Mechanical Engineering Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/2795

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SPECTRAL METHODS FOR MODELING AND ESTIMATING VIBRATION FATIGUE DAMAGE IN ELECTRONIC INTERCONNECTS
(2023) Welch, Jacob Adam; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The purpose of this thesis is to explore the accuracy of fatigue damage estimation in printedwiring assembly (PWA) interconnects, using purely frequency-domain (also known as spectral) information such as the power spectral density (PSD) of the input excitation. The test case used in this study is the estimation of fatigue damage accumulation rate in the critical interconnects of low profile quad flat-pack (LQFP) components on a PWA, under broad-band random vibration excitation. this study examines whether the fatigue predictions made with this frequency-domain approach are consistent with those obtained from a direct time-domain approach. The frequency-domain response modeling is achieved using a two-stage global-local modeling process using a finite element model (in ABAQUS©), where the dominant modal participation factors for the dynamic response is obtained using a dynamic global simplified dynamic finite element model consisting of shell elements to represent the entire PWA. The PSD of the input excitation is applied as a boundary condition and the PSD of the PWA strain response is recorded at the base of critical components. The corresponding PSD for the dynamic strain response at critical interconnects is estimated with strain-transfer functions (STFs) for each dominant mode, obtained from detailed 3D quasi-static nonlinear local models of the component, adjacent PWB, and the interconnects. The global-local STF provides a relationship between the level of equivalent strain in the critical interconnects and the flexural strain at the adjacent surface of the PWB. The STF for each of the dominant vibration modes is obtained by imposing the corresponding mode-shape predicted by the dynamic global model on the PWB, in the quasistatic local model, using multi-point constraint equations. The PSD of the equivalent strain in the critical interconnect is then estimated via linear modal superposition. A deterministic estimate of the cyclic fatigue damage accumulation rate in the critical interconnect is then conducted with the Basquin high cycle fatigue (HCF) model and linear damage superposition approach, by using three different spectral approaches for representing the strain severity with estimated probability density functions (PDFs). The three approaches include: (i) Raleigh method; (ii) Dirlik method and (iii) Range distribution function created with the Rainflow cycle counting method. Methods (ii) and (iii) are derived from a pseudo time-history created with an inverse Fourier transform. These frequency-domain results are compared to corresponding fatigue damage estimates from a multi-modal time-domain analysis method, to assess the consistency of the two approaches.
GRAIN-SCALE ANISOTROPIC STUDY OF TENSILE VS. SHEAR MECHANICAL CONSTITUTIVE AND FATIGUE BEHAVIOR IN OLIGOCRYSTALLINE SAC305 SOLDER JOINTS
(2021) Deshpande, Abhishek Nitin; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Solder joints in microelectronic assemblies experience a multiaxial combination of cyclic extensional and shear loads due to combinations of thermal expansion mismatch and flexure of printed circuit assemblies (PCAs) during thermal cycling or during vibrational loading of constrained PCAs. Although, a significant amount of research has been conducted to study cyclic fatigue failures of solder joints under pure-shear loading, most of the current literature on cyclic tensile loading of solders is on long dog-boned monolithic solder coupons. Unfortunately, such coupon specimens do not capture the critical interactions between key micro-scale morphological features (such as grain orientation, grain boundaries, intermetallic compounds [IMCs] and substrates) that are believed to play important roles in the fatigue of functional solder joints under life-cycle loading. Therefore, Part I of this study uses a combination of experiments and finite element analysis to investigate the differences in mechanisms of cyclic fatigue damage in Sn-3.0Ag-0.5Cu (SAC305) few-grained (oligocrystalline) microscale solder joints under shear, tensile and multiaxial loading modes at room temperature. Cyclic fatigue durability test results indicate that tensile loads are more detrimental compared to shear loads. Tensile vs. shear loading modes are found to cause distinctly different combinations of interfacial damage vs. internal damage in the bulk of the solder (transgranular and intergranular damage), which correlates with the differences observed in the resulting fatigue durability. The test results also confirm that this type of multimodal fatigue damage cannot be modeled with the traditional approach of a power-law dependence on the cyclic amplitude of equivalent deviatoric strain. Instead, multiaxial fatigue damage results are seen to be affected not only by the cyclic equivalent strain amplitudes, but also by the severity of the stress-triaxiality, as hypothesized in models such as Chaboche model.Estimating the true deviatoric strains and triaxiality ratios at the failure sites is not a trivial task in typical oligocrystalline SAC305 solder joints, because the strong anisotropy of the individual grains - and the interactions of such grains with surrounding grains as well as with the interfacial boundaries - make the strain field unique in each joint. Thus, the current approach of modeling solder joints as homogenous isotropic structures, are clearly inadequate because they fail to capture the true grain-scale stress fields at the failure sites. The joint-to-joint variation in the grain morphology leads to variability in fatigue damage accumulation rates under cyclic loading. Part II of this study thus focuses on grain-scale study of the fatigue results presented in Part I, by: (a) characterizing multi-scale anisotropic elastic-plastic properties of SAC305 single crystals, using a hybrid combination of experiments and finite element simulation, (b) applying a grain-scale parametric study to explain the variability seen in Part I, in the bimodal fatigue failures under multiaxial cyclic loading. The anisotropic elastic-plastic properties in Part IIa were determined by conducting monotonic tensile and shear tests on SAC305 single crystal specimens. The anisotropic elastic behavior is modeled using anisotropic elastic stiffness constants for SAC305, whereas anisotropic plasticity is modeled using Hill’s potential in conjunction with a Holloman-type power-law plastic constitutive model. Microstructurally motivated scaling factors are empirically developed, to assess the effect of dendritic and eutectic microstructural features on single-crystal stress-strain properties. This facilitates extrapolation of constitutive properties across different cooling rates and different isothermal aging protocols. Additional empirical scaling factors are also developed to account for the influence of characteristic grain sizes and grain aspect ratios (relative to principal loading directions). The parametric study in Part IIb, was conducted using the anisotropic properties of Part IIa, to quantify the effect of grain anisotropy on variability in cyclic mechanical fatigue curves of SAC305 solder. This study demonstrates an efficient computational approach for determining variability in mechanical response and fatigue behavior of Sn-rich solder joints, thereby reducing the time and costs associated with physical testing.
Design and Characterization of Additively Manufactured Lightweight Metal Structures with Equivalent Compliance and Fatigue Resistance
(2021) Santos, Luis S; Bruck, Hugh A; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Additive Manufacturing (AM) has been a disruptive manufacturing technology allowing for control of geometric features and material distributions, potentially starting at the atomistic level, to realize structures with lighter weights. However, it is still begin used primarily as a rapid prototyping tool due to challenges arising from various issues that need to be addressed before commercial parts can be deployed. Three of those issues are: (1) characterization of mechanical properties that may vary spatially, (2) identification of novel defects in the parts, and (3) new design approaches that account for the unique capabilities of AM processes and their impact on fatigue resistance.This dissertation addresses these three issues by developing a cyclical indentation technique to characterize the fatigue properties of geometric features only capable with AM. The method produces the degradation of the material stiffness as the number of cyclic loads increases and is capable of generating an entire S-N curve with a single test at sub-millimeter scales. Geometric features are then analyzed by running a thermal and mechanical simulation of a Direct Metal Laser Sintering (DMLS) printing process. The new simulation can account for buckling of features with high aspect ratios, such as low percentage infills or high levels of unit cell porosity, and predicts distortions with less than 5% error. This computational approach is useful for analyzing parts before printing and informs designers about regions in the part that may need modification to prevent buckling. Finally, the experimental and computational techniques are combined to design structures with macroscale topological features and microscale unit cell features that are fatigue resistant.
PARAMETRIC DESIGN AND EXPERIMENTAL VALIDATION OF CONJUGATE STRESS SENSORS FOR STRUCTURAL HEALTH MONITORING
(2021) Kordell, Jonathan; Dasgupta, Abhijit; Yu, Miao; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
In this dissertation, conjugate stress (CS) sensing is advanced through a parametric evaluation of a surface-mounted design and through experimental validation in monotonic and cyclic tensile tests. The CS sensing concept uses a pair of sensors of significantly different mechanical stiffness for direct query of the instantaneous local stress-strain relationship in the host structure, thus offering measurement of important health indicators such as stiffness (modulus), yield strength, strain hardening, and cyclic hysteresis. In this study, surface-mounted CS sensor designs are parametrically evaluated with finite element modeling, with respect to the sensors’ location, thickness, and modulus and the external loading state. An analytic pin-force model is developed to infer the host structure’s stress-strain state, based on the strain outputs of the CS sensor-pair. Two CS sensor designs are fabricated – one employs resistive foil strain gauges and the second employs fiber optic sensors – and paired with the pin-force model for experimental demonstration of the measurement of: (i) stress-strain history of three different isotropic metal bars (aluminum, copper, and steel) as they experience monotonic tensile loads well into plasticity and (ii) stress-strain hysteresis of a steel bar as it is subject to cyclic tensile fatigue. In the cyclic tests, two machine learning algorithms – anomaly detection and neural net classification – are used in conjunction with the estimated host stiffness from the CS sensor and pin force model to predict the onset of damage in the steel beams.
Entropic Approaches for Assessment of Metal Fatigue Damage
(2019) Yun, Huisung; Modarres, Mohammad; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Prognostics and Health Management (PHM), a promising technique assessing individual life of engineering systems, requires metrics that indicate the current level of degradation and aging. However, traditional methods of fatigue life estimation have a restriction to apply to PHM due to scale dependency of measurements. An alternative to the conventional fatigue assessment is the entropic approach, initially de-rived from the second law of thermodynamics. The entropic approach is scale-independent and able to monitor degradation and aging from the early periods of life. The entropic endurance indicates a certain level of damage that a component can tolerate before failure. Not only the thermodynamic theory but also information and statistical mechanics laws introducing entropy apply to the various modes of energy dissipations. This dissertation introduces the extension of the entropic approaches as the representation of damage by empirically examining the theoretical basis of three en-tropic theorems. Metallic coupons were fatigue tested to confirm the applicability of three entropic measures: irreversible thermodynamic entropy, information (Shannon) entropy, and Jeffreys divergence, by measuring variables used to compute energy dissipations during fatigue. In addition to the entropic approaches to damage, short-term loading process (STLP) is designed to minimize the difficulties associated with acoustic emission background noise when used to measure information entropy of the generated signals. Without damaging the material, high-frequency/low-amplitude loading is expected to generate acoustic signals through quiet background noise excitation loading to infer the current damage status. The results of this research help identifying multiple damage measurement methods and will broaden understanding and selecting practical applications, and reduce the prognosis uncertainty in PHM applications.
Evaluation of Information Entropy from Acoustic Emission Waveforms as a Fatigue Damage Metric for Al7075-T6
(2016) Sauerbrunn, Christine Marie; Modarres, Mohammad; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Information entropy measured from acoustic emission (AE) waveforms is shown to be an indicator of fatigue damage in a high-strength aluminum alloy. Several tension-tension fatigue experiments were performed with dogbone samples of aluminum alloy, Al7075-T6, a commonly used material in aerospace structures. Unlike previous studies in which fatigue damage is simply measured based on visible crack growth, this work investigated fatigue damage prior to crack initiation through the use of instantaneous elastic modulus degradation. Three methods of measuring the AE information entropy, regarded as a direct measure of microstructural disorder, are proposed and compared with traditional damage-related AE features. Results show that one of the three entropy measurement methods appears to better assess damage than the traditional AE features, while the other two entropies have unique trends that can differentiate between small and large cracks.
Response and Durability of Large Radius of Gyration Structures Subjected to Biaxial Vibration
(2013) Ernst, Matthew Ross; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Multiaxial vibration tests were conducted using an electrodynamic shaker capable of controlled vibration in six degrees of freedom. The test specimen consisted of six large inductors insertion mounted on a printed wiring board. Average damage accumulation rate was measured for random excitation in-plane, out-of-plane, and both directions simultaneously. Under simultaneous biaxial excitation, the damage rate was found to be 2.2 times larger than the sum of the in-plane and out-of-plane rates. The conclusion was that multiple-step single-degree-of-freedom testing can significantly overestimate the durability of some structures in a multiaxial environment. To examine the mechanics behind this phenomenon, the response of a simple rod structure was analyzed with the finite element method. Axial vibrations, which produce negligible stress on their own, were found to contribute significant additional stress when combined with transverse vibration. This additional stress contribution was found to be highly dependent on the frequency ratio and phase relationship between the two participating axes.
Fatigue Damage Accumulation Due to Complex Random Vibration Environments: Application to Single-Axis and Multi-Axis Vibration
(2011) Paulus, Mark E.; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
A combination of experiments and modeling are used to address the vibration durability of structures subjected to different random vibration environments. Presented in this work are a set of experimental data comparing the rate of change of the first natural frequency and the measured time to failure, of simple structural members under repetitive shock (RS) vibration, single-axis electrodynamic (ED) vibration and multi-axis ED vibration. It was found that multi-axis testing is more severe than single-axis testing at the same level. In addition the RS system low frequency amplitude is often too weak to efficiently propagate the crack. Smoothing of the input power spectral density (PSD) or poor line resolution was also shown to change the time to failure of a test. A poor correlation was shown between the PSD and the rate of natural frequency change (RFC) over a wide frequency shift. The change in natural frequency caused the initial PSD to be ineffective in determining the total time to failure. A predictive, analytic methodology to quantify the RFC was developed to predict the fatigue life of a structure experiencing random vibration excitation. This method allows the estimation of fatigue life using the frequency domain, where only the input power spectral density, damping factor and structural information are required. The methodology uses linear elastic fracture mechanics for fatigue crack propagation and accounts for the frequency shifting that occurs due to fatigue crack evolution. The analytic model has been shown to compare favorably to both finite element analysis (FEA) and experimental results, for mild-steel cantilever beams. Monte Carlo simulations have been conducted to assess the sensitivity of the model predictions to uncertainties in the input parameters. In addition a semi-empirical model was developed whereby the input PSD and damping factor are measured from life tests, and the resulting time to failure and the acceleration factors between different vibration environments can be determined. The improved modeling methodology developed by this work are of value not only to structural designers who wish to design for dynamic environments, but also to test engineers who wish to qualify products through accelerated life testing, and to vibration engineers who wish to compare the relative severity of different random vibration environments, in terms of their potential to cause fatigue damage accumulation.
HARMONIC AND RANDOM VIBRATION DURABILITY INVESTIGATION FOR SAC305 (Sn3.0Ag0.5Cu) SOLDER JOINT
(2009) Zhou, Yuxun; dasgupta, abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Vibration loading is commonly encountered during the service life of electronic products. However, compared to thermal cycling durability, vibration durability is more complex and has been less investigated. In surface mount technology, solder joints are the primary mechanical, thermal and electrical interconnects between the component and the PWB. So the reliability of solder joints is very crucial for most electronic assemblies. The vibration durability of Pb-free solder joints is the focus of this dissertation. The characteristics of the stress from vibration loading are low amplitude and high frequency, while those from cyclic thermal loading are high amplitude and low frequency. In this study, several exploratory vibration tests were conducted, using both narrow band and broad-band, step-stress excitation at several different isothermal and thermal cycling conditions. The effect of thermal pre-aging on solder joint vibration failures was also investigated. Some of the vibration durability results were analyzed in detail, to obtain quantitative insights into the vibration fatigue behavior of the SAC305 solder material. A time-domain approach was adopted to investigate the durability of solder interconnects under different kinds of vibration and quasi-static mechanical loading. First, the solder interconnects were subjected to narrow-band (harmonic) vibration loading. The test were conducted at the first natural frequency of the test board using constant-amplitude excitation and solder fatigue properties were extracted with the help of a time-domain analysis that is based on quasi-static finite element simulation. Compared to broad-band step-stress vibration durability tests, the advantage of the harmonic constant-amplitude test is less complexity in the model extraction process, hence, less uncertainty in the desired fatigue constants. Generalized strain-based S-N curves have been obtained for both SAC305 and Sn37Pb solder materials. The strain-life model constants show that SAC305 solder material has superior fatigue properties compared to Sn37Pb solder material under low-cycle fatigue loading, while the reverse is true for high-cycle fatigue loading. These results are consistent with test results from other researchers. In actual application, SAC305 assemblies almost always fail before Sn37Pb assemblies under comparable vibration excitation because of (i) higher solder strain at a given excitation level; and (ii) multiple failure modes such as copper trace cracking. Next, durability was investigated under step-stress, broad-band (random) excitation. These test results show that SAC305 interconnects are less durable than Sn37Pb interconnects under the random excitation used in this study, which agrees with the harmonic durability results. The random and harmonic durability results were quantitatively compared with each other in this study. Finite element simulation was used to investigate the stress-strain response in the interconnects. The output of this simulation is the strain transfer function due to the first flexural mode of the PWB. This transfer function is used to obtain the solder strain from the measured board strain. This fatigue assessment method demonstrated that the model constants obtained from the harmonic test overestimate the fatigue life under random excitation by an order of magnitude. The causes for this discrepancy were systematically explored in this study. The effects of cyclic loading and mean stress on the vibration durability were addressed and found to be minimal in this study. The stress-strain curves assumed for the solder material were found to have a very large effect on the durability constants, thus affecting the agreement between harmonic and random durability results. The transient response of the components on the test board under both harmonic and random excitation was also included in the strain transfer function with the help of dynamic implicit simulation, and found to have a much stronger effect on the vibration durability at the high frequencies used in broad-band excitation compared to the low frequency used in narrow-band test. Furthermore, the higher PWB vibration modes may play a strong role and may need to be included in the strain transfer-function. This study clearly reveals that the solder strain analysis for broad-band random excitation cannot be limited to the quasi-static strain transfer-function based on the first PWB flexural mode, that has been used in some earlier studies in the literature. The time-domain approach used in this study provided fundamental and comprehensive insights into the key factors that affect vibration durability under different types of excitation, thus leading to a generalized S-N modeling approach that works for both harmonic and random vibration loading.
Damage Initiation and Evolution in Voided and Unvoided Lead Free Solder Joints Under Cyclic Thermo-Mechanical Loading
(2007-02-05) Jannesari Ladani, Leila; Dasgupta, Abhijit; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The effect of process-induced voids on the durability of Sn-Pb and Pb-free solder interconnects in electronic products is not clearly understood and researchers have reported conflicting findings. Studies have shown that depending on the size and location, voids are not always detrimental to reliability, and in fact, may sometimes even increase the durability of joints. This debate is more intensified in Pb-free solders; since voids are more common in Pb-free joints. Results of experimental studies are presented in this study to empirically explore the influence of voids on the durability of Ball Grid Array (BGA) Pb-free solder joints. In order to quantify the detailed influence of size, location, and volume fraction of voids, extensive modeling is conducted, using a continuum damage model (Energy Partitioning model), rather than the existing approaches, such as fracture mechanics, reported in the literature. The E-P approach is modified in this study by use of a successive initiation method, since depending on their location and size; voids may influence either the time to initiate cyclic fatigue damage or time to propagate fatigue damage, or both. Modeling results show competing interactions between void size and location, that results in a non-monotonic relationship between void size and durability. It also suggests that voids in general are not detrimental to reliability except when a large portion of the damage propagation path is covered with either a large void or with many small voids. In addition, this dissertation also addresses several fundamental issues in solder fatigue damage modeling. One objective is to use experimental data to identify the correct fatigue constants to be used when explicitly modeling fatigue damage propagation in Pb-free solders. Explicit modeling of damage propagation improves modeling accuracy across solder joints of vastly different architectures, since the joint geometry may have a strong influence on the ratio of initiation-life to propagation-life. Most solder fatigue models in the literature do not provide this capability since they predict failure based only on the damage accumulation rates during the first few cycles in the undamaged joint. Another objective is to incorporate into cyclic damage propagation models, the effect of material softening caused by cyclic micro-structural damage accumulation in Pb-free solder materials. In other words the model constants of the solder viscoplastic constitutive model are continuously updated with the help of experimental data, to include this cyclic softening effect as damage accumulates during the damage-propagation phase. The ability to model this damage evolution process increases the accuracy of durability predictions, and is not available in most current solder fatigue models reported in the literature. This mechanism-based microstructural damage evolution model, called the Energy Partitioning Damage Evolution (EPDE) model is developed and implemented in Finite Element Analysis of solder joints with the successive initiation technique and the results are provided here. Experimental results are used as guidance to calibrate the Energy Partitioning fatigue model constants, for use in successive initiation modeling with and without damage evolution. FEA results show 15% difference between the life predicted by averaging technique and successive initiation. This difference could significantly increase in the case of long joints such as thermal pads or die-attach, hence validating the use of successive initiation in these cases. The difference between using successive initiation with and without damage evolution is about 10%. Considering the small amount of effort that has to be made to update the constitutive properties for progressive degradation, it is recommended that softening be included whenever damage propagation needs to be explicitly modeled. However the damage evolution exponents and the corresponding E-P model constants obtained in this study, using successive initiation with damage evolution, are partially dependent on the specimen geometry. Hence, these constants may have to be re-calibrated for other geometries.

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