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A novel method of micromechanical stereoinference is reported which yields components and gradients of Nye’s GND tensor which are inaccessible by surface EBSD. In particular, it determines the Nye’s tensor gradients going into the sample bulk. The method overcomes limitations imposed by metal’s electron opacity by combining experimentally-accessible Nye’s tensor components and measured infinitesimal elastic distortion tensors with a solution to the underlying stress equilibrium equations. The full Nye’s tensor can be transformed into a crystal coordinate frame and interpreted in the context of slip systems, a more physical sense than in the sample or experimental frame. A demonstration of the method is given for a simulated microstructure. The method is largely robust to random experimental noise but may be sensitive to pattern-center errors.

A mesoscale model, shear transformation zone dynamics (STZ dynamics), is employed to investigate the connections between the structure and deformation of metallic glasses. The present STZ dynamics model is adapted to incorporate a structure-related state variable, and evolves via two competing processes: STZ activation, which creates free volume, vs. diffusive rearrangement, which annihilates it. The dynamical competition between these two processes gives rise to an equilibrium excess free volume that can be connected to flow viscosity via the phenomenological Vogel–Fulcher–Tammann relation in relaxed structures near the glass transition temperature. On the other hand, the excess free volume allows glasses to deform at low temperatures via shear localization into shear bands, even in the presence of internal stress distributions that arise upon cooling after processing., Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies, United States. Defense Threat Reduction Agency (Contract HDTRA-11-1-0062)

In this work, we introduce and demonstrate a hybrid model that combines elements of the Monte Carlo Potts Model with those of the phase field model. This hybrid model is introduced as a method to simulate microstructural evolution processes that are kinetically controlled by long-range diffusion in multi-component systems. The hybrid model uses a digitized microstructure with each site characterized by its microstructural features and its composition. The total free energy of the system is defined by bulk chemical free energy as well as interfacial energy. The coupling between the microstructure and composition is achieved by using the total free energy to drive the evolution in both fields. The kinetics are simulated by a combination of Monte Carlo methods and solution of the Cahn–Hilliard equation. This model is applied to several example problems to demonstrate its capabilities. These are diffusion in single- and two-phase diffusion couples, grain growth in a two-phase system controlled by diffusion and diffusion phase transformation by nucleation and growth of a second phase.

Shear-coupled grain boundary motion is examined for a large number of grain boundaries including 73 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 symmetric tilt boundaries. In the present work, the grain boundary motion is induced by a synthetic driving force as opposed to prior studies of shear coupling induced by applied shear. For those boundaries that are observed to undergo shear-coupled motion, the results based on the two driving forces agree well, both for experiments and simulations. This agreement also confirms the generality of the shear coupling mechanism over numerous boundaries and boundary types. The examination of boundary structure provides insight into the different trends that are observed. Shear coupling according to modes not predicted by the Frank–Bilby equation are also demonstrated. The temperature dependence of shear coupling is examined, and is consistent with prior work for symmetric tilt boundaries. While prior studies have emphasized symmetric tilt boundaries, some general grain boundaries exhibit shear coupling as well. In these boundaries, it is found that the shear coupling is either temperature independent, decreases in magnitude with increasing temperature or, in some cases, changes direction with temperature.

High-resolution (or “cross-correlation”) electron backscatter diffraction analysis (HR-EBSD) utilizes cross-correlation techniques to determine relative orientation and distortion of an experimental electron backscatter diffraction pattern with respect to a reference pattern. The integrity of absolute strain and tetragonality measurements of a standard Si/SiGe material have previously been analyzed using reference patterns produced by kinematical simulation. Although the results were promising, the noise levels were significantly higher for kinematically produced patterns, compared with real patterns taken from the Si region of the sample. This paper applies HR-EBSD techniques to analyze lattice distortion in an Si/SiGe sample, using recently developed dynamically simulated patterns. The results are compared with those from experimental and kinematically simulated patterns. Dynamical patterns provide significantly more precision than kinematical patterns. Dynamical patterns also provide better estimates of tetragonality at low levels of distortion relative to the reference pattern; kinematical patterns can perform better at large values of relative tetragonality due to the ability to rapidly generate patterns relating to a distorted lattice. A library of dynamically generated patterns with different lattice parameters might be used to achieve a similar advantage. The convergence of the cross-correlation approach is also assessed for the different reference pattern types.

Low-load nanoindentation can be used to assess not only the plastic yield point, but the distribution of yield points in a material. This paper reviews measurements of the so-called nanoscale strength distribution (NSD) on two classes of materials: crystals and metallic glasses. In each case, the yield point has a significant spread (10–50% of the mean normalized stress), but the origins of the distribution are shown to be very different in the two materials classes. In crystalline materials the NSD can arise from thermal fluctuations and is attended by significant rate and temperature dependence. In metallic glasses well below their glass-transition temperature, the NSD is reflective of fluctuations in the sampled structure and is not very sensitive to rate or temperature. Computer simulations using shear transformation zone dynamics are used to separate the effects of thermal and structural fluctuations in metallic glasses, and support the latter as dominating the NSD of those materials at low temperatures. Finally, the role of the NSD as a window on structural changes due to annealing or prior deformation is discussed as a direction for future research on metallic glasses in particular.

A combined program of experiments and simulations is used to study the problem of cyclic indentation loading on metallic glasses. The experiments use a spherical nanoindenter tip to study shear band formation in three glasses (two based on Pd and one on Fe), after subjecting the glass to cycles of load in the nominal elastic range. In all three glasses, such elastic cycles lead to significant increases in the load required to subsequently trigger the first shear band. This cyclic hardening occurs progressively over several cycles, but eventually saturates. The effect requires cycles of sufficient amplitude and is not induced by sustained loading alone. The simulations employed a new shear transformation zone (STZ) dynamics code to reveal the local STZ operations that occur beneath an indenter during cycling. These results reveal a plausible mechanism for the observed cyclic hardening: local regions of confined microplasticity can develop progressively over several cycles, without being detectable in the global load–displacement response. It is inferred that significant structural change must attend such microplasticity, leading to hardening of the glass., United States. Office of Naval Research (Grant No. N00014-08-10312), United States. Army Research Office (National Defense Science and Engineering Graduate Fellowship), King Fahd University of Petroleum and Minerals

A new mesoscale modeling technique for the thermo-mechanical behavior of metallic glasses is proposed. The modeling framework considers the shear transformation zone (STZ) as the fundamental unit of deformation, and coarse-grains an amorphous collection of atoms into an ensemble of STZs on a mesh. By employing finite element analysis and a kinetic Monte Carlo algorithm, the modeling technique is capable of simulating glass processing and deformation on time and length scales greater than those usually attainable by atomistic modeling. A thorough explanation of the framework is presented, along with a specific two-dimensional implementation for a model metallic glass. The model is shown to capture the basic behaviors of metallic glasses, including high-temperature homogeneous flow following the expected constitutive law, and low-temperature strain localization into shear bands. Details of the effects of processing and thermal history on the glass structure and properties are also discussed., United States. Office of Naval Research (contract N00014-08-1-0312)

The nanomechanics of amorphous systems span significant time and length scales that are difficult to access. Shear transformation zone (STZ) dynamics is a mesoscale approach that combines the kinetic Monte Carlo (kMC) algorithm with coarse-graining techniques to bridge the relevant time and length scales associated with deformation in these systems. This work discusses the fundamental details of these scale bridging techniques as well as their specific application in the STZ dynamics framework. The modeling framework is applied in various scenarios to demonstrate the versatility of the mesoscale approach. These applications include: (1) simulating the overall deformation behaviors of amorphous metals, (2) investigating the influence of thermomechanical processing by tracking a structural state variable, excess free volume, (3) assessing the nanomechanics that lead to shear banding in amorphous metals, (4) elucidating structural evolution that occurs during nanoindentation, and (5) examining the influence of various microstructural factors that influence the mechanical properties of metallic glass matrix (MGM) composites.

Designers have traditionally simplified the consideration of material properties because of the diffi culty in incorporating anisotropy and non-homogeneity into design problems. Microstructure sensitive design for performance optimization (MSDPO) introduces the necessary tools to optimize both geometric design and anisotropic material properties concurrently, while also considering heterogeneous placement. In this paper a case study is presented wherein the geometry and microstructure of a micro-electro-mechanical system switch are optimized to minimize the actuation voltage, while ensuring that plastic yielding does not occur during operation. This is accomplished by varying both beam width and crystallographic texture along the length of the beam. The designed switch is predicted to reduce the actuation voltage by 90%. While this case study does not identify the manufacturing processes required to produce the optimized microstructure, such considerations can be included in MSDPO, but lie beyond the scope of this paper.

A method for the retrieval of grain-boundary inclination parameters of the grain-boundary character distribution (GBCD) by oblique double sectioning (ODS) is proposed. In this hybrid approach, grain-boundary inclination parameters are directly measured by double sectioning, while a statistically reliable sampling of the microstructure is achieved by oblique sectioning. The solution to the fundamental equations is posed in a manner similar to the recovery of the orientation distributions from sets of incomplete pole figures, using classical Fourier representations of the distribution functions. The ODS is validated by and compared to the L A /S V stereology through simulations and experimental implementation in a sample of 439 stainless steel. Simulations show that the grain-boundary normal distributions recovered by ODS and stereology are comparable, giving errors on the order of 10−2. Experimental implementation of ODS and the L A /S V stereology in alloy 439 stainless steel demonstrate additional practical limitations of the ODS methodology when applied to materials of large or uneven grain size.

Grain boundary plane orientation is a profoundly important determinant of character in polycrystalline materials that is not well understood. This work demonstrates how boundary plane orientation fundamental zones, which capture the natural crystallographic symmetries of a grain boundary, can be used to establish structure-property relationships. Using the fundamental zone representation, trends in computed energy, excess volume at the grain boundary and temperature-dependent mobility naturally emerge and show a strong dependence on the boundary plane orientation. Analysis of common misorientation axes even suggests broader trends of grain boundary energy as a function of misorientation angle and plane orientation. Due to the strong structure-property relationships that naturally emerge from this work, boundary plane fundamental zones are expected to simplify analysis of both computational and experimental data. This standardized representation has the potential to significantly accelerate research in the topologically complex and vast five-dimensional phase space of grain boundaries.

A method for the retrieval of the complete grain boundary character distribution by oblique double-sectioning is proposed. The method, which is similar to the recovery of the orientation distribution from sets of incomplete pole-figures, is efficient and provides many advantages as compared to calibrated serial sectioning. As compared to standard stereological approaches, the new methodology retains the advantage of direct measurement of the grain boundary inclination parameters. Solutions to the fundamental equation of oblique double-sectioning are provided in the Fourier space, and some specifics in sample preparation are introduced.

A method for estimating the variance of the grain boundary character distribution from experimental recovery of the two-point correlation functions is derived. The method is illustrated in 2-D to analyze the variance of “susceptible” boundaries in alloy 304 stainless steel. Comparison of these estimates with results obtained directly from OIM measurements is presented. Introduction When the phenomena governing failure in crystalline materials by fracture or crack propagation is intergranular in nature or a mixture of intergranular and transgranular behaviors, the character of the grain boundaries in the region surrounding the point of interest will govern much of the resulting behavior. Although conditions affecting this behavior will also be governed largely by the ductility and temperature under which the fracture occurs, the intergranular interfaces will affect the ability of the material to drive or stop this fracture [1,2]. Studies regarding stress corrosion cracking (SCC) have shown the effect of special boundaries upon the propagation of cracks in experimental samples [3-7]. Boundaries of low misorientation angle along with coincident site lattice (CSL) boundaries of low value inhibited the propagation of cracks in the material whereas boundaries with large misorientation angles were prone to propagate the crack. Accordingly, all references to “susceptible” grain boundaries in this publication will be of large misorientation angle excluding low value CSLs. The connectivity or percolation of grain boundaries of certain character has also proven to be a governing factor in the fracture mechanics of materials [8]. These percolative paths were found to be largely dependent upon percolation “red bonds” which have the ability or inability to impede these percolation paths [7]. Although these two conditions are clearly related in the failure of materials, the difficulty in relating the two is that percolation theory governs the behavior for infinite lattices and failure by fracture often only occurs in a small region; therefore linking the two becomes the probability of the two effects occurring in the same place and at the point of heightened stress. Therefore these two ideas may only be related when the region of interest is large. Research Perspective. The subject of interest is to develop a model which will link the fraction of grain boundaries necessary to develop a connected path of “susceptible” boundaries across a region of interest where the connected length would pose a serious threat to the integrity of the material. Although the probability of finding a cluster of connected length in a specified area has proven difficult because of the nature of percolation, the ability to determine the fraction of “susceptible” boundaries in a given region can be extracted readily. The authors are currently studying the percolative behavior of grain boundaries in alloy 304 stainless steel in order to establish this connection, but this discussion will be presented elsewhere. The focus of this paper will be on the determination of the variance of “susceptible” boundaries as a function of window size by a new method employing a two-point correlation function. The derivation along with experimental procedures and findings for the variance will be discussed. Variance of LA The Microstructure Function ) , ( s x M . In deriving the new method for sampling the variance of the grain boundary character distribution (GBCD), SV (s) , it is illustrative to consider the 2-D function LA(s), which is the line length per unit area of boundaries of local state s. Here local state refers to any selected set of parameters defining local grain boundary character, such as lattice misorientation, boundary inclination, etc. In 2-D measurements the latter is normally inaccessible. Consider the semi-continuous grain boundary network contained in a given field of view . LA(s) for the region can be recovered in two ways; the first of which is by deconstructing the data points from an Orientation Imaging Microscopy (OIM) dataset into discrete line segments, or grain boundary traces. By adding up the length of all the grain boundary traces of state s and dividing by the area of the scan, the true value for LA(s) can be obtained for the region . The second, new method requires allowing the grain boundary traces from the OIM scan to have a finite thickness, t, and then by sampling the region of interest with the vector x . Define a new microstructure function ) , ( s x M where ± = otherwise 0 type of boundary the from 2 within lies if 1 ) , ( s t x t s x M . (1) Integrating over the region of interest, and taking the limit as the thickness goes to zero one obtains the function LA(s) Ω = → 2 ) ( ) , ( ) ( 1 lim ) ( 0 R t A x d x s x M A s L θ (2)

Zhou and Mohles [J. Zhou, and V. Mohles, Acta Materialia 59, 5997 (2011)] recently presented a molecular dynamics (MD) simulation of grain boundary motion that contradicts the results of all previous such simulations. Here we show: (i) the Zhou–Mohles (Z–M) model incorporates a fundamental error in the definition of the atomic energy and forces; (ii) because of this error, the driving force for boundary motion is unknown; (iii) the Z–M model contains an additional, unrecognized, nonlinear driving force; and (iv) these observations explain and invalidate the Z–M results.

This report documents the development, demonstration and validation of a mesoscale, microstructural evolution model for simulation of zirconium hydride δ-ZrH{sub 1.5} precipitation in the cladding of used nuclear fuels that may occur during long-term dry storage. While the Zr-based claddings are manufactured free of any hydrogen, they absorb hydrogen during service, in the reactor by a process commonly termed ‘hydrogen pick-up’. The precipitation and growth of zirconium hydrides during dry storage is one of the most likely fuel rod integrity failure mechanisms either by embrittlement or delayed hydride cracking of the cladding (Hanson et al., 2011). While the phenomenon is well documented and identified as a potential key failure mechanism during long-term dry storage (Birk et al., 2012 and NUREG/CR-7116), the ability to actually predict the formation of hydrides is poor. The model being documented in this work is a computational capability for the prediction of hydride formation in different claddings of used nuclear fuels. This work supports the Used Fuel Disposition Research and Development Campaign in assessing the structural engineering performance of the cladding during and after long-term dry storage. In this work, a model to numerically simulate hydride precipitation at the microstructural scale, in a wide variety ofmore » Zr-based claddings, under dry-storage conditions is being developed. It will be used to aid in the evaluation of the mechanical integrity of used fuel rods during dry storage and transportation by providing the structural conditions from the microstructural scale to the continuum scale to engineering component scale models to predict if the used fuel rods will perform without failure under normal and off-normal conditions. The microstructure, especially, the hydride structure is thought to be a primary determinant of cladding failure, thus this component of UFD’s storage and transportation analysis program is critical. The model development, application and validation of the model are documented and the limitations of the current model are discussed. The model has been shown to simulate hydride precipitation in Zircaloy-4 cladding with correct morphology, thermodynamics and kinetics. An unexpected insight obtained from simulations hydride formation in Zircaloy-4 is that small (sub-micron) precipitates need to order themselves to form the larger hydrides typically described as radially-reoriented precipitates. A limitation of this model is that it does not currently solve the stress state that forms dynamically in the precipitate or matrix surrounding the precipitate. A method to overcome the limitations is suggested and described in detail. The necessary experiments to provide key materials physics and to validate the model are also recommended.« less

This report documents the development, demonstration and validation of a mesoscale, microstructural evolution model for simulation of zirconium hydride {delta}-ZrH{sub 1.5} precipitation in the cladding of used nuclear fuels that may occur during long-term dry storage. While the Zr-based claddings are manufactured free of any hydrogen, they absorb hydrogen during service, in the reactor by a process commonly termed ‘hydrogen pick-up’. The precipitation and growth of zirconium hydrides during dry storage is one of the most likely fuel rod integrity failure mechanisms either by embrittlement or delayed hydride cracking of the cladding. While the phenomenon is well documented and identified as a potential key failure mechanism during long-term dry storage (NUREG/CR-7116), the ability to actually predict the formation of hydrides is poor. The model being documented in this work is a computational capability for the prediction of hydride formation in different claddings of used nuclear fuels. This work supports the Used Fuel Disposition Research and Development Campaign in assessing the structural engineering performance of the cladding during and after long-term dry storage. This document demonstrates a basic hydride precipitation model that is built on a recently developed hybrid Potts-phase field model that combines elements of Potts-Monte Carlo and the phase-fieldmore » models. The model capabilities are demonstrated along with the incorporation of the starting microstructure, thermodynamics of the Zr-H system and the hydride formation mechanism.« less

Most materials microstructural evolution processes progress with multiple processes occurring simultaneously. In this work, we have concentrated on the processes that are active in nuclear materials, in particular, nuclear fuels. These processes are coarsening, nucleation, differential diffusion, phase transformation, radiation-induced defect formation and swelling, often with temperature gradients present. All these couple and contribute to evolution that is unique to nuclear fuels and materials. Hybrid model that combines elements from the Potts Monte Carlo, phase-field models and others have been developed to address these multiple physical processes. These models are described and applied to several processes in this report. An important feature of the models developed are that they are coded as applications within SPPARKS, a Sandiadeveloped framework for simulation at the mesoscale of microstructural evolution processes by kinetic Monte Carlo methods. This makes these codes readily accessible and adaptable for future applications.

A recently introduced hybrid Potts-phase field method has demonstrated the ability to evolve microstructures in conjunction with compositional fields tied to different phases. In this approach, Monte Carlo Potts methods are used to evolve the microstructure while phase field methods are used to evolve the composition, and the two fields are coupled through free energy functionals. Recent developments of the model allow different multi-component alloy systems to be simulated by using thermodynamic databases and kinetic quantities to dictate the behavior. An example of the method using the aluminum-silicon binary system is demonstrated.

Shear transformation zone (STZ) dynamics simulations, which are based on the kinetic Monte Carlo algorithm, are used to model the mechanical response of amorphous metals and provide insight into the collective aspects of the microscopic events underlying deformation. The present analysis details the activated states of STZs in such a model, as well as the statistics of their activation and how these are affected by imposed conditions of stress and temperature. The analysis sheds light on the spatial and temporal correlations between the individual STZ activations that lead to different macroscopic modes of deformation. Three basic STZ correlation behaviors are observed: uncorrelated activity, nearest-neighbor correlation, and self-reactivating STZs. These three behaviors correspond well with the macroscopic deformation modes of homogeneous flow, inhomogeneous deformation, and elastic behavior, respectively. The effect of pre-existing stresses in the simulation cell is also studied and found to have a homogenizing effect on STZ correlations, suppressing the tendency for localization.

Resolving the mechanisms associated with grain boundary migration is a difficult task. This work is focused on detailing techniques to utilize atomistic simulations to better understand the energy, structure and mobility of grain boundaries (GBs). Various techniques are detailed on how to construct different simulation cells, select boundary plane normals, and measure simulated mobility. A limited number of GBs, inspired by experimental observations, are selected for the present work. The GBs studied indicate that the structure of the theoretical set of GBs has a structure consistent with an overall minimization of energy. The mobility simulations indicate that shear coupling is the preferred migration mechanism. However, when the same GBs are constrained, as might occur in polycrystalline networks, the relative mobilities of the set of GBs are significantly altered. Finally, the influence of deformation structures, as they pertain to GB migration during recrystallization, are discussed.

A fully three-dimensional (3D) mesoscale modeling framework for the mechanical behavior of amorphous metals is proposed. The model considers the coarse-grained action of shear transformation zones (STZs) as the fundamental deformation event. The simulations are controlled through the kinetic Monte Carlo algorithm and the mechanical response of the system is captured through finite-element analysis, where STZs are mapped onto a 3D finite-element mesh and are allowed to shear in any direction in three dimensions. Implementation of the technique in uniaxial creep tests over a wide range of conditions validates the model's ability to capture the expected behaviors of an amorphous metal, including high temperature flow conforming to the expected constitutive law and low temperature localization in the form of a nascent shear band. The simulation results are combined to construct a deformation map that is comparable to experimental deformation maps. The flexibility of the modeling framework is illustrated by performing a contact test (simulated nanoindentation) in which the model deforms through STZ activity in the region experiencing the highest shear stress.