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The mechanical behavior of Pb-free solder alloys is important, since they must maintain mechanical integrity under thermomechanical fatigue, creep, and mechanical shock conditions. Mechanical shock, in particular, has become an increasing concern in the electronics industry, since electronic packages can be subjected to mechanical shock by mishandling during manufacture or by accidental dropping. In this study, the mechanical shock behavior of Sn and Sn-Ag-Cu alloys was systematically analyzed over the strain rate range 10-3 - 30 s-1 in bulk samples, and over 10-3 - 12 s-1 on the single solder joint level. More importantly, the influences of solder microstructure and intermetallic compounds (IMC) on mechanical shock resistance were quantified. A thorough microstructural characterization of Sn-rich alloys was conducted using synchrotron x-ray computed tomography. The three-dimensional morphology and distribution of contiguous phases and precipitates was analyzed. A multiscale approach was utilized to characterize Sn-rich phases on the microscale with x-ray tomography and focused ion beam tomography to characterize nanoscale precipitates. A high strain rate servohydraulic test system was developed in conjunction with a modified tensile specimen geometry and a high speed camera for quantifying deformation. The effect of microstructure and applied strain rate on the local strain and strain rate distributions were quantified using digital image correlation. Necking behavior was analyzed using a novel mirror fixture, and the triaxial stresses associated with necking were corrected using a self-consistent method to obtain the true stress-true strain constitutive behavior. Fracture mechanisms were quantified as a function of strain rate. Finally, the relationship between solder microstructure and intermetallic compound layer thickness with the mechanical shock resistance of Sn-3.8Ag-0.7Cu solder joints was characterized. It was found that at low strain rates the dynamic solder joint strength was controlled by the solder microstructure, while at high strain rates it was controlled by the IMC layer. The influences of solder microstructure and IMC layer thickness were then isolated using extended reflow or isothermal aging treatments. It was found that at large IMC layer thicknesses the trend described above does not hold true. The fracture mechanisms associated with the dynamic solder joint strength regimes were analyzed.
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.
With the increasing focus on developing environmentally benign electronic packages, lead-free solder alloys have received a great deal of attention. Mishandling of packages, during manufacture, assembly, or by the user may cause failure of solder joint. A fundamental understanding of the behavior of lead-free solders under mechanical shock conditions is lacking. Reliable experimental and numerical analysis of lead-free solder joints in the intermediate strain rate regime need to be investigated. This dissertation mainly focuses on exploring the mechanical shock behavior of lead-free tin-rich solder alloys via multiscale modeling and numerical simulations. First, the macroscopic stress/strain behaviors of three bulk lead-free tin-rich solders were tested over a range of strain rates from 0.001/s to 30/s. Finite element analysis was conducted to determine appropriate specimen geometry that could reach a homogeneous stress/strain field and a relatively high strain rate. A novel self-consistent true stress correction method is developed to compensate the inaccuracy caused by the triaxial stress state at the post-necking stage. Then the material property of micron-scale intermetallic was examined by micro-compression test. The accuracy of this measure is systematically validated by finite element analysis, and empirical adjustments are provided. Moreover, the interfacial property of the solder/intermetallic interface is investigated, and a continuum traction-separation law of this interface is developed from an atomistic-based cohesive element method. The macroscopic stress/strain relation and microstructural properties are combined together to form a multiscale material behavior via a stochastic approach for both solder and intermetallic. As a result, solder is modeled by porous plasticity with random voids, and intermetallic is characterized as brittle material with random vulnerable region. Thereafter, the porous plasticity fracture of the solders and the brittle fracture of the intermetallics are coupled together in one finite element model. Finally, this study yields a multiscale model to understand and predict the mechanical shock behavior of lead-free tin-rich solder joints. Different fracture patterns are observed for various strain rates and/or intermetallic thicknesses. The predictions have a good agreement with the theory and experiments.
Gels are three-dimensional polymer networks with entrapped solvent (water etc.). They bear amazing features such as stimuli-responsive (temperature, PH, electric field etc.), high water content and biocompatibility and thus find a lot of applications. To understand the complex physics behind gel's swelling phenomenon, it is important to build up fundamental mechanical model and extend to complicated cases. In this dissertation, a coupled large deformation and diffusion model regarding gel's swelling behavior is presented. In this model, free-energy of the total gel is constituted by polymer stretching energy and polymer-solvent mixing energy. In-house nonlinear finite element code is implemented with fast computational capability. Complex phenomenon such as buckling and healing of cracked gel by swelling are studied. Due to the wide coverage of polymeric materials and solvents, solvent diffusion in gels not only follows Fickian diffusion law where concentration map is continuous but also follows non-Fickian diffusion law where concentration map shows high gradient. Phenomenological model with viscoelastic polymer constitutive and concentration dependent diffusivity is created. The model well captures this special diffusion phenomenon such as sharp diffusion front and distinctive swollen and unswollen region.
Hydrogen embrittlement (HE) is a phenomenon that affects both the physical and chemical properties of several intrinsically ductile metals. Consequently, understanding the mechanisms behind HE has been of particular interest in both experimental and modeling research. Discrepancies between experimental observations and modeling results have led to various proposals for HE mechanisms. Therefore, to gain insights into HE mechanisms in iron, this dissertation aims to investigate several key issues involving HE such as: a) the incipient crack tip events; b) the cohesive strength of grain boundaries (GBs); c) the dislocation-GB interactions and d) the dislocation mobility.
The crack tip, which presents a preferential trap site for hydrogen segregation, was examined using atomistic methods and the continuum based Rice-Thompson criterion as sufficient concentration of hydrogen can alter the crack tip deformation mechanism. Results suggest that there is a plausible co-existence of the adsorption induced dislocation emission and hydrogen enhanced decohesion mechanisms. In the case of GB-hydrogen interaction, we observed that the segregation of hydrogen along the interface leads to a reduction in cohesive strength resulting in intergranular failure. A methodology was further developed to quantify the role of the GB structure on this behavior.
GBs play a fundamental role in determining the strengthening mechanisms acting as an impediment to the dislocation motion; however, the presence of an unsurmountable barrier for a dislocation can generate slip localization that could further lead to intergranular crack initiation. It was found that the presence of hydrogen increases the strain energy stored within the GB which could lead to a transition in failure mode. Finally, in the case of body centered cubic metals, understanding the complex screw dislocation motion is critical to the development of an accurate continuum description of the plastic behavior. Further, the presence of hydrogen has been shown to drastically alter the plastic deformation, but the precise role of hydrogen is still unclear. Thus, the role of hydrogen on the dislocation mobility was examined using density functional theory and atomistic simulations. Overall, this dissertation provides a novel atomic-scale understanding of the HE mechanism and development of multiscale tools for future endeavors.
Al 7075 alloys are used in a variety of structural applications, such as aircraft wings, automotive components, fuselage, spacecraft, missiles, etc. The mechanical and corrosion behavior of these alloys are dependent on their microstructure and the environment. Therefore, a comprehensive study on microstructural characterization and stress-environment interaction is necessary. Traditionally, 2D techniques have been used to characterize microstructure, which are inaccurate and inadequate since the research has shown that the results obtained in the bulk are different from those obtained on the surface. There now exist several techniques in 3D, which can be used to characterize the microstructure. Al 7075 alloys contain second phase particles which can be classified as Fe-bearing inclusions, Si-bearing inclusions and precipitates. The variation in mechanical and corrosion properties of aluminum alloys has been attributed to the size, shape, distribution, corrosion properties and mechanical behavior of these precipitates and constituent particles. Therefore, in order to understand the performance of Al 7075 alloys, it is critical to investigate the size and distribution of inclusions and precipitates in the alloys along with their mechanical properties, such as Young's modulus, hardness and stress-strain behavior. X-ray tomography and FIB tomography were used to visualize and quantify the microstructure of constituent particles (inclusions) and precipitates, respectively. Microscale mechanical characterization techniques, such as nanoindentation and micropillar compression, were used to obtain mechanical properties of inclusions. Over the years, studies have used surface measurements to understand corrosion behavior of materials. More recently, in situ mechanical testing has become more attractive and advantageous, as it enables visualization and quantification of microstructural changes as a function of time (4D). In this study, in situ X-ray synchrotron tomography was used to study the SCC behavior of Al 7075 alloys in moisture and deionized water. Furthermore, experiments were performed in EXCO solution to study the effect of applied stress on exfoliation behavior in 3D. Contrary to 2D measurements made at the surface which suggest non-uniform crack growth rates, three dimensional measurements of the crack length led to a much more accurate measurement of crack growth rates.
The objective of this research is to develop robust, accurate, and adaptive algorithms in the framework of the extended finite element method (XFEM) for fracture analysis of highly heterogeneous materials with complex internal geometries. A key contribution of this work is the creation of novel methods designed to automate the incorporation of high-resolution data, e.g. from X-ray tomography, that can be used to better interpret the enormous volume of data generated in modern in-situ experimental testing. Thus new algorithms were developed for automating analysis of complex microstructures characterized by segmented tomographic images.
A centrality-based geometry segmentation algorithm was developed to accurately identify discrete inclusions and particles in composite materials where limitations in imaging resolution leads to spurious connections between particles in close contact.To allow for this algorithm to successfully segment geometry independently of particle size and shape, a relative centrality metric was defined to allow for a threshold centrality criterion for removal of voxels that spuriously connect distinct geometries.
To automate incorporation of microstructural information from high-resolution images, two methods were developed that initialize signed distance fields on adaptively-refined finite element meshes. The first method utilizes a level set evolution equation that is directly solved on the finite element mesh through Galerkins method. The evolution equation is formulated to produce a signed distance field that matches geometry defined by a set of voxels segmented from tomographic images. The method achieves optimal convergence for the order of elements used. In a second approach, the fast marching method is employed to initialize a distance field on a uniform grid which is then projected by least squares onto a finite element mesh. This latter approach is shown to be superior in speed and accuracy.
Lastly, extended finite element method simulations are performed for the analysis of particle fracture in metal matrix composites with realistic particle geometries initialized from X-ray tomographic data. In the simulations, particles fracture probabilistically through a Weibull strength distribution. The model is verified through comparisons with the experimentally-measured stress-strain response of the material as well as analysis of the fracture. Further, simulations are then performed to analyze the effect of mesh sensitivity, the effect of fracture of particles on their neighbors, and the role of a particles shape on its fracture probability.
Nanolaminate composite materials consist of alternating layers of materials at the nanoscale (≤100 nm). Due to the nanometer scale thickness of their layers, these materials display unique and tailorable properties. This enables us to alter both mechanical attributes such as strength and wear properties, as well as functional characteristics such as biocompatibility, optical, and electronic properties. This dissertation focuses on understanding the mechanical behavior of the Al-SiC system. From a practical perspective, these materials exhibit a combination of high toughness and strength which is attractive for many applications. Scientifically, these materials are interesting due to the large elastic modulus mismatch between the layers. This, paired with the small layer thickness, allows a unique opportunity for scientists to study the plastic deformation of metals under extreme amounts of constraint.
Previous studies are limited in scope and a more diverse range of mechanical characterization is required to understand both the advantages and limitations of these materials. One of the major challenges with testing these materials is that they are only able to be made in thicknesses on the order of micrometers so the testing methods are limited to small volume techniques. This work makes use of both microscale testing techniques from the literature as well as novel methodologies. Using these techniques we are able to gain insight into aspects of the material’s mechanical behavior such as the effects of layer orientation, flaw dependent fracture, tension-compression asymmetry, fracture toughness as a function of layer thickness, and shear behavior as a function of layer thickness.
Electromigration (EM) has been a serious reliability concern in microelectronics packaging for close to half a century now. Whenever the challenges of EM are overcome newer complications arise such as the demand for better performance due to increased miniaturization of semiconductor devices or the problems faced due to undesirable properties of lead-free solders. The motivation for the work is that there exists no fully computational modeling study on EM damage in lead-free solders (and also in lead-based solders). Modeling techniques such as one developed here can give new insights on effects of different grain features and offer high flexibility in varying parameters and study the corresponding effects. In this work, a new computational approach has been developed to study void nucleation and initial void growth in solders due to metal atom diffusion. It involves the creation of a 3D stochastic mesoscale model of the microstructure of a polycrystalline Tin structure. The next step was to identify regions of current crowding or ‘hot-spots’. This was done through solving a finite difference scheme on top of the 3D structure. The nucleation of voids due to atomic diffusion from the regions of current crowding was modeled by diffusion from the identified hot-spot through a rejection free kinetic Monte-Carlo scheme. This resulted in the net movement of atoms from the cathode to the anode. The above steps of identifying the hotspot and diffusing the atoms at the hot-spot were repeated and this lead to the initial growth of the void. This procedure was studied varying different grain parameters. In the future, the goal is to explore the effect of more grain parameters and consider other mechanisms of failure such as the formation of intermetallic compounds due to interstitial diffusion and dissolution of underbump metallurgy.
Sn and Al alloys are widely used in various industries. Environmental-induced damage resulting in whiskering in Sn and corrosion in Al account for numerous failures globally every year. Therefore, for designing materials that can better withstand these failures, a comprehensive study on the characterization of the damage is necessary. This research implements advanced characterization techniques to study the above-mentioned environmental-induced damage in Sn and Al alloys.
Tin based films are known to be susceptible to whisker growth resulting in numerous failures. While the mechanisms and factors affecting whisker growth have been studied extensively, not much has been reported on the mechanical properties of tin whiskers themselves. This study focuses on the tensile behavior of tin whiskers. Tensile tests of whiskers were conducted in situ a dual beam focused ion beam (FIB) with a scanning electron microscope (SEM) using a micro electro-mechanical system (MEMS) tensile testing stage. The deformation mechanisms of whiskers were analyzed using transmission electron microscopy (TEM).
Due to the heterogenous nature of the microstructure of Al 7075, it is susceptible to corrosion forming corrosion products and pits. These can be sites for cracks nucleation and propagation resulting in stress corrosion cracking (SCC). Therefore, complete understanding of the corrosion damaged region and its effect on the strength of the alloy is necessary. Several studies have been performed to visualize pits and understand their effect on the mechanical performance of Al alloys using two-dimensional (2D) approaches which are often inadequate. To get a thorough understanding of the pits, it is necessary for three-dimensional (3D) studies. In this study, Al 7075 alloys were corroded in 3.5 wt.% NaCl solution and X-ray tomography was used to obtain the 3D microstructure of pits enabling the quantification of their dimensions accurately. Furthermore, microstructure and mechanical property correlations helped in a better understanding of the effect of corrosion. Apart from the pits, a surface corrosion layer also forms on Al. A subsurface damage layer has also been identified that forms due to the aggressive nature of NaCl. Energy dispersive X-ray spectroscopy (EDX) and nanoindentation helped in identifying this region and understanding the variation in properties.