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Homework Help: Stress strain diagram

  1. Dec 9, 2009 #1
    given the following points of the stress strain graph
    points.JPG
    and knowing that the stages are defined

    linear σ=Eε
    uniform plastic σ=Kδ2
    necking σ=αδ

    where ε is an elastic strain and δ plastic strain

    find the values of the constants E K n α

    using the given data i plotted σ(ε) and got the following
    Capture.JPG

    now to find the constant E, i take the linear portion and find its incline, i get
    E=33.33MPa

    as for the others
    for the platic deformation, can i take an of the points after (3,9) ?
    for each point i chose i get a different value
    K=σ/δ2
    K=4e4/(13e-4)2=2.366864e10
    K=4.5e4/(20e-4)2=1.125e10

    is the necking portion not meant to be after a maximum point in the graph? in this graph i have no such point.
     
  2. jcsd
  3. Dec 9, 2009 #2

    chemisttree

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    Linear, curved, linear.
     
  4. Dec 9, 2009 #3
    okay i see what you are saying, so then i can find the curve of the last part as i did for the first part, but how about the curved portion?
     
  5. Dec 9, 2009 #4
    as i said for each point i take i get a different value
    K=σ/δ^2
    K=4e4/(13e-4)^2=2.366864e10
    K=4.5e4/(20e-4)^2=1.125e10
     
  6. Dec 10, 2009 #5
    i think that the problem is the relationship between δ and ε, since the graph i have and the data given is for is σ(ε), but the constants i need are for σ(δ) what is the connection between δ and ε?
    i thought that δ=ε+c (c being the permanent deformation after the linear portion of the graph,) but i solved the equations using δ=ε+c

    σ=αδ
    σ=Kδ^2
    using the given data

    but i cannot solve for K, α, every time i plug in different data i get different values,

    i have been using the 1st 3 sets of data for the 1st linear section
    the second 3 sets for the parabolic section
    the last 2 sets for the final linear section

    clearly the δ cannot be raplaced directly by ε since when the stress=0 the function MUST also be 0, and the strain will not be 0 after plastic deformation, looking at the graph we can also see that the parabolic and linear sections will not reach (0,0)
    i can find the functions for these curves as a function of the strain ε but not δ which i need in order to find the constants
     
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