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Why Do Ductile Materials Neck in the Middle?

  1. Jun 10, 2017 #1
    For materials that have a propensity for necking, assuming they're heterogeneously structured/have equal strength throughout and are without defects- why do these materials have a propensity for necking in the center when forces are applied to both ends?

    I'm trying to use physics to explain why, when you pull a piece of pizza dough apart, it will thin out/neck in the center, and then, if you keep pulling, it will eventually break at that center point.
     
  2. jcsd
  3. Jun 10, 2017 #2
    That sounds like an interesting problem but does it really happen? I just tried stretching thin strips of paper but in most cases the strip broke close to one of the ends where I was gripping the paper. Of course paper is not pizza dough. Please let us know the results of any experiment that you try out.
     
  4. Jun 10, 2017 #3
    The fibers in paper might stretch a tiny bit when pulled apart, but, for the most part, it isn't ductile. Here's a good photo of taffy being stretched:

    https://littlehousebliss.files.wordpress.com/2014/07/taffy-after-pulling.jpg

    This is typical for taffy and dough- and chewing gum, and molten glass- off the top of my head.
     
  5. Jun 11, 2017 #4
  6. Jun 11, 2017 #5
    Isn't it true for ductile materials in general, including metal? Here are a couple examples:





    That being said, I have no formal education in material properties, and I might just be misunderstanding the discussion.
     
  7. Jun 11, 2017 #6


    From your videos necking does appear to start close to the middle of the specimen but in the video I linked necking is a fair distance from the centre (go to 5.17). It would be nice to get access to other results.

    One thing that should be considered is that the tested samples had a wider cross section at each end. On the plus side I think this prevents necking and breakage at the places where the sample is gripped. On the minus side I think that these two discontinuities in cross sectional area can cause some sort of discontinuity in the crystal structure along the length of the bar which is possibly, assuming everything else is perfect, symmetrical about the centre. It would be interesting to test this possible effect further by using either longer bars and or bars where the two ends have different cross sectional areas.

    I think the biggest problem is that ductile metals and indeed pizza dough are not heterogeneously structured and of equal strength throughout. The only materials I'm familiar with which come close to having such characteristics are intrinsic semiconductors and glass of the type used in fibre optic cables.

    I think there are experts in this forum who could give better advice than us.
     
  8. Jun 11, 2017 #7


    I don't know how the error occurred above but this shows the result i referred to.
     
  9. Jun 11, 2017 #8
    After being properly kneaded and proofed, pizza dough, if formed into a column and pulled apart, will fail in the center point at least 99 out of 100 times. It may not be homogenously* structured enough to happen 100% of the time, but it's enough to happen almost all the time- and it's the 99 times- when a material is of equal strength throughout that it fails in the middle- that's what I'm trying to understand.

    *I had been using 'heterogeneous' when I meant 'homogeneous.'
     
  10. Jun 11, 2017 #9
    When you tested the dough was it stretched sideways so that the dough was kept approximately horizontal and straight? I mention this because I imagine the dough bending under its own weight and forming a curve with the central part of the dough being at the lowest point. If this happens the tension will not be even at all points at any particular cross section of the dough but can be a maximum at the bottom part of the central section. It's analogous to bending a stick of wood, the outside of the bend will have the greatest stretch and the greatest tension.

    (Whoops I used heterogeneous as well)
     
  11. Jun 11, 2017 #10
    That's a good question. Yes, gravity would play a role if pulling horizontally, but I'm talking about pulling vertically, like the steel in the video.
     
  12. Jun 12, 2017 #11

    Stephen Tashi

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    Can we find a simple model for a homogeneous material that exhibits necking?

    Suppose we model a rod as chain of "identical" coiled springs connected end-to-end along the x-axis. Pulling on the ends of the rod (slowly) would cause the coils of the springs to form narrower coils, but there is no reason one spring would coil narrower than another.

    Suppose we model a rod as a two parallel chains of such springs and connect each junction of two coils on chain A with a vertical spring from that junction to the corresponding junction of chain B. I see no reason why stretching the rod would pull the two x-axis chains of springs closer together near the middle (assuming there is no initial tension in the springs that go in the y-direction.)

    Now suppose we join the two chains of springs that go in the x-direction using other springs that are not parallel to the y-axis. For example, we could join chains of springs A and B with springs that go from junction A[n] to B[n+1] and springs that go from junction A[n+1] to B[n]. If this configuration is stretched then do the two chains of springs in the x-direction remain parallel?

    In tensile testing or pizza dough pulling, the very ends of the specimen are constrained so the specimen can't change its cross sectional area at its ends. To model that with chains of springs, we impose a similar constraint on the y-distance between the two x-axis chains of springs at their ends. Intuitively (to me) the force needed to keep the two springs apart that that constant y-distance increases as the rod is stretched. So the x-axis chains of springs won't remain parallel because if they did then, at their ends, they would not exert any force in the y-direction.
     
  13. Jun 13, 2017 #12

    Nidum

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    Flat tensile specimen v3.png


    FEA showing VonMises stress in a flat test specimen under axial load .
     
    Last edited: Jun 13, 2017
  14. Jun 13, 2017 #13
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