Publications

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Residual stress is a common result of manufacturing processes, but it is one that is often overlooked in design and qualification activities. There are many reasons for this oversight, such as lack of observable indicators and difficulty in measurement. Traditional relaxation-based measurement methods use some type of material removal to cause surface displacements, which can then be used to solve for the residual stresses relieved by the removal. While widely used, these methods may offer only individual stress components or may be limited by part or cut geometry requirements. Diffraction-based methods, such as X-ray or neutron, offer non-destructive results but require access to a radiation source. With the goal of producing a more flexible solution, this LDRD developed a generalized residual stress inversion technique that can recover residual stresses released by all traction components on a cut surface, with much greater freedom in part geometry and cut location. The developed method has been successfully demonstrated on both synthetic and experimental data. The project also investigated dislocation density quantification using nonlinear ultrasound, residual stress measurement using Electronic Speckle Pattern Interferometry Hole Drilling, and validation of residual stress predictions in Additive Manufacturing process models.

The 2019 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 17 to August 1, 2019. NOMAD brings together participants with diverse technical backgrounds to work in small teams to cultivate new ideas and approaches in engineering mechanics and dynamics research. NOMAD provides an opportunity for researchers especially early career researchers - to develop lasting collaborations that go beyond what can be established from the limited interactions at their institutions or at annual conferences. A total of 20 students came to Albuquerque, New Mexico to participate in the seven-week long program held at the Mechanical Engineering building on the University of New Mexico campus. The students collaborated on one of seven research projects that were developed by various mentors from Sandia National Laboratories, the University of New Mexico, and academic institutions. In addition to the research activities, the students attended weekly technical seminars, various tours, and socialized at various off-hour events including an Albuquerque Isotopes baseball game. At the end of the summer, the students gave a final technical presentation on their research findings. Many of the research discoveries made at NOMAD are published as proceedings at technical conferences and have direct alignment with the critical mission work performed at Sandia.

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Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. This work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.

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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.

Meshfree methods for solid mechanics have been in development since the early 1990's. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both mesh-free and meshbased Lagrangian discretizations are compared using manufactured extreme-deformation fields. For the meshfree discretizations, both moving least squares and maximum entropy are considered. Quantitative error and convergence results are presented for the best approximation in the H¹ norm.

Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. Furthermore, this work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.

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The mechanical response of additively manufactured (AM) stainless steel 304L has been investigated across a broad range of loading conditions, covering 11 decades of strain rate, and compared with the behaviors of traditional ingot-derived (wrought) material. In general, the AM material exhibits a greater strength and reduced ductility compared with the baseline wrought form. These differences are consistently found from quasi-static and high strain rate tests. A detailed investigation of the microstructure, the defect structure, the phase, and the composition of both forms reveals differences that may contribute to the differing mechanical behaviors. Compared with the baseline wrought material, dense AM stainless steel 304L has a more complex grain structure with substantial sub-structure, a fine dispersion of ferrite, increased dislocation density, oxide dispersions and larger amounts of nitrogen. In-situ neutron diffraction studies conducted during quasi-static loading suggest that the increased strength of AM material is due to its initially greater dislocation density. The flow strength of both forms is correlated with dislocation density through a square root dependence akin to a Taylor-like relationship. Neutron diffraction measurements of lattice strains also correlate with a crystal plasticity finite element simulations of the tensile test. Other simulations predict a significant degree of elastic and plastic anisotropy due to crystallographic texture. Hopkinson tests at higher strain rates $\dot{ε}$ = 500 and 2500 s^-1 ) also show a greater strength for AM stainless steel 304L; although, the differences compared with wrought are reduced at higher strain rates. Gas gun impact tests, including reverse ballistic, forward ballistic and spall tests, consistently reveal a larger dynamic strength in the AM material. The Hugoniot Elastic Limit (HEL) of AM SS 304L exceeds that of wrought material although considerable variability is observed with the AM material. Forward ballistic testing demonstrates spall strengths of AM material (3.27 -- 3.91 GPa) that exceed that of the wrought material (2.63 -- 2.88 GPa). The Hugoniot equation-of-state for AM samples matches archived data for this metal alloy.

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Here, a stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Finally, several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.

This research applies nonlinear ultrasonic techniques for the quantitative characterization of additively manufactured materials. The characterization focuses on identifying the dislocation density produced during the additive constructive process in order to increase confidence on a part's performance and the success of the manufacturing process. Second harmonic generation techniques based on the transmission of Rayleigh surface waves are used to measure the ultrasonic nonlinearity parameter, β, which has proven a quantitative indicator of dislocations but has not been fully proven in additive manufactured materials. 316L and 304L stainless steel parts made from Powder Bed Fusion and Laser Engineered Net Shaping are compared between AM techniques and with wrought manufactured counterparts. β is consistently higher for additive manufactured parts. An annealing heat treatment is applied to each specimen to reduce dislocation density. β expectedly decreases by annealing in all specimens. A linear ultrasonic measurement is made to evaluate the effectiveness of using nonlinear techniques. The ultrasonic attenuation is higher for additive manufactured parts and increases at higher frequencies.

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

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