Coefficient of Thermal Expansion

6 Key excerpts on "Coefficient of Thermal Expansion"

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  eBook - PDF

  Metal Matrix Composites

  Thermomechanical Behavior

  • Minoru Taya, Richard J. Arsenault(Authors)
  • 2016(Publication Date)
  • Pergamon

    (Publisher)

  5.2 Coefficient of Thermal Expansion Of the possible thermal behavior characteristics, the behavior of thermal expansion of metal matrix composites has been the characteristic most extensively studied, since it affects the mechanical behavior of the composites in severe thermal environments, especially the application of composites in engine components and space structures. In these applications the stability of components and structures made of metal matrix composites over a long period of time becomes the critical design consideration. The stability can be described in two aspects, geometrical changes and mechanical property changes. In the former case the Coefficient of Thermal Expansion (CTE) of composite structures and components plays a key role, while in the latter case 177 178 Metal Matrix Composites the mismatch of CTEs between the metal matrix and fibers has a dominant effect. In this section we will discuss CTEs of metal matrix composites which can be either obtained experimentally or can be predicted by analytical models. There exist two different CTEs, linear and volumetric ones. The linear CTE is the more commonly measured one. The measurement of the linear CTE (CTE, hereafter) is usually made by a quartz tube dilatometer [1, 2]. A typical quartz tube dilatometer consists of a heating unit, a quartz tube connecting rod, a displacement measurement unit where the change in the length of the specimen is measured through the quartz tube in contact with the specimen, which in turn is measured by a displacement measurement unit. Two types of displacement measurement unit are popular: the linear variable differential transformer (LVDT) and the optical device. A schematic view of the dila-tometer with the optical displacement measurement unit is shown in Fig. 5.1. With the dilatometer the length change AL of the specimen of length L is measured.

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  The Science and Engineering of Materials, Enhanced, SI Edition

  • Donald Askeland, Wendelin Wright, Donald Askeland(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  22-2 Thermal Expansion An atom that gains thermal energy and begins to vibrate behaves as though it has a larger atomic radius. The average distance between the atoms and therefore the overall dimen- sions of the material increase. The change in the dimensions of the material Dl per unit length is given by the linear Coefficient of Thermal Expansion a:  5 l f 2 l 0 l 0 sT f 2 T 0 d 5 Dl l 0 DT (22-4) where T 0 and T f are the initial and final temperatures and l 0 and l f are the initial and final dimensions of the material. A volume Coefficient of Thermal Expansion (a v ) also can be defined to describe the change in volume when the temperature of the material is changed. If the material is isotropic,  v 5 3. An instrument known as a dilatometer Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 785 22-2 Thermal Expansion is used to measure the thermal-expansion coefficient. It is also possible to trace thermal expansion using x-ray diffraction (XRD). Coefficients of thermal expansion for several materials are included in Table 22-2. The Coefficient of Thermal Expansion of a material is related to the atomic bonding. In order for the atoms to vibrate about their equilibrium positions, energy must be supplied to the material. If the potential well is asymmetric, the atoms sepa- rate to a larger extent with increased energy compared to a symmetric well, and the material has a high thermal-expansion coefficient (Chapter 2).

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  eBook - ePub

  Materials Under Extreme Conditions

  Recent Trends and Future Prospects

  • A.K. Tyagi, S. Banerjee, A. K. Tyagi(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  Materials with moderate thermal expansion have TEC of about 10–30 × 10 − 6 /°C), whereas TEC of about 50–60 × 10 − 6 /°C places materials in the category of high thermal expansion. Typical examples are materials with low melting points such as metals and ionic solids, where the TEC can be as high as about 80–100 × 10 − 6 /°C. On the other hand, materials like silica and diamond, which have strong covalent bonds, are categorized as low TEC materials (TEC about 0.5–5 × 10 − 6 /°C). There are several materials that show negative thermal expansion behavior also. Typical examples of this class of materials are AX 2 O 8, AX 2 O 7 (A = Zr, Hf; X = W, Mo) [ 34 – 38 ], M 2 (MO 4) 3 (M = trivalent rare-earth cations like, Sc 3+, Y 3+, Er 3+, and Yb 3+ or transition metals ions and M = W 6+ or Mo 6+) [ 39 – 48 ], M 2 O (M = Cu +, Ag +) [49], ABO 2 (A = Cu +, Ag + and B = Al 3+, Sc 3+, Ln 3+) [50]. Likewise, there are materials that exhibit zero thermal expansion behavior. 5.1. Tailoring of Thermal Expansion Behavior Using a Solid Solution Formation Approach The discussions covered in the previous sections suggest that the thermal expansion of materials can be tailored in several ways, such as by making appropriate solid solutions, introducing an optimum level of defects, fine tuning crystal structure, tailoring the microstructure, altering the chemical bonding, or designing suitable composites. The subsequent sections of this chapter will discuss strategies to prepare materials with tailored thermal expansion behavior. Because thermal expansion by and large is an additive property, it follows the rule of addition. Thus it is possible to prepare appropriate solid solutions in such a way so as to obtain a material with desired thermal expansion. Of course, it must be added that there could be other properties also, in addition to thermal expansion, which might govern the composition of solid solutions

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  Measurement of Temperature and Chemical Composition

  Jones' Instrument Technology

  • B E Noltingk(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  the coefficient of superficial expansion is approximately twice the coefficient of linear expansion. The coefficient of cubic expansion is almost three times the coefficient of linear expansion. In engineering practice it is necessary, especially in large structures, to make allowance for thermal expansion. For instance bridges are built with expansion joints. Many instruments are designed with temperature compensation to accommodate thermal expansion. Thermal expansion can be made use of for temperature measurement, as is dealt with in Section 1.3. If great accuracy is required when measuring lengths with a scale made of metal, allowance should be made for the increase in length of the scale when its temperature is greater than that at which it was calibrated. Owing to the expansion of the scale, a length which was originally / t at the temperature t l9 at which the scale was calibrated, will have increased to / 2 where / 2 = /i[l+«('2-'i)] (1.2) Here t 2 is the temperature at which the measurement is made, and a the coefficient of expansion of the metal of the scale. A 1 mm division on the scale will therefore now measure +a(t 2 -t l )mm (1.3) An actual length / 2 mm will therefore measure +CL(t 2 -t x ) (1.4) The length will therefore appear to be smaller than it actually is. To make this error negligibly small, secondary standards of length are made of Invar, a nickel steel alloy whose linear coefficient of expansion is nearly zero. Expansion of liquids and gases In dealing with the expansion of liquids and gases it is necessary to consider the volume expansion, or cubical expansion. Both liquids and gases have to be held by a container, which will also expand, so that the apparent expansion of the liquid or gas will be less than the true or absolute expansion. The true coefficient of expansion of a liquid is equal to the coefficient of apparent expansion plus the coefficient of cubical expansion of the containing vessel.

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  Dynamic Mechanical Analysis

  • Kevin P. Menard, Noah Menard(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  g is collected by thermal expansion, not by the flexure or penetration method. This is in many ways the simplest or most essential form of TMA measurement. A sample is prepared with parallel top and bottom surfaces and the sample is allowed to expand under minimal load (normally 5 mN or less, ideally it would be 0 mN) as it is slowly heated and cooled. Samples range down to micron-thick films but as thick a sample as possible should be used to minimize errors. For polymers, 5-mm tall blocks are common. Heating rates are normally kept low to allow equilibration of the sample to the furnace temperature. CTE is calculated by:

  α 1 = 1 / l 0   ( δ l/ δ T ) F

  (4.1)

  where α1 is the linear CTE, l0 is the original length, δl is the change in length, and δT is the change in temperature. The F indicates this is done under constant force. Once this value is obtained, it can be used to compare the other materials used in the same produce. Large differences in the CTE can lead to motors binding, solder joints failing, composites splitting on bond lines, or internal stress build up. The Tg is obtained from the same data by measuring the inflection point in changes of slope of the baseline. As a material’s CTE changes dramatically at Tg , one would expect this to be an easily detected transition. It can be but for highly crosslinked materials, the Tg can be so broad and the change in CTE so slight as to be undetectable. Other approaches, like flexure testing, are therefore used. Different Tg values will be seen for each mode of testing15 (see Figure 4.5 ) and it is necessary to report the method one used to get the Tg by TMA. Values on CTE vary greatly from quartz (~0.5 ppm) to stainless steel (11 ppm) to high polymers (~25 ppm). In tension, where metal fixtures are often used, it is common to subtract the baseline signal from the data (see Figure 4.5c

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  Physics for O.N.C. Courses

  • R.A. Edwards(Author)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER 6

  Thermal Expansion

  Publisher Summary

  This chapter presents the concept of thermal expansion and its different properties. Most substances expand when they are heated. The expansion that any substance undergoes when heated through a few tens of degrees, Celsius, is usually quite small relative to the total bulk of the substance and, particularly, in the case of solids, may be far from being apparent by direct observation. The problem of the measurement of thermal expansion, at least for solids and liquids, is a problem of the accurate measurement of very small dimensions. Coefficient of linear expansion can be defined as the fractional increase in length of the solid per unit temperature rise. The chapter also presents the results of the experimental determination of the coefficient of expansion of liquids. Sufficient accuracy of measurement for most practical purposes of the linear coefficient of expansion of solids, particularly of metals, may be obtained using the micrometer screw gauge method. A thermostat is any device that regulates automatically the supply of heat to, and in consequence controls the temperature of, any system. Many thermostats operate by the expansion of liquids and solids or, in particular, the difference in expansion between one metal and another.

  6.1 Introduction

  Most substances expand when they are heated although this is not always the case, a notable exception being that of water when heated between 0° and 4°C. Water contracts when heated over this range, but beyond 4°C expansion occurs and continues right up to the boiling point at 100°C. A given mass of water thus has a minimum volume at 4°C, i.e. water has a maximum density at this temperature (Fig. 6.1 ). The original definition of the unit of mass known as the kilogram was the mass of a cubic decimetre of water (1 litre of water) at 4°C.

  FIG. 6.1

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