Theses and Dissertations from UMD
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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.Item Probabilistic Models for Creep-Fatigue in a Steel Alloy(2013) Ibisoglu, Fatmagul; Modarres, Mohammad; Reliability Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In high temperature components subjected to long term cyclic operation, simultaneous creep and fatigue damage occur. A new methodology for creep-fatigue life assessment has been adopted without the need to separate creep and fatigue damage or expended life. Probabilistic models, described by hold times in tension and total strain range at temperature, have been derived based on the creep rupture behavior of a steel alloy. These models have been validated with the observed creep-fatigue life of the material with a scatter band close to a factor of 2. Uncertainties of the creep-fatigue model parameters have been estimated with WinBUGS which is an open source Bayesian analysis software tool that uses Markov Chain Monte Carlo method to fit statistical models. Secondly, creep deformation in stress relaxation data has been analyzed. Well performing creep equations have been validated with the observed data. The creep model with the highest goodness of fit among the validated models has been used to estimate probability of exceedance at 0.6% strain level for the steel alloy.Item CLASSIFICATION AND PROBABILISTIC MODEL DEVELOPMENT FOR CREEP FAILURES OF STRUCTURES: STUDY OF X-70 CARBON STEEL AND 7075-T6 ALUMINUM ALLOYS(2011) Nuhi Faridani, Mohammad; Modarres, Mohammad; Reliability Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Creep and creep-corrosion, which are the most important degradation mechanisms in structures such as piping used in the nuclear, chemical and petroleum industries, have been studied. Sixty two creep equations have been identified, and further classified into two simple groups of power law and exponential models. Then, a probabilistic model has been developed and compared with the mostly used and acceptable models from phenomenological and statistical points of view. This model is based on a power law approach for the primary creep part and a combination of power law and exponential approach for the secondary and tertiary part of the creep curve. This model captures the whole creep curve appropriately, with only two major parameters, represented by probability density functions. Moreover, the stress and temperature dependencies of the model have been calculated. Based on the Bayesian inference, the uncertainties of its parameters have been estimated by WinBUGS program. Linear temperature and stress dependency of exponent parameters are presented for the first time. The probabilistic model has been validated by experimental data taken from Al-7075-T6 and X-70 carbon steel samples. Experimental chambers for corrosion, creep-corrosion, corrosion-fatigue, stress-corrosion cracking (SCC) together with a high temperature (1200 0C) furnace for creep and creep-corrosion furnace have been designed, and fabricated. Practical applications of the empirical model used to estimate the activation energy of creep process, the remaining life of a super-heater tube, as well as the probability of exceedance of failures at 0.04% strain level for X-70 carbon steel.Item The Effect of Phase Constitution and Morphology on Room Temperature Deformation Behavior of Binary Titanium Alloys(2011) Wyatt, Zane W.; Ankem, Sreeramamurthy; Material Science and Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Currently, titanium alloys are used in a variety of applications, including defense, aerospace, biomedicine, and even common consumer products such as bicycles and golf clubs. In many applications such as the landing gear of aircraft and geothermal energy production, titanium components may be subjected to stresses for extended periods of time. It has long been known that single-phase α (HCP), single-phase β (BCC), and two-phase α + β Ti alloys can creep at low temperatures (<0.25Tm). For this reason, creep is an important factor to consider when designing titanium alloys for various applications. The first part of this investigation is concerned with single-phase α-Ti alloys. It was found that the twin size (lamellar thickness) decreases with an increase in strain rate. This behavior is unexpected based on the classical understanding of instantaneous twinning. This investigation was able to for the first time demonstrate a time-dependent twinning phenomenon during high strain rate tensile deformation. The second part of this investigation is concerned with experimentally and theoretically studying low-temperature creep deformation behavior of two-phase α + β Ti alloys. Deformation mechanisms were seen in two-phase α + β Ti alloys that are not present during creep of the respective single-phase alloys with compositions equivalent to the individual phases. To investigate the possible interphase interaction stresses, 3D anisotropic Finite element modeling (FEM) was used. These simulations revealed that due to the Burgers orientation relationship between the two phases, deformation such as slip or twinning in the α phase can create very high additional shear stresses on different slip systems in the β phase. This work also revealed that the interfacial stresses that develop between the two phases during elastic deformation will often be much greater than the applied stress. These results were used to help explain the additional deformation mechanisms seen in two-phase alloys that are not seen in the respective single-phase alloys during creep. This work was supported by the National Science Foundation under Grant Number DMR-0906994.Item Investigation of Low Temperature Creep Deformation Behavior of a Metastable Beta Titanium-14.8Wt%Vanadium Alloy(2004-07-13) Hudson, Candi Monica; Ankem, Sreeramamurthy; Material Science and Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation presents the results of investigated low temperature creep behavior of a metastable beta phase Ti-14.8Weight%V alloy (Ti-14.8V). It is the first such study which relates the activation energy and microstructure with low temperature creep deformation mechanisms in the temperature range of 298K to 800K. A Ti-14.8V alloy with a grain size of 350 m was tensile and creep tested in the temperature range of 298 - 458 K; creep tests were conducted at 95% of the 0.2% yield stress. Activation energies were determined by utilizing strain rate models and resulting least squared Arrhenius plots, which were found to be in the range of 36.6-112.42 kJ/mole for the measured temperature range of 298 - 458K. The resulting activation energies plotted as a function of strain was found to be linear dependent. The determined activation energy values of 36.6 57.55 kJ/mole at the low end of the strain are within the range of activation energy values for dislocation motion. The higher activation energy value of 112.42 kJ/mole is within range of for activation energy value for diffusion of oxygen in beta titanium alloy. These activation energy values are consistent with SEM and TEM observations of deformation mechanisms as dislocations, slip, and stress induced plates (SIP) in the form of twinning were the dominant creep deformation mechanisms for this alloy. The deformation mechanisms changed from predominantly slip to SIP in the form of twins at the higher test temperatures. Further, these findings are consistent with observations, characterization by TEM analysis identified slip dislocations of the 1/2<111> type and twins of the {332}<113> type, which are consistent with time dependent twinning deformation. The results strongly support the mechanism of oxygen controlled time dependent twinning deformation as proposed earlier.