Showing papers in "Modelling and Simulation in Materials Science and Engineering in 2019"

Impact of dataset uncertainties on machine learning model predictions: the example of polymer glass transition temperatures

Abstract: Over the past decade, there has been a resurgence in the importance of data-driven techniques in material science and engineering. The utilization of state-of-the art algorithms, coupled with the increased availability of experimental and computational data, has led to the development of surrogate models offering the promise of rapid and accurate predictions of materials properties based solely on their structure or composition. Such machine learning models are trained on available past data and are thus susceptible to the intrinsic uncertainties/errors associate with these past measurements. The glass transition temperature (Tlsubggl/subg) of polymers, a property of paramount interest in polymer science, is one strong example of a material property that can show widespread variation in the final reported value as a result of a variety of intrinsic and extrinsic factors that occur during the experimental measurement process. In the current work, we curate a large database of Tlsubggl/subg measurements from a variety of data sources and proceed to investigate the statistical nature of the inherent uncertainties in the database. Through the partitioning of the dataset using statistically relevant measures, we investigate the effect of variations in the dataset on the performance of the final machine learning model. We demonstrate that measures of central tendency (such as mean and median) are valid approximations when dealing with multiple reported values of Tlsubggl/subg for the same polymeric material. Moreover, the Bayesian model noise/uncertainty that emerges from our machine-learning pipeline is able to represent quantitatively the underlying noise/uncertainties in the experimental measurement of Tlsubggl/subg.

Atomistic modeling of fracture

Abstract: Atomistic modeling of fracture is intended to illuminate the complex response of atoms in the very high stressed region just ahead of a sharp crack. Accurate modeling of the atomic scale fracture is crucial for describing the intrinsic nature of a material (intrinsic ductility/brittleness), chemical effects in the crack-tip vicinity, the crack interaction with different defects in solids such as grain boundaries, solutes, precipitates, dislocations, voids, etc. Here, different methods for atomistic modeling of fracture are compared in their ability to obtain quantitatively useful results that are in agreement with the basic principles of linear elastic fracture mechanics (LEFM). We demonstrate that the complicated atomic crack-tip behavior is precisely described in simulations of semi-infinite cracks, where the loading is uniquely controlled by the applied stress intensity factor K. Such 'K-test' simulations are shown to be equally applicable in crystalline and amorphous materials, and to be suitable for quantitative evaluation of various critical stress intensity factors, the overall material fracture toughness, and quantitative comparison with theories. We further demonstrate that the simulation of a nanoscale center-crack tension (CCT) specimen often leads to the results that do not satisfy the conditions for application of LEFM. The simulated intrinsic fracture toughness, one of the basic material properties, using CCT test geometry is shown to be dependent on the crack size and far-field loading. In general, this study resolves quantitative differences between several methods for atomistic modeling of fracture and recommends that application of simulations based on nanoscale finite size cracks not be pursued.

A multi-scale, multi-physics modeling framework to predict spatial variation of properties in additive-manufactured metals

Abstract: The microstructure of additively manufactured (AM) metals has been shown to be heterogeneous and spatially non-uniform when compared to conventionally manufactured metals. Consequently, the effective mechanical properties of AM-metal parts are expected to vary both within and among builds. Here, we present a framework for simulating process–(micro)structure– property relationships of AM metals produced via direct laser deposition (DLD). The framework predicts grain nucleation and competitive growth as a function of thermal history for a multi-pass, multi-layer DLD process. The resulting three-dimensional microstructure is automatically sub-sampled to perform virtual mechanical testing throughout the build domain using a parallelized elasto-viscoplastic fast Fourier transform code, accounting for grainboundary strengthening. The effective stress–strain response of each subsampled volume is automatically analyzed to extract effective mechanical properties, which are used to generate property maps showing the spatial variability of effective mechanical properties throughout the simulated build volume. As a demonstration, the framework is applied to different DLD stainless steel 316L build volumes having different process-induced microstructures. The multi-physics framework and property maps could provide a path toward qualification of AM-metal parts. Supplementary material for this article is available online Modelling and Simulation in Materials Science and Engineering Modelling Simul. Mater. Sci. Eng. 27 (2019) 025009 (23pp) https://doi.org/10.1088/1361-651X/aaf753 0965-0393/19/025009+23$33.00 © 2019 IOP Publishing Ltd Printed in the UK 1

A comparison of different continuum approaches in modeling mixed-type dislocations in Al

Abstract: Mixed-type dislocations are prevalent in metals and play an important role in their plastic deformation. Key characteristics of mixed-type dislocations cannot simply be extrapolated from those of dislocations with pure edge or pure screw characters. However, mixed-type dislocations traditionally received disproportionately less attention in the modeling and simulation community. In this work, we explore core structures of mixed-type dislocations in Al using three continuum approaches, namely, the phase-field dislocation dynamics (PFDD) method, the atomistic phase-field microelasticity (APFM) method, and the concurrent atomistic-continuum (CAC) method. Results are benchmarked against molecular statics. The PFDD and APFM methods are advanced in several aspects such that they can better describe the dislocation core structure. In particular, in these two approaches, the gradient energy coefficients for mixed-type dislocations are determined based on those for pure-type ones using a trigonometric interpolation scheme, which is shown to provide better prediction than a linear interpolation scheme. The dependence of in-slip-plane spatial numerical resolution in FPDD and CAC is also quantified.

Understanding the mechanisms of electroplasticity from a crystal plasticity perspective

Abstract: Electroplasticity is defined as the reduction in flow stress of a material undergoing deformation on passing an electrical pulse through it. The lowering of flow stress during electrical pulsing has been attributed to a combination of three mechanisms: softening due to Joule-heating of the material, de-pinning of dislocations from paramagnetic obstacles, and the electron-wind force acting on dislocations. However, there is no consensus in literature regarding the relative magnitudes of the reductions in flow stress resulting from each of these mechanisms. In this paper, we extend a dislocation density based crystal plasticity model to incorporate the mechanisms of electroplasticity and perform simulations where a single electrical pulse is applied during compressive deformation of a polycrystalline FCC material with random texture. We analyze the reductions in flow stress to understand the relative importance of the different mechanisms of electroplasticity and delineate their dependencies on the various parameters related to electrical pulsing and dislocation motion. Our study establishes that the reductions in flow stress are largely due to the mechanisms of de-pinning of dislocations from paramagnetic obstacles and Joule-heating, with their relative dominance determined by the specific choice of crystal plasticity parameters corresponding to the particular material of interest.

Ab initio-informed phase-field modeling of dislocation core structures in equal-molar CoNiRu multi-principal element alloys

Abstract: In this work, selecting the equal-molar CoNiRu multi-principal element alloy (MPEA) as a model material, we study dislocation core structures starting from first principles. We begin by sifting through all possible configurations to find those corresponding to elastic stability and energetically favored facecentered cubic (fcc) phases and, then, for these configurations, employ a phase field-based model to predict the extent of dislocations lying within them. The main findings are that for the fcc phase, (i) large variations in atomic configuration for the same chemical composition can cause significant changes in the generalized stacking fault energy surface and (ii) the dispersion in defect fault energies are chiefly responsible for substantial variations in the intrinsic stacking fault (ISF) widths of screw and edge dislocations. For instance, positive the ISF energy can vary by 10 times, with the lower values correlated with entirely Ni and Ru atoms and higher values with only Co and Ru atoms across the slip plane. Variations in lattice parameter and stiffness tensor accompany local differences in atomic configuration are also taken into account but shown to play a lesser role. We find that the dislocation can experience profound variations (3–7-fold changes) in its associated ISF width along its line, with the screw dislocation experiencing a greater variation than the edge dislocation (6.02–43.22Å for the screw dislocation, and 19.6–62.62Å for the edge dislocation). We envision that the ab initio -informed phase-field modeling method developed here can be readily adapted to MPEAs with other chemical compositions. Modelling and Simulation in Materials Science and Engineering Modelling Simul. Mater. Sci. Eng. 27 (2019) 084001 (26pp) https://doi.org/10.1088/1361-651X/ab3b62 0965-0393/19/084001+26$33.00 © 2019 IOP Publishing Ltd Printed in the UK 1

Modeling of grain growth under fully anisotropic grain boundary energy

Abstract: A level set formulation is proposed that can accurately trace the evolution of grain boundary networks in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Commonly adopted simplifying assumptions related to the grain boundary energy variation with local microstructure conditions are avoided and the grain boundary energy dependence on both crystallographic misorientation and boundary plane inclination is respected. Key components in the formulation are discussed, such as an efficient and simple scheme for unequivocal identification of crystal neighbors at grain boundary junctions where an arbitrary number of crystals intersect. The method works without modifications in both two and three dimensions and is shown to provide grain boundary junction configurations that comply with classical equilibrium conditions as well as topological transforms of the grain boundary network that agree with theoretical predictions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as previously proposed by Bulatov et al 2014 Acta Mater. 65:161–75. Examples are provided to illustrate the relevance of the level set framework for simulations of microstructure evolution in polycrystalline solids. For example, it is clearly shown that the proposed modeling framework provides a grain boundary inclination dependence of the grain boundary energy that cannot be neglected in mesoscale simulations of grain growth. (Less)

A multiscale model of protein adsorption on a nanoparticle surface

Abstract: We present a methodology to quantify the essential interactions at the interface between inorganic solid nanoparticles (NPs) and biological molecules. Our model is based on pre-calculation of the repetitive contributions to the interaction from molecular segments, which allows us to efficiently scan a multitude of molecules and rank them by their adsorption affinity. The interaction between the biomolecular fragments and the nanomaterial are evaluated using a systematic coarse-graining scheme starting from all-atom molecular dynamics simulations. The NPs are modelled using a two-layer representation, where the outer layer is parameterized at the atomistic level and the core is treated at the continuum level using Lifshitz theory of dispersion forces. We demonstrate that the scheme reproduces the experimentally observed features of the NP protein coronas. To illustrate the use of the methodology, we compute the adsorption energies for human blood plasma proteins on gold NPs of different sizes as well as the preferred orientation of the molecules upon adsorption. The computed energies can be used for predicting the composition of the NP-protein corona for the corresponding material.

Application of Gaussian process autoregressive models for capturing the time evolution of microstructure statistics from phase-field simulations for sintering of polycrystalline ceramics

Abstract: While phase-field models have been demonstrated to be highly versatile in performing physics-based simulations of a large variety of materials phenomena involving microstructure evolution (e.g., phase transformation, recrystallization, sintering), they are not practical for rapid exploration of the process design space due to their high demand for computational resources. The extraction of reliable and robust reduced-order models from the microstructure evolution datasets produced by such sophisticated physics-based models continues to be an unsolved problem. Recent advances in the fast computation of a comprehensive set of microstructure statistics and their data-driven low-dimensional representations using principal component analyses (PCA) have resulted in the successful extraction of practically useful reduced-order models connecting the microstructure statistics and the effective properties exhibited by the material. In this paper, we explore for the first time, the viability of these low-dimensional representations of the microstructure statistics for establishing reduced-order models capable of learning the important details of the microstructure evolution predicted by the computationally expensive phase-field models. More specifically, we will explore the viability of applying the Gaussian process autoregressive (GPAR) models used in the fields of statistics and signal processing for problems in microstructure evolution. This will be accomplished using a specific case study dealing with the time evolution of porous microstructures in sintering of polycrystalline ceramics.

Phase field modeling to transformation induced plasticity in super-elastic NiTi shape memory alloy single crystal

Abstract: A crystal plasticity based phase field model was established to investigate the occurrence of transformation induced plasticity (TRIP) and its effect on the cyclic transformation of super-elastic NiTi shape memory alloy (SMA) single crystal. The simulation shows that the martensite transformation and its reverse result in the occurrence of plastic deformation in the NiTi SMA single crystal and the mode of phase transition changes from a localized mode into a homogeneous one with the cycles. When the single crystal exhibits a localized martensite transformation, the TRIP occurs regularly at the interfaces between the martensite-dominated and austenite-dominated domains and then the strips of equivalent plastic strain are formed; meanwhile the TRIP hinders the martensite transformation in the austenite-dominated domains but promotes that in the martensite-dominated ones. When the transformation becomes homogeneous, the TRIP occurs in a scattered mode and with a high value, and promotes the martensite transformation in the whole single crystal. In addition, the interaction between the residual martensite phase and TRIP is investigated, and the results demonstrate that they promote each other to some extent.

Molecular dynamics studies on the sintering and mechanical behaviors of graphene nanoplatelet reinforced aluminum matrix composites

Abstract: The sintering process of graphene nanoplatelet (GNP) reinforced aluminum matrix composite powder was simulated by molecular dynamics method. The effects of Al nanoparticle size and sintering temperature on sintering behavior were studied. Uniaxial tensile simulation was applied to study the mechanical properties of sintered composites. The results show that the nanoparticle size and sintering temperature have significant effects on the sintering behavior of the composites. Smaller size nanoparticle system has lower melting point, which requires lower sintering temperature. Larger size particle system requires longer sintering time and higher sintering temperature. At lower temperatures, the main coalescence mechanisms of nanoparticle systems are surface diffusion and grain boundary diffusion. When the temperature is close to the melting point, volume diffusion and surface diffusion dominate. Tensile simulation results of sintered composites show that the addition of GNP can greatly improve the mechanical properties of the composites. Dislocation reinforcement and stress transfer are the main reinforcement mechanisms.

Acceleration of phase-field lattice Boltzmann simulation of dendrite growth with thermosolutal convection by the multi-GPUs parallel computation with multiple mesh and time step method

Abstract: Thermosolutal convection inevitably occurs during the solidification of alloys owing to the nonuniform distribution of temperature and/or solute concentration, and this can drastically alter the resulting solidification microstructures. In this study, we present a large-scale simulation scheme for the phase-field lattice Boltzmann model, which can express dendrite growth upon considering the solute, heat transport, and liquid flow. A multiple mesh and time step method was employed to reduce computational costs, where different mesh sizes and time steps are used to solve the phase-field equation, the advection–diffusion equations of heat and solute, and the lattice Boltzmann equations for fluid flow. Furthermore, we implemented parallel computations using multiple graphics processing units (GPUs) to accelerate the large-scale simulation. Through the application of the multiple mesh and time step method, the computation was accelerated by approximately one hundred times compared to the case using a constant mesh and time step for all equations. Moreover, we confirmed that the developed parallel-GPU computation combined with the multiple mesh and time step method could achieve good acceleration and scaling through increasing the number of GPUs. We also confirmed that the developed method could simulate multiple dendrite growth with thermosolutal convection.

Quantifying uncertainty in the process-structure relationship for Al–Cu solidification

Abstract: Phase field method (PFM) is a simulation tool to predict microstructural evolution during solidification and is helpful to establish the process-structure relationship for alloys. The robustness of the relationship however is affected by model-form and parameter uncertainties in PFM. In this paper, the uncertainty associated with the thermodynamic and process parameters of PFM is studied and quantified. Surrogate modeling is used to interpolate four quantities of interests (QoIs), including dendritic perimeter, area, primary arm length, and solute segregation, as functions of thermodynamic and process parameters. A sparse grid approach is applied to mitigate the curse-of-dimensionality computational burden in uncertainty quantification. Polynomial chaos expansion is employed to obtain the probability density functions of the QoIs. The effect of parameter uncertainty on the Al–Cu dendritic growth during solidification simulation are investigated. The results show that the dendritic morphology varies significantly with respect to the interface mobility and the initial temperature.

An efficient numerical framework for the amplitude expansion of the phase-field crystal model

Abstract: The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase-field crystal model allows for describing crystal lattice properties on diffusive timescales by focusing on continuous fields varying on length scales larger than the atomic spacing. Thus, it allows for the simulation of large systems still retaining details of the crystal lattice. Fostered by the applications of this approach, we present here an efficient numerical framework to solve its equations. In particular, we consider a real space approach exploiting the finite element method. An optimized preconditioner is developed in order to improve the convergence of the linear solver. Moreover, a mesh adaptivity criterion based on the local rotation of the polycrystal is used. This results in an unprecedented capability of simulating large, three-dimensional systems including the dynamical description of the microstructures in polycrystalline materials together with their dislocation networks.

Basal dislocation/precipitate interactions in Mg–Al alloys: an atomistic investigation

Abstract: The interaction between edge basal dislocations and β-Mg17Al12 precipitates was studied using atomistic simulations. A strategy was developed to insert a lozenge-shaped Mg17Al12 precipitate with Burgers orientation relationship within the Mg matrix in an atomistic model ensuring that the matrix/precipitate interfaces were close to minimum energy configurations. It was found that the dislocation bypassed the precipitate by the formation of an Orowan loop that entered the precipitate. Within the precipitate, the dislocation was not able to progress further until more dislocations overcome the precipitate and push the initial loop to shear the precipitate along the (110) plane, parallel to the basal plane of Mg. This process was eventually repeated as more dislocations overcome the precipitate and this mechanism of dislocation/precipitate interaction was in agreement with experimental observations. Moreover, the initial resolved shear stress to bypass the precipitate was in agreement with the predictions of the Bacon–Kocks–Scattergood model.

A general method to construct dislocations in atomistic simulations

Abstract: An important aspect of atomistic simulations of dislocations is the construction of the initial dislocation configurations. However, limited configurations can be constructed by previous methods, impeding the simulations of a general dislocation configuration in real materials. In this paper, we develop a simple and general method for constructing dislocations with arbitrary shapes specified by the users, realising the Volterra process at the atomic level. Examples of its applications to a dislocation helix, the partial dislocations, the multi-dislocation configurations, and the dislocations in the imperfect crystal are presented, showing the capacity and robustness of the present method.

Structural and elastic properties of amorphous carbon from simulated quenching at low rates

Abstract: We generate representative structural models of amorphous carbon (a-C) from constant-volume quenching from the liquid with subsequent relaxation of internal stresses in molecular dynamics simulations using empirical and machine-learning interatomic potentials. By varying volume and quench rate we generate structures with a range of density and amorphous morphologies. We find that all a-C samples show a universal relationship between hybridization, bulk modulus and density despite having distinct cohesive energies. Differences in cohesive energy are traced back to slight changes in the distribution of bond-angles that will likely affect thermal stability of these structures.

Uncertainty quantification and propagation in CALPHAD modeling

Abstract: Design is about making decisions bounded by a quantifiable degree of certainty. In the context of alloy design, Integrated Computational Materials Engineering (ICME) provides the framework whereby performance requirements are ultimately transformed into alloy/processing specifications through the combination of (complex) computational models connecting process-structure-property-performance relationships and experiments. Most ICME approaches consider the models used as deterministic and thus do not provide the means to make alloy design decisions with proper confidence measures. At the root of ICME lie CALPHAD models that describe the thermodynamics and phase stability of phases under specific thermodynamic boundary conditions. To date, the vast majority of efforts within the CALPHAD community have been deterministic in that thermodynamic models and the resulting thermodynamic properties and phase diagram features do not explicitly account for the uncertainties inherent in the model formulation or in the experimental/computational data used. In this contribution, we provide an overview of the state of the field. We review major efforts thus far and we then provide a (brief) tutorial on basic concepts of uncertainty quantification and propagation (UQ/UP) in CALPHAD. We discuss the major features of frequentist and Bayesian interpretations of uncertainty and proceed with a discussion of recent case studies in which UQ has been used to parameterize models for the thermodynamic properties of phases. We follow our discussion by presenting frameworks and demonstrating the propagation of uncertainty in thermodynamic properties and phase diagram predictions and briefly discuss how we can use Bayesian frameworks for rigorous model selection as well as for model fusion. We close our contribution by providing context for what has been done and what remains to be accomplished in order to fully embrace the management of uncertainty in CALPHAD modeling, a foundational element of ICME.

Atomistic simulation of the obstacle strengths of radiation-induced defects in an Fe–Ni–Cr austenitic stainless steel

Abstract: A molecular dynamics method is employed to simulate the interaction of an edge dislocation with a combined solute cluster-dislocation loop defect, as well as independent faulted interstitial dislocation loops and solute clusters in an Fe–12Ni–20Cr at a temperature of 300 K. The examined defects are typical radiation-induced defects in austenitic stainless steels used as core structural components in nuclear reactors, while the selected composition matches with commercial grade 304L alloy. The dislocation-defect interaction is examined, and the peak shear stress required to overcome the obstacle array, and its dependence on obstacle size, solute concentration, and orientation is determined. The peak shear stress is then converted to an effective obstacle strength (α). Results show that dislocation loops are stronger obstacles than solute clusters, and their strength is heavily dependent on orientation, while the strength of solute clusters is largely dependent on the solute concentration. The total strength of the combined solute cluster-dislocation loop defect is largely contributed by the dislocation loop, though a fraction of the cluster strength is added as well.

Size effect in molecular dynamics simulation of nucleation process during solidification of pure metals: investigating modified embedded atom method interatomic potentials

Abstract: Due to the significant increase in computing power in recent years, the simulation size of atomistic methods for studying the nucleation process during solidification has been gradually increased, even to billion atom simulations (sub-micron length scale). But the question is how big of a model is required for size-independent and accurate simulations of the nucleation process during solidification? In this work, molecular dynamics simulations with model sizes ranging from ~2000 to ~8 million atoms were used to study nucleation during solidification. To draw general conclusions independent of crystal structures, the most advanced second nearest-neighbor modified embedded atom method interatomic potentials for Al (face-centered cubic), Fe (body-centered cubic), and Mg (hexagonal-close packed) were utilized for molecular dynamics simulations. We have analyzed several quantitative characteristics such as nucleation time, density of nuclei, nucleation rate, self-diffusion coefficient, and change in free energy during solidification. The results showed that by increasing the model size to about two million atoms, the simulations and measurable quantities become entirely independent of simulation cell size. The prediction of cell size required for size-independent computed data can considerably reduce the computational costs of atomistic simulations and at the same time increase the accuracy and reliability of the computational data.