Stress analysis of 3-dimensional IC package as function of structural design parameters

Solid Liquid Inter-Diffusion (SLID) is a technology that has recently been utilized to fabricate 3D ICs. Since application of this technology is in its infancy stages, manufacturability and reliability of these bonds are still under heavy investigations. This study presents an elastic-plastic finite element and analytical analyses that were implemented to evaluate effect of package design parameters on thermo-mechanical reliability of the SLID bonds and copper interconnects. A numerical experiment is designed in which several design parameters; die thickness, bond size, underfill stiffness and substrate thickness, are varied in 3 levels. Stress in SLID bonds and in copper interconnects were evaluated using the 3-dimensional finite element analysis as well as an analytical approach. The results show that die and substrate thicknesses are the most influential factors among the selected parameters on stress at the interface and on copper interconnects. Main effect results for stress analysis in SLID bonds using finite element shows that die thickness and underfill stiffness are the most influential factors in defining stress at SLID bonds. Results of the analytical approach confirm the finite element analysis. It is shown that effect of interconnect size and pitch is very small compared to die thickness. In average increasing die thickness increases both shear and peeling stresses at the interfaces and copper interconnects.     

Extension of the non-uniform warping theory to an orthotropic composite beam

This Note proposes an extension to composite section of the non-uniform (out-of-plane) warping beam theory recently established for homogeneous and isotropic beam by R. El Fatmi (C. R. Mecanique 335 (2007) 467–474). For the present work, which constitutes a first step of this extension, the cross-section is assumed to be symmetric and made by orthotropic materials; however, Poisson's effects (called here in-plane warping) are also taken into account. Closed form results are given for the structural behavior of the composite beam and for the expressions of the 3D stresses; these ones, easy to compare with 3D Saint Venant stresses, make clear the additional contribution of the new internal forces induced by the non-uniformity of the (in and out) warpings. As first numerical applications, results on torsion and shear-bending of a cantilever sandwich beam are presented.     

Contact separation and failure analysis of a rotating thermo-elastoplastic shrink-fit assembly

Gas turbine propulsion and aircraft engines involve a great number of rotating shrink-fit assemblies. In presence of high-speed rotations and thermal effects, the reliability of such components with respect to contact separation and failure occurrences needs to be analyzed in the very early design of those structures. In particular, engineers and designers are to prescribe an adequate shrink interference to ensure a structural safe life for a given range of operating conditions. This paper is devoted to the determination of those critical contact and plastic states. To that end, a thermo-elastic–plastic analytical model of a rotating shrink-fit assembly is studied. The stress distributions and contact/plasticity/failure conditions are then derived analytically. In the last part, the determination of the safe operating domain and optimum shrink interference is illustrated through a numerical example.     

The effects of the rock bridge ligament angle and the confinement on crack coalescence in rock bridges: An experimental study and discrete element method

The present article investigates the influences of the rock bridge ligament angle, β, and the confinement on crack coalescence patterns by conducting laboratory and numerical tests on rock-like specimens. Laboratory tests show that no coalescence in the rock bridge occurred for low β. With an increase of β, tensile-shear coalescence and tensile coalescences subsequently occurred. In addition, the increase in the confinement first promoted shear coalescence and then restrained crack coalescence for low β, whereas the tensile coalescence was restrained by the increase in confinement for high β. The numerical results corroborate the laboratory tests in the coalescence patterns. In addition, the numerical study shows that tensile and shear cracks subsequently initiated near crack tips because of the concentrated tensile and shear stresses, respectively. Regarding the influence of β on crack coalescence, tensile or shear stress failed to concentrate in rock bridges for low β. Therefore, the cracks failed to coalesce, whereas with the increase in β, tensile and shear stress concentrations occurred in the bridge and led to either tensile shear or tensile coalescence. Regarding the influence of confinement on crack coalescence, the increase in confinement restrained the tensile stress concentrations and further hindered tensile crack coalescence in rock bridges for high values of β.     

Two-dimensional Raman Imaging Analysis of Microcrystal Diamond Film

Two-dimensional distributions of the impurity carbon (sp²-bonded carbon), crystallinity, and tensile stresses in a(Ⅲ) oriented diamond crystal of a diamond thin film were studied by using Raman imaging microscopy. The amount of the impurity carbon was more in the center of (Ⅲ) plane than in the circumference of the plane. The crystallinity and tensile stress were also higher in the center than in the circumference. Based on those two-dimesional distributions, we discuss the boundary structure between diamond carbon and sp²-bonded carbon in CVD diamond.     

Linear wave-induced dynamic structural stress analysis of a 2D semi-flexible closed fish cage

Closed fish cages in the sea are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A closed fish cage can be compared to a floating tank structure with an internal free surface. Several types of closed cages have been suggested, and they are categorised according to structural properties as flexible membrane structures (fabric), semi-flexible structures (glass fibre) and rigid structures (steel or concrete). To be able to develop safe and reliable structures, more knowledge is required on the seakeeping behaviour of closed cages in waves and the structural response to the wave loads. This paper builds on a theory presented in Strand and Faltinsen (2019) on the linear wave loads on a 2D closed flexible fish cage. A modelling error has been found in Strand and Faltinsen (2019), however, all the main conclusions are in hold. The error has been corrected in the model in the present paper. The present paper extends the model to include bending in the structural model to be able to handle semi-flexible structures where bending stiffness is significant. In this paper, the linear theory of a 2D semi-flexible closed fish cage in waves is developed and analysed to investigate the structural response of the semi-flexible closed cage in waves. We have compared a quasi-static analysis with a fully coupled hydroelastic analysis to investigate if it is a valid and conservative assumption to assume that the stresses in the structure can be assumed quasi-static. If a hydroelastic analysis is necessary or not, is dependent on the stiffness of the structure. We have investigated what happens with the stress in the curved beam part of the closed fish cage for increasing and decreasing stiffness relative to a reference composite structure. One stiffer and two softer cases have been analysed. One major concern for the structural stresses in a closed cage is the effect of sloshing. Sloshing is internal wave motion inside the cage and have multiple resonance periods. The results indicate that to use the quasi-static assumption in structural stress calculation is conservative within the given frequency range for all examined stiffnesses and frequencies, except the frequencies very close to the second sloshing frequency. Close to the second sloshing frequency for all the examined stiffnesses, a localised peak can be observed in the coupled hydroelastic results. The second sloshing frequency is a frequency connected to a symmetric sloshing mode. Rigid body motion is not affected at the symmetric sloshing frequency for an assumed rigid structure, and are therefore also not visible in the stress results from the quasi-static analysis. The structural stress in irregular sea was calculated. These results show no indication of increased stress close to the second sloshing frequency. However, this is not a surprising result since the stress peak is very localised in frequency, and the accumulated effect on the stress standard deviation is therefore small.     

Stress intensity factors for ring-shaped crack surrounded by spherical inclusions

Interaction of a ring-shaped crack with inhomogeneities such as inclusions is analyzed for the resulting three-dimensional stress field. Considered for the composite solid with a given volume fraction of inclusions are the two cases of (a) spherical voids and (b) spherical inclusions with elastic moduli different from the matrix. A ring-shaped crack is initiated at the equator of one of the voids or inclusions. A three-phase model is used to examine the interaction between the crack and surrounding inhomogeneities. Finite element method is then applied to calculate the stress intensity factor for different configurations. The effects of volume fraction of inhomogeneities, relative size of crack to inclusions, and material constants on crack behavior are discussed.     

复杂工况下光学元件变形及应力的有限元研究

航天及其它特殊领域的工作环境,会使光学元件的形状及内部应力发生变化,进而对其光学特性产生明显的影响.本文运用有限元法,在考虑大加速度引起的惯性载荷的影响的同时,对不同环境温度下元件形状及内部应力的变化亦作了初步的研究.     

Application of stereo vision to the study of mixed-mode crack-tip deformations

A stereo vision is applied to evaluate crack-tip parameters for fracture specimens subjected to a mixed-mode loading (tension and shear). By using a special loading device, the applied remote loading is oriented at an angle with respect to the axis of the crack. At each loading angle, the calibrated vision system was rotated so that the axis of the crack is parallel to the horizontal or vertical axis of the image frame. At a load close to the crack initiation, the displacement field around the crack-tip region of the fracture specimen was measured relative to a specimen coordinate system located at the crack tip of the fracture specimen. During the experiment, the fracture specimen was subjected to rigid body translation and rotation. Hence, the displacement fields are affected by the rigid body translation and rotation. Using the experimentally determined displacements and the analytically determined displacements with several higher order terms being included, the stress intensity factors and the amount of rigid body translation and rotation were calculated through a least-squares fit. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. Experimental results indicate that a K_I and K_II dominant region is observed in the corrected displacement fields.