scholarly journals Unified geometric formulation of material uniformity and evolution

2016 ◽  
Vol 4 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Marcelo Epstein ◽  
Manuel de León
Keyword(s):  
Material Uniformity ◽  
Geometric Formulation

scholarly journals Geometric Formulation of BRS and BRS* Transformations in T4 Theory

1984 ◽  
Vol 71 (1) ◽  
pp. 174-182
Author(s):  
H. Kikukawa ◽  
J. Kikukawa
Keyword(s):  
Geometric Formulation

A New Stress-Intensity Factor Solution for an External Surface Crack in Spheres

2021 ◽  
Author(s):  
James C. Sobotka ◽  
Yi-Der Lee ◽  
Joseph W. Cardinal ◽  
R. Craig McClung
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Crack Front ◽  
Surface Crack ◽  
Degrees Of Freedom ◽  
External Surface ◽  
Crack Plane ◽  
Finite Element Analyses ◽  
Stress Variations ◽  
Geometric Formulation

Abstract This paper describes a new stress-intensity factor (SIF) solution for an external surface crack in a sphere that expands capabilities previously available for this common pressure vessel geometry. The SIF solution employs the weight function (WF) methodology that enables rapid calculations of SIF values. The WF methodology determines SIF values from the nonlinear stress variations computed for the uncracked geometry, e.g., from service stresses and/or residual stresses. The current approach supports two degrees of freedom that denote the two crack tips located normal to the surface and the surface of the sphere. The geometric formulation of this solution enforces an elliptical crack front, maintains normality of the crack front with the free surface, and supports two degrees of freedom for fatigue crack growth from an internal crack tip and a surface crack tip. The new SIF solution accommodates spherical geometries with an exterior diameter greater than or equal to four times the thickness. This WF SIF solution has been combined with stress variations common for spherical pressure vessels: uniform internal pressure on the interior surface, uniform tension on the crack plane, and uniform bending on the crack plane. This paper provides a complete overview of this solution. We present for the first time the geometric formulation of the crack front that enables the new functionality and set the geometric limits of the solution, e.g., the maximum size and shape of the crack front. The paper discusses the bivariant WF formulation used to define the SIF solution and details the finite element analyses employed to calibrate terms in the WF formulation. A summary of preliminary verification efforts demonstrates the credibility of this solution against independent results from finite element analyses. We also compare results of this new solution against independent SIFs computed by finite element analyses, legacy SIF solutions, API 579, and FITNET. These comparisons indicate that the new WF solution compares favorably with results from finite element analyses. This paper summarizes ongoing efforts to improve and extend this solution, including formal verification and development of an internal surface crack model. Finally, we discuss the capabilities of this solution’s implementation in NASGRO® v10.0.

scholarly journals The one-loop tadpole in the geoSMEFT

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Power Counting ◽  
Leading Order ◽  
The Standard Model ◽  
The One ◽  
Near Future ◽  
Geometric Formulation

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

Use of Wafer Applied Underfill for 3D Stacking

2011 ◽  
Vol 2011 (1) ◽  
pp. 000008-000016 ◽  
Author(s):  
Antonio La Manna ◽  
K. J. Rebibis ◽  
C. Gerets ◽  
E. Beyne
Keyword(s):  
Flip Chip ◽  
Solder Bump ◽  
Initial Assessment ◽  
Test Vehicle ◽  
Differential Movement ◽  
The Right ◽  
3D Stacking ◽  
Material Uniformity ◽  
Work Done

A key element for improving 3D stacking reliability is the choice of the right Underfill materials. The Underfill is a specialized adhesive that has the main purposes of locking top and bottom dies; it must fill the gap between bumps and between dies, while reducing the differential movement that would occur during thermal cycling. Traditional underfill processes are based on local dispensing after solder bump reflow (Capillary dispensing), or before flip chip operation with no need of reflow (No Flow Underfill, NUF). In case of 3D stacking, such processes present some limitations: need of a dispensing area (die size increase); material flowing (spacing between dies) and cost (low throughput). After an introduction on typical underfill applications like die-to-package and die-die assembly, we report the work done to assess the properties of several Wafer Applied Underfill (WAUF) materials and their integration in 3D stacking. These materials have been initially applied on silicon wafers in order to assess the minimum achievable thickness and the material uniformity. The wafers have been coated by using different methods: spin coating and film lamination. After this initial assessment, the most promising materials have been used for 3D stacking. The test vehicle used has Cu/Sn μbumps with a pitch of 40μm. The quality of the materials is judged by electrical test, SAM (Surface Acoustic Microscope) and X-SEM (Scanning Electron Microscope).

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