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2 May, 09:57

Calculate the Engineering Ultimate Tensile Strength and the maximum load in tension testing of an annealed copper specimen with an original diameter of 5 mm. Assume that the strain hardening coefficient for annealed copper is 0.50 and that the true stress at necking is 290 MPa.

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  1. 2 May, 11:49
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    Original diameter = 5mm

    d = 0.005m. r=0.0025m

    True stress (σ) = 290MPa

    Coefficient of annealing copper (n) = 0.5

    True stress is given as force/area

    σ=F/A

    Ao=πr^2

    Ao=1.963*10^-5m2

    F=σ * A

    F=290*10^6 * π * (0.0025) ^2

    F = 5694.13N

    Given that

    σ=Kε^n

    290=Kε^0.5

    n=ε=0.5 at necking

    Therefore

    290=K*0.5^0.5

    K=410.12MPa

    ε=In (Ao/A)

    0.5=In (π*0.0025^2/A)

    exp (0.5) = 1.96*10^-5/A

    A=1.96*10^-5/exp (0.5)

    A = 1.2*10^-5m2

    This is the new area

    Then the Ultimate Tensile Stress

    σ=F/A

    σ=5694.13/1.2*10^-5

    σ=4.75*10^8Pa

    σ=475MPa

    Therefore,

    The ultimate tensile stress is 475MPa.

    The maximum tension is

    Fo/Ao=F/A

    F = (Fo/Ao) * A

    F = (5694.13/1963*10^-5) * 1.2*10^-5

    F = 3479.99

    F=3480N.
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