Dynamic crack nucleation and propagation in polycrystalline aluminum aggregates subjected to large inelastic deformations

The major objective of this work has been to apply a new compatibility-based fracture theory to the investigation of dynamic failure of polycrystalline metals and alloys. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, a general fracture criterion based on the integral law of compatibility is used. This new fracture criterion, was coupled with rate-dependent dislocation-density based crystalline plasticity formulations to elucidate the microstructural mechanisms related to the evolution of intergranular and transgranular failure and to understand how grain sizes and strain-rate sensitivity affect aggregate strength, ductility, and dynamic damage tolerance. It is shown that cracks commonly nucleate at triple junctions and at grain boundaries as intergranular cracks, and that slip bands through grains result in transgranular cracks.     

Three‐dimensional modelling of intergranular fatigue failure of fine grain polycrystalline metallic MEMS devices

This paper presents a 3D finite element model to investigate intergranular fatigue damage of microelectromechanical systems (MEMS) devices and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of MEMS material grain structures is modelled using randomly generated 3D Voronoi tessellations. Continuum Damage Mechanics is used to model progressive material degradation due to fatigue. A new 3D micro‐grain debonding procedure is developed to consider both intergranular crack initiation and propagation stages. The fatigue damage model is then used to investigate the effects of microstructure randomness on the variability in fatigue life of cantilever MEMS devices. Three different types of randomness are considered: (1) topological disorder due to random shapes and sizes of the material grains, (2) variation in material properties considering a normally (Gaussian) distributed elastic modulus and (3) material defects or internal voids. The stress–life results obtained are in good agreement with experimental data. The progression of damage and the overall crack pattern obtained from the microcantilever beam model are consistent with empirical observations.     

Micromechanics of dislocation channeling in intergranular stress corrosion crack nucleation

While driven by a combination of stress, a susceptible microstructure and an aggressive environment, the mechanistic origin of stress corrosion cracking remains poorly understood. The emergence of localized deformation as a key process in SCC has resulted in considerable experiment and simulation studies. The effectiveness of irradiation in localizing deformation into dislocation channels has provided a tool for studying the interaction between channels and grain boundaries. Experiment and simulation have shown that normal stress can be in excess of twice the applied stress and that cracking correlates well with the high normal stress. Shear stresses in the channel can add an additional component to the normal stress at the channel-boundary intersection. While the exact role of localized deformation in stress corrosion cracking is not yet full understood, it is known that the degree of localized deformation correlates well with SCC susceptibility. Further, both experiments and simulations indicate that cracks preferentially nucleate in grain boundaries that are perpendicular to the loading direction, are non-special high angle boundaries, are not oriented for easy deformation under the applied load, and are effective barriers to slip transmission. This paper will review recent progress in understanding the behavior of localized deformation and the impact on stress corrosion cracking.     

Effects of grain size on cyclic plasticity and fatigue crack initiation in nickel

Fatigue experiments were conducted on polycrystalline nickel of two grain sizes, 24 and 290 μm, to evaluate the effects of grain size on cyclic plasticity and fatigue crack initiation. Specimens were cycled at room temperature at plastic strain amplitudes ranging from 2.5×10⁻⁵ to 2.5×10⁻³. Analyses of the cyclic stress–strain response and evolution of hysteresis loop shape indicate that the back stress component of the cyclic stress is significantly affected by grain size and plastic strain amplitude, whereas these parameters have little effect on friction stress. A nonlinear kinematic hardening framework was used to study the evolution of back stress parameters with cumulative plastic strain. These are related to substructural evolution features. In particular, long range back stress components are related to persistent slip bands. The difference in cyclic plasticity behavior between the two grain sizes is related to the effect of grain size on persistent slip band (PSB) morphology, and the effect this has on long range back stress. Fine grain specimens had a much longer fatigue life, especially at low plastic strain amplitude, as a result of the influence of grain size on fatigue crack initiation characteristics. At low plastic strain amplitude (2.5×10⁻⁴), coarse grain specimens initiated cracks where PSBs impinged on grain boundaries. Fine grain specimens formed cracks along PSBs. At high plastic strain amplitude (2.5×10⁻³), both grain sizes initiated cracks at grain boundaries.     

Prediction of fatigue crack nucleation life in polycrystalline AA7075‐T651 using energy approach

A crystal plasticity (CP) simulation and an energy‐based model is presented to predict the fatigue nucleation onset for polycrystalline AA 7075‐T651. Different microstructure morphology and grain sizes are employed in the simulations. Using a simple method, statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) as decoupled with crystal plasticity model are estimated using a double round‐notch specimen test data, and CP simulation. The dislocation density parameter approximated from plastic energy density, stored energy density, elastic energy and accumulated slip validated with double hole experimental data. Sensitivity analysis is performed with respect to different microstructures and dislocation density parameters. Roughly, maximum 30% difference between experimental nucleation life and the simulated one is observed. The simulated predictions are in fair agreement with test data. The proposed strategy is suitable to study the scatter of fatigue nucleation life.     

An energy analysis of triple junction crack nucleation due to the wedging action of grain boundary dislocations

A physical model of wedge crack formation at triple junctions in polycrystalline materials is analyzed in this paper. The origin of the crack formation is the sliding of grain boundaries meeting at triple junctions. Based on the dislocation model of grain boundaries, the sliding is attributed to the gliding of grain boundary dislocations (GBDs). Consequently, the resulting crack formation can be analyzed theoretically in terms of the energetics of the piling up of interacting GBDs. The model permits the determination of crack stability or instability as well as the length of the stable crack. Results are obtained in this paper for polycrystalline ice and aluminium.     

Probabilistic description of fatigue crack growth in polycrystalline solids

A stochastic model describing the crack evolution and scatter associated with the crack propagation process has been built on the basis of the discontinuous Markovian process. The evolution and scatter are identified in terms of constant probability curves whose equation is derived as In P_r(i) = B(e^KI₀ − e^Ki), i ≥ I₀, where i is the number of cycles, B and K are crack-length-dependent variables, P_r(i) is the probabiliity of the crack being at position r along the fracture surface after i cycles elapse and I₀ is the minimum number of cycles required for the crack to advance from one position on the fracture surface to the next. The validity of the model is established by comparing the crack growth curves generated for Al 2024-T3 at a specific loading condition with those experimentally obtained.     

A theory of crack nucleation in high strain fatigue

From previous observations of the surfaces of metals cycled in high strain fatigue, the mechanism of crack nucleation is considered a plastic instability phenomenon. A model for crack nucleation based on this conclusion is now developed quantitatively and a simple relationship between the number of cycles to nucleate a crack and the applied, plastic, strain range thus predicted. Since the model is valid for any material capable of plastic deformation, plasticine has been cycled in reversed bending to test its prediction. Cracks were observed to form in the plasticine by puckering of the surface at stress concentrations, in direct confirmation of the model. Moreover, the crack nucleation measurements on the plasticine and data on metals, taken from the literature, are considered to be in reasonable agreement with the prediction of the model.

---

Zusammenfassung Ausgelrend von früheren Experimenten an Metalloberflächen, die starken Ermüdungs-verformungen unterworfen wurden, wird die Art der Rissentstehung als ein plastisches Instabilitätsphänomen betrachtet. Ein darauf aufbauendes Modell für die Rissentstehung wird quantitativ entwickelt and eine einfache Beziehung zwischen der Anzahl der zur Rissentstehung führenden Ermüdungsvorgänge and dem angewandten Verformungsbereich angegeben. Da das Modell auf jedes plastisch verformbare Material anwendbar ist, wurde seine Gültigkeit an Plastilin getestet, das periodischen Biegungen unterworfen wurde. Es wurden Risse im Plastilin beobachtet, die sich, entsprechend dem Modell, durch Faltenbildung der Oberfläche bei Stellen erhöhter Spannung ausbildeten. Ausserdern lässt sich feststellen, dass sowohl die Messergebnisse über Rissentstehung an Plastilin als auch die, der Literatur entnommenen, Messergebnisse an Metallen in brauchbarer Übereinstimmung mit den Aussagen des Modells stehen.

---

Résumé A partir d'observations précédentes faites sur la surface des métaux soumis à la fatigue oligocyclique, on a déduit que le mécanisme de formation de la fissure relevait d'un phénomène d'instabilité plastique.Sur la base de cette conclusion, on développe à présent quantitativement un modèle de formation de la fissure, ce qui permet de prédire use relation simple entte le sombre de cycles nécessaires pour amorcer une fissure et l'écart de déformation plastique appliquée par cycle.Le modèle étant appliquable à tout materiau susceptible de déformation plastiques, on a soumis à flexion alternée de la plasticise afin d'en vérifier les prédictions.On a observé que, pour ce matériau, les fissures prenaient naissance par un processus de plissement de la surface aux endroits de concentration de tension, ce qui confirme directement le modèle proposé. En outre, les mesures de formation des fissures dans la plasticise ont été comparées aux données existantes dans la littérature, et qui se refèrent aux métaux.Cette comparaison prêche en faveur d'une concommitence raisonnable des observations expérimentales et des prédictions du modèle.

     

Influence of corrosion and creep on intergranular fatigue crack path in 2XXX aluminium alloys

In this paper, two examples of the influence of time-dependent processes on crack path in two 2XXX aluminium alloys are presented. The first example is concerned with corrosion-fatigue crack growth resistance of a 2024 T351 alloy cracked in the S-L direction in 3.5% NaCl solution at free corrosion potential. The second example deals with the elevated temperature crack growth resistance of a 2650 T6 alloy that might be used in future supersonic aircraft fuselage panels. The common idea is to correlate quantitative measurements of relevant fractographic features of crack path to the effects of time-dependent processes on crack growth rates.     

The influence of a multilayered metallic coating on fatigue crack nucleation

A thorough review of the literature on fatigue crack initiation indicates that for optimum resistance to fatigue crack initiation, a surface coating needs more than just a high hardness and that a combination of properties including toughness, cyclic work hardenability, residual compressive stresses, and adherence, in addition to a hardness higher than that of the substrate are required. Based on this assumption, it was hypothesized that nanometer-scale, multilayer coatings will posses a combination of these required properties enabling significant increases in fatigue crack initiation resistance. To test this hypothesis, fatigue experiments were conducted on Cu samples with different surface treatments including a nanoscale Cu–Ni multilayer. The fatigue lives of the multilayer coated samples were significantly greater than those of uncoated samples or samples coated with a monolithic coating of Cu or Ni indicating that the nanodimensional layering of the multilayer coating is responsible for retarding fatigue crack initiation and failure. The samples were examined with various analytical techniques including scanning and transmission electron microscopy and atomic force microscopy.     

A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials

In this paper, a cohesive grain boundary integral formulation is proposed, for simulating intergranular microfracture evolution in polycrystalline brittle materials. Artificially generated polycrystalline microstructures are discretized using the proposed anisotropic boundary element method, considering the random location, morphology and material orientation of each grain. Each grain is assumed as a single crystal with general elastic orthotropic mechanical behaviour. Crack initiation and propagation along the grain boundaries interfaces are modelled using a linear cohesive law, considering mixed mode failure conditions. Furthermore, a non‐linear frictional contact analysis is performed over cracked grain interfaces to encounter cases where crack surfaces come into contact, slide or separate. The effect of randomly located pre‐existing flaws on the overall behaviour and microcracking evolution of a polycrystalline material is also investigated for different Weibull moduli. The stochastic effects of each grain morphology‐orientation, internal friction and randomly distributed pre‐existing flaws, under different loading conditions, are studied probabilistically by simulating various randomly generated microstructures. Copyright © 2006 John Wiley & Sons, Ltd.     

A stored energy criterion for fatigue crack nucleation in polycrystals

A series of microstructurally-differing, large-grained, notched, polycrystal BCC ferritic steel bend test samples have been analysed to extract the experimentally observed sites of fatigue crack nucleation together with the numbers of cycles to cause crack nucleation. The samples have been modelled with explicit representation of both grain morphologies and crystallographic orientations using crystal plasticity which has enabled a detailed assessment to be made of key microstructure-level quantities such as accumulated slip, slip rate, and densities of both statistically stored and geometrically necessary dislocations local to the experimentally observed sites of crack nucleation. These quantities when considered independently have not been found to correlate with experimentally observed cycles to nucleation.A new criterion for fatigue crack nucleation has been introduced in which a critical stored energy density, G_c, is argued to be necessary in order for crack nucleation. The rate of stored energy density determined at the sites of crack nucleation has been shown to correlate well with experimental measurement of cycles to nucleation, and the number of cycles to cause fatigue crack nucleation, for the samples for which such measurements are available, is well predicted. The criterion enables prediction of cycles to crack nucleation for all of the experimental samples and has been shown to demarcate correctly the crack nucleation lives observed over the range of differing experimental microstructures.     

Microstructural statistics for fatigue crack initiation in polycrystalline nickel-base superalloys

In advanced engineering alloys where inclusions and pores are minimized during processing, the initiation of cracks due to cyclic loading shifts to intrinsic microstructural features. Criteria for the identification of crack initiation sites, defined using elastic-plastic loading parameters and twin boundary length, have been developed and applied to experimental datasets following cyclic loading. The criteria successfully quantify the incidence of experimentally observed cracks. Statistical microstructural volume elements are defined using a convergence approach for two nickel-base superalloys, IN100 and René 88DT. The material element that captures the fatigue crack-initiating features in René 88DT is smaller than IN100 due to a combination of smaller grain size and higher twin density.     

Depth of intergranular oxygen diffusion during environment-dependent fatigue crack growth in alloy 718

The elevated-temperture fatigue crack growth behavior in alloy 718, when subjected to a loading frequency lower than the transitional frequency of this alloy, is viewed as fully environment dependent. In this process, the crack growth increment per loading cycle is assumed to be equal to the intergranular oxygen diffusion depth at the crack tip during the cycle effective oxidation time. In order to identify the trend of this diffusion depth an experimental program was carried out on compact tension specimens made of alloy 718 at 650 °C in which fatigue crack growth measurements were made for cyclic load conditions with and without hold time periods at minimum load level. This work resulted in establishing a relationship correlating the intergranular oxygen diffusion depth and the value of the stress intensity factor range ΔK. This relationship, when integrated over the cycle effective oxidation time, results in a closed-form solution describing the environment-dependent fatigue crack growth rate. A comparison is made between the results of this solution when applied to different loading frequencies and the corresponding experimental results. This comparison shows good agreement between the two sets of results. Furthermore, by combining the parabolic rate law of diffusion and the equation for the intergranular oxygen diffusion depth, an explicit expression for the oxygen diffusivity of grain boundaries is derived. It is found that this diffusivity is both a ΔK- and a frequency-dependent parameter.     

A theoretical investigation into the nucleation of stable crack precursors in polycrystalline ice

The possible formation of small stable cracks (crack precursors) at grain triple points in polycrystalline S2 ice subjected to stresses below that required to nucleate grain-size cracks is examined theoretically at –10° C. The investigation is based on the theory that stress concentrations can arise from the crystal elastic anisotropy and the pile-up of grain boundary dislocations at the triple point. Using an energy approach, numerical simulations of a model show that (i) small stable cracks can initiate from triple points under small stresses, (ii) unstable Griffith cracks can also nucleate, (iii) the smallest nucleation stresses are weakly dependent on hydrostatic compression and crystal orientation, and obey approximately the Hall-Petch relation with respect to the mean grain size, (iv) the crack to grain boundary length ratios are statistically distributed rather than constant, and (v) crack nucleation is strongly influenced by the orientations of the grain boundaries with respect to the applied stress and by the grain boundary dislocation configurations (positive or negative).