Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm, a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems.
SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.
Additive manufactured Ti-5Al-5V-5Mo-3Cr (Ti-5553) is being considered as an AM repair material for engineering applications because of its superior strength properties compared to other titanium alloys. Here, we describe the failure mechanisms observed through computed tomography, electron backscatter diffraction (EBSD), and scanning electron microscopy (SEM) of spall damage as a result of tensile failure in as-built and annealed Ti-5553. We also investigate the phase stability in native powder, as-built and annealed Ti-5553 through diamond anvil cell (DAC) and ramp compression experiments. We then explore the effect of tensile loading on a sample containing an interface between a Ti-6Al-V4 (Ti-64) baseplate and additively manufactured Ti-5553 layer. Post-mortem materials characterization showed spallation occurred in regions of initial porosity and the interface provides a nucleation site for spall damage below the spall strength of Ti-5553. Preliminary peridynamics modeling of the dynamic experiments is described. Finally, we discuss further development of Stochastic Parallel PARticle Kinteic Simulator (SPPARKS) Monte Carlo (MC) capabilities to include the integration of alpha (α)-phase and microstructural simulations for this multiphase titanium alloy.
Thermal spray processes involve the repeated impact of millions of discrete particles, whose melting, deformation, and coating-formation dynamics occur at microsecond timescales. The accumulated coating that evolves over minutes is comprised of complex, multiphase microstructures, and the timescale difference between the individual particle solidification and the overall coating formation represents a significant challenge for analysts attempting to simulate microstructure evolution. In order to overcome the computational burden, researchers have created rule-based models (similar to cellular automata methods) that do not directly simulate the physics of the process. Instead, the simulation is governed by a set of predefined rules, which do not capture the fine-details of the evolution, but do provide a useful approximation for the simulation of coating microstructures. Here, we introduce a new rules-based process model for microstructure formation during thermal spray processes. The model is 3D, allows for an arbitrary number of material types, and includes multiple porosity-generation mechanisms. Example results of the model for tantalum coatings are presented along with sensitivity analyses of model parameters and validation against 3D experimental data. The model's computational efficiency allows for investigations into the stochastic variation of coating microstructures, in addition to the typical process-to-structure relationships.
Grain-scale microstructure evolution during additive manufacturing is a complex physical process. As with traditional solidification methods of material processing (e.g. casting and welding), microstructural properties are highly dependent on the solidification conditions involved. Additive manufacturing processes however, incorporate additional complexity such as remelting, and solid-state evolution caused by subsequent heat source passes and by holding the entire build at moderately high temperatures during a build. We present a three-dimensional model that simulates both solidification and solid-state evolution phenomena using stochastic Monte Carlo and Potts Monte Carlo methods. The model also incorporates a finite-difference based thermal conduction solver to create a fully integrated microstructural prediction tool. The three modeling methods and their coupling are described and demonstrated for a model study of laser powder-bed fusion of 300-series stainless steel. The investigation demonstrates a novel correlation between the mean number of remelting cycles experienced during a build, and the resulting columnar grain sizes.
Additive manufacturing is a transformative technology with the potential to manufacture designs which traditional subtractive machining methods cannot. Additive manufacturing offers fast builds at near final desired geometry; however, material properties and variability from part to part remain a challenge for certification and qualification of metallic components. AM induced metallic microstructures are spatially heterogeneous and highly process dependent. Engineering properties such as strength and toughness are significantly affected by microstructure morphologies resulting from the manufacturing process Linking process parameters to microstructures and ultimately to the dynamic response of AM materials is critical to certifying and qualifying AM built parts and components and improving the performance of AM materials. The AM fabrication process is characterized by building parts layer by layer using a selective laser melt process guided by a computer. A laser selectively scans and melts metal according to a designated geometry. As the laser scans, metal melts, fuses, and solidifies forming the final geometry in a layerwise fashion. As the laser heat source moves away, the metal cools and solidifies forming metallic microstructures. This work describes a microstructure modeling application implemented in the SPPARKS kinetic Monte Carlo computational framework for simulating the resulting microstructures. The application uses Bzier curves and surfaces to model the melt pool surface and spatial temperature profile induced by moving the laser heat source; it simulates the melting and fusing of metal at the laser hot spot and microstructure formation and evolution when the laser moves away. The geometry of the melt pool is quite flexible and we explore effects of variances in model parameters on simulated microstructures.
Determining a process–structure–property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials design are often considered in the context of process–property linkage by bypassing the materials structure, or in the context of structure–property linkage as in microstructure-sensitive design problems. However, there is a lack of research effort in studying materials design problems in the context of process–structure linkage, which has a great implication in reverse engineering. In this work, given a target microstructure, we propose an active learning high-throughput microstructure calibration framework to derive a set of processing parameters, which can produce an optimal microstructure that is statistically equivalent to the target microstructure. The proposed framework is formulated as a noisy multi-objective optimization problem, where each objective function measures a deterministic or statistical difference of the same microstructure descriptor between a candidate microstructure and a target microstructure. Furthermore, to significantly reduce the physical waiting wall-time, we enable the high-throughput feature of the microstructure calibration framework by adopting an asynchronously parallel Bayesian optimization by exploiting high-performance computing resources. Case studies in additive manufacturing and grain growth are used to demonstrate the applicability of the proposed framework, where kinetic Monte Carlo (kMC) simulation is used as a forward predictive model, such that for a given target microstructure, the target processing parameters that produced this microstructure are successfully recovered.
Generally, scientific simulations load the entire simulation domain into memory because most, if not all, of the data changes with each time step. This has driven application structures that have, in turn, affected the design of popular IO libraries, such as HDF-5, ADIOS, and NetCDF. This assumption makes sense for many cases, but there is also a significant collection of simulations where this approach results in vast swaths of unchanged data written each time step.This paper explores a new IO approach that is capable of stitching together a coherent global view of the total simulation space at any given time. This benefit is achieved with no performance penalty compared to running with the full data set in memory, at a radically smaller process requirement, and results in radical data reduction with no fidelity loss. Additionally, the structures employed enable online simulation monitoring.
Porosity in additively manufactured metals can reduce material strength and is generally undesirable. Although studies have shown relationships between process parameters and porosity, monitoring strategies for defect detection and pore formation are still needed. In this paper, instantaneous anomalous conditions are detected in-situ via pyrometry during laser powder bed fusion additive manufacturing and correlated with voids observed using post-build micro-computed tomography. Large two-color pyrometry data sets were used to estimate instantaneous temperatures, melt pool orientations and aspect ratios. Machine learning algorithms were then applied to processed pyrometry data to detect outlier images and conditions. It is shown that melt pool outliers are good predictors of voids observed post-build. With this approach, real time process monitoring can be incorporated into systems to detect defect and void formation. Alternatively, using the methodology presented here, pyrometry data can be post processed for porosity assessment.
Additive manufacturing (AM) of metal parts can save time, energy, and produce parts that cannot otherwise be made with traditional machining methods. Near final part geometry is the goal for AM, but material microstructures are inherently different from those of wrought materials as they arise from a complex temperature history associated with the additive process. It is well known that strength and other properties of interest in engineering design follow from microstructure and temperature history. Because of complex microstructure morphologies and spatial heterogeneities, properties are heterogeneous and reflect underlying microstructure. This report describes a method for distributing properties across a finite element mesh so that effects of complex heterogeneous microstructures arising from additive manufacturing can be systematically incorporated into engineering scale calculations without the need for conducting a nearly impossible and time consuming effort of meshing material details. Furthermore, the method reflects the inherent variability in AM materials by making use of kinetic Monte Carlo calculations to model the AM process associated with a build.
This report outlines the fiscal year (FY) 2019 status of an ongoing multi-year effort to develop a general, microstructurally-aware, continuum-level model for representing the dynamic response of material with complex microstructures. This work has focused on accurately representing the response of both conventionally wrought processed and additively manufactured (AM) 304L stainless steel (SS) as a test case. Additive manufacturing, or 3D printing, is an emerging technology capable of enabling shortened design and certification cycles for stockpile components through rapid prototyping. However, there is not an understanding of how the complex and unique microstructures of AM materials affect their mechanical response at high strain rates. To achieve our project goal, an upscaling technique was developed to bridge the gap between the microstructural and continuum scales to represent AM microstructures on a Finite Element (FE) mesh. This process involves the simulations of the additive process using the Sandia developed kinetic Monte Carlo (KMC) code SPPARKS. These SPPARKS microstructures are characterized using clustering algorithms from machine learning and used to populate the quadrature points of a FE mesh. Additionally, a spall kinetic model (SKM) was developed to more accurately represent the dynamic failure of AM materials. Validation experiments were performed using both pulsed power machines and projectile launchers. These experiments have provided equation of state (EOS) and flow strength measurements of both wrought and AM 304L SS to above Mbar pressures. In some experiments, multi-point interferometry was used to quantify the variation is observed material response of the AM 304L SS. Analysis of these experiments is ongoing, but preliminary comparisons of our upscaling technique and SKM to experimental data were performed as a validation exercise. Moving forward, this project will advance and further validate our computational framework, using advanced theory and additional high-fidelity experiments.
The ability to simulate wireless networks at large-scale for meaningful amount of time is considerably lacking in today's network simulators. For this reason, many published work in this area often limit their simulation studies to less than a 1,000 nodes and either over-simplify channel characteristics or perform studies over time scales much less than a day. In this report, we show that one can overcome these limitations and study problems of high practical consequence. This work presents two key contributions to high fidelity simulation of large-scale wireless networks: (a) wireless simulations can be sped up by more than 100X in runtime using ideas from spatial indexing algorithms and clipping of negligible signals and (b) clustering and task-oriented programming paradigm can be used to reduce inter- process communication in a parallel discrete event simulation resulting in a better scaling efficiency.
Welding is one of the most wide-spread processes used in metal joining. However, there are currently no open-source software implementations for the simulation of microstructural evolution during a weld pass. Here we describe a Potts Monte Carlo based model implemented in the SPPARKS kinetic Monte Carlo computational framework. The model simulates melting, solidification and solid-state microstructural evolution of material in the fusion and heat-affected zones of a weld. The model does not simulate thermal behavior, but rather utilizes user input parameters to specify weld pool and heat-affect zone properties. Weld pool shapes are specified by Bézier curves, which allow for the specification of a wide range of pool shapes. Pool shapes can range from narrow and deep to wide and shallow representing different fluid flow conditions within the pool. Surrounding temperature gradients are calculated with the aide of a closest point projection algorithm. The model also allows simulation of pulsed power welding through time-dependent variation of the weld pool size. Example simulation results and comparisons with laboratory weld observations demonstrate microstructural variation with weld speed, pool shape, and pulsed-power.
The primary goal of this work is to develop and implement analytic methods for quantitative analysis of microstructure. These analytic methods are demonstrated on microstructures generated by the Sandia kinAic Monte Carlo code SPPARKS. This report documents progress to that end as well as incremental work towards larger aspirations of making process-structure-property connections for complex processes such as welding and additive manufacturing.
A C++ library (called Eshelby) was implemented in fiscal year 2015 based upon the formulas documented in this report. The library implements a generalized version of Eshelby's inclusion problem. The library was written as a set of functions which can be called from another program; the principle intended use cases are kinetic models of precipitate formation in zirconium claddings where use of the Eshelby library provides needed elastic energy density calculations, as well as calculations of stress and strain in and around precipitates; it is intended that the library will be made open source. For isotropic inclusions in the form of oblate and prolate ellipsoids, the Eshelby library can be used for nearly any relevant/appropriate shape parameters to calculate strains, stresses and energy density at interior and exterior points. The Eshelby library uses a combination of analytical formulas and numerical routines making it very extensible. For example, the library can can easily be extended to include inclusions such as spheres since analytical expressions exist for the required elliptic integrals; similarly, general ellipsoids do not have analytical results for the required elliptic integrals but those integrals can be numerically evaluated and thus fit naturally into the Eshelby library. This report documents all formulas implemented in the Eshelby library and presents some demonstration calculations relevant to the intended application.
In this report, we present a thermodynamic-based model of hydride precipitation in Zr-based claddings. The model considers the state of the cladding immediately following drying, after removal from cooling-pools, and presents the evolution of precipitate formation upon cooling as follows: The pilgering process used to form Zr-based cladding imparts strong crystallographic and grain shape texture, with the basal plane of the hexagonal α-Zr grains being strongly aligned in the rolling-direction and the grains are elongated with grain size being approximately twice as long parallel to the rolling direction, which is also the long axis of the tubular cladding, as it is in the orthogonal directions.
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves conver- gence behavior. Finally, a novel approach for modeling ductile failure has been developed, moti- vated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software im- plementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.
The elastic properties and mechanical stability of zirconium alloys and zirconium hydrides have been investigated within the framework of density functional perturbation theory. Results show that the lowest-energy cubic Pn3m polymorph of δ-ZrH1.5 does not satisfy all the Born requirements for mechanical stability, unlike its nearly degenerate tetragonal P42/mcm polymorph. Elastic moduli predicted with the Voigt-Reuss-Hill approximations suggest that mechanical stability of α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates is limited by the shear modulus. According to both Pugh's and Poisson's ratios, α-Zr, Zr-alloy and Zr-hydride polycrystalline aggregates can be considered ductile. The Debye temperatures predicted for γ-ZrH, δ-ZrH1.5 and ε-ZrH2 are D = 299.7, 415.6 and 356.9 K, respectively, while D = 273.6, 284.2, 264.1 and 257.1 K for the α-Zr, Zry-4, ZIRLO and M5 matrices, i.e. suggesting that Zry-4 possesses the highest micro-hardness among Zr matrices.
A position-aware linear solid (PALS) peridynamic constitutive model is proposed for isotropic elastic solids. The PALS model addresses problems that arise, in ordinary peridynamic material models such as the linear peridynamic solid (LPS), due to incomplete neighborhoods near the surface of a body. Improved model behavior in the vicinity of free surfaces is achieved through the application of two influence functions that correspond, respectively, to the volumetric and deviatoric parts of the deformation. The model is position-aware in that the influence functions vary over the body and reflect the proximity of each material point to free surfaces. Demonstration calculations on simple benchmark problems show a sharp reduction in error relative to the LPS model.
This report develops and documents nonlinear kinematic relations needed to implement piezoelectric constitutive models in ALEGRA-EMMA [5], where calculations involving large displacements and rotations are routine. Kinematic relationships are established using Gausss law and Faradays law; this presentation on kinematics goes beyond piezoelectric materials and is applicable to all dielectric materials. The report then turns to practical details of implementing piezoelectric models in an application code where material principal axes are rarely aligned with user defined problem coordinate axes. This portion of the report is somewhat pedagogical but is necessary in order to establish documentation for the piezoelectric implementation in ALEGRA-EMMA. This involves transforming elastic, piezoelectric, and permittivity moduli from material principal axes to problem coordinate axes. The report concludes with an overview of the piezoelectric implementation in ALEGRA-EMMA and small verification examples.
A non-local, ordinary-state-based, peridynamics viscoelasticity model is developed. In this model, viscous effects are added to deviatoric deformations and the bulk response remains elastic. The model uses internal state variables and is conceptually similar to linearized isotropic viscolelasticity in the local theory. The modulus state, which is used to form the Jacobian matrix in Newton-Raphson algorithms, is presented. The model is shown to satisfy the 2nd law of thermodynamics and is applicable to problems in solid continuum mechanics where fracture and rate effects are important; it inherits all the advantages for modeling fracture associated with peridynamics. By combining this work with the previously published ordinary-state-based plasticity model, the model may be amenable to viscoplasticity problems where plasticity and rate effects are simultaneously important. Also, the model may be extended to include viscous effects for spherical deformations as well. The later two extensions are not presented and may be the subject of further work.
This report details efforts to deploy Agile Components for rapid development of a peridynamics code, Peridigm. The goal of Agile Components is to enable the efficient development of production-quality software by providing a well-defined, unifying interface to a powerful set of component-based software. Specifically, Agile Components facilitate interoperability among packages within the Trilinos Project, including data management, time integration, uncertainty quantification, and optimization. Development of the Peridigm code served as a testbed for Agile Components and resulted in a number of recommendations for future development. Agile Components successfully enabled rapid integration of Trilinos packages into Peridigm. A cost of this approach, however, was a set of restrictions on Peridigm's architecture which impacted the ability to track history-dependent material data, dynamically modify the model discretization, and interject user-defined routines into the time integration algorithm. These restrictions resulted in modifications to the Agile Components approach, as implemented in Peridigm, and in a set of recommendations for future Agile Components development. Specific recommendations include improved handling of material states, a more flexible flow control model, and improved documentation. A demonstration mini-application, SimpleODE, was developed at the onset of this project and is offered as a potential supplement to Agile Components documentation.
An implicit time integration algorithm for a non-local, state-based, peridynamics plasticity model is developed. The flow rule was proposed in [3] without an integration strategy or yield criterion. This report addresses both of these issues and thus establishes the first ordinary, state-based peridynamics plasticity model. Integration of the flow rule follows along the lines of the classical theories of rate independent J{sub 2} plasticity. It uses elastic force state relations, an additive decomposition of the deformation state, an elastic force state domain, a flow rule, loading/un-loading conditions, and a consistency condition. Just as in local theories of plasticity (LTP), state variables are required. It is shown that the resulting constitutive model does not violate the 2nd law of thermodynamics. The report also develops a useful non-local yield criterion that depends upon the yield stress and horizon for the material. The modulus state for both the ordinary elastic material and aforementioned plasticity model is also developed and presented.
Progress in MEMS fabrication has enabled a wide variety of force and displacement sensing devices to be constructed. One device under intense development at Sandia is a passive shock switch, described elsewhere (Mitchell 2008). A goal of all MEMS devices, including the shock switch, is to achieve a high degree of reliability. This, in turn, requires systematic methods for validating device performance during each iteration of design. Once a design is finalized, suitable tools are needed to provide quality assurance for manufactured devices. To ensure device performance, measurements on these devices must be traceable to NIST standards. In addition, accurate metrology of MEMS components is needed to validate mechanical models that are used to design devices to accelerate development and meet emerging needs. Progress towards a NIST-traceable calibration method is described for a next-generation, 2D Interfacial Force Microscope (IFM) for applications in MEMS metrology and qualification. Discussed are the results of screening several suitable calibration methods and the known sources of uncertainty in each method.
This report summarizes design and modeling activities for the MEMS passive shock sensor. It provides a description of past design revisions, including the purposes and major differences between design revisions but with a focus on Revisions 4 through 7 and the work performed in fiscal year 2008 (FY08). This report is a reference for comparing different designs; it summarizes design parameters and analysis results, and identifies test structures. It also highlights some of the changes and or additions to models previously documented [Mitchell et al. 2006, Mitchell et al. 2008] such as the way uncertainty thresholds are analyzed and reported. It also includes dynamic simulation results used to investigate how positioning of hard stops may reduce vibration sensitivity.