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.
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.
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.
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.
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.
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.
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.