Micromechanical modelling of ductile crack growth in the binder phase of WC–Co

This study focuses on numerical simulation of ductile failure in the Co binder phase of WC–Co hardmetal. The growth of edge cracks under mode I loading is considered. A computational micromechanics approach is taken where the Co binder ligaments are explicitly represented in finite element models. An embedding technique is employed. Crystal plasticity theory is used to represent plastic deformation in the Co ligaments. Crack propagation in the binder is simulated using an element removal technique based on a modified Rice and Tracey model for ductile void growth, and fracture resistance curves are generated. Parameter studies are performed for variations in microstructrual parameters such as numbers of Co ligaments ahead of the crack tip and local Co volume fraction. The importance of thermal residual stresses and finite element mesh density are also investigated.     

Interaction between anisotropic plastic deformation and damage evolution in Al 2198 sheet metal

Deformation anisotropy of sheet aluminium alloy 2198 (Al-Cu-Li) has been investigated by means of mechanical testing of notched specimens and Kahn-type fracture specimens, loaded in the rolling direction (L) or in the transverse direction (T). Fracture mechanisms were investigated via scanning electron microscopy. Contributions to failure are identified as growth of initial voids accompanied by a significant nucleation of a second population of cavities and transgranular failure. A model based on the Gurson-Tvergaard-Needleman (GTN) approach of porous metal plasticity incorporating isotropic voids, direction-dependent void growth, void nucleation at a second population of inclusions and triaxiality-dependent void coalescence has been used to predict the mechanical response of test samples. The model parameters have been calibrated by means of 3D unit cell simulations, revealing the interaction between the plastic anisotropy of the matrix material and void growth. The model has been successfully used to describe and predict direction-dependent deformation behaviour, crack propagation and, in particular, toughness anisotropy.     

Mechanics and mechanisms of fatigue in a WC–Ni hardmetal and a comparative study with respect to WC–Co hardmetals

There is a major interest in replacing cobalt binder in hardmetals (cemented carbides) aiming for materials with similar or even improved properties at a lower price. Nickel is one of the materials most commonly used as a binder alternative to cobalt in these metal-ceramic composites. However, knowledge on mechanical properties and particularly on fatigue behavior of Ni-base cemented carbides is relatively scarce. In this study, the fatigue mechanics and mechanisms of a fine grained WC–Ni grade is assessed. In doing so, fatigue crack growth (FCG) behavior and fatigue limit are determined, and the attained results are compared to corresponding fracture toughness and flexural strength. An analysis of the results within a fatigue mechanics framework permits to validate FCG threshold as the effective fracture toughness under cyclic loading. Experimentally determined data are then used to analyze the fatigue susceptibility of the studied material. It is found that the fatigue sensitivity of the WC–Ni hardmetal investigated is close to that previously reported for Co-base cemented carbides with alike binder mean free path. Additionally, fracture modes under stable and unstable crack growth conditions are inspected. It is evidenced that stable crack growth under cyclic loading within the nickel binder exhibit faceted, crystallographic features. This microscopic failure mode is rationalized on the basis of the comparable sizes of the cyclic plastic zone ahead of the crack tip and the characteristic microstructure length scale where fatigue degradation phenomena take place in hardmetals, i.e. the binder mean free path.     

A continuum damage mechanics model for void growth and micro crack initiation

A damage mechanics model is proposed to study the void growth and crack initiation. J₂ incremental flow theory along with a damage variable is used to model the material behaviour in elasto-plastic regime. Large deformation (large rotation and finite strain) finite element analysis is carried out for five different cases. In all the cases it is observed that the triaxiality and the plastic strain play an important role in void growth and crack initiation in ductile material. A failure curve is obtained for the material AISI-1090 spheroidised steel. Finally, it is concluded that the critical value of the damage variable can be taken as a crack initiation parameter.     

Crack growth in lamellar titanium aluminide

In-situ compact tension tests on binary lamellar titanium aluminide (TiAl) possessing the colony ``polycrystalline' microstructure illustrate a range of damage phenomena and toughening mechanisms including crack nucleation across colony boundaries, plastic deformation of bridging ligaments, and multiple cracking within colonies. Here, the effects of relative lamellae misorientation and offsets between neighboring colonies on crack growth are investigated computationally through an idealized microstructure of multiple colonies. Within each colony, the brittle Ti₃Al lamellae are represented as parallel planes of comparatively low toughness embedded in a matrix of ductile TiAl lamellae that are collectively modeled as an elastic-viscoplastic solid with higher fracture toughness. Plane strain calculations of crack growth are carried out on a compact tension geometry. The calculations are in good qualitative agreement with the in-situ observations, capturing many features of crack growth such as multiple microcrack nucleation and plastic deformation of residual ligaments. Experiments and numerical analyses show that changes in lamellar orientation and alignment across a colony boundary can contribute significantly to the fracture resistance. The numerical results demonstrate that the fracture resistance of these alloys is determined by an intricate interplay between matrix ductility, Ti₃Al and TiAl fracture toughnesses, and colony boundary toughness. This suggests the possibility of computationally-guided material optimization through microstructural control of these material properties.     

Effect of submillimeter size holes on the fatigue limit of a high strength tool steel

The very high cycle fatigue and small fatigue crack growth behaviour of a generic tool steel material for diesel fuel injector application are described. The small crack growth tests for the tool steel material with and without the hardening heat treatment revealed the mechanisms of crack propagation and threshold behaviour. Based on the small fatigue crack propagation threshold value, an elastic plastic fracture mechanics methodology for the prediction of the endurance limit of specimens with submillimeter holes is proposed. The advantages of the new methodology are discussed in relation to existing methodologies for endurance limit prediction of specimens with small holes.     

Fatigue behaviour and lifing of two single crystal superalloys

A model has been developed to predict the high temperature cyclic life of single crystal superalloys RR2000 and CMSX-4 under conditions of creep and fatigue. A combined creep–fatigue model is used, although it is found that failure always occurs by creep or fatigue separately, and that creep–fatigue interaction has a minor influence. Microstructural investigation of a series of interrupted high- and low-frequency tests are presented, these are combined with the results of a series of interrupted creep tests to identify the separate and interactive mechanisms of creep and fatigue. When creep damage is present the material behaves homogeneously. Under these conditions crack growth is initiation controlled, the mechanism of failure is surface or casting pore-initiated planar crack growth followed by shear on crystallographic planes. As the temperature is lowered or the cyclic frequency increased, the material behaves less homogeneously and shear bands are formed during cycling. Crack growth under these conditions is again initiation controlled and failure is by rapid crystallographic crack growth along shear bands. Such a failure is a distinct fatigue failure and occurs when little creep damage is present. Under certain cyclic conditions, mainly those where the crystallographic failure mechanism is dominant, the material shows an anomalous increase in fatigue resistance with temperature up to approximately 950 °C. This behaviour has been quantified by relating it to the effect of strain rate and temperature on the yield strength of the material.     

Modelling the softening within the fracture process zone associated with the fissuring mode of crack growth in Zr-2.5Nb CANDU pressure tube material

The fissuring mode of fracture in CANDU pressure tube material, and in particular Stage 1 crack growth (essentially flat J _R curve) as observed in some irradiated compact toughness specimens has been investigated. Models are presented of the fracture process zone associated with a crack that tunnels at the specimen mid-section, which extends preliminary work reported earlier. Various types of process zone behaviour are analysed, and based on an appropriate value for J _c, the J value associated with the cumulative mode of crack propagation in irradiated material, together with an estimate of the tensile stress at the leading edge of the process zone, the known failure mechanism (formation, growth and coalescence of voids) of the ligaments between the fissures is shown to be reasonably consistent with the experimental measurements of the fissure spacing and fissure length.     

Multiple mechanisms controlling fatigue crack growth

Recognizing that fatigue is a two‐parameter problem requiring two load parameters to define cyclic loads unambiguously, a unified approach has been developed to account for crack growth behaviour in terms of ΔK and K_max . Since both driving forces govern the crack growth rate, any analysis based on either ΔK or K_max will provide only partial information about the fatigue behavior of materials. It is shown that ΔK–K_max plots and the associated crack growth trajectory maps reflect the basic mechanisms that contribute to crack growth in a material. These plots also provide a convenient basis to recognize the changes in the micromechanisms that can occur as a function of load ratio or crack growth rate, or both. Taking examples from the literature, crack growth trajectory maps are provided showing such changes in the governing mechanisms of crack growth. It is shown that the ΔK–K_max approach is not an alternative to crack closure models, but it reflects the intrinsic material behaviour that must be understood before reliable crack prediction models can be developed.     

Discrete modelling of ductile crack growth by void growth to coalescence

Ductile crack growth is analyzed by discrete representation of the voids growing near a blunting crack-tip. Coalescence of the nearest void with the crack-tip is modeled, followed by the subsequent coalescence of other discretely represented voids with the newly formed crack-tip. Necking of the ligaments between the crack-tip and a void or between voids involves the development of very large strains, which are included in the model by using remeshing at several stages of the plastic deformation. The material is here described by standard isotropic hardening Mises theory. For a very small void volume fraction the crack-tip tends to interact with one void at a time, while larger void volume fractions lead to simultaneous interaction of multiple voids on the plane ahead of the crack-tip. In some cases a change from one of these mechanisms to the other is seen during growth through the many voids represented here. First uniformly spaced voids of equal size are considered, but also a few computations for a random distribution of the void spacings or of the void sizes are carried out.     

History effect in fatigue crack growth under mixed-mode loading conditions

Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth. Consequently, fatigue crack growth models should include plasticity-induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed-mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ_I/dt and dρ_II/dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale. Evolutions of dρ_I/dt and dρ_II/dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic–plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed-mode crack tip plasticity (dρ_I/dt and dρ_II/dt), it becomes possible to predict fatigue crack growth under I/II mixed-mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was setup. It allows applying any mixed-mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

A finite element study of crack growth in WC-Co

A finite element analysis of crack growth in tungsten carbide cobalt has been used to study the plastic deformation of binder ligaments bridging the crack faces in the wake of a matrix crack. A multiligament zone observed on the intersection of an arrested crack with a free surface is used to model the crack tip region. The plane stress results demonstrate that plasticity is confined to a band linking the ligament tips well in accordance with experimentally found deformation patterns. The plane strain calculations for the same microstructure supply information about hole nucleotion and growth which are known to control the failure process of the ligaments. It is concluded from a recent analysis of void growth in homogeneous materials, that plastic deformation in the binder of WC-Co is concentrated in the neck between a blunting crack tip and a void growing ahead of it. Thus in both cases, plane stress and plane strain, non bridging binder regions deform purely elastically in contrast to the results of recent finite element calculations. It is seen that the previously used concept of a plastic zone size in the binder of cemented carbides equal to or larger than the mean intercept length of the binder, 305-1, must be modified. 305-2 constitutes only an upper limit for the mean size of the plastic zone while the actual extension of plasticity is smaller.

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Résumé On utilise une analyse par éléments finis de la croissance d'une fissure dans un alliage Cobalt-Carbure de Tungstène pour l'étude de la déformation plastique des ligaments de liaison entre les faces d'une fissure prenant naissance dans une matrice. Pour représenter la région à l'extrémité de la fissure, on utilise la zone multiligamentaire observée à l'intersection d'une fissure ouverte et d'une surface libre. Les résultats correspondent à un état plan de tension démontrant que la plasticité est confinée à une bande reliant les extrémités des ligaments, ce qui est bien en accord avec les aspects de déformation trouvés expérimentalement. Les calculs en état plan de déformation pour la même microstructure fournissent une information sur le processus de nucléation et de croissance des lacunes, qui est connu pour contrôler le processus de rupture d'un ligament. On conclut de l'analyse pour des matériaux homogènes que la déformation plastique dans une liaison de WC-Co est concentrée dans la position rétrécie entre l'extrémité arrondie d'une fissure et une lacune en croissance en amont de celle-ci. Dès lors, dans les deux cas de tension plane ou de déformation plane, les régions de liaison qui ne relient pas les faces de la rupture se déforment de manière purement élastique, ceci en contraste avec les résultats de calculs récents par éléments finis. On constate que le concept de taille de zone plastique égale ou supérieure à la longueur moyenne 317-3 de la liaison doit être modifié. 317-4 ne représente qu'une limite supérieure pour la taille moyenne de la zone plastique, tandis que l'étendue réelle de la plasticité est plus petite.

     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

An approximation for the cyclic state of stress ahead of cracks and its implications under fatigue crack growth

Numerical methods are mostly used in the field of fatigue to derive the stress intensity factor (SIF) or J-integral solutions to be employed in damage tolerance analysis of cracked components. In this frame, simple assumptions about material properties are taken into account.More refined approaches try to describe the plasticity-induced crack closure in order to account for retardation effects under variable amplitude loading. In these approaches, the cyclic plasticity is used and cyclic finite element analyses are carried out.In the present work, a novel strategy is presented for the calculation of the relevant parameters to the fatigue crack growth, based on the evaluation of local field parameters (J-integral, T-stress) and cyclic material properties. It is demonstrated that, in case of mild steels and under the assumption of a stress ratio R = −1, the global constraint factor α_g widely employed in fatigue crack growth algorithms such as the strip-yield model, can be calculated in a closed-form on the basis of the expression of the crack-tip fields. Moreover, α_g provides a reasonable explanation of the fatigue crack growth behaviour of the A1N steel for different geometrical and loading configurations. Further investigations carried out on different medium and high strength steel grades show that the plastic radius ahead of small and long cracks at their fatigue limits can be considered as a constant for the material.     

PREDICTING THE EFFECTS OF LOAD RATIO ON THE FATIGUE CRACK GROWTH RATE AND FATIGUE THRESHOLD

The effect of the load ratio, R, on fatigue crack growth behaviour is analysed on the basis of the recently proposed inelastic discrete asperities model. A wide range of load ratios, both positive and negative, are examined. Particular emphasis is placed on compressive excursions, i.e. negative R loadings. The inelastic discrete asperities model is a micro-mechanical analysis based on the plastic crushing of a single asperity (or multiple asperities) located on the crack face close to the crack tip and under dominantly plane strain conditions. Experimental data have indicated that the primary crack face contacts which obstruct closure are immediately adjacent to the crack tip, although segments of the crack face more distant from the crack tip are not neglected. However, the more distant asperities are a part of the past crack advance history which does not influence current behaviour. By use of this model, it is shown that the effect of the load ratio can be adequately predicted once some baseline information on mechanical material properties and surface roughness is provided. The model also provides useful trend information and explains many of the observed phenomena, e.g. the ‘saturation’ of the compressive underload effects. For a constant applied nominal stress intensity factor range, ΔK_nom , it is shown that the effective stress intensity factor range, ΔK_eff , initially decreases as the positive R decreases (corresponding to the increasing influence of closure), reaches a minimum around R = 0, and then starts increasing with negative R (corresponding to the plastic crushing of the asperities which reduces closure), eventually reaching a saturation level below ΔK_nom . Conversely, for an assumption of a constant ΔK_eff , the applied ΔK_nom increases as the positive load ratio decreases, reaching a maximum around R = 0, and then decreases with more negative R values, eventually reaching again a saturation level (above ΔK_eff ). It is also shown that the effect of material hardness can be directly analysed based on this model.     

Fatigue crack growth analysis of 2024 T3 aluminium specimens under aircraft service spectra

The fatigue crack growth behaviour of 2024 T3 aluminium was investigated experimentally. The fatigue experiments were performed under constant stress amplitude, constant amplitude with single and multiple overloads and aircraft service spectra. The fatigue spectra used correspond to the air-to-air, air-to-ground and instrumentation and navigation flight phases. They were applied for different stress levels. In total 11 different random flight service spectra were examined. The retardation effects caused by the overloads on the fatigue crack growth behaviour and the fatigue crack growth under aircraft service spectra were predicted using an in-house-developed code. The code makes use of the strip plastic zone approximation to account for material hardening effects along the path of prospective crack growth. Crack growth is treated incrementally and corresponds to failure of material elements ahead of an existing crack after a certain critical number of fatigue cycles. For the simulation of irregular service spectra by equivalent sequences of distinguished stress cycles a modified rainflow counting method is utilized. Spectrum simulation accounts also for non-linearity in fatigue damage accumulation and load sequence effects. The computed fatigue curves fit well with the experimental results.     

Ductile crack propagation by plastic collapse of the intervoid ligaments

In the present study ductile crack initiation and propagation is investigated by means of a micro-mechanical model under small-scale yielding conditions. Voids are resolved discretely in the fracture process zone where steep gradients occur during the loading history and are taken into accounted by a homogenized porous plasticity law elsewhere. The size of the region of discrete voids is not set a priori but is determined consistently. The results show that effective crack growth occurs by plastic collapse, i.e. purely geometric softening of the intervoid ligaments without incorporating material separation. Due to this mechanism a limit load exists coinciding with the maximum fracture toughness. In addition, it turns out that the shielding due to the growth of voids around the crack plane has a considerable influence on the computed R-curves compared to models neglecting this effect. Depending on the void arrangement a diffuse softening zone or even crack branching is observed. A comparison with experimental data from literature indicates that plastic collapse and the formation of diffuse zones of void growth are realistic mechanisms of ductile crack propagation.     

Fatigue crack growth with overloads/underloads: Interaction effects and surface roughness

The generalization of damage tolerance to variable amplitude fatigue is of prime importance in order to maintain the reliability of structures and mechanical components subjected to severe loading conditions. Engineering spectra usually contain overloads and underloads which distribution may not be random. However for predicting the life of a structure, a simplified spectrum is usually determined from the real one, in order to reduce testing periods on prototypes. Therefore it is thus important to know which cycles can contribute to crack growth and which can be neglected. This paper presents an analysis of fatigue crack growth on M (T) specimens made of a medium carbon steel DIN Ck45. The specimens are subjected to repeated blocks of cycles made up of one or several (1, 2, 6 or 10) overloads (or underloads) separated by a variable number (10, 1000 or 10 000) of baseline cycles. The main objective of this study is to better understand the mechanisms at the origin of interactions effects due to the presence of overloads (or underloads) at different locations of each block loading. Under constant amplitude loading, single variables ΔK and K_max are required in crack growth relationships. The transferability of fatigue laws, obtained under constant amplitude loading to variable amplitude fatigue, requires at least an additional variable, whose evolution with crack length accounts for the interactions effects between cycles of different types. Results have shown that the interaction effects in fatigue crack growth are closely related to the mechanisms of crack growth: cyclic plastic behaviour of the material and fracture surface roughness. Measurements of roughness of the surface fracture were carried out in both constant amplitude and variable amplitude tests. The roughness characterization helped to determine the importance of the mechanisms on variable amplitude fatigue crack growth and determine the influence of overloads/underloads on fatigue crack growth.     

The fracture of hybrid-particulate composites

The fracture behaviour of hybrid-particulate composites has been examined. These novel materials contain both dispersed rubbery and rigid glass particles, and values of the stress-intensity factorK _lc and fracture energyG _lc have been determined using a double-torsion test. Considerable increases in toughness have been recorded and the mechanisms of toughening have been identified. The rigid glass particles increase the crack resistance mainly through a crack-pinning mechanism whilst the rubbery particles, which have a much greater effect, enhance the extent of localized plastic shear deformations around the crack tip. Quantitative failure theories and criteria are suggested for these mechanisms.