Fracture Of Polycrystals Research Articles

Yield criterion for intergranular void coalescence under combined tension and shear

Intergranular ductile fracture is a failure mode that may arise in many metallic alloys used in industrial applications. It manifests as the successive nucleation, growth, and coalescence of cavities at grain boundaries. Thus, simulation of intergranular ductile fracture in polycrystals requires modeling those three different stages at the scale of grain boundaries, i.e. at the interface between two different crystals. In this study, a yield criterion for the coalescence of cavities at the interface between two isotropic materials obeying Mises plasticity is first developed by limit analysis in order to provide some insights into that phenomenon. This criterion is checked against numerical limit analysis under combined tension and shear and is found to agree with unit-cell simulations quantitatively. The model is then extended to crystals so as to account for the complex coupling between loading state, crystallographic orientations, and void microstructure in intergranular coalescence. This second criterion is also assessed through comparisons to numerical limit analysis for an FCC crystal lattice. The agreement is very good in the case of coalescence by internal necking and the trends displayed by coalescence under combined tension and shear are captured correctly. Some implications of the model on the competition between transgranular and intergranular ductile fracture are discussed. Finally, by combining this model with an existing criterion for void growth at grain boundaries, a multi-surface yield function relevant to intergranular ductile fracture is obtained and compared to unit-cell simulations.

Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of [formula omitted

The multiphase-field method has great potential to advance future research on battery materials. In this work, we discuss the modeling of phase-separating intercalation compounds based on the Cahn-Hilliard equation as well as a multi-phase, multi-component model operating in an Allen-Cahn framework. Modeling assumptions are introduced step-by-step to facilitate future developments and bridging the gap across scales. Dimensionality reduction reflecting the material anisotropies can be critical for combining the phase-field approach with Newman-type models. Furthermore, we discuss a nano-particle battery model starting from intercalation in a defect-free, single-crystalline platelet. The underlying modelling assumptions are reduced step-by-step, first, including in-plane diffusion as a result of crystal defects and finally accounting for a polycrystalline material section. We show how faster in-plane diffusion promotes phase separation while higher C-rates and coherency strain lead to the opposite effect. This work highlights the importance to consider pre-existing grain boundaries for nucleation at higher-order junctions, heterogeneity of the intercalation fluxes and grain-by-grain filling behaviour. Anisotropic elastic deformation leads to high stresses at the evolving phase boundaries, especially at high misorientations between neighbouring grains. The maximum principle stress is used as an estimate for degradation by fracture in polycrystals.

Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue

Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J-integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.

Probing Atomic-Scale Fracture of Grain Boundaries in Low-symmetry 2D Materials.

Grain boundaries (GBs) play a central role in the fracture of polycrystals. However, the complexity of GBs and the difficulty in monitoring the atomic structure evolution during fracture greatly limit the understanding of the GB mechanics. Here, in situ aberration-corrected scanning transmission electron microscopy and density functional theory calculations are combined to investigate the fracture mechanics in low-symmetry, polycrystalline, 2D rhenium disulfide (ReS2 ), unveiling the distinctive crack behaviors at different GBs with atomic resolution. Brittle intergranular fracture prefers to rip through the GBs that are parallel to the Re chains of at least one side of the GBs. In contrast, those GBs, which do not align with Re chains on either side of the GBs, are highly resistant to fracture, impeding or deflecting the crack propagation. These results disclose the GB type-dependent mechanical failure of anisotropic 2D polycrystals, providing new ideas for material reinforcement and controllable cutting via GB engineering.

A two-set order parameters phase-field modeling of crack deflection/penetration in a heterogeneous microstructure

Modeling of crack deflection/penetration or manifested as intergranular/transgranular fracture in polycrystals has long been a challenge in both fracture mechanics and materials science. A phase-field model formulated with two-set order parameters describing the crack field and the microstructure field respectively, is herein established to investigate the competition between crack penetration and deflection at an interface. The advantages of the proposed model are three-fold: (1) the fracture toughness of grain boundaries and/or interfaces, besides single crystal properties (e.g., Young’s modulus, Poisson ratio, and fracture toughness), can be automatically incorporated, (2) cohesive interfaces are treated in one phase-field framework in comparison with the integrated phase-field and cohesive zone model in which cohesive elements have to be manually placed at the interface, and (3) two-set order parameters enable to describe the concurrent crack propagation and microstructure evolution. The proposed model is validated by comparing the simulated critical deflection angles with the results from theoretical analysis of the linear elastic fracture mechanics and the experiments. The model is then applied to a heterogeneous Silicon Nitride polycrystal to determine the effect of interface fracture toughness on the intergranular/transgranular fracture transition and the effective toughness of the materials.

Analytical homogenization modeling and computational simulation of intergranular fracture in polycrystals

Failure at grain boundaries has a critical effect on the overall fracture behaviour of polycrystalline aggregates, as is the case in many metals. In the case of dynamic embrittlement, segregation of impurities occurs at grain boundaries, lowering their cohesive strength. The material response is then dominantly determined by grain boundary properties. The self-consistent scheme is extended to account for grain boundary decohesion by using a cohesive law to represent crack initiation and propagation. After introducing the imperfect interface conditions into the Eshelby’s equivalent inclusion solution, the effective tensile response and brittle intergranular fracture of a Cu–Ni–Si alloy is predicted. The proposed analytical model allows for the identification of parameters for both crystal plasticity and cohesive constitutive laws, from a single macroscopic tensile curve. Afterwards, multiscale computations of artificial microstructures are done using the analytically calibrated values of material parameters. Comparison of the results with experimental data shows a satisfactory agreement.

Challenges in Continuum Modelling of Intergranular Fracture

Abstract: Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five‐dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.

The effect of plastic flow in the neck on the scale levels of fracture in polycrystals. Experiment and modeling

A multiscale approach to the study of the plastic flow evolution pattern in the neck of high-strength structural steel and submicrocry stalline armco iron and titanium specimens is used to describe the physical nature underlying the difference in the fracture mechanisms between these materials. An important role of local regions of bulk tension in micropore and crack formation and subsequent fracture of the materials is demonstrated by experiments and numerical simulations.

A comparison of finite element and atomistic modelling of fracture

Are the cohesive laws of interfaces sufficient for modelling fracture in polycrystals using the cohesive zone model? We examine this question by comparing a fully atomistic simulation of a silicon polycrystal with a finite element simulation with a similar overall geometry. The cohesive laws used in the finite element simulation are measured atomistically. We describe in detail how to convert the output of atomistic grain boundary fracture simulations into the piecewise linear form needed by a cohesive zone model. We discuss the effects of grain boundary microparameters (the choice of section of the interface, the translations of the grains relative to one another and the cutting plane of each lattice orientation) on the cohesive laws and polycrystal fracture. We find that the atomistic simulations fracture at lower levels of external stress, indicating that the initiation of fracture in the atomistic simulations is likely dominated by irregular atomic structures at external faces, internal edges, corners and junctions of grains. Thus, the cohesive properties of interfaces alone are not likely to be sufficient for modelling the fracture of polycrystals using continuum methods.

Localized deformation and fracture of polycrystals at mesolevel

Recent experiments have shown that shear band formation and rotation of structural elements at the mesolevel are fundamental to the development of plastic deformation and fracture of solids. Attention should be focused on a mesovolume of deformed material because the local stress and strain differ from those averaged at the macroscale. The discrete nature of the microshears and restricted deformation of the mesofragments should be accounted for. Rotation of the different mesofragments being parts of a grain, grains, grain conglomerates, etc., plays an important role in plasticity. Moreover, knowledge of the local parameters is needed for developing plasticity theories and fracture criteria. Models have been proposed within the framework of the physical mesomechanics. They take into account structural elements of different scales for simulating shear band nucleation and propagation in addition to mesofragment rotations. Calculations have been made for different mesovolumes under dynamic loading. In this work, a new criterion of plasticity is considered at the mesolevel. It accounts for the nucleation of plastic shears at the surfaces and interaction of structural elements. The numerical technique combines both the continuum mechanics approach and discrete cellular automata method.

Evolution of deformation domains and kinetics of fatigue fracture of Duralumin polycrystals at the mesoscopic level

Laws governing the buildup of fatigue fracture under cyclic loading of aluminum alloy polycrystals under conditions of multicycle fatigue have been studied by analyzing the spacetime dynamics of mesoscopic structures. It has been shown that under the periodic action of an external mechanical field, deformation domains form in the material at the mesoscopic level. The evolution of these dynamic mesoscopic domain substructures determines the kinetics of the fatigue fracture of the polycrystals.

The impact of grain boundary character distribution on fracture in polycrystals

The importance of structural effects on intergranular fracture is discussed in order to understand, predict and control fracture in polycrystals. The heterogeneity of fracture in a polycrystal has been found to be due to the difference in structure-dependent propensity to intergranular fracture among grain boundaries. The grain boundary character distribution (GBCD) which describes the type and frequency of grain boundaries is shown to be one of important microstructural factors affecting fracture processes and characteristics. A recent prediction of GBCD-controlled toughness and brittle-ductile transition is introduced. The importance of the connectivity of grain boundaries, the so-called grain boundary correlation number, is also discussed. Recent successful achievement of the control of intergranular brittleness is presented as an application of the result of basic research on fracture to the control of intergranular brittleness by grain boundary design and control in advanced materials.

Grain boundary design and control for high temperature materials

Abstract Recent experimental work has been reviewed concerning the effects of grain boundary structure on grain boundary sliding and migration, and other boundary phenomena involved in high temperature plasticity. A basic knowledge of the structure-dependent intergranular phenomena is important for a full understanding of the heterogeneity and characteristic features of high temperature deformation and fracture, because the structural effects of grain boundaries enhance the boundary-induced heterogeneity of deformation and fracture in polycrystals. The grain boundary character distribution (GBCD) has been shown to be important and useful in explaining and controlling high temperature plasticity, superplasticity and fragility in polycrystals. The potential use of grain boundary design and control for high temperature materials has been discussed on the basis of recent work concerning GBCD, texture and other microstructural factors. The recent achievement of grain boundary design and control for high temperature materials has been briefly introduced.

Materials interfaces: atomic-level structure and properties

Contributors. Introduction. Atomic-level geometry of crystalline interfaces D. Wolf. Experimental investigation of internal interfaces in solids D.N. Seidman. Bulk interfaces. Part I: Bulk interfaces. Correlation between the structure and energy of grain boundaries in metals D. Wolf, K.L. Merkle. Grain and interphase boundaries in ceramics and ceramic composites M.G. Norton, C.B. Carter. Special properties of E grain boundaries G. Palumbo, K.T. Aust. Grain boundary structure and migration D.A. Smith. Role of interfaces in melting and solid-state amorphization S.R. Phillpot, S. Yip, P.R. Okamoto, D. Wolf. Wetting of surfaces and grain boundaries D.R. Clarke, M. Gee. Part II: Semi-bulk and thin-film interfaces. Structural, electronic and magnetic properties of thin films and superlattices A. Continenza, C.Li, A.J. Freeman. Surfaces and interfaces as studied by scanning-tunneling microscopy R. Hamers. Epitaxy of semiconductor thin films J. Batstone. Phase behavior of monolayers S.G.J. Mochrie, D. Gibbs, D.M. Zehner. Elastic and structural properties of superlattices M. Grimsditch, I.K. Schuller. Computer simulation of the elastic behavior of interface materials D. Wolf, J. Jasczak. Interfaces within intercalation compounds M.S. Dresselhaus, G. Dresselhaus. Nanophase materials: structure-property correlations R.W. Siegel. Part III: Role of interface chemistry. Interfacial segregation, bonding and reactions C.L. Briant. Physics and chemistry of segregation at internal interfaces R. Kirchheim. Atomic resolution study of solute-atom segregation at grain boundaries: experiments and Monte Carlo simulations S.M. Foiles, D. Seidman. Amorphization by interfacial reaction W.L. Johnson. Relationship between structural and electronic properties of metal-semiconductor interfaces R. Tung. Electronic properties of semiconductor-semiconductor interfaces and their control using interface chemistry D.W. Niles, G. Margaritondo. Microscopic nature of metal-polymer interfaces P.S. Ho, B.D. Silverman, S-L. Chiu. Part IV: Fracture behavior. Tensile strength of interfaces A.S. Argon, V. Gupta. Microstructure and fracture resistance of metal/ceramic interfaces A.G. Evans, M. Ruhle. Role of interface dislocations and surface ledges in the work of adhesion D. Wolf, J. Jaszczak. Microstructural and segregation effects in the fracture of polycrystals D.J. Srolovitz, W. Yang.

Brittle to ductile transition in cleavage fracture

In many cleavable solids, cleavage cracks can propagate at steady state by laying down a trail of dislocations emanating from the crack tip and lying on planes inclined to the crack front. These crack-tip initiated dislocations produce shielding at the crack tip that reduces both the crack tip tensile stresses and the shear stresses on the inclined planes. They also blunt the crack. Cleavage cracks, can nevertheless, still propagate under appropriately increased stress intensity conditions to keep the crack tip tensile stress constant. A condition is reached in the propagation of such slightly blunted cracks where a small increment in temperature or a decrement in the crack velocity permits the nucleation of a new set of dislocations that produce additional shielding and blunting which tip the balance against the crack-tip tensile stresses. This results in a transition from brittle cleavage to ductile behavior. The steady state specific plastic work that can just be tolerated by a propagating cleavage crack before it catastrophically blunts is calculated to be only of the order of 10% of the specific surface energy. Although most geometrical details of the dislocation emission process are adequately modeled, the calculated brittle to ductile transition temperatures are found to be more than an order of magnitude higher than those that have been experimentally measured. This discrepancy is a result of the present inadequate methods of modeling activation configurations by considering the dislocation loop radius as the only activation parameter, while proper modeling of such configurations must consider also the Burgers shear displacement of the loop as an activation parameter. Such two parameter analyses, however, require accurate information on interlayer atomic shear resistance profiles for specific crystals which are presently not available. The analysis furnishes ready explanations of the toughening effects of so-called “ductilization” treatments and embrittling effect of aging and dislocation locking, as well as the relatively large difference between the lowest levels of toughness between fracture in polycrystals and in single crystals.

Yield, flow and fracture of polycrystalsedited by T. N. Baker

<i>Yield, flow and fracture of polycrystals</i>edited by T. N. Baker

Intergranular fracture in bicrystals—II

In this paper results of stress rupture experiments on bicrystals of a structural alloy, 316 stainless steel, are reported and contrasted with equivalent results from copper-bicrystals which were reported earlier. In both instances the boundary was aligned normal to the tensile axis to minimize the influence of grain boundary sliding. In contrast with the experiments on copper, where it was found that the time to fracture could be reasonably well predicted on the basis of cavity growth only, in 316SS it is found that predictions based upon cavity growth considerably underestimate the failure times. It is inferred that cavity nucleation takes up a dominant fraction of the fracture time in the 316SS bicrystals. The data asymptotically approaches a threshold stress at low stresses. It is suggested that the threshold stress, so measured, may be used as a parameter in the design of structures which operate under steady state, long term, elevated temperature conditions. Fracture in bicrystal specimens always occurred sooner than fracture in polycrystals of 316SS.