure of these materials scale nonlinearly with the structure size due to the presence of a significant Fracture Process Zone (FPZ) ahead of the crack tip induced by graphene nanomodification. Such a complicated size effect and scaling in either quasi-static or fatigue scenario cannot be described by the Linear Elastic Fracture Mechanics (LEFM), but can be well captured by…
High field pulsed magnets at the NHMFL use high strength conductor wires up to 90% of their ultimate tensile strength. Therefore it is very important to ensure that the wires are free of flaws. It is known that in the conductors cold drawing process, internal chevron crack could occur due to unsuitable drawing die schedule or inadequate lubrication. These internal cracks occurs infrequently along the wire, so tensile tests of short samples cut from the ends of a long length conductor often miss the problem. In addition, small inclusions on the wire surface can compromise wires fatigue properti…
Environmentally assisted cracking phenomena are widespread across the transport, defence, energy and construction sectors. However, predicting environmentally assisted fractures is a highly cross-disciplinary endeavour that requires resolving the multiple material-environment interactions taking place. In this manuscript, an overview is given of recent breakthroughs in the modelling of environmentally assisted cracking. The focus is on the opportunities created by two recent developments: phase field and multi-physics modelling. The possibilities enabled by the confluence of phase field method…
