Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress–strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid–liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.     

Flow Curve and Failure Modeling for High‐Mn Steels on a Microstructural Scale

A microstructural model for flow curve and failure modeling based on the representative volume element (RVE) approach is developed for high‐Mn steels. The polycrystalline structure is generated by discrete Voronoi tessellation. Physically based material models for mechanical twinning and the ε‐martensite phase transformation are implemented for describing the hardening behavior. A ductile damage model based on the multiaxial state of strain calculates the fracture and failure. Uniaxial tensile tests were carried out for the steel 22Mn0.6C with varying grain size and for a temperature range of 123–423 K. Experimental results are in good agreement with the calculated RVE models.     

On composite-structure weaknesses: Part I. Simulation,properties, and numerical approach

Composite material samples were created by means of computer simulation to duplicate short-fiber-reinforced metal-matrix composites (MMCs). Each sample contains a fairly large number of Voronoi grains and ellipsoidal short fibers, which orient and distribute in a random manner, to mimic composite microstructures for investigating the coherent interconnections of composite-structure weaknesses (CSWs) with local microstructure. It is supposed that the samples are subjected to coupled boundary traction due to mechanical loading and thermal cycling. A Kr?ner-Kneer structure-based model and Waldvogel-Rodin algorithm were used for numerical computations of the mesoscopic stress distribution in constituent grains. The computations are based on the grain-volume average of local fields. Polycrystal elastic/thermal properties and effective elastic/thermal properties of simulated MMC samples were predicted, respectively, in terms of micromechanics models, in favor of incorporating the influences of macroscopic material properties on the formation of CSWs. An analytically-numerically-based approach is proposed for analyzing peak mesoscopic stress and strain distributions in short fibers. Three crucial aspects constitute a kernel of the approach, i.e., (1) segmentation of short fibers, (2) establishment of the geometric relations of a short fiber to the surrounding grains, and (3) the local nature of micromechanics. The analytically-numerically-based approach takes into account the grain orientation, fiber orientation, grain geometry, fiber geometry, and macroscopic properties of simulated MMC samples. The Numerical Assessment of Computer-Imitated Weaknesses-MMCs (NACIW-MMCs) software program has been developed for performing simulation of the microstructure of short-fiber-reinforced MMCs and executing all involved numerical computations.     

An examination of the interparticle contact area during sintering of W-0.3 Wt Pct Co

As a powder compact sinters, its microstructure evolves. One way to quantify the scale of the microstructure is to consider the interparticle contact area. This study examines two known models for calculating the interparticle contact area: the classic two-sphere model and the Voronoi cell model. Both models have particular assumptions about the microstructure that make them not applicable for treating densification to near full density with concurrent grain growth. The classic two-sphere model assumes a regular packing of particles and a perfectly spherical particle geometry and neglects an increasing particle coordination number with sintering. The Voronoi cell model assumes that the scale of the microstructure remains constant; i.e., as long as the compact is densifying, grain growth does not occur. We propose a modified Voronoi cell that accounts for an increasing grain size, making it applicable to a general case where grain growth occurs during sintering. The three models are compared to the interparticle contact area data, obtained by stereology techniques, for W-0.3 wt pct Co sintered from green state to near full density. The original Voronoi cell model fits the data only at low temperatures, before the onset of grain growth. Below approximately 90 pct relative density, the two-sphere model with an assumed coordination number of six (coordination number in a green compact) and the modified Voronoi cell model provide a good fit to the data. At higher densities, both models overestimate the interparticle contact area.     

Characterizing the Local Primary Dendrite Arm Spacing in Directionally Solidified Dendritic Microstructures

Characterizing the spacing of primary dendrite arms in directionally solidified microstructures is an important step for developing process–structure–property relationships by enabling the quantification of (i) the influence of processing on microstructure and (ii) the influence of microstructure on properties. In this work, we utilized a new Voronoi-based approach for spatial point pattern analysis that was applied to an experimental dendritic microstructure. This technique utilizes a Voronoi tessellation of space surrounding the dendrite cores to determine nearest neighbors and the local primary dendrite arm spacing. In addition, we compared this technique to a recent distance-based technique and a modification to this using Voronoi tessellations. Moreover, a convex hull-based technique was used to include edge effects for such techniques, which can be important for thin specimens. These methods were used to quantify the distribution of local primary dendrite arm spacings, their spatial distribution, and their correlation with interdendritic eutectic particles for an experimental directionally solidified Ni-based superalloy micrograph. This can be an important step for correlating processing and properties in directionally solidified dendritic microstructures.     

Structure-dependence of intergranular corrosion in high purity nickel

Electrochemical studies were conducted in 2 N H₂SO₄ at 303 K in order to assess the applicability of the CSL/DSC model of interface structure to intergranular corrosion susceptibility at grain boundaries in high purity (99.999%) polycrystalline nickel. Susceptibility to the initiation of localized corrosion at grain boundaries was manifested through characteristic overpotentials for passive film breakdown. These characteristic overpotentials were found to (1) decrease with increasing bulk sulphur concentration (0.3–50 ppm), and (2) be strongly dependent on interface structure (CSL/DSC). Boundaries close (Δθ) to low ΣCSL relationships were observed to be most resistant to the initiation of localized corrosion. A limiting structural field was determined, not extending beyond Σ25, and restricted to an angular deviation limit defined by a relation of the type: Δθ = 15° Σ^−5/6. Results were determined to be consistent with a mechanism whereby susceptibility to intergranular corrosion is dictated by the (1) geometry, and (2) chemistry (i.e. solute concentration) of intrinsic grain boundary dislocations.     

Grain boundaries in rapidly solidified and annealed Fe-6.5 mass% Si polycrystalline ribbons with high ductility

The type and frequency of grain boundaries in rapidly solidified and subsequently annealed ribbons of Fe-6.5 mass% Si alloy have been determined to discuss the origin of high ductility of the annealed ribbons. The electron channelling pattern (ECP) technique for crystallographic orientation determination was applied. Ribbons subjected to slight annealing after the solidification have a random grain orientation distribution and contain higher frequencies (86–87%) of high-energy boundaries or so called random boundaries. On the other hand, rapidly solidified and fully annealed ribbons with a large grain size of 600 μm and {100} texture contain low-energy boundaries such as low-angle and low Σ, coincidence boundaries in high frequencies. Nearly one half of the boundaries are of low-energy type. Some coincidence boundaries such as Σ5, Σ13 and S 25 occur 3–8 times more frequently than those predicted for a polycrystal with randomly oriented grains. Similarly, low-angle boundaries compose 25% of the total boundaries in the fully annealed ribbon. The inverse cubic root Σ dependence of the frequency for the coincidence boundaries has been discussed. The high ductility of fully annealed Fe-6.5 mass% Si alloy polycrystalline ribbons is attributed to a high frequency of the low-energy boundaries with strong resistance to intergranular fracture.     

A Microstructure-Based Constitutive Model for Superplastic Forming

A constitutive model is proposed for simulations of hot metal forming processes. This model is constructed based on dominant mechanisms that take part in hot forming and includes intergranular deformation, grain boundary sliding, and grain boundary diffusion. A Taylor type polycrystalline model is used to predict intergranular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three-dimensional macro stress?Cstrain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. The proposed model is first used to simulate step strain-rate tests and the results are compared with experimental data. It is shown that the model can be used to predict flow stresses for various grain sizes and strain rates. The yield locus is then predicted for multiaxial stress states, and it is observed that it is very close to the von Mises yield criterion. It is also shown that the proposed model can be directly used to simulate hot forming processes. Bulge forming process and gas pressure tray forming are simulated, and the results are compared with experimental data.     

Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

A 3D model has been developed to predict the average ferrite grain size and grain size distribution for an austenite-to-ferrite phase transformation during continuous cooling of an Fe-C-Mn steel. Using a Voronoi construction to represent the austenite grains, the ferrite is assumed to nucleate at the grain corners and to grow as spheres. Classical nucleation theory is used to estimate the density of ferrite nuclei. By assuming a negligible partition of manganese, the moving ferrite–austenite interface is treated with a mixed-mode model in which the soft impingement of the carbon diffusion fields is considered. The ferrite volume fraction, the average ferrite grain size, and the ferrite grain size distribution are derived as a function of temperature. The results of the present model are compared with those of a published phase-field model simulating the ferritic microstructure evolution during linear cooling of an Fe-0.10C-0.49Mn (wt pct) steel. It turns out that the present model can adequately reproduce the phase-field modeling results as well as the experimental dilatometry data. The model presented here provides a versatile tool to analyze the evolution of the ferrite grain size distribution at low computational costs.     

Probabilistic Models and Simulation of Irregular Masonry Walls

A method is proposed for generating samples of irregular masonry walls that capture the essential statistics of a given population. The method first entails characterizing the geometry of scaled star-like inclusions by means of a non-Gaussian random field model and second packing these inclusions together to form a virtual material specimen. The model used in the first step is a nonlinear memoryless mapping of a sum of harmonic functions with Gaussian coefficients while in the second step the model proposed transforms Poisson fields into a domain of inclusions with a sieving curve that matches the sample specimen. The two random field models are used to develop Monte Carlo algorithms which produce virtual material specimens that include two levels of probabilistic characterization, a first level that is correlated to the inclusion geometry, and a second that is dictated by the global morphology of the sample material specimen.     

Surface intergranular cracking in large strain fatigue

The formation of surface intergranular cracks has been investigated with a coarse-grained polycrystal of nickel, deformed in low-cycle fatigue at 573 K. The evolution of the cracks was followed as a function of fatigue life fractions, and the factors favoring their formation were identified. It was found that in air, surface intergranular cracking occurs early in fatigue life and is induced by the impinging slip traces at the interface. Grain boundaries other than coherent twin boundaries and those with Σ < 5 are susceptible to such cracking. Depending on the boundary plane orientation and on the geometry of the operative slip vectors relative to the specimen surface, the grain boundary cracks may or may not grow to any appreciable extent. Crack growth is accelerated if the boundary plane makes a large angle with the stress axis and if the differential out-of-surface component of the operative slip vectors in the adjoining grains is large. In vacuum, slip is dispersed and surface rumplings become effective in grain boundary crack nucleation. The evolution of surface intergranular cracks, however, is delayed as opposed to tests conducted in air. The results are interpreted in terms of the interaction between crystal dislocations and grain boundaries and on the state of stress at the grain boundaries.     

Scaling in linear bubble models of grain growth

We have numerically solved a linear bubble model of grain growth to study orientation effects in a polycrystal on power law growth of the average grain size and on the existence of a scaling form for the normalized grain size distribution function. We consider a binary linear bubble model such that the inter-bubble permeability between like bubbles (unity) is different from that (M) between unlike bubbles. We have also defined a continuous orientation linear bubble model that allows for a continuous distribution of orientations. The inter-bubble permeability in this case depends on the relative orientation of the two bubbles on either side. Our results suggest that scaling and the exponent in the power growth law, in grain growth models that assume uniform grain boundaries, are not altered by introducing anisotropic grain boundary properties provided the initial distribution of orientations is random.     

Creep–Environment Interactions in Dwell-Fatigue Crack Growth of Nickel Based Superalloys

A multi-scale, mechanistic model is developed to describe and predict the dwell-fatigue crack growth rate in the P/M disk superalloy, ME3, as a function of creep–environment interactions. In this model, the time-dependent cracking mechanisms involve grain boundary sliding and dynamic embrittlement, which are identified by the grain boundary activation energy, as well as, the slip/grain boundary interactions in both air and vacuum. Modeling of the damage events is achieved by adapting a cohesive zone (CZ) approach which considers the deformation behavior of the grain boundary element at the crack tip. The deformation response of this element is controlled by the surrounding continuum in both far field (internal state variable model) and near field (crystal plasticity model) regions and the intrinsic grain boundary viscosity which defines the mobility of the element by scaling up the motion of dislocations into a mesoscopic scale. This intergranular cracking process is characterized by the rate at which the grain boundary sliding reaches a critical displacement. A damage criterion is introduced by considering the grain boundary mobility limit in the tangential direction leading to strain incompatibility and failure. Results of simulated intergranular crack growth rate using the CZ model are generated for temperatures ranging from 923 K to 1073 K (650 °C to 800 °C), in both air and vacuum. These results are compared with those experimentally obtained and analysis of the model sensitivity to loading conditions, particularly temperature and oxygen partial pressure, are presented.     

Crystal Plasticity Model Validation Using Combined High-Energy Diffraction Microscopy Data for a Ti-7Al Specimen

High-Energy Diffraction Microscopy (HEDM) is a 3-d X-ray characterization method that is uniquely suited to measuring the evolving micro-mechanical state and microstructure of polycrystalline materials during in situ processing. The near-field and far-field configurations provide complementary information; orientation maps computed from the near-field measurements provide grain morphologies, while the high angular resolution of the far-field measurements provides intergranular strain tensors. The ability to measure these data during deformation in situ makes HEDM an ideal tool for validating micro-mechanical deformation models that make their predictions at the scale of individual grains. Crystal Plasticity Finite Element Models (CPFEM) are one such class of micro-mechanical models. While there have been extensive studies validating homogenized CPFEM response at a macroscopic level, a lack of detailed data measured at the level of the microstructure has hindered more stringent model validation efforts. We utilize an HEDM dataset from an alpha-titanium alloy (Ti-7Al), collected at the Advanced Photon Source, Argonne National Laboratory, under in situ tensile deformation. The initial microstructure of the central slab of the gage section, measured via near-field HEDM, is used to inform a CPFEM model. The predicted intergranular stresses for 39 internal grains are then directly compared to data from 4 far-field measurements taken between ~4 and ~80 pct of the macroscopic yield strength. The evolution of the elastic strain state from the CPFEM model and far-field HEDM measurements up to incipient yield are shown to be in good agreement, while residual stress at the individual grain level is found to influence the intergranular stress state even upon loading. Implications for application of such an integrated computational/experimental approach to phenomena such as fatigue are discussed.     

分簇无线传感器网络中提高网络连通性的协作算法

针对分簇无线传感器网络提出了一种基于虚拟天线阵列的协作算法.该算法通过节点间的协作来提高网络连通性,所有节点均按照泊松Voronoj网格模型进行分簇,簇首根据通信链路决定是否激活节点协作;若节点协作算法被激活,簇首从其成员中选择适合的节点作为协作节点共同组成虚拟天线阵列.通过协作,可扩展簇间的通信范围从而与远方节点直接通信以避免出现通信覆盖盲区,或者可补偿信道增益以防止由于信道深衰落所导致的传输失败.仿真结果表明,协作算法在通信过程中具有更好的连通性及能量效率,可有效降低接收端的丢包率,维持网络的连通性,从而延长网络的工作时间.     

Sulphur segregation and high-temperature brittle intergranular fracture in alloy steels

High temperature brittle intergranular fracture has recently been identified as a mode of failure in alloy steels. It is associated with the dynamic segregation of sulphur to cracks in hard microstructures stressed at elevated temperatures in a manner analogous to hydrogen embrittlement at ambient temperature. Several models have been proposed to describe the action of sulphur, but insufficient experimental data have been available for their evaluation. The present study characterises sulphur enrichment at cracks and on free surfaces at high temperature in detail using scanning Auger spectroscopy. Both intergranular and transgranular surfaces were studied at pressures of air from 10⁻⁹ to 10⁻³ torr. Two types of sulphur enrichment at cracks were identified; general segregation to crack faces and local enrichment close to crack tips. The source of sulphur was largely that dissolved in the ferrite matrix. Large sulphides, intersecting grain boundaries, made a minor contribution, while small “overheated” intergranular sulphides were inoperative as sulphur sources. The role of stress in encouraging sulphur segregation was confirmed. In addition, an intermediate pressure of air was found to enhance sulphur enrichment, but only at surface oxygen coverages of 15–25 at.%. These observations were generally consistent with the influence of the crack tip stress field on migration of the sulphur solute, described by the “pure drift” model of high temperature brittle intergranular fracture. Refinement of the model, using finite element stress analysis, is included.     

Grain Selection in Spiral Selectors During Investment Casting of Single-Crystal Components: Part II. Numerical Modeling

In this article, grain selection in spiral selectors during investment casting of single-crystal (SX) components is simulated using a cellular automaton grain structure model (CAFE) within a finite element thermal model (PROCAST). The models were validated against experimental observations and then were applied to model the effect of geometry of the spiral selectors on grain selection through a systematic approach. It was found that the efficiency of the spiral selector is significantly dependent on its geometry; the spiral becomes more efficient in selecting single grain with a smaller wax wire diameter; larger spiral rotation diameter, and smaller take-off angle. Recommendations for optimizing the spiral geometry are provided.     

Finite-element calculations of the lattice rotation field of a tensile-loaded nickel-based alloy multicrystal and comparison with topographical X-ray diffraction measurements

A new experimental measurement technique using synchrotron radiation is applied to determine the curvature of the crystallographic lattice within a grain of a multicrystalline specimen after uniaxial tensile loading. The experimental results are compared to a three-dimensional finite-element model, which is based on a classical crystal-plasticity law. The model takes the entire microstructure of the multicrystal into account. A small-strain and small-rotation formalism allows calculation of the orientation matrix at each integration point for each deformation step. A good agreement of the experimental and numerical data has been found. The experimental technique is based on image-data processing. The development of data-treatment algorithms allows distinction to be made between the regular crystallographic curvature and the random mosaic distribution always present in polycrystalline materials.     

Ferroelectric/ferroelastic interactions and a polarization switching model

Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs electric field curves and the corresponding electric displacement vs electric field loops [1]. It is also the source of a stress—strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress [2, 3]. In this work, ceramic lead lanthanum zirconate titanate (PLZT) is polarized by loading with a strong electric field. The resulting strain and polarization hysteresis loops are recorded. The polarized sample is then loaded with compressive stress parallel to the polarization and the stress vs strain curve is recorded. The experimental results are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops and the nonlinear stress—strain curve for the polycrystalline ceramic are reproduced by the simulation.