We will spend most of our time examining materials loaded in uniaxial tension but there are many other applied stress modes 1 Typical mechanical testing machine the load cell measures force and the extensometer measures displacement 2 The same material can exhibit varied force displacement responses depending on the sample size To make material property measurements independent of sample size we use the concepts of stress and strain 3 Converting force displacement to stress strain Ao cross sectional sample area l0 is the initial sample length Engineering stress Units of N m2 or Pa Engineering strain Dimensionless m m F A0 l lo l lo lo 4 Typical stress strain curve for a ductile metal Let s focus first on the linear or elastic portion of the curve 5 The elastic region obeys Hooke s law E E is Young s modulus and is a measure of the stiffness or rigidity of a material 6 Young s modulus values are typically provided for room temperature but E can definitely change with temperature 7 Poisson Effect occurs during elastic deformation For example applying a tensile stress along the z axis results in a positive strain along the z axis and a negative strain along the x and y axes The Poisson ratio is the ratio of axial to radial strain and is in the range of 0 25 0 35 for most ductile metals Volume is typically not conserved during elastic deformation The exception is when a material has a Poisson ratio of 0 50 8 z x Let s look at the case of triaxial tension the magnitude of the strain in each direction depending on the relative magnitudes of x y and z y 9 Once you understand the triaxial case the uniaxial case is relatively straightforward z 10 Plastic or Irreversible Deformation Note the relatively small strain associated with elastic deformation 11 The stress at which the curve becomes nonlinear is called the yield stress y On the atomic scale it is the point where planes of atoms slide past one another For structural design the yield stress y is important because stresses should stay well below the yield stress Otherwise your structure experiences permanent deformation 12 Since it can be difficult for multiple observers to agree on the stress at which nonlinearity commences an offset yield stress is sometimes used 13 When a material is unloaded after plastic deformation the unloading curve runs parallel to the elastic portion of the loading curve nonrecoverable recoverable 14 Generalities About Ceramics Metals and Polymers Ceramics High E very high y such that at room temperature ceramics fracture before they yield Metals Moderate to high E moderate y Polymers Low E low y y in quotes because deformation occurs by chain sliding not by movement of atomic planes Below their glass transition temperature polymers are brittle 15 on top of having a low Young s modulus If stress is force per unit area then why does the stress drop in an engineering stress strain curve when the area of the cross section decreases Hint look at how engineering stress is calculated 16 What is the difference between engineering strain and true strain Consider the following experiment Two wires both with an initial length of 10 cm Wire A stretched to 12 cm in two steps step one from 10 to 11 cm step two from 11 to 12 cm Wire B Stretch from 10 to 12 cm in one step We should get the same value of total strain for wires A and B right l lo l lo lo li T ln lo Engineering Strain True Strain 17 T F Ai F A0 Notice that the difference between engineering and true stress is not significant until well after yielding Why should we care any structure would have collapsed by then 18 Strain hardening notice that the reloaded material has a higher yield stress than the material during initial 19 loading Different ductile metals exhibit different true stress true strain responses Large n Small n High strain portion We can fit the high strain portion of the curve with T K where K and n are constants 20 n T T K n T 21 Hardness is a measure of the localized resistance to plastic deformation Advantages over tensile testing a quick and easy b does not require a large amount of material c nondestructive 22 Mechanical Behavior of Polymers room temperature A brittle e g plexiglass B ductile e g bulk polyethylene C elastomeric e g rubber bands 23 Many polymers exhibit temperature dependent mechanical behavior The data below is for poly methylmethacrylate PMMA or plexiglass 24 Polymer chains within the neck region develop a degree of molecular orientation during tensile deformation Taken to the extreme one may fabricate high modulus polymer fibers 25 Many polymers exhibit viscoelastic behavior resulting in mechanical behavior that can be highly dependent on strain rate For example some silicone based polymers stretched slowly act like taffy but if you stretch the material rapidly it will snap or break This is an example of shear thickening behavior 26
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