Elastic Stability of a Cantilever Beam (Rod) Supported by an Elastic Foundation, With Application to Nano-Composites

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
E. Suhir
Keyword(s):  
Elastic Foundation ◽  
Cantilever Beam ◽  
Elevated Temperatures ◽  
Flexural Rigidity ◽  
Elastic Stability ◽  
Critical Force ◽  
The Matrix ◽  
Practical Guidelines ◽  
Low Modulus ◽  
Lower Temperature

A simple analytical (“mathematical”) predictive model is developed with an objective to establish the condition of elastic stability for a compressed cantilever beam (rod) of finite length lying on a continuous elastic foundation. Based on the developed model, practical guidelines are provided for choosing the adequate length of the beam and/or its flexural rigidity and/or the spring constant of the foundation, so that the beam remains elastically stable. The obtained solution can be used, perhaps with some additional assumptions and modifications, for the assessment of the critical force for high-modulus and low-expansion fibers (including nano-fibers) embedded into a low-modulus and high-expansion medium (matrix). Composite systems are often fabricated at elevated temperatures and operated at lower temperature conditions. It is imperative that an embedded fiber remains elastically stable, i.e., does not buckle as a result of the thermal contraction mismatch of its material with the material of the matrix. If buckling occurs, the functional (e.g., thermal) and/or the structural (“physical”) performance of the composite might be compromised.

MICROSTRUCTURAL EVOLUTION OF Al-Cu-Mg-Ag ALLOY WITH TRACE Zr ADDITION DURING TWO-STEP HOMOGENIZATION

2009 ◽  
Vol 23 (06n07) ◽  
pp. 855-862 ◽  
Author(s):  
FEIYUE MA ◽  
ZHIYI LIU
Keyword(s):  
Melting Point ◽  
Grain Boundaries ◽  
Microstructural Evolution ◽  
Cast Alloy ◽  
Scanning Calorimetry ◽  
Zr Addition ◽  
Homogenization Time ◽  
The Matrix ◽  
Higher Temperature ◽  
Lower Temperature

The microstructural evolution in an Al - Cu - Mg - Ag alloy with trace Zr addition during homogenization treatment was characterized by Differential Scanning Calorimetry (DSC), Scanning Electron Microscopy (SEM) and Energy-dispersive X-ray Spectroscopy (EDS). It was shown that the low-melting-point phase segregating toward grain boundaries is Al 2 Cu , with a melting point of 523.52°C. A two-step homogenization process was employed to optimize the microstructure of the as-cast alloy, during which the alloy was first homogenized at a lower temperature, then at a higher temperature. After homogenized at 420°C for 6 h, Al 3 Zr particles were finely formed in the matrix. After that, when the alloy was homogenized at an elevated temperature for a longer time, i.e., 515°C for 24 h, most of the precipates at the grain boundaries were removed. Furthermore, the dispersive Al 3 Zr precipitates were retained, without coarsening greatly in the final homogenization step. A kinetics model is employed to predict the optimal homogenization time at a given temperature theoretically, and it confirms the result in present study, which is 420°C/6h+515°C/24h.

Application of an Epoxy Cap in a Flip-Chip Package Design

1989 ◽  
Vol 111 (1) ◽  
pp. 16-20 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Thermal Expansion ◽  
Flip Chip ◽  
Coefficient Of Thermal Expansion ◽  
Preliminary Test ◽  
Elastic Stability ◽  
Thermally Induced ◽  
Package Design ◽  
Silicone Gels ◽  
Low Modulus ◽  
Supporting Frame

In order to combine the merits of epoxies, which provide good environmental and mechanical protection, and the merits of silicone gels, resulting in low stresses, one can use an encapsulation version, where a low modulus gel is utilized as a major encapsulant, while epoxy is applied as a protecting cap. Such an encapsulation version is currently under consideration, parallel with a metal cap version, for the Advanced VLSI package design which is being developed at AT&T Bell Laboratories. We recommend that the coefficient of thermal expansion for the epoxy be somewhat smaller than the coefficient of thermal expansion for the supporting frame. In this case the thermally induced displacements would result in a desirable tightness in the cap/frame interface. This paper is aimed at the assessment of stresses, which could arise in the supporting frame and in the epoxy cap at low temperatures. Also, the elastic stability of the cap, subjected to compression, is evaluated. The calculations were executed for the Advanced VLSI package design and for a Solder Test Vehicle (STV), which is currently used to obtain preliminary information regarding the performance of the candidate encapsulants. It is concluded that in order to avoid buckling of the cap, the latter should not be thinner than 15 mils (0.40 mm) in the case of VLSI package design and than 17.5 mils (0.45 mm) in the case of STV. At the same time, the thickness of the cap should not be greater than necessary, both for smaller stresses in the cap and for sufficient undercap space, required for wirebond encapsulation. The obtained formulas enable one to evaluate the actual and the buckling stresses. Preliminary test data, obtained by using STV samples, confirmed the feasibility of the application of an epoxy cap in a flip-chip package design.

Mechanical Properties of Matrix Hybrid Thick-Composites

Materials ◽  
2004 ◽  
Author(s):  
Hiroyuki Hamada ◽  
Asami Nakai ◽  
Kazuya Eto ◽  
Kenichi Sugimoto
Keyword(s):  
Mechanical Properties ◽  
Hybrid Composite ◽  
High Performance ◽  
Impact Load ◽  
Unsaturated Polyester ◽  
In Situ Observation ◽  
Impact Properties ◽  
The Matrix ◽  
Low Modulus ◽  
Thick Composites

For the purpose of more safety boats, the large thickness of outer plates is required to increase flexural stiffness, strength and impact properties. Some problems in mechanical properties are generated by increasing in thickness because the effect of interlaminar shearing of Thick-composites on whole mechanical properties is greater than that of thin-composites. We have investigated the matrix hybrid composite with two kinds of unsaturated polyester, one was hard type resin with low toughness and the other was flexible type resin with low modulus and high toughness. In this study, matrix hybrid composite was focused and applied to Thick-composites. First, the flexural properties were investigated and the micro fracture progress was precisely observed with in-situ observation using replica method. Then, impact properties of the Thick-composites were examined and the availability of matrix hybrid composite was investigated. It was concluded that the matrix hybrid composite achieved high performance in both static and impact load.

Characteristics of an Eigensystem Describing the Elastic Stability of a Thin Cantilever Beam

1962 ◽  
Vol 66 (623) ◽  
pp. 722-724 ◽  
Author(s):  
B. Saravanos
Keyword(s):  
Equilibrium Problem ◽  
Cantilever Beam ◽  
Elastic Stability ◽  
Additional Component ◽  
Connecting Rod ◽  
The Stability

The stability of a uniform cantilever beam subjected to an articulated tip load has been analysed as an equilibrium problem of static elastic stability. It was found there that the articulation of the connecting rod applying the tip load introduced additional component forces during the process of beam deformation.

Small Lead and Indium Inclusions in Aluminium

1991 ◽  
Vol 235 ◽  
Author(s):  
E. Johnson ◽  
K. Hjemsted ◽  
B. Schmidt ◽  
K. K. Bourdelle ◽  
A. Johansen ◽  
...  
Keyword(s):  
Melting Point ◽  
Elevated Temperatures ◽  
Supersaturated Solution ◽  
In Situ Tem ◽  
Initial Growth ◽  
Heating And Cooling ◽  
Moiré Fringes ◽  
The Matrix ◽  
Spontaneous Phase

ABSTRACTIon implantation of lead or indium into aluminium results in spontaneous phase separation and formation of lead or indium precipitates. The precipitates grow in topotactical alignment with the matrix, giving TEM images characterized by moiré fringes. The size and density of the precipitates increase with increasing fluence until coalescence begins to occur. Implantations at elevated temperatures lead to formation of larger precipitates with well developed facets. This is particularly significant for implantations above the bulk melting point of the implanted species. Melting and solidification have been followed by in-situ TEM heating and cooling experiments. Superheating up to ∼ 50 K above the bulk melting point has been observed, and the largest inclusions melt first. Melting is associated with only partial loss of facetting of the largest inclusions. Initial growth of the inclusions occurs by trapping of atoms retained in supersaturated solution. Further growth occurs by coalescence of neighbouring inclusions in the liquid phase. Solidification is accompanied by a strong undercooling ∼ 30 K below the bulk melting point, where the smallest inclusions solidify first. Solidification is characterized by spontaneous restoration of the facets and the topotactical alignment.

scholarly journals High-Resolution Microstructure Characterization of Additively Manufactured X5CrNiCuNb17-4 Maraging Steel during Ex and in Situ Thermal Treatment

2021 ◽  
Author(s):  
Mihaela Albu ◽  
Bernd Panzirsch ◽  
Hartmuth Schröttner ◽  
Stefan Mitsche ◽  
Klaus Reichmann ◽  
...  
Keyword(s):  
Maraging Steel ◽  
Elevated Temperatures ◽  
Scanning Transmission Electron Microscope ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
The Matrix ◽  
Powder Particles ◽  
In Situ Heating ◽  
Heating Up

Powder and SLM additively manufactured parts of X5CrNiCuNb17-4 maraging steel were systematically investigated by electron microscopy to understand the relationship between the properties of the powder grains and the microstructure of the printed parts. We prove that satellites, irregularities and superficial oxidation of powder particles can be transformed into an advantage through the formation of nanoscale (AlMnSiTiCr)-oxides in the matrix during the printing process. The nano-oxides showed extensive stability in terms of size, spherical morphology, chemical composition and crystallographic disorder upon in situ heating up to 950°C in the scanning transmission electron microscope. Their presence thus indicates a potential for oxide-dispersive strengthening of this steel, which may be beneficial for creep resistance at elevated temperatures. The nucleation of copper clusters and their evolution into nanoparticles as well as the precipitation of Ni and Cr particles upon in situ heating have as well been systematically documented.

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