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- Creators: Arizona State University
- Creators: Peralta, Pedro
Description
Pb-free solders are used as interconnects in various levels of micro-electronic packaging. Reliability of these interconnects is very critical for the performance of the package. One of the main factors affecting the reliability of solder joints is the presence of porosity which is introduced during processing of the joints. In this thesis, the effect of such porosity on the deformation behavior and eventual failure of the joints is studied using Finite Element (FE) modeling technique. A 3D model obtained by reconstruction of x-ray tomographic image data is used as input for FE analysis to simulate shear deformation and eventual failure of the joint using ductile damage model. The modeling was done in ABAQUS (v 6.10). The FE model predictions are validated with experimental results by comparing the deformation of the pores and the crack path as predicted by the model with the experimentally observed deformation and failure pattern. To understand the influence of size, shape, and distribution of pores on the mechanical behavior of the joint four different solder joints with varying degrees of porosity are modeled using the validated FE model. The validation technique mentioned above enables comparison of the simulated and actual deformation only. A more robust way of validating the FE model would be to compare the strain distribution in the joint as predicted by the model and as observed experimentally. In this study, to enable visualization of the experimental strain for the 3D microstructure obtained from tomography, a three dimensional digital image correlation (3D DIC) code has been implemented in MATLAB (MathWorks Inc). This developed 3D DIC code can be used as another tool to verify the numerical model predictions. The capability of the developed code in measuring local displacement and strain is demonstrated by considering a test case.
ContributorsJakkali, Vaidehi (Author) / Chawla, Nikhilesh K (Thesis advisor) / Jiang, Hanqing (Committee member) / Solanki, Kiran (Committee member) / Arizona State University (Publisher)
Created2011
Description
Pb-free solder joints are commonly used as interconnects in semiconductor packaging. One of the major defects affecting the mechanical performance of solder joints are reflow pores that form during processing. These pores exhibit significant variability in size and distribution, and understanding the effects of pore geometry on failure is an important reliability concern. In this thesis, the pore microstructures of solder joint samples and the localized plastic deformation around individual pores was characterized in 3D using lab scale X-ray Microtomography. To observe the deformation of a solder joint in 3D, a solder joint was imaged with Microtomography after reflow and then deformed in shear in several loading steps with additional tomography data taken between each. The 3D tomography datasets were then segmented using the 3D Livewire technique into regions corresponding to solder and pores, and used to generate 3D models of the joint at each strain value using Mimics software. The extent of deformation of individual pores in the joint as a function of strain was quantified using sphericity measurements, and correlated with the observed cracking in the joint. In addition, the error inherent in the data acquisition and 3D modeling process was also quantified. The progression of damage observed with X-ray Microtomography was then used to validate the deformation and failure predicted by a Finite Element (FE) simulation. The FE model was based on the as-reflowed tomography data, and incorporated a ductile damage failure model to simulate fracture. Using the measured sphericity change and cracking information obtained from the tomography data, the FE model is shown to correctly capture the broad plastic deformation and strain localization seen in the actual joint, as well as the crack propagation. Lastly, Digital Image Correlation was investigated as a method of obtaining improved local strain measurements in 3D. This technique measures the displacement of the inherent microstructural features of the joint, and can give localized strain measurements that can be directly comparable to that predicted by modeling. The technique is demonstrated in 2D on Pb-Sn solder, and example 3D data is presented for future analysis.
ContributorsPadilla, Erick (Author) / Chawla, Nikhilesh (Thesis advisor) / Alford, Terry (Committee member) / Krause, Stephen (Committee member) / Arizona State University (Publisher)
Created2012
Description
Aromatic polymers, with benzene-like rings in their main chains, include materials such as polyurea, an amorphous elastomer capable of dissipating large amounts of energy under dynamic loading, which makes it a promising coating for defensive systems. Although computational research exists that investigates the atomic-level response of polyurea and other amorphous aromatic polymers to extreme conditions, there is little experimental work to validate these models 1) at the atomic-scale and 2) under high pressures characteristic of extreme dynamic loading. Understanding structure-property relationships at the atomic-level is important for polymers, considering many of them undergo pressure and temperature-induced structural transformations, which must be understood to formulate accurate predictive models. This work aims to gain a deeper understanding of the high-pressure structural response of aromatic polymers at the atomic-level, with emphasis into the mechanisms associated with high-pressure transformations. Hence, atomic-level structural data at high pressures was obtained in situ via multiangle energy dispersive X-ray diffraction (EDXD) experiments at the Advanced Photon Source (APS) for polyurea and another amorphous aromatic polymer, polysulfone, chosen as a reference due to its relatively simple structure. Pressures up to 6 GPa were applied using a Paris Edinburgh (PE) hydraulic press at room temperature. Select polyurea samples were also heated to 277 °C at 6 GPa. The resulting structure factors and pair distribution functions, along with molecular dynamics simulations of polyurea provided by collaborators, suggest that the structures of both polymers are stable up to 6 GPa, aside from reductions in free-volume between polymer backbones. As higher pressures (≲ 32 GPa) were applied using diamond anvils in combination with the PE press, indications of structural transformations were observed in both polymers that appear similar in nature to the sp2-sp3 hybridization in compressed carbon. The transformation occurs gradually up to at least ~ 26 GPa in PSF, while it does not progress past ~ 15 GPa in polyurea. The changes are largely reversible, especially in polysulfone, consistent with pressure-driven, reversible graphite-diamond transformations in the absence of applied temperature. These results constitute some of the first in situ observations of the mechanisms that drive pressure-induced structural transformations in aromatic polymers.
ContributorsEastmond, Tyler (Author) / Peralta, Pedro (Thesis advisor) / Hoover, Christian (Committee member) / Hrubiak, Rostislav (Committee member) / Mignolet, Marc (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2022
Description
The characterization of spall microstructural damage metallic samples is critical to predicting and modeling modes of failure under blast, ballistic, and other dynamic loads. In this regard, a key step to improve models of dynamic damage is making appropriate connections between experimental characterization of actual damage in the form of discrete voids distributed over a given volume of the specimens, and the output of the models, which provide a continuous measure of damage, for example, void fraction as a function of position. Hence, appropriate homogenization schemes to estimate, e.g., continuous void fraction estimations from discrete void distributions, are key to calibration and validation of damage models. This project seeks to analyze 3D tomography data to relate the homogenization parameters for the discrete void distributions, i.e., homogenization volume size and step, as well as representative volume element size, to the local length scales, e.g., grain size as well as void size and spacing. Copper disks 10 mm in diameter and 1 mm thick with polycrystalline structures were subjected to flyer plate impacts resulting in shock stresses ranging from 2 to 5 GPa. The spall damage induced in samples by release waves was characterized using X-ray tomography techniques. The resulting data is thresholded to differentiate voids from the matrix and void fraction is obtained via homogenization using various parameterization schemes to characterize void fraction distributions along the shock and transverse directions. The representative volume element is determined by relating void fraction for varying parameterized window sizes to the void fraction in the overall volume. Results of this study demonstrate that the optimal representative volume element (RVE) to represent void fraction within 10% error of the overall sample void fraction for this Hitachi copper sample is .2304 mm3. The RVE is found to contain approximately 255 grains. Statistical volume elements of 1300 µm3 or smaller are used to quantify void fraction as a function of position and while the results along the shock direction, i.e., the presence of a clear peak at the expected location of the spall plane, are expected, the void fraction along the transverse direction show oscillatory behavior. The power spectra and predominant frequencies of these distributions suggest the periodicity of the oscillations relates to multiples of local material length scales such as grain size. This demonstrates that the grain size in the samples, about 120 µm, is too large compared to the sample size to try to capture spatial variability due to applied loads and the microstructure, since the microstructure itself produces variability on the order of a few grain sizes. These results may play a role for the design of experiments to collect real-world 3D damage data for validating and enhancing the accuracy and definition of simulation models for damage characterization by providing frameworks for microstructural strain variability when modeling spall behavior under dynamic damage.
ContributorsNimbkar, Sharmila (Author) / Peralta, Pedro (Thesis director) / Oswald, Jay (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2023-12
Description
The study of deflagration to detonation transition (DDT) in explosives is of prime importance with regards to insensitive munitions (IM). Critical damage owing to thermal or shock stimuli could translate to significant loss of life and material. The present study models detonation and deflagration of a commonly used granular explosive: cyclotetramethylene-tetranitramine, HMX. A robust literature review is followed by computational modeling of gas gun and DDT tube test data using the Sandia National Lab three-dimensional multi-material Eulerian hydrocode CTH. This dissertation proposes new computational practices and models that aid in predicting shock stimulus IM response. CTH was first used to model experimental data sets of DDT tubes from both Naval Surface Weapons Center and Los Alamos National Laboratory which were initiated by pyrogenic material and a piston, respectively. Analytical verification was performed, where possible, for detonation via empirical based equations at the Chapman Jouguet state with errors below 2.1%, and deflagration via pressure dependent burn rate equations. CTH simulations include inert, history variable reactive burn and Arrhenius models. The results are in excellent agreement with published HMX detonation velocities. Novel additions include accurate simulation of the pyrogenic material BKNO3 and the inclusion of porosity in energetic materials. The treatment of compaction is especially important in modeling precursory hotspots, caused by hydrodynamic collapse of void regions or grain interactions, prior to DDT of granular explosives. The CTH compaction model of HMX was verified within 11% error via a five pronged validation approach using gas gun data and employed use of a newly generated set of P-α parameters for granular HMX in a Mie-Gruneisen Equation of State. Next, the additions of compaction were extended to a volumetric surface burning model of HMX and compare well to a set of empirical burn rates. Lastly, the compendium of detonation and deflagration models was applied to the aforementioned DDT tubes and demonstrate working functionalities of all models, albeit at the expense of significant computational resources. A robust hydrocode methodology is proposed to make use of the deflagration, compaction and detonation models as a means to predict IM response to shock stimulus of granular explosive materials.
ContributorsMahon, Kelly Susan (Author) / Lee, Taewoo (Thesis advisor) / Herrmann, Marcus (Committee member) / Chen, Kangping (Committee member) / Jiao, Yang (Committee member) / Huang, Huei-Ping (Committee member) / Arizona State University (Publisher)
Created2015
Description
Improved knowledge connecting the chemistry, structure, and properties of polymers is necessary to develop advanced materials in a materials-by-design approach. Molecular dynamics (MD) simulations can provide tremendous insight into how the fine details of chemistry, molecular architecture, and microstructure affect many physical properties; however, they face well-known restrictions in their applicable temporal and spatial scales. These limitations have motivated the development of computationally-efficient, coarse-grained methods to investigate how microstructural details affect thermophysical properties. In this dissertation, I summarize my research work in structure-based coarse-graining methods to establish the link between molecular-scale structure and macroscopic properties of two different polymers. Systematically coarse-grained models were developed to study the viscoelastic stress response of polyurea, a copolymer that segregates into rigid and viscous phases, at time scales characteristic of blast and impact loading. With the application of appropriate scaling parameters, the coarse-grained models can predict viscoelastic properties with a speed up of 5-6 orders of magnitude relative to the atomistic MD models. Coarse-grained models of polyethylene were also created to investigate the thermomechanical material response under shock loading. As structure-based coarse-grained methods are generally not transferable to states different from which they were calibrated at, their applicability for modeling non-equilibrium processes such as shock and impact is highly limited. To address this problem, a new model is developed that incorporates many-body interactions and is calibrated across a range of different thermodynamic states using a least square minimization scheme. The new model is validated by comparing shock Hugoniot properties with atomistic and experimental data for polyethylene. Lastly, a high fidelity coarse-grained model of polyethylene was constructed that reproduces the joint-probability distributions of structural variables such as the distributions of bond lengths and bond angles between sequential coarse-grained sites along polymer chains. This new model accurately represents the structure of both the amorphous and crystal phases of polyethylene and enabling investigation of how polymer processing such as cold-drawing and bulk crystallization affect material structure at significantly larger time and length scales than traditional molecular simulations.
ContributorsAgrawal, Vipin (Author) / Oswald, Jay (Thesis advisor) / Peralta, Pedro (Committee member) / Chamberlin, Ralph (Committee member) / Solanki, Kiran (Committee member) / Jiao, Yang (Committee member) / Arizona State University (Publisher)
Created2016
Description
The exceptional mechanical properties of polymers with heterogeneous structure, such as the high toughness of polyethylene and the excellent blast-protection capability of polyurea, are strongly related to their morphology and nanoscale structure. Different polymer microstructures, such as semicrystalline morphology and segregated nanophases, lead to coordinated molecular motions during deformation in order to preserve compatibility between the different material phases. To study molecular relaxation in polyethylene, a coarse-grained model of polyethylene was calibrated to match the local structural variable distributions sampled from supercooled atomistic melts. The coarse-grained model accurately reproduces structural properties, e.g., the local structure of both the amorphous and crystalline phases, and thermal properties, e.g., glass transition and melt temperatures, and dynamic properties: including the vastly different relaxation time scales of the amorphous and crystalline phases. A hybrid Monte Carlo routine was developed to generate realistic semicrystalline configurations of polyethylene. The generated systems accurately predict the activation energy of the alpha relaxation process within the crystalline phase. Furthermore, the models show that connectivity to long chain segments in the amorphous phase increases the energy barrier for chain slip within crystalline phase. This prediction can guide the development of tougher semicrystalline polymers by providing a fundamental understanding of how nanoscale morphology contributes to chain mobility. In a different study, the macroscopic shock response of polyurea, a phase segregated copolymer, was analyzed using density functional theory (DFT) molecular dynamics (MD) simulations and classical MD simulations. The two models predict the shock response consistently up to shock pressures of 15 GPa, beyond which the DFT-based simulations predict a softer response. From the DFT simulations, an analysis of bond scission was performed as a first step in developing a more fundamental understanding of how shock induced material transformations effect the shock response and pressure dependent strength of polyurea subjected to extreme shocks.
ContributorsLi, Yiyang (Author) / Oswald, Jay (Thesis advisor) / Rajan, Subramaniam D. (Committee member) / Solanki, Kiran (Committee member) / Chamberlin, Ralph (Committee member) / Rajagopalan, Jagannathan (Committee member) / Arizona State University (Publisher)
Created2017
Description
Polyurea is a highly versatile material used in coatings and armor systems to protect against extreme conditions such as ballistic impact, cavitation erosion, and blast loading. However, the relationships between microstructurally-dependent deformation mechanisms and the mechanical properties of polyurea are not yet fully understood, especially under extreme conditions. In this work, multi-scale coarse-grained models are developed to probe molecular dynamics across the wide range of time and length scales that these fundamental deformation mechanisms operate. In the first of these models, a high-resolution coarse-grained model of polyurea is developed, where similar to united-atom models, hydrogen atoms are modeled implicitly. This model was trained using a modified iterative Boltzmann inversion method that dramatically reduces the number of iterations required. Coarse-grained simulations using this model demonstrate that multiblock systems evolve to form a more interconnected hard phase, compared to the more interrupted hard phase composed of distinct ribbon-shaped domains found in diblock systems. Next, a reactive coarse-grained model is developed to simulate the influence of the difference in time scales for step-growth polymerization and phase segregation in polyurea. Analysis of the simulated cured polyurea systems reveals that more rapid reaction rates produce a smaller diameter ligaments in the gyroidal hard phase as well as increased covalent bonding connecting the hard domain ligaments as evidenced by a larger fraction of bridging segments and larger mean radius of gyration of the copolymer chains. The effect that these processing-induced structural variations have on the mechanical properties of the polymer was tested by simulating uniaxial compression, which revealed that the higher degree of hard domain connectivity leads to a 20% increase in the flow stress. A hierarchical multiresolution framework is proposed to fully link coarse-grained molecular simulations across a broader range of time scales, in which a family of coarse-grained models are developed. The models are connected using an incremental reverse–mapping scheme allowing for long time scale dynamics simulated at a highly coarsened resolution to be passed all the way to an atomistic representation.
ContributorsLiu, Minghao (Author) / Oswald, Jay (Thesis advisor) / Muhich, Christopher (Committee member) / Jiang, Hanqing (Committee member) / Peralta, Pedro (Committee member) / Jiao, Yang (Committee member) / Arizona State University (Publisher)
Created2020