Using genetic algorithms to evolve three-dimensional microstructures from two-dimensional micrographs

The article describes work to bring together the topics of evolutionary computing and stereology and asks the reader to judge whether such an approach can be genuinely useful or just represents a clever application of computer science. The problem we address is that of constructing three-dimensional (3-D) microstructures from two-dimensional (2-D) micrographs. Our solution is a computer program called MicroConstructor that evolves 3-D discrete computer microstructures, which are statistically equivalent to the 2-D inputs in terms of the microstructural variables of interest. The core of Micro-Constructor is a genetic algorithm that evolves the 3-D microstructure so that its stereological parameters match the 2-D data. MicroConstructor uses a general method of pattern construction, the EmbryoCA, that does not require intervention from the user and is highly evolvable. This article presents initial results from successful experiments to evolve 3-D two-phase microstructures from 2-D input microstructures. The advantages and disadvantages of the method are discussed, and we conclude that the method, though delightfully elegant and full of potential, has yet to prove itself capable of constructing 3-D microstructures that would interest experimentalists and computer modelers. This article is based on a presentation made in the symposium entitled “Three Dimensional Materials Science” during the 2003 MS&T ’03: Materials Science & Technology Conference 2003 in Chicago, Illinois, on November 11 & 12, 2003, under the auspices of the ASM/MSCTS: Materials Science Critical Technology Sector Committee and the TMS/SMD: Structural Materials Division Committee.     

An accelerated methodology for the evaluation of critical properties in polyphase alloys

A system for more rapidly determining the strength and stiffness of polyphase alloys is presented that is based on a digital representation of the material structure. Working in concert with the representation are a number of digital tools and probes that are analogues of testing equipment and instrumentation of traditional laboratory methods. These are combined with nontraditional mechanical testing methods to complete the system. An example of an Fe-Cu system is used to illustrate the methodology. This article is based on a presentation made in the symposium entitled “Three Dimensional Materials Science” during the 2003 MS&T ’03: Materials Science & Technology Conference 2003 in Chicago, Illinois, on November 11 & 12, 2003, under the auspices of the ASM/MSCTS: Materials Science Critical Technology Sector Committee and the TMS/SMD: Structural Materials Division Committee.     

Stress and strain localization three-dimensional modeling for particle-reinforced metal matrix composites

The ductility of particle-reinforced metal matrix composites (PR MMCs) is reduced by the localization of stress and strain, which is exacerbated by microstructural heterogeneity, especially particle clustering. Herein, the effect of particle distribution on the macroscopic and microscopic response has been studied using three distinct types of three-dimensional (3D) finite-element model: a repeating unit cell, a multiparticle model, and a clustered particle model. While the repeating unit cell model represents a cubic periodic array of particles, the multiparticle model represents a random distribution of particles contained in a cube of matrix material, and the clustered particle model represents an artificially clustered distribution of particles. These models were used to study the macroscopic tensile stress-strain response as well as the underlying stress and strain fields. The results indicate that a clustered microstructure leads to a stiffer response with more hardening than that of random and periodic microstructures. Plastic flow and hydrostatic stress localization in the matrix and maximum principal stress localization in the particles are significantly higher in the clustered microstructure. Damage is expected to initiate in the cluster regions leading to low ductility. This article is based on a presentation made in the symposium entitled “Three Dimensional Materials Science” during the 2003 MS&T ’03: Materials Science & Technology Conference 2003 in Chicago, Illinois, on November 11–12, 2003, under the auspices of the ASM/MSCTS: Materials Science Critical Technology Sector Committee and the TMS/SMD: Structural Materials Division Committee.     

Anisotropy of point defect diffusion in alpha-zirconium

Two types of intrinsic defect, i.e., vacancy and self-interstitial atom (SIA), are formed in metals during irradiation with energetic particles. The evolution of defect population leads to significant changes in microstructure and causes a number of radiation-induced property changes. Some phenomena, such as radiation growth of anisotropic materials, are due to anisotropy in the atomic mass transport by point defects. Detailed information on atomic-scale mechanisms is, therefore, necessary to understand such phenomena. In this article, we present results of a computer simulation study of mass transport via point defects in alpha-zirconium. The matrix of self-diffusion coefficients and activation energies for vacancy and SIA defects have been obtained, and different methods of treatment of diffusion have been tested. Molecular dynamics (MD) shows that vacancy diffusion is approximately isotropic in the temperature range studied (1050 to 1650 K), although some preference for basalplane diffusion was observed at the lower end of the range. The mechanism of interstitial diffusion changes from one-dimensional (1-D) in a 〈11 0〉 direction at low temperature (<300 K) to two-dimensional (2-D) in the basal plane and, then, three-dimensional (3-D) at higher temperatures. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Equal-channel angular extrusion of beryllium

The equal-channel angular extrusion (ECAE) technique has been applied to a powder metallurgy (P/M) source Be alloy. Extrusions have been successfully completed on Ni-canned billets of Be at approximately 425 °C. No cracking was observed in the billets, and significant grain refinement was achieved. In this article, microstructural features and dislocation structures are discussed for a single-pass extrusion, including evidence of 〈c〉 and 〈c+a〉 dislocations. Significant crystallographic texture developed during ECAE, which is discussed in terms of this unique deformation processing technique and the underlying physical processes which sustain the deformation. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Advances in deformation twin characterization using electron backscattered diffraction data

This article reports on recent progress in the effort to develop an automated, crystallographically based twin identification and quantification routine using large sets of spatially correlated electron backscattered diffraction (EBSD) data. The proposed analysis scheme uses information about the most probably occurring twin types and the macroscopic stress state, taken together with the crystallographic theory of deformation twinning, to identify and classify twinned areas in a scanned cross section of a material. The key features of the analysis are identification of potential twin boundaries by their misorientation character, validation of these boundaries through comparison with the actual boundary position and twin-plane matching across the boundary, and calculation of the Schmid factors for the orientations on either side of the boundary. This scheme will allow researchers to quantify twin area fractions from statistically significant regions and, in turn, estimate twinned volume fractions with reasonable reliability. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Advances in deformation twin characterization using electron backscattered diffraction data

This article reports on recent progress in the effort to develop an automated, crystallographically based twin identification and quantification routine using large sets of spatially correlated electron backscattered diffraction (EBSD) data. The proposed analysis scheme uses information about the most probably occurring twin types and the macroscopic stress state, taken together with the crystallographic theory of deformation twinning, to identify and classify twinned areas in a scanned cross section of a material. The key features of the analysis are identification of potential twin boundaries by their misorientation character, validation of these boundaries through comparison with the actual boundary position and twin-plane matching across the boundary, and calculation of the Schmid factors for the orientations on either side of the boundary. This scheme will allow researchers to quantify twin area fractions from statistically significant regions and, in turn, estimate twinned volume fractions with reasonable reliability. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Deformation twinning in polycrystalline Zr: Insights from electron backscattered diffraction characterization

The response of polycrystalline α-zirconium to various deformation conditions was investigated through electron backscattered diffraction (EBSD) characterization. The range of deformation conditions included quasi-static compression and tension at room and cryogenic temperatures, along with a Taylor cylinder impact experiment. The resultant data provided spatial resolution of individual with system activity as a function of the progression of deformation. Over 300 deformation twins were analyzed to identify the type of twin system and active variant, along with the Schmid factor in the parent orientation. These data supplied information on the distribution of Schmid factor and variant rank as a function of twin system and deformation condition. Results showed significant deviation from a maximum Schmid factor activation criterion and suggest deformation twinning is greatly affected by local internal stress heterogeneities and the sense of the applied stress. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Deformation twinning in polycrystalline Zr: Insights from electron backscattered diffraction characterization

The response of polycrystalline α-zirconium to various deformation conditions was investigated through electron backscattered diffraction (EBSD) characterization. The range of deformation conditions included quasi-static compression and tension at room and cryogenic temperatures, along with a Taylor cylinder impact experiment. The resultant data provided spatial resolution of individual twin system activity as a function of the progression of deformation. Over 300 deformation twins were analyzed to identify the type of twin system and active variant, along with the Schmid factor in the parent orientation. These data supplied information on the distribution of Schmid factor and variant rank as a function of twin system and deformation condition. Results showed significant deviation from a maximum Schmid factor activation criterion and suggest deformation twinning is greatly affected by local internal stress heterogeneities and the sense of the applied stress. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Anisotropy of point defect diffusion in alpha-zirconium

Two types of intrinsic defect, i.e., vacancy and self-interstitial atom (SIA), are formed in metals during irradiation with energetic particles. The evolution of defect population leads to significant changes in microstructure and causes a number of radiation-induced property changes. Some phenomena, such as radiation growth of anisotropic materials, are due to anisotropy in the atomic mass transport by point defects. Detailed information on atomic-scale mechanisms is, therefore, necessary to understand such phenomena. In this article, we present results of a computer simulation study of mass transport via point defects in alpha-zirconium. The matrix of self-diffusion coefficients and activation energies for vacancy and SIA defects have been obtained, and different methods of treatment of diffusion have been tested. Molecular dynamics (MD) shows that vacancy diffusion is approximately isotropic in the temperature range studied (1050 to 1650 K), although some preference for basal-plane diffusion was observed at the lower end of the range. The mechanism of interstitial diffusion changes from one-dimensional (1-D) in a direction at low temperature (<300 K) to two-dimensional (2-D) in the basal plane and, then, three-dimensional (3-D) at higher temperatures. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Mobility of interstitial clusters in alpha-zirconium

Clusters of self-interstitial atoms (SIAs) formed in displacement cascades in metals irradiated with energetic particles play an important role in microstructure evolution under irradiation. They have been studied in the fcc and bcc metals by atomic-scale computer simulation, and in this article, we present the results of a similar study in a hexagonal close-packed (hcp) crystal. Static and dynamic properties of clusters of up to 30 SIAs were studied using a many-body Finnis-Sinclair type interatomic potential for Zr. The results show a qualitative similarity of some properties of clusters to those for cubic metals. In particular, all clusters larger than four SIAs exhibit fast thermally activated one-dimensional (1-D) glide, which is in a <1120> direction in the hcp lattice. Due to the structure of the hcp lattice, this mechanism leads to two-dimensional mass transport in basal planes. Some clusters exhibit behavior peculiar to the hcp structure, for they can migrate two-dimensionally (2-D) in the basal plane. The jump frequency, activation energy, and correlation factors of clusters have been estimated, and comparisons drawn between the behavior of SIA clusters in different structures. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Equal-channel angular extrusion of beryllium

The equal-channel angular extrusion (ECAE) technique has been applied to a powder metallurgy (P/M) source Be alloy. Extrusions have been successfully completed on Ni-canned billets of Be at approximately 425°C. No cracking was observed in the billets, and significant grain refinement was achieved. In this article, microstructural features and dislocation structures are discussed for a singlepass extrusion, including evidence of <c> and <c+a> dislocations. Significant crystallographic texture developed during ECAE, which is discussed in terms of this unique deformation processing technique and the underlying physical processes which sustain the deformation. S.R. AGNEW, formerly with the Oak Ridge National Laboratory, Oak Ridge, TN 37831-6115 This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Mobility of interstitial clusters in alpha-zirconium

Clusters of self-interstitial atoms (SIAs) formed in displacement cascades in metals irradiated with energetic particles play an important role in microstructure evolution under irradiation. They have been studied in the fcc and bcc metals by atomic-scale computer simulation, and in this article, we present the results of a similar study in a hexagonal close-packed (hcp) crystal. Static and dynamic properties of clusters of up to 30 SIAs were studied using a many-body Finnis-Sinclair type interatomic potential for Zr. The results show a qualitative similarity of some properties of clusters to those for cubic metals. In particular, all clusters larger than four SIAs exhibit fast thermally activated one-dimensional (1-D) glide, which is in a 〈11 0〉 direction in the hcp lattice. Due to the structure of the hcp lattice, this mechanism leads to two-dimensional mass transport in basal planes. Some clusters exhibit behavior peculiar to the hcp structure, for they can migrate two-dimensionally (2-D) in the basal plane. The jump frequency, activation energy, and correlation factors of clusters have been estimated, and comparisons drawn between the behavior of SIA clusters in different structures. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Intergranular stresses in ZIRCALOY-2

The development of the understanding of the intergranular stresses in ZIRCALOY-2 is reviewed. Neutron diffraction measurements of the intergranular strains were made on rod-textured material and highly textured plate. The elastoplastic self-consistent (EPSC) model provides a sound theoretical foundation for our understanding of the behavior. The strain response of ZIRCALOY-2 to applied tensile stress is well described for two very different textures with the same slip and hardening parameters. It is almost certain that tensile twinning is the explanation for the response to compressive stress and rolling that is, as yet, incompletely understood. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Intergranular stresses in ZIRCALOY-2

The development of the understanding of the intergranular stresses in ZIRCALOY-2 is reviewed. Neutron diffraction measurements of the intergranular strains were made on rod-textured material and highly textured plate. The elastoplastic self-consistent (EPSC) model provides a sound theoretical foundation for our understanding of the behavior. The strain response of ZIRCALOY-2 to applied tensile stress is well described for two very different textures with the same slip and hardening parameters. It is almost certain that tensile twinning is the explanation for the response to compressive stress and rolling that is, as yet, incompletely understood. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Neutron and Synchrotron X-ray Studies of Recrystallization Kinetics

An overview is given on recrystallization kinetics investigated by neutron and synchrotron X-ray methods. It is shown that during recrystallization, grains belonging to different texture components may have very different growth kinetics. Also, every single grain has its own kinetics different from the other grains. Effects hereof on recrystallization modeling are discussed and an outlook for future experiments and modeling is finally given. This article is based on a presentation given in the symposium entitled “Neutron and X-Ray Studies for Probing Materials Behavior,” which occurred during the TMS Spring Meeting in New Orleans, LA, March 9–13, 2008, under the auspices of the National Science Foundation, TMS, the TMS Structural Materials Division, and the TMS Advanced Characterization, Testing, and Simulation Committee.     

Diffusion along grain and interphase boundaries in alpha Zr and Zr-2.5 wt pct Nb alloy

Diffusion parameters of Cr diffusion along the α/β interphase boundaries of a Zr-2.5 wt pct Nb alloy are presented. The conventional radiotracer technique combined with serial sectioning of the samples was applied. In the Arrhenius plot, it is possible to consider only one straight line (with Q=133 kJ/mol for 615<T<953 K) or two zones (with Q=230 kJ/mol for 773<T<953 K and Q=77 kJ/mol for 615<T<773 K). An analysis is made of these results together with previous data concerning diffusion along short circuits paths in α-Zr (grain boundaries) and Zr-2.5 wt pct Nb (interphase boundaries): Zr and Nb as the alloy component elements and Ni, Fe, and Co as other relevant impurities. Different mechanisms are proposed: a vacancy mechanism for Zr and Nb and an interstitial-like mechanism for the impurities, for both kind of boundaries. The influence on diffusion and the estimated values of the impurities segregation in the α phase are discussed in the work. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting February 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.     

Microstructure evolution in Zr under equal channel angular pressing

Pure polycrystalline Zr was deformed by equal channel angular pressing (ECAP), and the microstructural characteristics were analyzed. By repeated alternating ECAP, it was possible to, refine the grain size from 200 to 0.2 μm. Subsequent annealing heat treatment at 550°C resulted in a grain growth of up to 6 μm. Mechanical twinning was an important deformation mechanism, particularly during the early stage of deformation. The most active twinning system was identified as 85.2 deg tensile twinning, followed by 57.1 deg compressive twinning. Crystal texture as well as grain-boundary misorientation distribution of deformed Zr were analyzed by X-ray diffraction (XRD) and electron backscattered diffraction (EBSD). The ECAP-deformed Zr showed a considerable difference in the crystallographic attributes from those of cold-rolled Zr or Ti, in that texture and boundary misorientation-angle distribution tend toward more even distribution with a slightly preferential distribution of boundaries of a 20 to 30 deg misorientation angle. Furthermore, unlike the case of cold rolling, the crystal texture was not greatly altered by subsequent annealing heat treatment. Overall, the present work suggests ECAP as a viable method to obtain significant grain refining in hexagonal close-packed (hcp) metals. This article is based on a presentation made in the symposium entitled “Defect Properties and Mechanical Behavior of HCP Metals and Alloys” at the TMS Annual Meeting, February, 11–15, 2001, in New Orleans, Louisiana, under the auspices of the following ASM committees: Materials Science Critical Technology Sector, Structural Materials Division, Electronic, Magnetic & Photonic Materials Division, Chemistry & Physics of Materials Committee, Joint Nuclear Materials Committee, and Titanium Committee.