Bi-Material Re-Entrant Triangle Cellular Structures Incorporating Tailorable Thermal Expansion and Tunable Poisson's Ratio1

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Xiaobing He ◽  
Jingjun Yu ◽  
Yan Xie

Abstract Based on the bi-material triangle lattice cell, a new cellular structure, bi-material re-entrant triangle (BRT) cellular structure, is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson's ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. A general thermoelasticity equation to systematically build the relationship among the external force, the temperature load, and the deformation for planar lattice structures with bounded joints is derived and then embedded into a theoretical model for the devised BRT structure. Using assembled thermoelasticity equation, effective PR, Young's modulus, as well as CTE are computed. In order to guide designers to construct initial concepts, the design domain for coupling negative CTE and negative PR properties is plotted. The material-property-combination region that can be achieved by this cellular structure is determined within an Ashby material selection chart of CTE versus PR. Nine available combinations of CTE and PR properties are extracted and demonstrated with abaqus simulation.

Author(s):  
He Xiaobing ◽  
Xie Yan ◽  
Yu Jingjun

Abstract Based on the bi-material triangle lattice material, a new cellular structure: bi-material re-entrant triangle (BRT) is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson’s ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. An equation to systematically build the relationship among the external force, the temperature increment and the deformation for the planar lattice material with bounded joints is derived and then embedded into a theoretical model for devised BRT structure. Using master stiffness equation, effective PR, effective Young’s modulus as well as effective CTE are computed. In order to guide designers to construct an initial concept quickly, the design domain for coupling negative CTE and negative PR properties is proposed. Nine available paired characteristics for coupling effect are extracted and demonstrated with ABAQUS simulation.


1982 ◽  
Vol 1 (1) ◽  
pp. 24-27 ◽  
Author(s):  
I. Taitl

Fired resistors exhibit variations which are minimised by abrasive and laser trimming. The latter may cause unstable behaviour which is further aggravated by thermal shock. The chemical structure of a thick film resistor is analysed with respect to mechanical stress, and the theoretical conclusion that the coefficient of thermal expansion of the resistor should be equal to or smaller than that of the substrate is verified experimentally. The thermal behaviour of ruthenium dioxide is examined and a range of CTE values are determined for materials of varying chemical composition. The relationship between CTE and post laser trimming stability is demonstrated on four thick film resistors which differ in thermal expansion. It is pointed out that formulations with high metallic content can absorb tensile stress by elastic deformation, thus minimising the formation or propagation of laser induced cracks.


2018 ◽  
Vol 52 (27) ◽  
pp. 3745-3758 ◽  
Author(s):  
Amin Bahrami ◽  
Niloofar Soltani ◽  
Martin I Pech-Canul ◽  
Shaghayegh Soltani ◽  
Luis A González ◽  
...  

In this study, wettability behavior of B4C substrate as well as B4C/crystalline rice husk ash and B4C/amorphous rice husk ash substrates with two aluminum alloys were studied. The electrical resistivity, thermal expansion coefficients, and thermal diffusivity of bilayer Al/B4C/rice husk ash composite fabricated by one-step pressureless infiltration were measured and the obtained data were systemically analyzed using the Taguchi method and analysis of variance. Boron carbide substrates after addition of amorphous or crystalline rice husk ash display good wettability with molten aluminum alloys. The results show that, electrical resistivity of Al/B4C/rice husk ash composites is mainly influenced by initial preform porosity, while the coefficient of thermal expansion of composites is determined by the chemical composition of infiltrated alloys. The measured values for coefficient of thermal expansion (10.5 × 10−6/℃) and electrical resistivity (0.60 × 10−5 Ω.m) of Al/B4C/rice husk ash composites, fabricated according to analysis of variance's optimal conditions are in good agreement with those of the projected values (11.02 × 10−6/℃ and 0.65 × 10−5 Ω.m, respectively). The difference between the corresponding values obtained from verification tests and projected values, for electrical resistivity and coefficient of thermal expansion are less than 5%. Finally, as a material selection approach, the strengths and weaknesses of the composites have been graphed in the form of radar diagrams.


Author(s):  
Kirsten Lovelace ◽  
Sonya Smith

Abstract This research investigates the effects of thermal cycling from room to cryogenic temperatures (300K–4K) on the thermal expansion coefficient of two ceramic substrates of Silicon Nitride (Si3N4) and alpha-Alumina/Sapphire (α-Al2O3). Due to the shortage of available data, a comparative study with reference materials, Copper, AISI Carbon Steel 1008 and Molybdenum, are compared to the National Institute of Standards and Technology (NIST) property data as a proof of concept. Accurate thermal contraction data of materials at low temperatures are important in material selection and thermal design of engineered systems, such as, space electronic devices. Thermal expansion mismatch causes substantial problems in space electronic device reliability because of the various stresses imposed on the joint materials undergoing extreme thermal cycles. Theory supports the advantage of utilizing Sapphire (Al2O3) and Silicon Nitride (Si3N4) within microchip configuration. However, there is limited data available that confidently supports this assertion beyond theory. An electro-mechanical method for in-situ strain measurements is presented as a tool to characterize thermomechanical behavior of Sapphire and Silicon Nitride at temperatures below 50 K. The calculated coefficient of thermal expansion for silicon nitride is 1.35 · 10−6 1/K and 0.994 · 10−6 1/K for sapphire at 5.7 K. The results from this validation have a mean error percentage of less than 6 %.


2011 ◽  
Vol 483 ◽  
pp. 78-82
Author(s):  
Xiao Wei Liu ◽  
Jia Lu Tang ◽  
Rong Yan Chuai ◽  
Hai Feng Zhang ◽  
Xi Lian Wang

In this paper, we make a detail analysis of some factors, which affects the electrostatic bonding process. According to the electrical properties of glass, combined with the principle of electrostatic bonding, we analysed the relationship of critical bonding time, voltage and temperature as well as the factors which affect electrostatic bonding. Then we come up with the mathematical model of the intensity and temperature of electrostatic bonding. In accordance with the above-mentioned formula and the experimental data, we can get the following conclusions: the intensity of electrostatic bonding is much greater between 280°C to 370°C; the best temperature for this bonding is about 350°C; however, when the temperature is below 280°C,the intensity of electrostatic bonding is lower due to the great impact of particles under low temperature; but when the temperature is higher than 370°C,the mismatch of coefficient of thermal expansion of silicon and glass gets larger, then as a result, the intensity of this bonding has a significant decrease with the increasing of temperature.


Author(s):  
Zhijun Ma ◽  
Mengge Liu ◽  
Wei Yang ◽  
Zhong Yang ◽  
Yongchun Guo ◽  
...  

Al-Si casting alloys are the most commonly used materials for piston alloys. The coefficient of thermal expansion is the key property of a piston material for improving the overall performance and service life of an engine. In the present study, the relationship between the morphology of the excess silicon phase and the coefficient of thermal expansion of Al-Si binary casting alloys was discussed. Optical and scanning electron microscopy were utilized to observe the morphology of the excess silicon phase in the Al-Si binary casting alloys before and after solution aging treatment. The results showed that the morphology of the excess silicon phase significantly influenced the coefficient of thermal expansion of the Al-Si binary casting alloys. After solution aging treatment, the coefficient of thermal expansion of the Al-Si binary casting alloys increased due to the rounding and granulating of the excess silicon phase precipitated during the casting process and decreased due to the precipitation of the finely dispersed Si phase in the α-Al matrix. The change in the coefficient of thermal expansion depended on which of the two kinds of morphological transformation of the excess silicon phase is dominant.


2015 ◽  
Vol 44 (24) ◽  
pp. 10932-10938 ◽  
Author(s):  
Ping Zhang ◽  
Yonggui Zhao ◽  
Xiuyu Wang

Bond ionicity, lattice energy, and coefficient of thermal expansion were calculated using a semiempirical method.


2005 ◽  
Vol 2 (3) ◽  
pp. 162-170 ◽  
Author(s):  
D. Sujan ◽  
M. V. V. Murthy ◽  
K. N. Seetharamu ◽  
A. Y. Hassan

Schmidt's trimaterial model for shearing stress for uniform temperature is upgraded to account for differential temperatures in the layers. Subsequently a model for peeling stress is proposed from the consideration of moment equilibrium combined with the above mentioned upgraded shear stress model. The results are presented in terms of two parameters m1 and m2, relating the two temperature ratios at die-die attach interface and at die attach-substrate interface respectively. The results are also presented in terms of another two parameters n1 and n2, representing coefficient of thermal expansion ratios between die and die attach materials and die attach and substrate materials respectively. The obtained results can be useful resources in future analysis of trimaterial assemblies for proper design and material selection.


2018 ◽  
Vol 202 ◽  
pp. 01005
Author(s):  
D. Sujan ◽  
L. Vincent ◽  
Y. W. Pok

In electronic packaging, typically two or more thin dissimilar plates or layers are bonded together by an extremely thin adhesive bond layer. Electronic assemblies are usually operated under high power conditions which predictably produces a high temperature environment in the electronic devices. Therefore, thermal mismatch shear and peeling stress inevitably arise at the interfaces of the bonded dissimilar materials due to differences in Coefficient of Thermal Expansion (CTE) typically during the high temperature change in the bond process. As a result, delamination failure may occur during manufacturing, machining, and field use. As such, these thermo-mechanical stresses play a very significant role in the design and reliability of the electronic packaging assembly. Consequently, critical investigations of interfacial stresses under variable load conditions in composite structure can result in a better design of electronic packaging with higher reliability and minimize or eliminate the risk of functional failure. In order to formulize bond material selection, analytical studies are carried out in order to study the influence of bond layer parameters on interfacial thermal stresses of a given package. These parameters include Coefficient of thermal expansion (CTE), poison’s ratio, temperature, thickness, and stiffness (compliant and stiff) of the bond layer. From the study, stiffness and bond layer thickness are identified as the key parameters influencing interfacial shearing and peeling stresses. The other parameters namely CTE, poisons ratio has shown insignificant influence on interfacial stresses due to the very thin section of bond layer compared to the top and bottom layers. The results also show that the interfacial stresses increases proportionally with the increase of temperature in the layers. Therefore, it is very important that the temperature is maintained as low as possible during the chip manufacturing and operating stages. Since only two parameters namely stiffness and bond layer thickness are identified as the key parameters, the interface thermal mismatch stresses can be reduced or eliminated by controlling these two parameters only. Therefore the identification of suitable bond layer parameters selection with reasonable accuracy is possible even without performing optimization process. Finally, this paper proposes a Metal Matrix Composite (MMC) bond material selection approach using rule of mixture material design. The outcome of this research can be seen in the forms of practical and beneficial tools for interfacial stress evaluation and physical design and fabrication of layered assemblies. The Engineers can utilize this research outcome in conjunction with guidelines for electronic packaging under variable thermal properties of layered composites.


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