<p dir="ltr">Non-Newtonian fluid models such as the Bingham and Herschel-Bulkley models are used to characterize the flow behavior of many complex fluids and soft solids. The three parameter Herschel-Bulkley model captures the yield stress behavior and the nonlinear power law behavior. In this thesis, the semi-analytical solution of Herschel-Bulkley fluids provided by Covey and Stanmore is used to experimentally characterize the squeeze flow behavior. A ‘Squeeze Flow and Thermal Resistance Tester’ was custom designed to perform velocity controlled squeeze flow experiments. The tester has an additional capability of performing thermal resistance characterization adhering to the ASTM-D5470 standard. A novel framework is described for characterizing the three Herschel-Bulkley parameters (τy, n and ηHB) using the developed tester. </p><p dir="ltr">Thermal Interface Materials (TIMs) are used to efficiently dissipate heat from a heat generating component to a heat sink in an electronic package. Thermal grease is a type of TIM comprising of a base material (e.g. polymer) loaded with highly conducting filler particles (e.g, boron nitride, alumina or sometimes conducting metals such as aluminum or silver). These greases are expected to exhibit Herschel-Bulkley flow behavior. Hence, thermal greases are used as candidate materials for squeeze flow characterization. In addition to the flow characterization, the thermal resistance across these thermal greases are also characterized using the custom designed tester. Characterization of mechanical and thermal behavior of TIMs is crucial to predicting their long-term reliability. </p><p dir="ltr">The effect of in-situ isothermal baking duration and test temperature on flow behavior is studied. The increase in duration of isothermal baking at test temperature of 55◦C showed that the material tends to stiffen with baking duration. The increase in test temperature from 5◦C to 100◦C resulted in a decrease in the power law index n and viscosity ηHB. </p><p dir="ltr">Finally, a numerical simulation strategy for performing squeeze flow simulations is described. The characterized flow parameters from the squeeze flow experiments were used as input material parameters for a dynamic mesh-based numerical simulation of squeeze flow between parallel surfaces. The results of the experimental force response and numerical simulation results were compared and found to be in close agreement. In order to simulate flow of thermal greases in a package undergoing deformation, a non-flat test setup was fabricated and squeeze experiments were performed. Numerical simulations were subsequently performed for the non-flat surface using material parameters extracted from previous experiments and the results were compared. The results from both experiments and numerical simulations showed that the force response of thermal greases under non-flat surfaces was significantly higher than the planar case.</p>

<p dir="ltr">Due to advances in 3D integration and miniaturization of chips, the power density and number of hotspots within electronic packages have increased rapidly. A major bottleneck in the chip-to-coolant thermal resistance pathway is the interfacial resistance at solid-solid contacts and, therefore, thermal interface materials (TIMs) are employed to minimize interfacial thermal resistance. To improve heat dissipation, thermal grease (a type of TIM) is generally employed to reduce the overall thermal resistance from a heat-generating component to the heat sink. However, these materials degrade throughout their lifetime and the process is not well understood.</p><p dir="ltr">The first part of this dissertation focuses on investigating the degradation behavior of thermal greases using traditional and accelerated reliability techniques. The performance of a thermal grease often worsens with time due to the thermomechanical cycling driven by the coefficient of thermal expansion mismatch between the substrates via pumpout (material moves out of the interface) and dryout (phase separation of the composite material) phenomena. I isolate the effect of thermal cycling (from mechanical cycling) on the degradation of thermal greases by subjecting them to power cycling while holding the bond line thickness constant. In addition to thermocouples in the system, a high-resolution temperature mapping of the thermal grease is leveraged using an infrared microscope for evaluation of local degradation <i>in situ</i>. The results demonstrate a novel pathway for evaluating thermal grease performance by showcasing the importance of the viscosity-temperature hysteresis. However, traditional reliability testing methods such as thermal cycling have long testing periods, often of the order of days or months. Therefore, to accelerate the degradation analysis of thermal greases, I propose adding mechanical cycling while maintaining a constant heat flow rate. The reliability of thermal greases is investigated at different mechanical oscillation amplitudes and squeezing pressures using a novel custom-designed and machined experimental rig. The results uncover that the mechanical reliability of thermal greases depends on the ratio of elastic modulus to viscosity, with higher ratios being more desirable. Meanwhile, the thermal reliability depends upon the synergy of material properties with higher elastic modulus and higher thermal conductivity, resulting in a lesser increase in thermal resistance over the lifetime of thermal greases. </p><p dir="ltr">The second part of this dissertation focuses on the characterization of the rheology of the thermal greases and the associated uncertainty. Thermal greases have complex rheological properties that impact the performance over their lifetime. I perform rheological experiments on thermal greases and observe both stress relaxation and stress buildup regimes, which are not captured by steady shear-thinning models. Instead, a thixo-elasto-visco-plastic and a nonlinear-elasto-visco-plastic constitutive model characterizes each of the observed regimes. I use the models within a data-driven approach based on physics-informed neural networks (PINNs) to solve the inverse problem of determining the rheological model parameters from the dynamic response in experiments. Further, from a microscopic point of view, these rheological behaviors and associated uncertainties arise from the microstructure rearrangements due to particles' inhomogeneous mixing or separation/settling over time. However, this model calibration approach does not address parameter uncertainty arising due to epistemic (limited rheological data) and aleatoric (randomness of rheological experiments) sources. The last part of this dissertation addresses this limitation and quantifies uncertainties arising in the model calibration process. A hierarchical Bayesian inference methodology is used to obtain distributions of the rheological parameters. The uncertainty is further propagated to shear stress distributions and thermal resistances of thermal grease to demonstrate that the rheological models considered are suitable representations of the experimentally observed regimes. </p><p dir="ltr">Therefore, the current dissertation addresses the thermomechanical degradation behaviors and associated complex rheological characteristics of thermal greases. Understanding the degradation and rheology of thermal greases can help design better thermal greases which are degradation-resistant and hence can improve the reliability of electronic packages.</p>