UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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Item Anisotropic Multi-scale Modeling for Steady-state Creep Behavior of Oligocrystalline SnAgCu (SAC) Solder Joints(2021) Jiang, Qian; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Heterogeneous integration is leading to unprecedented miniaturization of solder joints. The overall size of solder interconnections in current-generation microelectronics assemblies has length-scales that are comparable to that of the intrinsic heterogeneities of the solder microstructure. In particular, there are only a few highly anisotropic grains in each joint. This makes the mechanical response of each joint quite unique. Rigorous mechanistic approaches are needed for quantitative understanding of the response of such joints, based on the variability of the microstructural morphology. The discrete grain morphology of as-solidified oligocrystalline SAC (SnAgCu) solder joints is explicitly modeled in terms of multiple length scales (four tiers of length scales are used in the description here). At the highest length-scale in the joint (Tier 3), there are few highly anisotropic viscoplastic grains in each functional solder joint, connected by visoplastic grain boundaries. At the next lower tier (Tier 2), the primary heterogeneity within each grain is due to individual dendrites of pro-eutectic β-Sn. Additional microscale intermetallic compounds of Cu6Sn5 rods are located inside individual grains. Packed between the dendrite lobes is a eutectic Ag-Sn alloy, The next lower length-scale (Tier 1), deals with the microstructure of the Ag-Sn eutectic phase, consisting of nanoscale Ag3Sn IMC particles dispersed in a β-Sn matrix. The characteristic length scale and spacing of the IMC particles in this eutectic mix are important features of Tier 1. Tier 0 refers to the body-centered tetragonal (BCT) anisotropic β-Sn crystal structure, including the dominant slip systems for this crystal system. The objective of this work is to provide the mechanistic framework to quantify the mechanical viscoplastic response of such solder joints. The anisotropic mechanical behavior of each solder grain is modeled with a multiscale crystal viscoplasticity (CV) approach, based on anisotropic dislocation mechanics and typical microstructural features of SAC crystals. Model constants are calibrated with single crystal data from the literature and from experiments. This calibrated CV model is used as single-crystal digital twin, for virtual tests to determine the model constants for a continuum-scale compact anisotropic creep model for SAC single crystals, based on Hill’s anisotropic potential and an associated creep flow-rule. The additional contribution from grain boundary sliding, for polycrystalline structures, is investigated by the use of a grain-boundary phase, and the properties of the grain boundary phase are parametrically calibrated by comparing the model results with creep test results of joint-scale few-grained solder specimens. This methodology enables user-friendly computationally efficient finite element simulations of multi-grain solder joints in microelectronic assemblies and facilitates parametric sensitivity studies of different grain configurations. This proposed grain-scale modeling approach is explicitly sensitive to microstructural features such as the morphology of: (i) the IMC reinforcements in the eutectic phase; (ii) dendrites; and (iii) grains. Thus, this model is suited for studying the effect of microstructural tailoring and microstructural evolution. The developed multiscale modeling methodology will also empower designers to numerically explore the worst-case and best-case microstructural configurations (and corresponding stochastic variabilities in solder joint performance and in design margins) for creep deformation under monotonic loading, for creep-fatigue under thermal cycling as well as for creep properties under isothermal aging conditions.Item ERROR ESTIMATION, GRID SELECTION AND CONVERGENCE VERIFICATION IN LARGE EDDY SIMULATION(2019) Toosi, Siavash; Larsson, Johan; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Large eddy simulation (LES) is a modeling approach to simulation of turbulence, in which the large and energy containing eddies are directly resolved, while the smaller scales are modeled. The ``coarse-graining'' length scale (the length scale below which the turbulent eddies are modeled) is an important modeling parameter that is directly tied to the computational grid. As a result, the LES grid controls both the numerical and modeling errors and in most cases (given that the LES model is consistent) becomes the most important factor in determining the accuracy of the solution. The main goal of this dissertation is to enable a systematic approach to grid selection and convergence-verification in LES. Systematic grid selection consists of five essential ingredients: (i) an ``error-indicator'' that identifies the regions of error generation, (ii) some knowledge of the directional structure of error generation (i.e., an anisotropic measure of error generation at each location), (iii) a model that describes the connection between the error generation and the filter/grid resolution (i.e., how it changes with a change in the resolution), (iv) criteria that describe the most ``optimal'' distribution of the error-indicator in space and in direction, and (v) a robust method for convergence-verification. Items (i), (ii), (iv) and (v) are all addressed in this dissertation, while item (iii) has not been a subject of extensive research here (because of its somewhat lower importance compared to the other four). Three error-indicators are introduced that are different in terms of their underlying assumptions, complexity, potential accuracy, and extensibility to more complex flows and more sophisticated formulations of the problem of ``optimal'' grid selection. Two of these error-indicators are inherently anisotropic, while the third one is only a scalar but can be combined with either of the other two to enable anisotropic error-estimation. The ``optimal'' distributions of these error-indicators are discussed in detail, that, combined with a model to connect the error-indicator and the grid/filter resolution, describe our ``optimal'' grid selection criteria. Additionally, a more robust approach for convergence-verification in LES is proposed, and is combined with error-estimation and ``optimal'' grid selection/adaptation to form a systematic algorithm for large eddy simulation. The proposed error-estimation, grid selection, and convergence-verification methods are tested on the turbulent channel flow and the flow over a backward-facing step, with good results in all cases, and grids that are quite close to what is know as ``best practice'' for LES of these flows.Item Investigation into the Influence of Build Parameters on Failure of 3D Printed Parts(2016) Fornasini, Giacomo; Schmidt, Linda C; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Additive manufacturing, including fused deposition modeling (FDM), is transforming the built world and engineering education. Deep understanding of parts created through FDM technology has lagged behind its adoption in home, work, and academic environments. Properties of parts created from bulk materials through traditional manufacturing are understood well enough to accurately predict their behavior through analytical models. Unfortunately, Additive Manufacturing (AM) process parameters create anisotropy on a scale that fundamentally affects the part properties. Understanding AM process parameters (implemented by program algorithms called slicers) is necessary to predict part behavior. Investigating algorithms controlling print parameters (slicers) revealed stark differences between the generation of part layers. In this work, tensile testing experiments, including a full factorial design, determined that three key factors, width, thickness, infill density, and their interactions, significantly affect the tensile properties of 3D printed test samples.Item Optical and Thermal Properties of Nanoporous Material and Devices(2015) Kim, Kyowon; Murphy, Thomas E; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we investigate the optical and thermal properties of porous silicon and its applications. In first part, porous silicon's optical properties and application as a highly sensitive refractive index sensor is studied. An integrated Mach-Zehnder interferometer waveguide fabricated from nanoporous silicon is shown to exhibit high sensitivity and measurement stability that exceeds previously demonstrated porous sensors. In second part, we discuss experimental methods to characterize the thermal conductivity of nanoporous silicon films. We use the 3-ω method to characterize the exceptionally low thermal conductivity of porous silicon. Finally, we employ an improved heat conduction analysis method for the 3-ω method to measure the anisotropy in thermal conductivity. Our measurement show that porous silicon has very low in-plane thermal conductivity compared to cross-plane conductivity. We confirmed this anisotropy using direct numerical simulation of the anisotropic heat equation.Item Multiscale Modeling of the Anisotropic Creep Response of SnAgCu Single Crystal(2015) Mukherjee, Subhasis; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to their coarse grained microstructure, in conjunction with the severe anisotropy exhibited by single crystal Sn, renders each joint unique in terms of mechanical behavior. An anisotropic multiscale modeling framework is proposed in this dissertation to capture the influence of the inherent elastic anisotropy and grain orientation in single crystal Sn on the primary and secondary creep response of single crystal SnAgCu (SAC) solder. Modeling of microstructural deformation mechanisms in SnAgCu (SAC) solder interconnects requires a multiscale approach because of tiered microstructural heterogeneities. The smallest length scale (Tier 0) refers to the Body Centered Tetragonal (BCT) structure of the Sn matrix itself because it governs: (1) the associated dislocation slip systems, (2) dislocation line tension (3) dislocation mobility and (4) intrinsic orthotropy of mechanical properties in the crystal principal axis system. The next higher length scale, (Tier 1), consists of nanoscale Ag3Sn intermetallic compounds (IMCs) surrounded by Body Centered Tetragonal (BCT) Sn to form the eutectic Sn-Ag phase. The next higher length scale (Tier 2) consists of micron scale lobes of pro-eutectic Sn dendrites surrounded by eutectic Sn-Ag regions and reinforced with micron scale Cu6Sn5 IMCs. Unified modeling of above two length scales provides constitutive properties for SAC single crystal. Tier 3 in coarse-grained solder joints consists of multiple SAC crystals along with grain boundaries. Finally, Tier 4 consists of the structural length scale of the solder joint. Line tension and mobility of dislocations (Tier 0) in dominant slip systems of single crystal Sn are captured for the elastic crystal anisotropy of body centered tetragonal (BCT) Sn by using Stroh's matrix formalism. The anisotropic creep rate of the eutectic Sn-Ag phase of Tier I is then modeled using above inputs and the evolving dislocation density calculated for the dominant glide systems. The evolving dislocation density history is estimated by modeling the equilibrium between three competing processes: (1) dislocation generation; (2) dislocation impediment (due to backstress from forest dislocations in the Sn dendrites and from the Ag3Sn IMC particles in the eutectic phase); and (3) dislocation recovery (by climb/diffusion from forest dislocations in the Sn dendrites and by climb/detachment from the Ag3Sn IMC particles in the eutectic phase). The creep response of the eutectic phase (from Tier 1) is combined with creep of ellipsoidal Sn lobes at Tier 2 using the anisotropic Mori-Tanaka homogenization theory, to obtain the creep response of SAC305 single crystal along global specimen directions and is calibrated to experimentally obtained creep response of a SAC305 single crystal specimen. The Eshelby strain concentration tensors required for this homogenization process are calculated numerically for ellipsoidal Sn inclusions embedded in anisotropic eutectic Sn-Ag matrix. The orientations of SAC single crystal specimens with respect to loading direction are identified using orientation image mapping (OIM) using Electron Backscatter Diffraction (EBSD) and then utilized in the model to estimate the resolved shear stress along the dominant slip directions. The proposed model is then used for investigating the variability of the transient and secondary creep response of Sn3.0Ag0.5Cu (SAC305) solder, which forms the first objective of the dissertation. The transient creep strain rate along the [001] direction of SAC305 single crystal #1 is predicted to be 1-2 orders of magnitude higher than that along the [100]/[010] direction. Parametric studies have also been conducted to predict the effect of changing orientation, aspect ratio and volume fraction of Sn inclusions on the anisotropic creep response of SAC single crystals. The predicted creep shear strain along the global specimen direction is found to vary by a factor of (1-3) orders of magnitude due to change in one of the Euler angles (j1) in SAC305 single crystal #1, which is in agreement with the variability observed in experiments. The second objective of this dissertation focuses on using this proposed modeling framework to characterize and model the creep constitutive response of new low-silver, lead-free interconnects made of Sn1.0Ag0.5Cu (SAC105) doped with trace elements, viz., Manganese (Mn) and Antimony (Sb). The proposed multiscale model is used to mechanistically model the improvement in experimentally observed steady state creep resistance of above SAC105X solders due to the microalloying with the trace elements. The third and final objective of this dissertation is to use the above multiscale microstructural model to mechanistically predict the effect of extended isothermal aging on experimentally observed steady state creep response of SAC305 solders. In summary, the proposed mechanistic predictive model is demonstrated to successfully capture the dominant load paths and deformation mechanisms at each length scale and is also shown to be responsive to the microstructural tailoring done by microalloying and the continuous microstructural evolution because of thermomechanical life-cycle aging mechanisms in solders.