Lightweight structures are essential for reducing carbon dioxide emissions because lower structural mass directly decreases fuel consumption. Recent advancements in additive manufacturing have enabled the production of components with complex geometries, including Voronoi-type structures, which are commonly used to reduce weight in automotive and aerospace applications. Although often described as bioinspired, such structures are frequently generated using the Poisson point process, which involves a high level of randomness. Since tree leaves have evolved over time and possess important mechanical properties that enable them to withstand environmental conditions, this paper proposes a new heuristic, called BOTH, based on Bauhinia forficata. This heuristic initializes Voronoi structures with an emphasis on enhancing structural stiffness. To analyze leaf morphology and evaluate the mechanical behavior of the resulting structures, computer vision, machine learning algorithms, and finite element simulations were utilized. Validation of the heuristic showed that structures initialized with BOTH exhibit higher stiffness and less variability than those generated using the Poisson point process, with the minimum stiffness increasing from 14.85 to 176.12 kN/mm, corresponding to more than an elevenfold improvement in allowable design stress.

It is well known that grain boundaries are the preferred location for nucleation. Those nucleation sites are not located uniformly randomly in space as assumed by the KJMA theory. As the grains are polyhedra, they comprise faces, edges, and vertices, and nucleation may take place in all these geometrical features. In his pioneering paper, John W. Cahn proposed modeling nucleation and growth on each of these geometrical faces, making some approximations. One of his assumptions was that the grain faces were approximated by “random planes.” In this paper, we clarify the meaning of Cahn’s random planes by revisiting his derivation using modern methods of stochastic geometry. We illustrate our result with a computer simulation. In summary, this paper provides a mathematical explanation of when and why Cahn’s equation, a well-known model, can be used to approximate the volume fraction of phase transformations nucleated on grain faces. We consider both the site-saturated and the constant nucleation rate cases.

The advances in manufacturing technologies have enabled the production of Voronoi structures. The main advantage of these complex designs is their lightweight and enhanced mechanical properties, such as high buckling resistance. Some applications of Voronoi structures are in reducing the weight of automotive and aerospace parts and developing biomedical implants. Metaheuristics are being used to optimize these structures while improving their mechanical properties. Hence, in this study, a systematic review is conducted to identify the trends and gaps in the use of the Genetic Algorithm to optimize two and three-dimensional Voronoi structures. The results mapped seven application domains and suggest that future research should combine manufacturability and optimization constraints, such as additive manufacturing restrictions. In addition, alternative materials (e.g., ceramics and metals) could be used to create specimens for the mechanical tests, and other approaches to finite element simulation are required to speed up the optimization process. The quantitative analysis suggests that this is an emerging topic, with few researchers in local groups cooperating to develop the field.

In polycrystals, a new phase nucleation usually occurs on the grain boundaries. Cahn (J.W. Cahn: Acta Metall. 1956, 4, 449-459) proposed analytical expressions for transformations nucleated on the grain faces, edges, and vertices. Notwithstanding, there are no models for transformations that nucleate simultaneously on, for example, grain faces and vertices. Modeling simultaneous transformations fundamentally depends on whether the transformations are independent. For example, transformations located on random points and random faces are independent. Independent transformations can be modeled using the methodology developed by Rios and Villa (2011). The situation becomes much more difficult when the transformations are not independent but dependent. In this work, we study transformations nucleated simultaneously at the vertices and faces of PoissonVoronoi tessellations employing analytical methods and computer simulation. We develop an analytical mathematical treatment for the situation in which simultaneous transformations are not independent but are dependent in the probabilistic sense. Our mathematical approach specifically applies to the simultaneous nucleation on the faces and vertices of a Poisson Voronoi tessellation.

Reconstruction of random heterogeneous media has been an increasingly popular theme in materials science, as such media is primarily found in nature and manufactured materials. An ideal reconstruction includes every microstructural feature of the reference image and allows simulations of physical quantities that agree with experimental data. In this work, three 2D reconstructions and three 3D reconstructions are produced. All six are based on a single planar section. Its stereological and metallographic features are compared to those of the reference. 2D and 3D reconstructions from single planar sections were carried out with simulated annealing and a sampling method. The first reconstruction used the co-occurrence correlation function (CCF) and orthogonal sampling. The second employed the two-point correlation function ( S 2) and the lattice point algorithm (LPA) as the sampling method. Finally, the third reconstruction used the S 2 together with the two-point cluster function ( C 2) and the LPA as the sampling method. One of two sampling techniques (orthogonal and LPA) were used. The reconstructions that were done using S 2 and C 2 and LPA sampling provided the best results both in 2D and 3D cases, combining realistic morphology and good compatibility with the reference stereological measures.

This article analyses the spread of martensite nucleation in small particles and polycrystalline materials, considering the influence of thermal agitation on the diffusionless aspect of martensitic transformation. Henceforth, we propose a formal description of the initiation of the martensitic transformation supported by experimental data, which emphasises the conditioning of the austenite for martensite transformation and applies to martensitic transformation in general

One typically characterizes the transformation kinetics of a parent phase, alpha, into a single phase, beta, by measuring the volume fraction transformed, VV beta, against time. Sometimes one also reports the interfacial area density between the new and the parent phase, VS alpha beta, against the volume fraction transformed. S alpha beta V is a dynamic interface. It migrates as the growth of the new phase takes place. Interfaces between transformed phases might be called static interfaces. These may be present before transformation starts, for example, grain boundaries of a polycrystalline parent phase. Alternatively, static interfaces, S beta beta, may appear during the transformation because of impingement. Therefore, one V may better understand the microstructural evolution following the behavior of the volume fraction, dynamic and static interfaces. A more complicated situation occurs if the parent phase transforms into two or more product phases, for example, alpha ->beta,gamma. In this work, we apply parameters to describe the transformation of a parent phase into a single phase, the contiguity and the dispersion, to the situation in which the parent phase transforms into two or more phases. We tested these parameters against computer simulations and concluded that they combine a good description of the behavior of the simulated transformations and simplicity.

This work considers the autocatalytic spread of the martensitic transformation throughout the austenite grains in FeNiC and FeNiMn alloys. Formal descriptions were reviewed. The microstructural path concept was re-introduced. The model's analysis of scale factors reiterated the importance of the martensite–austenite interaction. We compared the initial heterogeneous martensite nucleation in a polycrystalline FeNiC with the nucleation in a Fe30Ni particulate alloy. A cluster of tetrakaidecahedral austenite grains might be a reasonable choice to describe the martensite spread in the FeNiC.

Anais do Simpósio de Engenharia Metalúrgica e de Materiais Sul Fluminense (978-85-5722-634-0) - Estudo Analítico De Transformações Simultâneas E Sequenciais Nucleadas Nos Contornos De Grão Para Definição De Parâmetros De Simulação Computacional

Anais do Simpósio de Engenharia Metalúrgica e de Materiais Sul Fluminense (978-65-5941-775-9) - Simulação Computacional E Descrição Analítica De Nucleação E Crescimento De Segunda Fase Nas Faces De Rede Elipsoidal E De Poliedros De Kelvin

Resumo: A reconstrução de meios aleatórios tem sido um tema cada vez mais popular em Materiais, pois este tipo de meio é amplamente encontrado em materiais naturais e em materiais desenvolvidos pelo homem.Uma reconstrução adequada permite simulações de grandezas físicas do material com alto grau de precisão e compatibilidade com medidas experimentais.O método de Yeong-Torquato, baseado em simulated annealing, é um dos mais consagrados na área, e sua correta aplicação depende de funções de correlação que caracterizem bem a microestrutura.O objetivo deste trabalho é avaliar dois descritores, a função de correlação de dois pontos (S2) e a função de correlação de co-ocorrência (CCF), tanto por inspeção visual, como por comparação estatística usando contraste, entropia e outras medidas.Foi possível observar que ambas as funções foram satisfatórias para padrões artificiais, mas careceram de informação de longo alcance na reconstrução de um ferro fundido nodular

A large number of engineering materials of interest are aggregate of many small crystals, called the grains of the polycrystal, which are often equiaxed. However, because of processing, the grain shape may become anisotropic; for instance, during recrystallization or phase transformations, the new grains may grow in the form of ellipsoids. Moreover, it is reasonable and it has also been found in experimental works, that the probability of a new nucleus forming very close to another one is likely to be low. From a mathematical point of view, such situation may be modelled by assuming hard-core nucleation processes. We collect here a series of recent results on mean volume and surface densities of suitable dynamical germ-grain models with ellipsoidal shape of the grains, with the aim to provide a unified approach in modelling phase transformations of this kind.

Anais do Simpósio de Engenharia Metalúrgica e de Materiais Sul Fluminense (978-65-5941-775-9) - Descrição Analítica Da Interface Formada Após A Ocorrência Do Impingement Na Recristalização De Duas Partículas Esféricas

The advent of new materials may increase transformations that involve two or more product phases. This transformation involving two or more product phases may occur simultaneously or sequentially. It is well-known that heterogeneous nucleation has advantages over homogeneous nucleation. Several sites may become preferred because they favor heterogeneous nucleation. The interface of precipitates and the grain boundaries are one of the preferred locations for nucleation. We model simultaneous and sequential transformations nucleated at the preferred sites. This work employs both computer simulation and exact analytical solutions. Two product phases, 1 and 2, were considered. The product phase 1 nucleated at the matrix/particle interface and the product phase 2 nucleated at the grain boundaries. The analytical model showed an excellent agreement with simulation data. For each case, computer simulation obtained the microstructural evolution. We discussed the effect of nucleation at the preferred sites on the microstructure.

This work aims to study cluster nucleation, whose solid–solid phase transformation kinetics considerably deviates from that forecasted by the Kolmogorov–Johnson–Mehl–Avrami (KJMA) model. In this scenario, nuclei do not appear homogeneously within the matrix; however, they appear in preferred regions called clusters. One of the principal parameters of this nucleation is the number of clusters in the matrix. This work uses a numerical model to simulate nucleation and growth reactions, which occur explicitly in spherical clusters. It was thus possible to analyze the cluster number variation affecting the microstructural evolution. During the numerical experiments, we compare the simulation outcomes with the analytical model from Villa & Rios. It was possible to observe that analytical solutions from Villa & Rios equations corroborated the numerical results. The computational model of this study agrees with the analytically exact modeling. This study expanded the analytical solution showing the microstructural evolution in 3D. The simulations also proved that the slower the phase transformation reaction occurs, the fewer clusters per unit volume. Also, the generated microstructures have their particular characteristics. Studies in cluster matrices that use only qualitative and visual analyses can lead to wrong interpretations regarding microstructural evolution when using conventional models of formal kinetics. Thus, the computer simulation study presented that Villa & Rios model is the most suitable for this case involving clustering nucleation. The research shows that clustering introduces microstructural heterogeneity into the matrix. This heterogeneity can be harmful to the materials' final properties that underwent a microstructural transformation with these characteristics.

This work introduces a deterministic approach to the martensite transformation curve. Martensite is a nucleation-controlled transformation that has two characteristics: autocatalysis and auto-accommodation. Only a small number of martensite units initially form owing to primary nucleation. These new units may cause the transformation of other units by autocatalysis. We call this kind of transformation chained autocatalysis. Moreover, as the transformation progresses, the auto-accommodation influences the arrangement of new units. This work assumes that the transformation-saturation relates to the exhaustion of the chained autocatalysis, which underlines the microstructure. To compare, we considered the KJMA’s extended-transformation concept that implies assuming exhaustion by impingement. Data from isothermal martensite transformations and anisothermal martensite transformations are used to validate the model. Those data comprised different grain sizes and carbon contents. The model is based upon Verhulst’s logistic concept. We propose that the model's high fitting-capability stems from its deterministic aspect combined with martensite’s self-similarity. Additionally, we suggest that chained autocatalysis controls the rate of martensite transformation. Therefore, the relaxation of transformation strains by plasticity assisted by mutual accommodation determines the transformation's martensite volume in the absence of post-propagation coarsening/coalescence.

The appearance of intermetallic phases in steels is a matter of great interest due to the harmful character they can confer to the material's mechanical properties. This study presents the effect of the sigma phase's appearance for duplex stainless steel through numerical computational modeling. First, this work simulates a duplex microstructure matrix by a computational stochastic method. Subsequently, it uses this matrix to simulate the sigma phase's nucleation and growth. The Causal Cone method is the base of the nucleation and growth algorithm. The phase transformation code developed gave good results. The computational method calculates many parameters to evaluate microstructural development by stereological measurements. With the Linear Mixing Rule, the computational code predicts the material's mechanical properties. The study compares the data found in the literature against the numerical simulation outcomes. It was possible to verify the increase of the hardness for more significant volumetric fractions of sigma. The results present the transformed microstructure, the growth kinetic, and the mechanical properties evolution in time. This new technology saves money, time, sample, and human resources in carrying out a practical laboratory experiment.

This paper revisits the transformation curves of martensite. We obtained a comparative function compatible with plate and lath transformation validated with independent experimental data in the scientific literature, starting with a power law. The model bears two fitting parameters, which could be interpreted after established aspects of the transformations described in the literature. The model provides a framework to analyse 'isothermal', 'athermal', 'bursting' and 'mechanical induced' martensitic transformation curves.