Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages Introduction to Mechanical Properties of Materials Questions
Introduction to Mechanical Properties of Materials AimsBefore you startIntroductionTensile test: force and extensionStress, strain and Poisson's ratioElastic deformation: Hooke's law and stiffnessViscoelasticityPlastic deformation: strength and ductilitySlip: resolved shear stress and Schmid factor, Taylor factorHardness and work hardeningCreepFracture: toughnessDuctile-brittle transition temperatureSummaryQuestionsGoing further
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Questions

Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

  1. Which are the conditions that define ideal elastic behaviour? (You may pick more than one answer)

    a The strain response at each level of applied stress (or vice versa) has a unique equilibrium value.
    b The equilibrium reponse is achieved instaneously.
    c The response is linear.
    d None of above.

  2. Which of the mechanical behaviours below is time dependent? (You may pick more than one answer)

    a Ideal elastic behaviour.
    b Viscoelastic behaviour.
    c Creep.
    d Diffusion.

  3. The animation below shows the linear elastic behaviour of copper, calculate its Young’s Modulus E.

    (a) 130 GPa
    (b) 130 MPa
    (c) 130 kPa
    (d) 130 Pa

  4. Select the mechanical process responsible for plastic deformation. (You may pick more than one answer)

    a Dislocation glide.
    b Deformation twinning.
    c Dislocation combination.
    d None of above.

  5. Dislocation glide is temperature dependent. As the temperature drops, a metal may transform from ductile to brittle (i.e. it undergoes less plastic deformation). The crystal structure affects the ductile brittle transition temperature because (you may pick more than one answer)

    a Different Burgers vector.
    b Different slip systems available.
    c Different energy barrier to plastic flow.
    d None of above.

  6. Calculate the stresses inside a pressurised thin-wall (i) spherical and (ii)cylindrical vessels from the diagrams below.


  7. The elastic properties of natural rubber (cis-1,4-polyisoprene) can be represented by the Maxwell model of a spring (with stiffness k) and a dashpot (with viscosity ν) in series. When subjected to an oscillating stress at angular frequency, ω, the effective Young’s modulus E of the rubber is given by

    where the characteristic relaxation time, tR, is given by

    (i)Obtain an expression for E at high and low ω.
    (ii) Sketch the variation of E as a function of ω2.
    (iii) If the temperature is higher, how will the sketch change?

  8. Consider a rolling mill below to reduce the cross section area of the workpiece.

    The increment of plastic work done on drawing a cylinder of cross sectional area A and length L an amount δL is given by where σy is the uniaxial yield stress of the component material. Here we assumed no work hardening, so the applied force is σyA.
    From this expression, find an expression for minimum amount of work per unit volume, Up required to deform plastically a component with reduction ratio R (> 1).

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