The Peeling Moment–A Key Rule for Delamination Resistance in I.C. Assemblies

2004 ◽  
Vol 126 (1) ◽  
pp. 106-109 ◽  
Author(s):  
Thomas D. Moore ◽  
John L. Jarvis
Keyword(s):  
Temperature Change ◽  
Beam Theory ◽  
Free Edge ◽  
Uniform Temperature ◽  
Physical Explanation ◽  
Delamination Resistance ◽  
Bimaterial Structure ◽  
The Moment ◽  
New Formula

The peeling stress near the free edge of a bimaterial beam under uniform temperature change creates a moment which causes both layers to have identical curvatures at the interface. A new formula from beam theory is given for this Peeling Moment. A beam with a negative Peeling Moment resists delamination at the free edge. A physical explanation for the moment is developed; the sign of the Peeling Moment is also the determinant of the location of the equivalent centroid of the bimaterial beam. This provides a valuable new rule for designing resistance to thermomechanical delamination of a bimaterial structure.

Effect of Bond Layer on Bimaterial Assembly Subjected to Uniform Temperature Change

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
D. Sujan ◽  
Dereje E. Woldemichael ◽  
M. V. V. Murthy ◽  
K. N. Seetharamu
Keyword(s):  
Temperature Change ◽  
Research Work ◽  
Interfacial Stress ◽  
Thin Plates ◽  
Rational Basis ◽  
Uniform Temperature ◽  
Stress Evaluation ◽  
Numerical Example ◽  
Bond Layer ◽  
Shear Compliance

When two thin plates or layers are bonded together, an extremely thin bond layer of third material exists between the two layers. This research work examines the effect of bond layer on the interfacial shearing and peeling stresses in a bimaterial model. Earlier papers on this topic are based on several mutually contradictory expressions for the shear compliance of the bond layer. This paper is aimed at resolving this ambiguity and presents derivation of shear compliance on a rational basis. A numerical example is carried out for a silicon-copper system with a gold-tin solder bond layer. The results obtained are likely to be useful in interfacial stress evaluation and physical design of bimaterial assemblies used in microelectronics and photonics applications.

Backtracking to Reformulate: Establishing the Bosnian Federation

1996 ◽  
Vol 1 (3) ◽  
pp. 525-545 ◽  
Author(s):  
George Rudman
Keyword(s):  
Side Payments ◽  
The Us ◽  
The Moment ◽  
New Formula

AbstractUpon the failure of the Vance-Owen and Owen-Stoltenberg efforts to devise a formula to deal with the Bosnian problem, the US took over the mediator's role. Instead of coming up with a new formula, it backtracked to parts of earlier proposals and led the parties to a solution based on an exchange of a Croat-Muslim federation in Bosnia for a confederation between that federation and Croatia. This was possible because the moment had become ripe through the development of a perception that continued war was a self-inflicted pain for no chance of unilateral gain, and through the application of side payments of aid and recognition that the mediator could deploy.

scholarly journals Modelling and analysis the effect of unbalanced moment directions on behaviour of edge column-slab connections

2018 ◽  
Vol 159 ◽  
pp. 01007 ◽  
Author(s):  
I Ketut Sudarsana ◽  
I Gede Gegiranang Wiryadi ◽  
Gede Adi Susila
Keyword(s):  
Experimental Data ◽  
Shear Force ◽  
Free Edge ◽  
Experimental Result ◽  
Element Analysis ◽  
Concrete Damage ◽  
Modelling Techniques ◽  
Concrete Damage Plasticity ◽  
The Moment ◽  
Punching Failure

This research investigates the effect of unbalanced moment directions on the behaviour of edge column slab connections using a finite element analysis. The analyses were done on subassembly edge column slab connections that were designed according to Indonesian Concrete Standard (SNI 2847:2013). Three unbalanced moment directions were considered namely perpendicular, parallel and inclined 45° to the slab free edge. The concrete damage plasticity (CDP) and truss elements in Abaqus were utilized to model and analyse the behaviour of concrete and reinforcement bars, respectively. The modelling techniques were first validated using an experimental result available in the literature. There are five parameters in the CDP model need to be validated to get convergent results with the experimental data. Using the CDP validated parameters, then seven specimen models were analysed under combined shear force and an unbalanced moment in three directions. The ratio of M/V was kept constant of 0.3. The results show that the punching failure capacity of connections having an unbalanced moment inclined 45° is smaller than that of an unbalanced moment perpendicular to the slab free edge, but higher than that of an unbalanced moment parallel to the slab free edge. The patterns of concrete strain are consistent with the moment directions. All tension rebars passing through column sections yield at the connection failures.

VIBRATION AND BUCKLING OF SS-F-SS-F RECTANGULAR PLATES LOADED BY IN-PLANE MOMENTS

2001 ◽  
Vol 01 (04) ◽  
pp. 527-543 ◽  
Author(s):  
JAE-HOON KANG ◽  
ARTHUR W. LEISSA
Keyword(s):  
Beam Theory ◽  
Free Edge ◽  
Free Vibrations ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
One Dimensional ◽  
Simply Supported ◽  
Free Vibration Frequency ◽  
Edge Conditions

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon the Poisson's ratio (ν), results are shown for 0≤ν≤0.5, valid for isotropic materials.

Die Cracking at Solder (In60-Pb40) Joints on Brittle (GaAs) Chips: Fracture Correlation Using Critical Bimaterial Interface Corner Stress Intensities

2003 ◽  
Vol 125 (3) ◽  
pp. 369-377 ◽  
Author(s):  
Bingzhi Su ◽  
Y. C. Lee ◽  
Martin L. Dunn
Keyword(s):  
Stress Intensity ◽  
Temperature Change ◽  
Failure Criterion ◽  
Critical Stress ◽  
Solder Bump ◽  
Bimaterial Interface ◽  
Uniform Temperature ◽  
Elastic Fields ◽  
Solder Bumps ◽  
Wide Range

We study cracking from the interface of an In60-Pb40 solder joint on a brittle GaAs die when the joint is subjected to a uniform temperature change. Our primary objective is to apply and validate a fracture initiation criterion based on critical values of the stress intensities that arise from an analysis of the asymptotic elastic stress fields at the interface corner. In some regards the approach is similar to interface fracture mechanics; however, it differs in that it is based on a singular field other than that for a crack. We begin by determining the shape that the solder bump will assume after reflow when constrained by a fixed diameter wetting pad on the GaAs. To simplify the interpretation of the results, we focus on a class of solder bumps of various sizes, but with a self-similar shape. The approach, though, can be applied to different size and shape solder bumps. We then compute the asymptotic interface corner fields when the system is subjected to a uniform temperature change. The asymptotic structure (radial and angular dependence) of the elastic fields is computed analytically, and the corresponding stress intensities that describe the scaling of the elastic fields with geometry and loading are computed by axisymmetric finite element analysis. In order to assess the validity of fracture correlation using critical stress intensities, we designed and fabricated a series of test structures consisting of In60-Pb40 solder bumps on a GaAs chip. The test structures were subjected to uniform temperature drops from room temperature to induce cracking at the interface corner. From the tests we determined the relationship between the solder bump size and the temperature change at which cracking occurred. Not unexpectedly, smaller bumps required larger temperature changes to induce cracking. The observed scaling between solder bump size and temperature change is well described by the critical stress intensity failure criterion based on only a single parameter, the critical value of the mode 1 stress intensity, K1crn. Interestingly, this is because over a significant region, the mode 2 and constant terms in the asymptotic expansion cancel each other. This failure criterion provides the necessary machinery to construct failure maps in terms of geometry and thermomechanical loading. We conclude by describing how to apply the approach in more general and more practical settings that are possibly applicable to a wide range of problems in microelectronics, optoelectronics, and microelectromechanical systems packaging.

Thermomechanical Modeling of a Wet Shape Memory Alloy Actuator

2006 ◽  
Author(s):  
Joel Ertel ◽  
Stephen Mascaro
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Temperature Change ◽  
Cold Water ◽  
Uniform Temperature ◽  
Thermomechanical Model ◽  
Martensite Fraction ◽  
Mechanical Models ◽  
Sma Actuator ◽  
The Wire

This paper presents combined thermal and mechanical models of a wet shape memory alloy (SMA) wire actuator. The actuator consists of a SMA wire suspended concentrically in a compliant tube. Actuation occurs as hot and cold water are alternately pumped through the tube to contract and extend the wire, respectively. Although other constitutive models of the behavior of SMA's exist, they generally assume uniform temperature change throughout the SMA actuator. The thermomechanical model presented in this paper accounts for the non-uniform temperature change of the SMA wire due to alternating the temperature of the flow along the wire. The thermal model consists of analysis of the heat transfer between the fluid and the SMA wire. Heat loss to the environment and the temperature change of the fluid through the actuator are taken into account. Based on this analysis the temperature of the wire at segments along its length can be determined as a function of time. The mechanical model approximates the strain-martensite fraction and martensite fraction-temperature relationships. By combining the thermal and mechanical models the strain of the wire can be determined as a function of time. The combined thermomechanical model will be used to model applications in which a wet SMA actuator is desired.

scholarly journals Timoshenko Beam Theory: Exact Solution for First-Order Analysis, Second-Order Analysis, and Stability

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Second Order ◽  
Bernoulli Beam ◽  
Order Analysis ◽  
First Order ◽  
The Moment ◽  
Relationship Of

This paper presents an exact solution to the Timoshenko beam theory (TBT) for first-order analysis, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory (EBBT) neglects shear deformations. Thus, the Euler–Bernoulli beam is a special case of the Timoshenko beam. The moment-curvature relationship is one of the governing equations of the EBBT, and closed-form expressions of efforts and deformations are available in the literature. However, neither an equivalent to the moment-curvature relationship of EBBT nor closed-form expressions of efforts and deformations can be found in the TBT. In this paper, a moment-shear force-curvature relationship, the equivalent in TBT of the moment-curvature relationship of EBBT, was presented. Based on this relationship, first-order and second-order analyses were conducted, and closed-form expressions of efforts and deformations were derived for various load cases. Furthermore, beam stability was analyzed and buckling loads were calculated. Finally, first-order and second-order element stiffness matrices were determined.

Aerodynamic Loading Considerations of Three-Shaft Engine Compression System During Surge

2020 ◽  
Author(s):  
Jose Moreno ◽  
John Dodds ◽  
Christopher Sheaf ◽  
Fanzhou Zhao ◽  
Mehdi Vahdati
Keyword(s):  
High Pressure ◽  
Physical Explanation ◽  
Compression System ◽  
High Pressure Compressor ◽  
Aero Engine ◽  
Compressor Surge ◽  
The Moment ◽  
Engine Components ◽  
Variable Stator ◽  
Pressure Compressor

Abstract Compressor surge imposes a limit on aero-engine operability and can compromise integrity because of significant aerodynamic loads imparted on the engine components. The aim of this paper is to use 3D unsteady CFD to predict the surge loadings on a modern three spool engine. The computations are performed using a whole-assembly approach. In this work, the effect of two types of surge initiation on the maximum loading recorded during surge are studied and a physical explanation of the main phenomena which contribute to those loadings is offered. The engine is matched at a high power condition and the surge inception is via throttling of the high pressure compressor (HPC) or turning of the intermediate pressure compressor (IPC) variable stator vanes. It was found that in an aero-engine surge event, the maximum overpressure are caused by a combined effect of the surge shock wave passing and high pressure gas blown towards the front of the engine during depressurisation. The overpressure is dictated by the compression system exit pressure at the moment of the surge inception. The surge initiation via HPC throttling produces larger overpressure and therefore, should be considered for design considerations.

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