Technology & Engineering
Thermal Strain
Thermal strain refers to the deformation or change in dimensions of a material due to changes in temperature. When a material is heated or cooled, its molecules expand or contract, causing the material to expand or contract as well. This can lead to stress and potential damage in materials and structures, making thermal strain an important consideration in engineering and design.
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6 Key excerpts on "Thermal Strain"
- Daryl Logan(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
We will concern ourselves only with the strains due to temperature variation, T « , and will consider both one- and two-dimensional problems. C H A P T E R 15 Copyright 2017 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. 15 | Thermal Stress 728 Temperature changes in a structure can result in large stresses if not considered properly in design. In bridges, improper constraint of beams and slabs can result in large compressive stresses and resulting buckling failures due to temperature changes. In statically indeterminate trusses, members subjected to large temperature changes can result in stresses induced in mem-bers of the truss. Similarly, machine parts constrained from expanding or contracting may have large stresses induced in them due to temperature changes. Composite members made of two or more different materials may experience large stresses due to temperature change if they are not thermally compatible; that is, if the materials have large differences in their coefficients of thermal expansion, stresses may be induced even under free expansion (Figure 15 –1). When a member undergoes a temperature change the member attempts to change dimensions. For an unconstrained member AB (Figure 15 –2) undergoing uniform change in temperature T , the change in the length L is given by d a 5 TL T (15.1.1) where a is called the coefficient of thermal expansion and T is the change in temperature. The coefficient a is a mechanical property of the material having units of 1 C / 8 (where 8 C is degrees Celsius).
eBook - PDF- Timothy A. Philpot(Author)
- 2014(Publication Date)
- Wiley(Publisher)
43 P2.13 A thin square plate PQRS is symmetrically deformed into the shape shown by the dashed lines in Figure P2.13. For the deformed plate, determine (a) the normal strain of diagonal QS. (b) the shear strain xy at corner P. 251.2 mm 249.7 mm 250 mm y x S R Q P Undeformed Deformed FIGURE P2.13 When unrestrained, most engineering materials expand when heated and contract when cooled. The Thermal Strain caused by a one-degree (1°) change in temperature is designated by the Greek letter (alpha) and is known as the coefficient of thermal expansion. The strain due to a temperature change of T is T T (2.6) The coefficient of thermal expansion is approximately constant for a considerable range of temperatures. (In general, the coefficient increases with an increase of temperature.) For a uniform material (termed a homogeneous material) that has the same mechanical properties in every direction (termed an isotropic material), the coefficient applies to all dimensions (i.e., all directions). Values of the coefficient of expansion for common materi- als are included in Appendix D. Total Strains Strains caused by temperature changes and strains caused by applied loads are essentially independent. The total normal strain in a body acted on by both temperature changes and applied load is given by total T (2.7) Since homogeneous, isotropic materials, when unrestrained, expand uniformly in all direc- tions when heated (and contract uniformly when cooled), neither the shape of the body nor the shear stresses and shear strains are affected by temperature changes. 2.4 Thermal Strain A material of uniform composition is called a homogeneous material. In materials of this type, local variations in composition can be considered negligible for engineering purposes. Furthermore, homogeneous materials cannot be mechanically separated into different materials (e.g., carbon fibers in a polymer matrix).
- C.K Maiti, S Chattopadhyay, L.K Bera(Authors)
- 2007(Publication Date)
- CRC Press(Publisher)
Furthermore, at these temperatures and/or stress levels, the amorphous mate-rials may exhibit viscoelastic behavior and the poly-crystalline materials may Strain Engineering in Microelectronics 27 FIGURE 2.2 Sources of various stresses in silicon microelectronics. After S. Chaudhry, “Analysis and Modeling of Stress Related Effects in Scaled Silicon Technol-ogy,” Doctoral Dissertation, University of Florida, 1996. have elastoplastic behavior as well. Residual stresses are critical in Si technol-ogy and can be experimentally determined using either optical techniques al-lowing the calculation of the substrate curvature, or directly by micro-Raman spectroscopy or x-ray/electron diffraction techniques. Fig. 2.2 is a summary of various stresses encountered in silicon microelectronics. The stresses can generally be classified into five groups: (a) the temperature change and the thermal growth of material (i.e., silicon dioxide and silicides), (b) the etching of materials, (c) the deposition processes which create intrinsic stresses, (d) the structural changes of deposited films due to densification, hydration or dehydration, crystallization, and (e) the implantation of dopants. The total measured stress is the sum of these five components. Thermal stresses are induced by the mismatch of the thermal expansion co-efficients between different materials. They arise when the system undergoes a temperature variation during the various stages of the integrated circuit pro-cessing. By introducing a number of assumptions; (i) materials are isotropic and homogeneous and (ii) there is no temperature gradient in the film or in the substrate, the Thermal Strain, induced by a variation in temperature can be calculated from 28 Strained-Si Heterostructure Field Effect Devices = α ( T ) · Δ T (2.1) where α (T) is the thermal expansion coefficient of the film. For silicon, it has been observed that this coefficient is temperature dependent.
eBook - ePub- Robert L. Mott, Joseph A. Untener(Authors)
- 2021(Publication Date)
- CRC Press(Publisher)
14 Thermal Effects and Elements of More than One MaterialThe Big Picture14–1 Objectives of This Chapter14–2 Deformation due to Temperature Changes14–3 Thermal Stress14–4 Members Made of More than One MaterialThe Big Picture Discussion Map-
Engineering drawings typically represent parts in one given condition, but when the temperature changes, the material responds accordingly. In many applications, these changes must be considered for proper performance and safety.
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Thermal changes when parts are free to grow or shrink without restriction will result in a change in part dimensions. If thermal changes occur while a part is restricted from growth or shrinkage, internal stresses will be induced.
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Some elements that carry loads are made of more than one material. Those materials share the load, but not necessarily evenly. Analysis of each material is required to ensure proper performance and safety.
To this point, elements considered in this text have been assumed to remain at the same temperature. Automotive engine components like those shown in Figure 14-1 , though, can go through extreme temperature conditions. When sitting in the morning in a northern climate, the entire engine might be well below freezing. Within minutes of starting the engine, however, an internal component near the combustion of fuel will reach extremely high temperatures. As a designer, you must anticipate the full range of conditions and ensure that your designs will perform as specified.FIGURE 14–1
eBook - PDF- Andrzej Weronski(Author)
- 1991(Publication Date)
- CRC Press(Publisher)
4 Thermal Fatigue 4.1 THERMAL STRESSES AND STRAINS Thermal stresses arising from thermal transients are commonly divided into: 1. Strain-controlled stresses , where the local expansion or contraction of mate-rial is hindered by the surrounding material; 2. Displacement-controlled stresses , where the overall expansion or contraction of the component is limited by another component. Displacement-controlled stresses can be calculated only in a limited number of cases. Figure 4.1 shows a number of examples illustrating the former type of stresses. Let us assume that the elastic plate has originally uniform temperature T q quenched from one face to the Tf temperature. The relevant temperature distri-bution and internal strain a,- are shown in Fig. 4.1. When one direction is restrained against expansion, a om compressive membrane stress must be applied: L/2 °m = ~ l J E a(T -T0) dx' = Ea@m(T0 -Tf ) -L/2 where L = plate thickness E = Young’s modulus a = coefficient of linear expansion 0 m = nondimensional mean temperature jc' = x -L/2, x being measured from the face T = temperature at the x position 108 Thermal Fatigue 109 QUENCHED FACE TEMPERATURE (a) TEMPERATURE DISTRIBUTION DISTORTED SHAPE AFTER QUENCHING ON TOP FACE ORIGINAL SHAPE ' f o * Y HOT (b) STRESSES -NO RESTRAINT COLD — è i t o T T —n HOT (c) STRESSES COLD +ve 0 —veO BENDING RESTRAINT +ve +ve (ip O^otTemp 'r r -j-jp — n HOT (d) STRESSES r-x -r 0 —ve 0 6¡ Ob TOTAL RESTRAINT Figure 4.1 Stress distribution in a plate quenched on one face under various degrees of restraint. (From Clayton, 1983.) If rotation of any plate section is prevented, then a bending stress of 2a^r7L must be applied, where +L/2 ab = -A ¡ E a (T -T 0)x'dx' -LI2 If both extension and rotation are prevented, the a t stress that must be applied is equal to a, = -E a(T -To) = EaG(T0 -Tf ) where there is restraint in two directions, Gm, o^, and <5t are multiplied by l/(l-v), v being Poisson’s ratio and ot = a/ + + o m.
eBook - PDF- J. Beddoes, M. Bibby(Authors)
- 1999(Publication Date)
- Butterworth-Heinemann(Publisher)
Stress and strain during deformation The ingot and continuous casting operations, outlined in the previous chapter, rarely yield a finished product that does not need further processing. Typically, ingots or strands are further processed by one of several bulk deformation operations, often followed by additional shaping via sheet deformation, machining or joining. The prin- ciples that underlie all of these processes are presented in Chapters 4-8. However, to analyse deformation processes, an understanding of the relationships between stress, strain and deformation is necessary. These relationships are presented in this chapter. During metal deformation, large changes in part geometry may occur. It is often important to understand the consequences of the geometrical shape change on the internal structure of the metal. Externally, force and power are applied to deform the part. Internally, the part reacts based on its microstructure and properties. These internal and external effects can usually be quantified to some degree by calcu- lations involving the stress-strain relationships of the workpiece. In this chapter basic stress-strain concepts are briefly introduced to illustrate their usefulness for metal deformation problems. The response of a material to mechanical loads is often measured by a uniaxial tension test. A tensile specimen, such as shown in Fig. 3.1, is loaded with a force, F. The exten- sion of the sample, typically measured by a change in gauge length, is recorded and the results displayed as a load-extension curve. Load-extension curves characteristic of low carbon steel and many nonferrous metals are shown in Fig. 3.1. Since both load and extension are clearly dependent on specimen size, they are not unique mate- rial properties. Consequently, tensile test results are almost always expressed as stress and strain. Engineering stress is defined as F (3.1) O'a = A-~ where: t7 a is the engineering stress
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