Exploding bridgewire (EBW) detonators are used to rapidly and reliably initiate energetic reactions by exploding a bridgewire via Joule heating. While the mechanisms of EBW detonators have been studied extensively in nominal conditions, comparatively few studies have addressed thermally damaged detonator operability. We present a mesoscale simulation study of thermal damage in a representative EBW detonator, using discrete element method (DEM) simulations that explicitly account for individual particles in the pressed explosive powder. We use a simplified model of melting, where solid spherical particles undergo uniform shrinking, and fluid dynamics are ignored. The subsequent settling of particles results in the formation of a gap between the solid powder and the bridgewire, which we study under different conditions. In particular, particle cohesion has a significant effect on gap formation and settling behavior, where sufficiently high cohesion leads to coalescence of particles into a free-standing pellet. This behavior is qualitatively compared to experimental visualization data, and simulations are shown to capture several key changes in pellet shape. We derive a minimum and maximum limit on gap formation during melting using simple geometric arguments. In the absence of cohesion, results agree with the maximum gap size. With increasing cohesion, the gap size decreases, eventually saturating at the minimum limit. We present results for different combinations of interparticle cohesion and detonator orientations with respect to gravity, demonstrating the complex behavior of these systems and the potential for DEM simulations to capture a range of scenarios.
There has always been a desire to port high-fidelity reactive flow models from one code to another. For example, the AWE reactive burn model known as CREST has been or is being implemented in several of the U.S. Department of Energy hydrocodes. Those involved with reactive burn model implementation recognize the challenges immediately, e.g., Eulerian versus Lagrangian frameworks, the form of the equation of state, the closure relations, etc. In this work, we report the development of the CREST reactive burn model in CTH, a multidimensional, multi-material hydrocode developed by Sandia National Laboratories, following an earlier implementation shown at the last International Detonation Symposium. Results include code-to-code comparisons between CTH and the AWE hydrocode PERUSE, focusing on the simulated particle velocity histories during a shock-to-detonation transition, and corresponding to previous gas gun impact experiments as well as new model verification studies. Lessons learned are provided, including discussions of the numerical accuracy, in addition to the role of artificial viscosity and artificial viscous work. Finally, simulation results are shown to compare the Snowplough versus P-Alpha porosity model options.
In polymer-filled granular composites, damage may develop in mechanical loading prior to material failure. Damage mechanisms such as microcracking or plastic deformation in the binder phase can substantially alter the material's mesostructure. For energetic materials, such as solid propellants and plastic bonded explosives, these mesostructural changes can have far reaching effects including degraded mechanical properties, potentially increased sensitivity to further insults, and changes in expected performance. Unfortunately, predicting damage is nontrivial due to the complex nature of these composites and the entangled interactions between inelastic mechanisms. In this work, we assess the current literature of experimental knowledge, focusing on the pressure-dependent shear response, and propose a simple simulation framework of bonded particles to study four limiting-case material formulations at both meso- and macro-scales. To construct the four cases, we systematically vary the relative interfacial strength between the polymer binder and granular filler phase and also vary the polymer's glass transition temperature relative to operating temperature which determines how much the binder can plastically deform. These simulations identify key trends in global mechanical response, such as the emergence of strain hardening or softening regimes with increasing pressure which qualitatively resemble experimental results. By quantifying the activation of different inelastic mechanisms, such as bonds breaking and plastically straining, we identify when each mechanism becomes relevant and provide insight into potential origins for changes in mechanical responses. The locations of broken bonds are also used to define larger, mesoscopic cracks to test various metrics of damage. We primarily focus on triaxial compression, but also test the opposite case of triaxial extension to highlight the impact of Lode angle on mechanical behavior.
There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.
Cookoff experiments of powdered and pressed TATB-based plastic bonded explosives (PBXs) have been modeled using a pressure-dependent universal cookoff model (UCM) in combination with a micromechanics pressurization (MMP) model described in a companion paper. The MMP model is based on the accumulation of decomposition gases at nucleation sites that load the surrounding TATB crystals and binder. This is the first cookoff model to use an analytical mechanics solution for compressibility and thermal expansion to describe internal pressurization caused by both temperature and decomposition occurring within closed-pore explosives. This approach produces more accurate predictions of ignition time and pressurization within high-density explosives than simple equation-of-state models. The current paper gives details of the reaction chemistry, model parameters, predicted uncertainty, and validation using experiments from multiple laboratories with errors less than 6 %. The UCM/MMP model framework gives more accurate thermal ignition predictions for high density explosives that are initially impermeable to decomposition gases.
In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. We verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. We then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.
Validated models of melt cast explosives exposed to accidental fires are essential for safety analysis. In the current work, we provide several experiments that can be used to develop and validate cookoff models of melt cast explosives such as Comp-B3 composed of 60:40 wt% RDX:TNT. We present several vented and sealed experiments from 2.5 mg to 4.2 kg of Comp-B3 in several configurations. We measured pressure, spatial temperature, and ignition time. Some experiments included borescope images obtained during both vented and sealed decomposition. We observed the TNT melt, the suspension of RDX particles in the melt, bubble formation caused by RDX decomposition, and bubble-induced mixing of the suspension. The RDX suspension did not completely dissolve, even as temperatures approached ignition. Our results contrast with published measurements of RDX solubility in hot TNT that suggest RDX would be completely dissolved at these high temperatures. These different observations are attributed to sample purity. We did not observe significant movement of the two-phase mixture until decomposition gases formed bubbles. Bubble generation was inhibited in our sealed experiments and suppressed mixing.
Metal additive manufacturing (AM) allows for the freeform creation of complex parts. However, AM microstructures are highly sensitive to the process parameters used. Resulting microstructures vary significantly from typical metal alloys in grain morphology distributions, defect populations and crystallographic texture. AM microstructures are often anisotropic and possess three-dimensional features. These microstructural features determine the mechanical properties of AM parts. Here, we reproduce three “canonical” AM microstructures from the literature and investigate their mechanical responses. Stochastic volume elements are generated with a kinetic Monte Carlo process simulation. A crystal plasticity-finite element model is then used to simulate plastic deformation of the AM microstructures and a reference equiaxed microstructure. Results demonstrate that AM microstructures possess significant variability in strength and plastic anisotropy compared with conventional equiaxed microstructures.
A parallel, adaptive overlay grid procedure is proposed for use in generating all-hex meshes for stochastic (SVE) and representative (RVE) volume elements in computational materials modeling. The mesh generation process is outlined including several new advancements such as data filtering to improve mesh quality from voxelated and 3D image sources, improvements to the primal contouring method for constructing material interfaces and pillowing to improve mesh quality at boundaries. We show specific examples in crystal plasticity and syntactic foam modeling that have benefitted from the proposed mesh generation procedure and illustrate results of the procedure with several practical mesh examples.
We describe an approach to predict failure in a complex, additively-manufactured stainless steel part as defined by the third Sandia Fracture Challenge. A viscoplastic internal state variable constitutive model was calibrated to fit experimental tension curves in order to capture plasticity, necking, and damage evolution leading to failure. Defects such as gas porosity and lack of fusion voids were represented by overlaying a synthetic porosity distribution onto the finite element mesh and computing the elementwise ratio between pore volume and element volume to initialize the damage internal state variables. These void volume fraction values were then used in a damage formulation accounting for growth of these existing voids, while new voids were allowed to nucleate based on a nucleation rule. Blind predictions of failure are compared to experimental results. The comparisons indicate that crack initiation and propagation were correctly predicted, and that an initial porosity field superimposed as higher initial damage may provide a path forward for capturing material strength uncertainty. The latter conclusion was supported by predicted crack face tortuosity beyond the usual mesh sensitivity and variability in predicted strain to failure; however, it bears further inquiry and a more conclusive result is pending compressive testing of challenge-built coupons to de-convolute materials behavior from the geometric influence of significant porosity.
The repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. Error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology and localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.
In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. The algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.
This SAND report fulfills the final report requirement for the Born Qualified Grand Challenge LDRD. Born Qualified was funded from FY16-FY18 with a total budget of ~$13M over the 3 years of funding. Overall 70+ staff, Post Docs, and students supported this project over its lifetime. The driver for Born Qualified was using Additive Manufacturing (AM) to change the qualification paradigm for low volume, high value, high consequence, complex parts that are common in high-risk industries such as ND, defense, energy, aerospace, and medical. AM offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this effort.
Damage mechanisms in elastomeric syntactic foams filled with glass microballoons (GMB) and resulting effects on the macroscale elastic constants have been investigated. Direct numerical simulations of the material microstructure, composite theory analyses, and uniaxial compression tests across a range of filler volume fractions were conducted. The room temperature and elastic behavior of composites with undamaged, fully debonded, and fully crushed GMBs were investigated for syntactic foams with a polydimethylsiloxane matrix. Good agreement was obtained between numerical studies, composite theory, and experiments. Debonding was studied via finite element models due to the difficulty of isolating this damage mechanism experimentally. The predictions indicate that the bulk modulus is insensitive to the state of debonding at low-GMB-volume fractions but is dramatically reduced if GMBs are crushed. The shear behavior is affected by both debonding and crush damage mechanisms. The acute sensitivity of the bulk modulus to crushed GMBs is further studied in simulations in which only a fraction of GMBs are crushed. We find that the composite bulk modulus drops severely even when just a small fraction of GMBs are crushed. Various material parameters such as GMB wall thickness, volume fraction, and minimum balloon spacing are also investigated, and they show that the results presented here are general and apply to a wide range of microstructure and GMB filler properties.
Sylgard® 184/Glass Microballoon (GMB) potting material is currently used in many NW systems. Analysts need a macroscale constitutive model that can predict material behavior under complex loading and damage evolution. To address this need, ongoing modeling and experimental efforts have focused on study of damage evolution in these materials. Micromechanical finite element simulations that resolve individual GMB and matrix components promote discovery and better understanding of the material behavior. With these simulations, we can study the role of the GMB volume fraction, time-dependent damage, behavior under confined vs. unconfined compression, and the effects of partial damage. These simulations are challenging and push the boundaries of capability even with the high performance computing tools available at Sandia. We summarize the major challenges and the current state of this modeling effort, as an exemplar of micromechanical modeling needs that can motivate advances in future computing efforts.
Previous numerical studies of Sylgard filled with glass microballoons (GMB) have relied on various microstructure idealizations to achieve a large range of volume fractions with high mesh quality. This study investigates how different microstructure idealizations and constraints affect the apparent homogenized elastic constants in the virgin state of the material, in which all GMBs are intact and perfectly bonded to the Sylgard matrix, and in the fully damaged state of the material in which all GMBs are destroyed. In the latter state, the material behaves as an elastomeric foam. Four microstructure idealizations are considered relating to how GMBs are packed into a representative volume element (RVE): (1) no boundary penetration nor GMB-GMB overlap, (2) GMB-GMB overlap, (3) boundary penetration, and (4) boundary penetration and GMB-GMB overlap. First order computational homogenization with kinematically uniform displacement boundary conditions (KUBCs) was employed to determine the homogenized (apparent) bulk and shear moduli for the four microstructure idealizations in the intact and fully broken GMB material states. It was found that boundary penetration has a significant effect on the shear modulus for microstructures with intact GMBs, but that neither boundary penetration nor GMB overlap have a significant effect on homogenized properties for microstructures with fully broken GMBs. The primary conclusion of the study is that future investigations into Sylgard/GMB micromechanics should either force GMBs to stay within the RVE fully and/or use periodic BCs (PBCs) to eliminate the boundary penetration issues. The implementation of PBCs requires the improvement of existing tools in Sandia’s Sierra/SM code.
The texture of a polycrystalline material refers to the preferred orientation of the grains within the material. In metallic materials, texture can significantly affect the mechanical properties such as elastic moduli, yield stress, strain hardening, and fracture toughness. Recent advances in additive manufacturing of metallic materials offer the possibility in the not too distant future of controlling the spatial variation of texture. In this work, we investigate the advantages, in terms of mechanical performance, of allowing the texture to vary spatially. We use an adjoint-based gradient optimization algorithm within a finite element solver (COMSOL) to optimize several engineering quantities of interest in a simple structure (hole in a plate) and loading (uniaxial tension) condition. As a first step to general texture optimization, we consider the idealized case of a pure fiber texture in which the homogenized properties are transversely isotropic. In this special case, the only spatially varying design variables are the three Euler angles that prescribe the orientation of the homogenized material at each point within the structure. This work paves a new way to design metallic materials for tunable mechanical properties at the microstructure level.
This work was done to support customer questions about whether a Sylgard/Glass Microballoon (GMB) potting material in current use could be replaced with pure Sylgard and if this would significantly change stresses imparted to internal components under thermal cycling conditions. To address these questions, we provide micromechanics analysis of Sylgard/GMB materials using both analytic composite theory and finite element simulations to better understand the role of the GMB volume fraction in determining thermal expansion coefficient, elastic constants, and behavior in both confined and unconfined compression boundary value problems. A key finding is that damage accumulation in the material from breakage of GMBs significantly limits the global stress magnitude and results in a plateau stress behavior over large ranges of compressive strain. The magnitude of this plateau stress is reduced with higher volume fractions of GMBs. This effect is particularly pronounced in confined compression, which we estimate bears the most similarity to the application of interest. This stress-limiting damage mechanism is not present in pure Sylgard, however, and the result is much higher stresses under confined compression. Thus, we recommend that some volume fraction greater than 10% GMBs be used for confined deformation applications.
We calibrate a linear thermoviscoelastic model for solid Sylgard 184 (90-10 formulation), a lightly cross-linked, highly flexible isotropic elastomer for use both in Sierra / Solid Mechanics via the Universal Polymer Model as well as in Sierra / Structural Dynamics (Salinas) for use as an isotropic viscoelastic material. Material inputs for the calibration in both codes are provided. The frequency domain master curve of oscillatory shear was obtained from a report from Los Alamos National Laboratory (LANL). However, because the form of that data is different from the constitutive models in Sierra, we also present the mapping of the LANL data onto Sandia’s constitutive models. Finally, blind predictions of cyclic tension and compression out to moderate strains of 40 and 20% respectively are compared with Sandia’s legacy cure schedule material. Although the strain rate of the data is unknown, the linear thermoviscoelastic model accurately predicts the experiments out to moderate strains for the slower strain rates, which is consistent with the expectation that quasistatic test procedures were likely followed. This good agreement comes despite the different cure schedules between the Sandia and LANL data.
A parallel, adaptive overlay grid procedure is proposed for use in generating all-hex meshes for stochastic (SVE) and representative (RVE) volume elements in computational materials modeling. The mesh generation process is outlined including several new advancements such as data filtering to improve mesh quality from voxelated and 3D image sources, improvements to the primal contouring method for constructing material interfaces and pillowing to improve mesh quality at boundaries. We show specific examples in crystal plasticity and syntactic foam modeling that have benefitted from the proposed mesh generation procedure and illustrate results of the procedure with several practical mesh examples.
An a posteriori error-estimation framework is introduced to quantify and reduce modeling errors resulting from approximating complex mesoscale material behavior with a simpler macroscale model. Such errors may be prevalent when modeling welds and additively manufactured structures, where spatial variations and material textures may be present in the microstructure. We consider a case where a <100> fiber texture develops in the longitudinal scanning direction of a weld. Transversely isotropic elastic properties are obtained through homogenization of a microstructural model with this texture and are considered the reference weld properties within the error-estimation framework. Conversely, isotropic elastic properties are considered approximate weld properties since they contain no representation of texture. Errors introduced by using isotropic material properties to represent a weld are assessed through a quantified error bound in the elastic regime. An adaptive error reduction scheme is used to determine the optimal spatial variation of the isotropic weld properties to reduce the error bound.
