125 research outputs found

    Analysis of stress partitioning in biphasic mixtures based on a variational purely-macroscopic theory of compressible porous media: recovery of Terzaghi’s law

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    The mechanics of stress partitioning in two-phase porous media is predicted on the basis of a variational purely-macroscopic theory of porous media (VMTPM) with compressible constituents. Attention is focused on applications in which undrained flow (UF) conditions are relevant, e.g., consolidation of clay soils and fast deformations in cartilagineous tissues. In a study of the linearized version of VMTPM we have recently shown that, as UF conditions are approached (low permeability or fast loading), Terzaghi’s effective stress law holds as a general property of rational continuum mechanics and is recovered as the characteristic stress partitioning law that a biphasic medium naturally complies with. The proof of this property is obtained under minimal constitutive hypotheses and no assumptions on internal microstructural features of a particular class of material. VMTPM predicts that such property is unrelated to compressibility moduli of phases and admits no deviations from Terzaghi’s expression of effective stress, in contrast with most of the currently available poroelastic theoretical frameworks. This result is presently illustrated and discussed. Simulations of compressive consolidation tests are also presented; they are obtained via a combined analytical-numerical integration technique, based on the employment of Laplace transforms inverted numerically via de Hoog et al.’s algorithm. The computed solutions consistently describe a transition from drained to undrained flow which confirms that Terzaghi’s law is recovered as the limit UF condition is approached and indicate a complex mechanical behavior

    An Empirical Model for Estimating the Probability of Electrical Short Circuits from Tin Whiskers

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    In this experiment, an empirical model to quantify the probability of occurrence of an electrical short circuit from tin whiskers as a function of voltage was developed. This empirical model can be used to improve existing risk simulation models. FIB and TEM images of a tin whisker confirm the rare polycrystalline structure on one of the three whiskers studied. FIB cross-section of the card guides verified that the tin finish was bright tin

    Tin Whisker Electrical Short Circuit Characteristics Part 2

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    Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that has a currently unknown probability associated with it. Due to contact resistance electrical shorts may not occur at lower voltage levels. In this experiment, we study the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From this data we can estimate the probability of an electrical short, as a function of voltage, given that a free tin whisker has bridged two adjacent exposed electrical conductors. In addition, three tin whiskers grown from the same Space Shuttle Orbiter card guide used in the aforementioned experiment were cross-sectioned and studied using a focused ion beam (FIB)

    An Empirical Model for Estimating the Probability of Electrical Short Circuits from Tin Whiskers-Part I

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    Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that has a currently unknown probability associated with it. Due to contact resistance, electrical shorts may not occur at lower voltage levels. In this experiment, we study the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From this data, we can estimate the probability of an electrical short, as a function of voltage, given that a free tin whisker has bridged two adjacent exposed electrical conductors. In addition, three tin whiskers grown from the same Space Shuttle Orbiter card guide used in the aforementioned experiment were cross sectioned and studied using a focused ion beam (FIB)

    Estimating the Probability of Electrical Short Circuits from Tin Whiskers

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    To comply with lead-free legislation, many manufacturers have converted from tin-lead to pure tin finishes of electronic components. However, pure tin finishes have a greater propensity to grow tin whiskers than tin-lead finishes. Since tin whiskers present an electrical short circuit hazard in electronic components, simulations have been developed to quantify the risk of said short circuits occurring. Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that had an unknown probability associated with it. Note however that due to contact resistance electrical shorts may not occur at lower voltage levels. In our first article we developed an empirical probability model for tin whisker shorting. In this paper, we develop a more comprehensive empirical model using a refined experiment with a larger sample size, in which we studied the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From the resulting data we estimated the probability distribution of an electrical short, as a function of voltage. In addition, the unexpected polycrystalline structure seen in the focused ion beam (FIB) cross section in the first experiment was confirmed in this experiment using transmission electron microscopy (TEM). The FIB was also used to cross section two card guides to facilitate the measurement of the grain size of each card guide's tin plating to determine its finish

    Developing an Empirical Model for Estimating the Probability of Electrical Short Circuits from Tin Whiskers

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    To comply with lead-free legislation, many manufacturers have converted from tin-lead to pure tin finishes of electronic components. However, pure tin finishes have a greater propensity to grow tin whiskers than tin-lead finishes. Since tin whiskers present an electrical short circuit hazard in electronic components, simulations have been developed to quantify the risk of said short circuits occurring. Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that had an unknown probability associated with it. Note however that due to contact resistance electrical shorts may not occur at lower voltage levels. In our first article we developed an empirical probability model for tin whisker shorting. In this paper, we develop a more comprehensive empirical model using a refined experiment with a larger sample size, in which we studied the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From the resulting data we estimated the probability distribution of an electrical short, as a function of voltage. In addition, the unexpected polycrystalline structure seen in the focused ion beam (FIB) cross section in the first experiment was confirmed in this experiment using transmission electron microscopy (TEM). The FIB was also used to cross section two card guides to facilitate the measurement of the grain size of each card guide's tin plating to determine its finish

    Tin Whisker Electrical Short Circuit Characteristics

    Get PDF
    Existing risk simulations make the assumption that when a free tin whisker has bridged two adjacent exposed electrical conductors, the result is an electrical short circuit. This conservative assumption is made because shorting is a random event that has an unknown probability associated with it. Note however that due to contact resistance electrical shorts may not occur at lower voltage levels. In our first article we developed an empirical probability model for tin whisker shorting. In this paper, we develop a more comprehensive empirical model using a refined experiment with a larger sample size, in which we studied the effect of varying voltage on the breakdown of the contact resistance which leads to a short circuit. From the resulting data we estimated the probability distribution of an electrical short, as a function of voltage. In addition, the unexpected polycrystalline structure seen in the focused ion beam (FIB) cross section in the first experiment was confirmed in this experiment using transmission electron microscopy (TEM). The FIB was also used to cross section two card guides to facilitate the measurement of the grain size of each card guide's tin plating to determine its finish
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