Elasticity of Materials
Elasticity of materials refers to the ability of a material to return to its original shape after being deformed by an external force. This property is important in engineering and technology as it helps determine how materials will behave under different conditions, such as stress and strain. Understanding the elasticity of materials is crucial for designing and constructing durable and reliable structures and products.
6 Key excerpts on "Elasticity of Materials"
eBook - ePub- John Bird(Author)
- 2019(Publication Date)
- Routledge(Publisher)
...Similar arguments lie in manufacturing engineering, where the engineer must be able to estimate the ability of his/her machines to bend, cut or shape the artefact s/he is trying to produce, and at a competitive price! This chapter provides explanations of the different terms that are used in determining the properties of various materials. The importance of knowing about the effects of forces on materials is to aid the design and construction of structures in an efficient and trustworthy manner. At the end of this chapter, you should be able to: define force and state its unit recognise a tensile force and state relevant practical examples recognise a compressive force and state relevant practical examples recognise a shear force and state relevant practical examples define stress and state its unit calculate stress σ from σ = F A define strain calculate strain e from ε = x L define elasticity, plasticity, limit of proportionality and elastic limit state Hooke’s law define Young’s modulus of elasticity E and stiffness appreciate typical values for E calculate Ε from E = σ ε perform calculations using Hooke’s law plot a load/extension graph from given data define ductility, brittleness and malleability, with examples of each Science and Mathematics for Engineering. 978-0-367-20475-4, © John Bird. Published by Taylor & Francis. All rights reserved. 26.1 Introduction A good knowledge of some of the constants used in the study of the properties of materials is vital in most branches of engineering, especially in mechanical, manufacturing, aeronautical and civil and structural engineering...
- Shashanka Rajendrachari, Orhan Uzun(Authors)
- 2021(Publication Date)
- Bentham Science Publishers(Publisher)
...Mechanical Properties of Materials R. Shashanka, Orhan Uzun Abstract The mechanical properties of a material reverberate the correlation between its response and deformation to an applied load. Some of the very important mechanical properties are ductility, strength, stiffness, and hardness. These properties can be studied by using various instruments available in the metallurgy or mechanical engineering laboratories. The mechanical properties of materials mainly depend upon the factors like nature of the applied load, its duration, and environmental conditions. The applied load may be tensile, compressive, or shear in nature; and its magnitude may be constant or may fluctuate continuously with time. Another important factor is time or duration, and it may vary from a fraction of a second to many years. Some of the important tests used to study mechanical properties are, creep test, tensile test, compression test, fatigue test, hardness test, impact tests, etc. Keywords: Creep, Ductility, Elastic region, Engineering stress-strain curves, Fracture stress, Hardness, Malleability, Necking, Proof stress, Proportional stress, Strain, Strain hardening, Stress, Toughness, Tensile test, Ultimate tensile strength, Yielding region, Yield stress. 1. INTRODUCTION Fig. (1) depicts the various mechanical properties of materials. Generally, the quality of a material can be investigated by studying their mechanical properties; then, materials will be rejected or accepted based upon the obtained results. Therefore, it is important to study the mechanical properties of materials. In this chapter, we have discussed various mechanical tests used to study the mechanical properties. 2. TENSILE TEST Generally, the tensile test is used to investigate the strength, toughness, resilience, ductility and many other mechanical properties [ 1 ]. Solid materials will undergo deformation when they are subjected to load; and applied load can be tensile, compressive or shear. Fig...
eBook - ePubIntroduction to Engineering Mechanics
A Continuum Approach, Second Edition
- Jenn Stroud Rossmann, Clive L. Dym, Lori Bassman(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
...Materials whose behavior is best described by such a combination are known as viscoelastic materials. For viscoelastic materials, both how much they deform and how fast they deform are important. Many, biomaterials exhibit some degree of viscoelasticity. The two primary characteristics of viscoelastic behavior are creep and stress relaxation. Creep occurs when a material is exposed to a constant load for a long time and the material deforms increasingly: it is why a rubber band used to suspend a weight will gradually lengthen, and why you will find that you are measurably shorter at the end of an active day during which your intervertebral cartilage has been subjected to constant compressive loading. Stress relaxation means that when a constant deformation is applied to a material, over time it will resist that deformation less, so that the experienced loading decreases with time. Another key feature of viscoelastic materials is hysteresis. This is the term used to describe the tendency of viscoelastic materials to dissipate energy, rather than to store all of the energy of deformation as linearly elastic solids do. A schematic of this behavior is shown on a stress–strain diagram in Figure 14.4a ; the area between the loading and unloading curves represents dissipated or lost energy. (For a Hookean solid, the loading and unloading curves are the same for small deformations.) Figure 14.4b shows an experimentally obtained hysteresis curve for bovine veins in which it becomes clear that for these vessels, the amount of energy dissipated increases with increasing strain rate. This energy dissipation is what makes viscoelastic materials well suited to absorbing or cushioning shock. FIGURE 14.4 Hysteresis of viscoelastic materials: (a) representative stress–strain diagram; and (b) experimentally obtained stress–strain diagram for bovine veins. (Data from J. S...
eBook - ePubStructure for Architects
A Case Study in Steel, Wood, and Reinforced Concrete Design
- Ashwani Bedi, Ramsey Dabby(Authors)
- 2019(Publication Date)
- Routledge(Publisher)
...Wood’s material strength is represented by values for bending stress (F b), tensile strength parallel to the grain (F t), compressive strength parallel to the grain (F c), compressive strength perpendicular the grain (F c⊥), and shear strength parallel to the grain (F v). Concrete’s most important material strength is its compressive strength, represented by (f′ c). Other important concrete properties such as shear strength, rupture strength, and modulus of elasticity, are expressed as a function of f′ c. Material Stiffness Robert Hooke in the late 1600s discovered that when stress is initially applied on a material, the strain increases proportionally. This proportional relationship, called Hooke’s Law, is represented by a straight line on a stress-strain curve and exists only to the proportional limit— a unique point for different materials, beyond which they behave differently. Within the proportional limit, when stress is removed, strain disappears and the material returns to its original shape—the material is said to behave elastically. Material stiffness is a measure of a material’s resistance to deformation. It is represented by the modulus of elasticity (E), also known as Young’s modulus, and is commonly found in beam deflection and column buckling formulae. Modulus of elasticity is defined as the ratio of stress to strain within the proportional limit of a material’s stress-strain curve, and is a linear relationship. E = STRESS / STRAIN The higher a material’s modulus of elasticity, the steeper its stress-strain slope and the greater its stiffness (Figure 3.4). Figure 3.4 Modulus of Elasticity Comparison on a Stress-Strain Diagram Let’s examine the stress-strain curves for steel, wood, and concrete to better understand their unique structural characteristics. 3.2 Stress-Strain Curves for Steel, Wood, and Concrete Stress-Strain Curve for Steel in Tension Steel’s stress-strain curve is similar in tension and compression for stresses within the elastic range...
eBook - ePub- Jack Hu, Zdzislaw Marciniak, John Duncan(Authors)
- 2002(Publication Date)
- Butterworth-Heinemann(Publisher)
...1 Material properties The most important criteria in selecting a material are related to the function of the part – qualities such as strength, density, stiffness and corrosion resistance. For sheet material, the ability to be shaped in a given process, often called its formability, should also be considered. To assess formability, we must be able to describe the behaviour of the sheet in a precise way and express properties in a mathematical form; we also need to know how properties can be derived from mechanical tests. As far as possible, each property should be expressed in a fundamental form that is independent of the test used to measure it. The information can then be used in a more general way in the models of various metal forming processes that are introduced in subsequent chapters. In sheet metal forming, there are two regimes of interest – elastic and plastic deformation. Forming a sheet to some shape obviously involves permanent ‘plastic’ flow and the strains in the sheet could be quite large. Whenever there is a stress on a sheet element, there will also be some elastic strain. This will be small, typically less than one part in one thousand. It is often neglected, but it can have an important effect, for example when a panel is removed from a die and the forming forces are unloaded giving rise to elastic shape changes, or ‘springback’. 1.1 Tensile test For historical reasons and because the test is easy to perform, many familiar material properties are based on measurements made in the tensile test. Some are specific to the test and cannot be used mathematically in the study of forming processes, while others are fundamental properties of more general application. As many of the specific, or nonfundamental tensile test properties are widely used, they will be described at this stage and some description given of their effect on processes, even though this can only be done in a qualitative fashion. A tensile test-piece is shown in Figure 1.1...
eBook - ePubPractical Plant Failure Analysis
A Guide to Understanding Machinery Deterioration and Improving Equipment Reliability, Second Edition
- Neville W Sachs, P.E.(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
...This property, the amount of deflection for a given load, is the modulus of elasticity, and is frequently called Young’s Modulus. For all carbon steels, whether the weak inexpensive stuff paper clips are made from or a super strong heat-treated alloy, the modulus of elasticity is about 30 × 10 6 and they elongate identically. (The reason we sometimes use higher strength materials is that they will elastically deform much more before taking a permanent set, i.e., before their yield strength is exceeded.) Figure 3.4 A typical stress-stain diagram showing how much a part distorts with a given load (stress). Other metals have differing moduli of elasticity as shown in Table 3.1. Table 3.1 Elastic Moduli (Young’s Modulus) for Some Common Materials Material Metric Units – GPa US Units – × 10 6 psi Aluminum 69 10 Beryllium 269 39 Cast Iron 90 to 150 13 to 22 Copper 105 15.5 Lead 14 2 Monel 175 25 Stainless Steel 190 28 Mild Steel 206 30 Titanium 103 15 Nylon 7.5 to 19 1.1 to 2.8 Polyethylene 48 to 95 7 to 14 Looking at the modulus of elasticity values in the chart, one sees that if identical pieces are made out of aluminum and steel and loaded in the same manner, the aluminum part will elongate or deflect almost three times as much as the steel one. By the same token, a copper piece with the same load would deflect about twice what the steel piece would do. This elongation (or strain) is relatively easy to calculate. The modulus of elasticity, E, is expressed in GPa or psi and can be visualized as the load that would cause a perfectly elastic part to double in length...
