Shear Stress and Stress-Strain Behavior Quiz
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Questions and Answers

What is the relationship between Brinell hardness (HB) and tensile strength for most steel alloys?

  • TS in MPa = 5.00 (HB)
  • TS in psi = 300 (HB)
  • TS in MPa = 3.45 (HB) (correct)
  • TS in psi = 500 (HB)

    • In the given illustrative problem of elongation computation for a piece of copper, what is the modulus of elasticity (E) for copper?

  • 110 GPa (correct)
  • 90 GPa
  • 100 GPa
  • 120 GPa

    • If a piece of copper is pulled in tension with a stress of 276 MPa and the deformation is entirely elastic, what will be the resultant elongation for a piece originally 305 mm long?

  • 1.020 mm
  • 0.765 mm (correct)
  • 0.500 mm
  • 0.350 mm

    • What is the diameter change in mm for a cylindrical brass rod with a diameter of 10 mm when subjected to a 2.5 x 10^3 mm load in an elastic deformation?

    <p>0.025 mm</p> Signup and view all the answers

    When a tensile stress is applied to a cylindrical brass rod, in which direction does the rod elongate?

    <p>z-direction</p> Signup and view all the answers

    In the context of material deformation, what relationship governs strain (𝜖) with stress (𝝈) according to the provided information?

    <p>𝜖 = 𝝈 / E</p> Signup and view all the answers

    What is the formula for computing shear stress?

    <p>𝜏 = 𝐹 / 𝐴₀</p> Signup and view all the answers

    What is the relationship described by Hooke's Law?

    <p>Stress is proportional to strain</p> Signup and view all the answers

    What does the modulus of elasticity represent?

    <p>Material's resistance to elastic deformation</p> Signup and view all the answers

    What does the slope of the linear segment in a stress-strain plot correspond to?

    <p>Modulus of Elasticity (E)</p> Signup and view all the answers

    In which type of deformation are stress and strain proportional?

    <p>Elastic deformation</p> Signup and view all the answers

    What does shear strain represent?

    <p>The tangent of the strain angle</p> Signup and view all the answers

    What is toughness defined as in materials science?

    <p>The ability to deform plastically before fracturing</p> Signup and view all the answers

    In the context of toughness, what does area ABC in a stress-strain curve represent?

    <p>Toughness of a brittle material</p> Signup and view all the answers

    What is the unit of measurement for toughness according to the information provided?

    <p>J/m3</p> Signup and view all the answers

    How is true stress defined in materials science?

    <p>Load divided by instantaneous cross-sectional area</p> Signup and view all the answers

    What happens beyond the onset of necking in terms of true stress and strain?

    <p>They are related by true stress = stress(1 + strain)</p> Signup and view all the answers

    Why must a metal display both strength and ductility to be considered tough?

    <p>To absorb energy and plastically deform before fracturing</p> Signup and view all the answers

    What is the minor load value for the Rockwell hardness test?

    <p>10 kg</p> Signup and view all the answers

    What is the purpose of the Brinell hardness test?

    <p>To measure the hardness of metal surfaces by forcing a hard, spherical indenter into the surface</p> Signup and view all the answers

    What is the diameter of the hardened steel (or tungsten carbide) indenter used in Brinell hardness tests?

    <p>10.00 mm</p> Signup and view all the answers

    What is the typical range of standard loads used in Brinell hardness tests?

    <p>500 to 3000 kg in 500-kg increments</p> Signup and view all the answers

    How is the Brinell hardness number (HB) determined?

    <p>By measuring the diameter of the resulting indentation and using a chart to convert to the appropriate HB number</p> Signup and view all the answers

    What is the purpose of the superficial Rockwell hardness test?

    <p>To measure the hardness of thin specimens</p> Signup and view all the answers

    What is the relationship between the modulus and the elastic strain of a material?

    <p>The greater the modulus, the stiffer the material, or the smaller the elastic strain that results from the application of a given stress.</p> Signup and view all the answers

    What is the purpose of the modulus as a design parameter?

    <p>The modulus is used for computing elastic deflections.</p> Signup and view all the answers

    What is the relationship between shear stress, shear strain, and the shear modulus?

    <p>Shear stress and shear strain are proportional through the expression $\tau = G\gamma$.</p> Signup and view all the answers

    What is the definition of Poisson's ratio?

    <p>Poisson's ratio is defined as the ratio of the lateral strain to the axial strains.</p> Signup and view all the answers

    What happens to the lateral strains when a tensile stress is applied to a metal specimen?

    <p>The lateral strains (in the x and y directions) are compressive and negative.</p> Signup and view all the answers

    What is the relationship between the axial strain and the lateral strains according to Poisson's ratio?

    <p>$\nu = -\epsilon_y/\epsilon_x = -\epsilon_z/\epsilon_z$</p> Signup and view all the answers

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