Stiffness

5 Key excerpts on "Stiffness"

• 

  eBook - ePub

  Materials

  Engineering, Science, Processing and Design

  • Michael F. Ashby, Hugh Shercliff, David Cebon(Authors)
  • 2009(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  mode of loading . The cover picture illustrates the common ones. Ties carry tension—often, they are cables. Columns carry compression—tubes are more efficient as columns than solid rods because they don’t buckle as easily. Beams carry bending moments, like the wing spar of the plane or the horizontal roof beams of the airport. Shafts carry torsion, as in the drive shaft of cars or the propeller shaft of the plane. Pressure vessels contain a pressure, as in the tires of the plane. Often they are shells: curved, thin-walled structures.

  Stiffness is the resistance to change of shape that is elastic , meaning that the material returns to its original shape when the stress is removed. Strength (Chapter 6 ) is its resistance to permanent distortion or total failure. Stress and strain are not material properties; they describe a stimulus and a response. Stiffness (measured by the elastic modulus E , defined in a moment) and strength (measured by the elastic limit σ y or tensile strength σ ts ) are material properties. Stiffness and strength are central to mechanical design, often in combination with the density, ρ . This chapter introduces stress and strain and the elastic moduli that relate them. These properties are neatly summarised in a material property chart —the modulus–density chart—the first of many that we shall explore in this book.

  Density and elastic moduli reflect the mass of the atoms, the way they are packed in a material and the Stiffness of the bonds that hold them together. There is not much you can do to change any of these, so the density and moduli of pure materials cannot be manipulated at all. If you want to control these properties you can either mix materials together, making composites, or disperse space within them, making foams. Property charts are a good way to show how this works.

  4.2 Density, stress, strain and moduli

  Density

  Many applications (e.g. sports equipment, transport systems) require low weight and this depends in part on the density of the materials of which they are made. Density is mass per unit volume. It is measured in kg/m3 or sometimes, for convenience, Mg/m3 (1 Mg/m3 = 1000 kg/m3 ).

  The density of samples with regular shapes can be determined using precision mass balance and accurate measurements of the dimensions (to give the volume), but this is not the best way. Better is the ‘double weighing’ method: the sample is first weighed in air and then when fully immersed in a liquid of known density. When immersed, the sample feels an upward force equal to the weight of liquid it displaces (Archimedes’ principle1 ). The density is then calculated as shown in Figure 4.1

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  eBook - ePub

  Introduction to Composite Materials

  • StephenW. Tsai(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  chapter 1 Stiffness of unidirectional composites

  The Stiffness of unidirectional composites, like any other structural material, can be defined by appropriate stress-strain relations. We will show that the coefficients or material constants of these relations can be packaged in a set of engineering constants, compliance components, or modulus components. The components of any one set are directly expressible in terms of the components of the other sets. The Stiffness of unidirectional composites is governed by the same stress-strain relation that is valid for conventional materials. Only the number of independent constants are four for composites and two for conventional materials.

  1.  stress

  Stress is a measure of internal forces within a body. This together with strain are the key variables for the determination of Stiffness and strength of a material. The mechanisms of deformation and failure are also interpreted in terms of the state of stress and strain. They are the fundamental variables for the mechanical behavior of materials similar to temperature and heat flux for heat conduction; or pressure, volume and temperature for gas.

  There is no direct measurement for stress. Instead, stress is inferred or derived from the following: •  Applied forces using stress analysis. •  Measured displacements also using stress analysis. •  Measured strains using stress-strain relations.

  When we talk about stress we usually mean the average stress over some physical dimension. This is similar to population measured over a city, county or state. In our study of composites we deal with three levels of average stress:

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  eBook - ePub

  Science and Mathematics for Engineering

  • John Bird(Author)
  • 2019(Publication Date)
  • Routledge

    (Publisher)

  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. For example, most steels look the same, but steels used for the pressure hull of a submarine are about five times stronger than those used in the construction of a small building, and it is very important for the professional and chartered engineer to know what steel to use for what construction; this is because the cost of the high-tensile steel used to construct a submarine pressure hull is considerably higher than the cost of the mild steel, or similar material, used to construct a small building. The engineer must not only take into consideration the ability of the chosen material of construction to do the job, but also its cost. 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. For example, most steels look the same, but steels used for the pressure hull of a submarine are about 5 times stronger than those used in the construction of a small building, and it is very important for the professional and chartered engineer to know what steel to use for what construction; this is because the cost of the high-tensile steel used to construct a submarine pressure hull is considerably higher than the cost of the mild steel, or similar material, used to construct a small building. The engineer must not only take into consideration the ability of the chosen material of construction to do the job, but also its cost. 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.

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  eBook - ePub

  The Science For Conservators Series

  Volume 3: Adhesives and Coatings

  • Conservation Unit Museums and Galleries Commission(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  Figure 4.3 . The data are for typical samples of a given material that have been prepared under controlled conditions and of standardised shape and size. Other samples tested in other conditions could give values somewhat different from those quoted and this is particularly likely with the objects you handle. Most of the properties of a material, especially tensile strength, are not immutable. The internal constitution of a material depends on its history — how it was produced and subsequently treated. A sample with cracks or holes in it will have a lower tensile strength than normal (see Section 4D), similarly so would those that have corroded, rotted or been degraded in some way. However, bearing these limitations in mind, such data can be useful. For instance, notice that the widely used adhesives epoxy resin and phenol formaldehyde have a much lower tensile strength when solid than metals, but that they are stronger than wood tested across the grain. This raises the possibility that a joint made between pieces of wood with one of these adhesives could break within the wood rather than in the joint.

  B Strain and Stiffness

  All solids change their shape (deform) when subjected to a weight or any other kind of force. When you stretch a rubber band or squeeze an eraser, the change of shape is obvious. If you try to squeeze a piece of glass, pottery, metal or wood between your fingers you will not detect a change of shape because a much greater force is needed in order to produce an observable change. These materials appear to have a greater intrinsic Stiffness. When large objects made from these stiff materials are subject to large forces the deformation is observable; trees sway in the wind, aeroplane wings flap, and the tops of tall skyscrapers move a metre or two in a gale.

  Stiffness

  It is clear that some objects are stiffer than others, that is, they are more resistant than others to changing their shape under an applied force. A branch is stiffer than a twig; they have the same intrinsic Stiffness (they are made of the same material) but differ in dimensions. You have to get rid of the effects of geometry to look at the material alone in order to study these phenomena in a scientific way. To understand why some materials are intrinsically stiffer than others you need to consider the bonds that hold atoms and molecules together in a solid. Envisage that the millions of bonds between atoms or molecules in a material behave like minute springs. When a material is stretched or compressed each of these bonds is stretched or compressed too, and the overall change of shape of the material is the result of the many very small changes at a microscopic level. The effect produced in the spring-like bonds in a material is illustrated in Figure 4.4 . Figure 4.4(a)

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  eBook - ePub

  Fundamentals of Materials Engineering - A Basic Guide

  • Shashanka Rajendrachari, Orhan Uzun(Authors)
  • 2021(Publication Date)
  • Bentham Science Publishers

    (Publisher)

  4 ]. Toughness is measured by calculating the area under the stress-strain curve from a tensile test and it is the unit of energy per volume. One of the metals having maximum toughness is Tungsten, and its toughness can be significantly increased by alloying with suitable metals.

  Fig. (7)) The stress-strain curve showing the toughness [4 ].

  5.8. Resilience

  It is the ability of a material to rebound elastically into the original shape. In other words, it is the total energy absorbed by the materials during elastic deformation. Fig. (

  8

  ) shows the resilience and modulus of resilience in load-extension and stress-strain diagrams, respectively [4 ]. It is the area up to the elastic limit, as shown in the figure.

  Fig. (8)) (a) Load-extension diagram showing resilience. (b) Stress-strain diagram showing modulus of resilience [4 ].

  The maximum amount of energy absorbed up to the elastic limit, without permanent distortion, is called proof resilience. Similarly, the modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without permanent distortion. The unit of resilience is joule per cubic meter (J/m3 ).

  5.9. Stiffness

  Stiffness is expressed by Young’s modulus, and it is defined as the resistance of material for elastic deformation. The values of both true stress and true strain are from the elastic region, and it does not affect by alloying or change in the microstructure.

  5.10. Ductility

  Ductility is an ability of a material to stretch under tensile stress before fracture. In other words, it can also be defined as an ability of a material to drawn in to thin wire. Generally, ductility can be expressed in terms of percentage elongation, and it is given as below;

  Ductility of a material can be graphically represented as below:

  Fig. (

  9

  ) represents the load-extension diagram showing the ductility of materials [4 ]. Examples of ductile materials are copper, aluminum, steel, and some more metals. Ductility is a physical property, and it is not having any unit.

  5.11. Malleability

  Malleability is just opposite to that of ductility. In the case of the ductility test, tensile forces are used, but here compressive forces are used. It is defined as the ability of a material to undergo plastic deformation before fracturing under compressive stress. It can also be defined as the ability of a material to undergo rolling or flattening into thin sheets. Most of the metals with high ductility also possess greater malleability, and it can be measured by % reduction in the cross-sectional area of the material under study.

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