The Coefficient of Linear Thermal Expansion

Like metals, plastics generally expand when heated and contract when cooled. Usually, for a given temperature change TPs have a greater change than metals. The coefficient 

The CLTE is an important consideration if dissimilar materials like one plastic to another or a plastic to metal and so forth are to be assembled. The CLTE is influenced by the type of plastic (liquid crystal, for example) and composite, particularly the glass-fiber content and its orientation. It is especially important if the temperature range includes a thermal transition such as Tg. Normally, all this activity with dimensional changes is available from material suppliers readily enough to let the designer apply a logical approach and understand what could happen. 

The design of products has to take into account the dimensional changes that can occur during fabrication (see Chapters 3-7) and during its useful service life. With a mismatched CLTE there could be destruction of plastics from factors such as cracking or buckling. 

Expansion and contraction can be controlled in plastic by its orientation, cross-linking, adding fillers or reinforcements (see Fig. 2-20), and so on. With certain additives the CLTE value could be zero or near zero. For example, plastic with a graphite filler contracts rather than expands during a temperature rise (see Fig. 1-5, Thermal Expansion ). As shown in Table 2-19, composites with only glass-fiber reinforcement can be used to match those of metal and other materials. In fact, TSs are especially compounded to have little or no change. 

In a TS the ease or difficulty of thermal expansion is dictated for the most part by the degree of cross-linking as well as the overall stiffness of the units between the crosslinks. The less flexible units are also more resistant to thermal expansion. Such influences as secondary bonds have much less effect on the thermal expansion of TSs. 

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The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

Coefficient of Linear Thermal Expansion. The coefficients of linear thermal expansion of polymers are higher than those for most rigid materials at ambient temperatures because of the supercooled-liquid nature of the polymeric state, and this applies to the cellular state as well. Variation of this property with density and temperature has been reported for polystyrene foams (202) and for foams in general (22). When cellular polymers are used as components of large stmctures, the coefficient of thermal expansion must be considered carefully because of its magnitude compared with those of most nonpolymeric stmctural materials (203). 

Thermal Expansion. The averaged value of the coefficient of linear thermal expansion of diamond over the range 20 to 100°C is 1.34 X 10 cm/cm/ C and 3.14 x 10 from 20 to 800°C. At room temperature the values for sihca glass and diamond ate 0.5 X 10 and 0.8 X 10 , respectively. The relatively low expansion combined with the low reactivity of diamonds, except for carbide formation, leads to some challenges in making strong bonds between diamond and other materials. 

An influence on dimensions and tolerances involves the coefficient of linear thermal expansion or contraction. This CLTE value has to be determined at the product s operating temperature (Chapter 2, THERMAL EXPANSION AND CONTRACTION) Plas tics can provide all extremes in CLTEs. As an... 

The coefficient of linear thermal expansion is almost constant, for most types of glass, for temperatures up to 400-600°C. The actual value depends on the chemical constitution of the glass. It then increases rapidly above a certain temperature, often called the... 

The coefficient of linear thermal expansion is the ratio of the change in length per degree C to the length at 0°C. 

The same models of mechanical conpling can be used to predict the coefficient of linear thermal expansion in the composite, ai, based on the moduli, and thermal expansion coefficients of the fiber and matrix, a/ and a, respectively ... 

When the wall of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands depending on the coefficient of linear thermal expansion of the steel. The parts at lower temperature impede the expansion of those parts with higher temperature, and induce additional thermal stresses. To estimate the transient thermal stresses which regularly appear e.g. during start-up or shut-down of process components or as well as a result of process interruptions and in the case of pulsating temperature conditions during operation. Informations about the temperature distribution across the vessel wall as a function of radius and time [12]... 

Notation strength limit in extension E is the modulus of elasticity is the elongation at break A is the impact strength a is the coefficient of linear thermal expansion... 

Taking derivatives of experimental data (i.e. for determining the coefficient of linear thermal expansion) is not quite as straightforward as taking derivatives of algebraic functions, since data tend to have some scatter. If, for example, a data set has a visually upward trend but two adjacent points are stacked on top of each other, the slope between these points is infinite. An improvement would be to average the slopes from a cluster of points, but if infinity is one of the values, the average value is still infinity. 

Since different instruments are designed to accept a variety of sample lengths, the change in length per unit starting length is conventionally recorded as a function of temperature, as shown in Figure 7.1. The slope of the trace is the coefficient of linear thermal expansion, defined by ... 

Since only the pressure is being measured directly, the volume Vmust remain constant or else vary in a known way with the temperature (and pressure). If a is the coefficient of linear thermal expansion of the material from which the bulb is constructed, the coefficient of volume expansion is 3a. If this is assumed constant with temperature, we can write... 

The coefficient of linear thermal expansion. If a piece of straight glass rod of any diameter and of length L cm is heated uniformly through At°C, it will expand by some amount /cm. We can now say that the increase in length/unit length/°C rise in temperature is a, and... 

The coefficient of linear thermal expansion of wood is so small that it may be ignored in long structures. This property can be most attractive in the construction of long ducts, eliminating the necessity for complicated and expensive expansion joints. Used alone, many wood constructions have served satisfactorily for very long periods in certain chemical services. 

Uses a vitreous silica dilatometer to measure the coefficient of linear thermal expansion of plastics which are not distorted by the thrust of the dilatometer on the specimen. 

ISO 4897-85 Cellular Plastics - Determination of the Coefficient of Linear Thermal Expansion of Rigid Materials at Sub-Ambient Temperatures, 9 pp... 

The coefficient of linear thermal expansion of wood-chip concrete was measured by the push rod meter at JTCCM. The result of measurement is shown in Table 6. Because of the influence of moisture content, the coefficient of linear thermal expansion are different with the temperature range below and over 40°C. Within the range of -8 40°C, when the packing ratio of wood-chip is increased, the coefficient of linear thermal expansion increases. 

Table 13 The coefficient of linear thermal expansion of a-alumina as a function of temperature...

The coefficient of linear thermal expansion (3 is another useful quantity that is commonly quoted in the literature. It simply equals one third of the coefficient of volumetric thermal expansion for an isotropic (unoriented) material ... 

Studies of the effects of various types of fiber and particulate fillers have shown that milled glass fibers are in the near term the most suitable means to achieve part stiffness and the required reduction in the coefficient of linear thermal expansion to allow practical mating of RIM polyurethane panels with steel. 

Effect of talc on the coefficient of linear thermal expansion-contraction was not pronounced (Table 4.10) and was actually superimposed with that of wood flour. In other words, the principal effect was just a displacement of plastic with a filler, regardless whether it was wood flour or talc. It certainly makes sense because both wood and mineral fillers have their own coefficients of thermal expansion-contraction by an order of magnitude lower than that of HDPE (see Chapter 10). 

The test method covers determination of the coefficient of linear thermal expansion for plastic materials, using a vitreous silica push-rod dilatometer. Vitreous silica is also known as fused silica quartz. Dilatometer is an expansion-meter, as dilation is expansion of materials when they are heated. The test method recommends that ASTM E 228 shall be used for temperature range other than -30 to 30°C, because ASTM E 228 operates in the temperature range of -30 to 140°F (-34°C to +60°C). 

After the measurements are done at 30°C (-22°F), the ASTM procedure prescribes to change the transfer the dilatometer to the +30°C (86°F) bath, and conduct the measurements as described above. Both the measurements should be repeated and finally conducted at room temperature. The coefficient of linear thermal expansion over the temperature range is calculated using the formula given above. Average coefficient is referenced to room temperature. 

Precision of the coefficient of linear thermal expansion is usually fair. ASTM D 696-98 lists an example with nine plastics, tested in five different laboratories (a round robin test). The data for three plastics are shown in Table 10.1. 

For isotropic solids, fi is related to the coefficient of linear thermal expansion a by... 

Table 1 lists the coefficients of linear thermal expansion for several commonly-encountered materials. 

The influence of temperature on rigid cellular materials can be studied using several available standards covering dimensional stability (BS 4370, Part 1, Method 5), compressive creep (ISO 7616 [41]). and the determination of the coefficient of linear thermal expansion (BS 4370, Part 3, Method 13). The first two of these tests are relatively easy to perform, and the dimensional stability in particular tends to be quoted widely. 

In general, the coefficient of thermal expansion of latex-modified mortar and concrete is directly influenced by that of the aggregates used, as in ordinary cement mortar and concrete. Latex-modified mortar and concrete usually have coefficients of thermal expansion equal to or slightly larger than that of ordinary mortar and concrete. Table 4.6l gives the coefficient of linear thermal expansion of SBR- and PVDC-modified mortars with variation of polymer-cement ratio. 

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