Effective Coefficient of Thermal Expansion

The structure is bonded to a substrate 24 which is chosen to have a coefficient of thermal expansion that is selected for providing the resultant read-out chip assembly with an effective coefficient of thermal expansion that is approximately the same as an HgCdTe detector array 36. The substrate material may be GaAs (4.5-5.9 x 10"6 m/mK), CdTe, Ge (5.5-6.4 x 10"6 m/mK), and a-plane sapphire (3.5-7 5 x 10" m/mK) where the coefficients of thermal expansion are given in parentheses. The coefficients of thermal expansion for silicon, HgCdTe and epoxy are 1.2 x 10"6 m/mK, 3.8-4.5 x 1 O 6m/mK and 30-50 x 10"6 m/mK, respectively. Next, the substrate 16 is removed and aluminium pads 34a are formed. Indium bumps 34b are cold welded to corresponding indium bumps 36b. 

Figure 5.5 Temperature-dependent effective coefficient of thermal expansion [12]. (With permission from Elsevier.)...

The conversion degree of glass transition, a, was obtained from Eq. (2.12). The resulting temperature-dependent effective coefficient of thermal expansion for the experimental GFRP material is shown in Figure 5.5. 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

ASTM D883 defines a filler as "...a relatively inert material added to a plastic to modify its strength, permanence, working properties, or other quaHties or to lower costs." EiHers (qv) that modify the properties and characteristics of epoxies are employed in epoxy resins for a variety of reasons. Then principal functions are to control viscosity, reduce shrinkage and the coefficient of thermal expansion, effect a cost reduction, and color the epoxy resins. 

The ceramic oxide carrier is bonded to the monolith by both chemical and physical means. The bonding differs for a ceramic monolith and a metallic monolith. Attrition is a physical loss of the carrier from the monolith from the surface shear effects caused by the exhaust gas, a sudden start-up or shutdown causing a thermal shock as a result of different coefficients of thermal expansion at the boundary between the carrier and the monolith, physical vibration of the cataly2ed honeycomb, or abrasion from particulates in the exhaust air (21) (see Fig. 6d). 

A rod of polypropylene, 10 mm in diameter, is clamped between two rigid fixed supports so that there is no stress in the rod at 20°C. If the assembly is then heated quickly to 60°C estimate the initial force on the supports and the force after 1 year. The tensile creep curves should be used and the effect of temperature may be allowed for by making a 56% shift in the creep curves at short times and a 40% shift at long times. The coefficient of thermal expansion for polypropylene is 1.35 x 10 °C in this temperature range. 

Hygroscopic (moisture) effects arise for polymer materials such as some epoxies that absorb moisture chemically after curing and therefore expand. These effects are directly analogous to thermal effects and are characterized by coefficients of moisture expansion and p2 in principal material coordinates in direct analogy to a.( and 02 for coefficients of thermal expansion. All calculations for thermal effects with the a can be replaced by or supplemented with analogous terms for moisture expansion. 

For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

Obviously, the discrepancy between the experimental data [238-241] and predictions of the theory [236,237] can be attributed to the difference of the coefficients of thermal expansion. The polymer exerts pressure on the filler, thereby masking the effect of the strength of adhesion on the modulus. The pressure on the filler may be sufficiently high. In [243] it was found, for example, that in PP, quartz particles experienced a compression force of about 100 MPa after cold drawing of the composite the force reduces to 50 MPa in the direction of drawing but at the same time increases to 300 MPa in the perpendicular direction. 

Products are affected dimensionally by the difference between their forming temperature and their product-use temperature. Thus, a plastic s coefficient of thermal expansion and contraction has a significant effect on service conditions. The thermoforming pressure, time, and temperature variations that can exist will affect the final dimensions. Of these factors, evenness in heating throughout the sheet thickness before forming is usually the most important control. Type of heater has a direct effect on obtaining uniform heat... 

Thermal expansion induced by insolation may be important in desert areas where rocky outcrops and soil surfaces are barren. In a desert, daily temperature excursions are wide and rocks are heated and cooled rapidly. Each type of mineral in a rock has a different coefficient of thermal expansion. Consequently, when a rock is heated or cooled, its minerals differentially expand and contract, thereby inducing stresses and strains in the rock and causing fractures. Ollier (1969) discussed examples of rock weathering due to insolation. Fire can develop temperatures far in excess of insolation and be quite effective in fracturing rocks (Black-welder, 1927). 

Figure 22. Effect of crack density on coefficient of thermal expansion of a T300/5208 composite laminate [OjAWJj. (Reproduced from reference 4.)...

The pressure effect on the enthalpy of liquid ethanol can be estimated from equation 2.15, now written in terms of the coefficient of thermal expansion, a ... 

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