Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy

Rowenhorst, David J.; Lewis, A. C.; Σπανός, Γ.

doi:10.1016/j.actamat.2010.06.030

Cited by 180 publications

(136 citation statements)

References 32 publications

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“…Meanwhile, Abbruzzese-Compopiano's quadratic model [7] also agrees well with the experimental results of Liu et al [9] when the sphere equivalent radius is used for grain size instead of mean tangent diameter. The Abbruzzese-Compopiano's [7] and Thorvaldsen's [8] quadratic models are also consistent with the experimental results of -titanium alloy [10] and aluminum alloy [11] as well as the results of surface evolver simulation [12]. These studies considered a mean field approach in describing topology-size relationships while neglected the effects of the neighboring grains.…”

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confidence: 65%

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Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

et al. 2013

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A new grain topology-size relationship in three-dimensional (3D) polycrystalline microstructures has recently been established by considering the effects of non-random first nearest neighbor grains. In this contribution, a generalized form for this relationship is presented by considering the interactions of kth (k=1, 2, 3…) nearest neighbor grains, and large scale Monte Carlo-Potts model simulation is used to investigate the general neighborhood topological effect on the topology-size relationship. The results show that, unlike their first nearest neighbors (k=1), the topological correlations of 3D grains with their kth layers (k2) of nearest-neighbors may have trivial effect on the topology-size relationship. Many macroscopic properties such as mechanical, thermal, magnetic and conductive properties of the material can be directly linked to microstructure; therefore, it is very important to predict the grain microstructure and its evolution [1][2][3][4]. The size and the shape of grains and their spatial correlation are likely to play a significant role in the microstructural evolution. Therefore, the grain topology-size relationship is of fundamental importance for a better understanding of polycrystalline materials. In 1985, by applying the methods of statistical mechanics to the structure of random, space-filling cellular structures, Rivier [5] revealed that the maximum entropy inference under a few constraints yields structural equations of state, relating the topology of cells to their size. These equations of state are namely Perimeter law (for metallurgical grains) and Lewis's law (for ideal soap froths). According to Perimeter law, the average radius of grains is proportional to the number of their edges. While, in three dimensions (3D), a parabolic relationship exists between the grain size and grain topology. DeHoff and Liu [6] have proposed a linear relationship between the number of grain faces and the mean tangent diameter of individual grains in 3D. Thereafter, Abbruzzese and Compopiano [7] and Thorvaldsen [8] proposed two independent forms of quadratic relationships between the number of grain faces and the sphere-equivalent radius of grains in 3D. The DeHoff-Liu's linear model has been verified experimentally by Liu et al. [9] and strongly recommended it when the mean tangent diameter is used for grain size. Meanwhile, Abbruzzese-Compopiano's quadratic model [7] also agrees well with the experimental results of Liu et al. [9] when the sphere equivalent radius is used for grain size instead of mean tangent diameter. The Abbruzzese-Compopiano's [7] and Thorvaldsen's [8] quadratic models are also consistent with the experimental results of -titanium

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confidence: 65%

“…The nonrandom nearest neighbor correlations in 3D grain structures have been studied both experimentally [10,15] and by simulations [12,16]. Recent studies strongly suggested the importance of considering the effects of first nearest-neighbor grains when studying grain growth [10,16] and also predicting the grain topology-size relationships.…”

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confidence: 99%

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

et al. 2013

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“…Various experimental techniques are available for microstructural characterization [25,26,27,28,29,71,72,73] and their output is sometimes used as input for finite element (FE) analysis [74,75,48,49]. However a complete 3D reconstruction still remains a challenging task.…”

Section: Artificial Microstructure Generationmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

116

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In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

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“…Actually, many of reported values are higher than the predicted value from the Mullins relation: for example, 13.7 (Suwa et al 24) ) and 14.7 (Kim et al 23) ) from phase-field simulations, 15 from the surface-evolver model 20) and 15.5 from the experimental measurement. 60) In general, it is considered that the threshold number of neighboring grains for three-dimensional grain growth is closely related to the regular packing of space filling objects with the Weaire-Phelan structure, 61) where the ideal surface-areato-volume ratio occurs for a structure consisting of one 12-sided polygon and one 14-sided polygon. However, most of reported values deviate from the ideal value, actual grains during the grain growth are not ideal polygons.…”

Section: Mullins Relation For Three-dimensional Grainmentioning

confidence: 99%

Grain Growth in Large-Scale Molecular Dynamics Simulation: Linkage between Atomic Configuration and von Neumann-Mullins Relation

Okita

Shibuta

2016

ISIJ Int.

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Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy

Cited by 180 publications

References 32 publications

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Grain Growth in Large-Scale Molecular Dynamics Simulation: Linkage between Atomic Configuration and von Neumann-Mullins Relation

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