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Homework Help: Discerning the Elasticity Modulus of Brittle Cast Iron from Test Data

  1. Nov 26, 2012 #1
    Here goes try number two, the forum deleted my last post. :cry:

    First time poster, so hopefully I'm following the rules, I do apologise if I'm not. I have a problem with my lab report, I would be very grateful if anyone could help. Thanks.

    1. The problem statement, all variables and given/known data

    I'm writing a tensile test lab report and have hit a snag along the way. We were given three unknown specimens and through analysis of the recorded data, are to make educated guesses as to what they are. I have all but confirmed the first two are high carbon steel and aluminium of some description. Young's modulus, UTS and 0.2% proof stress are all accurate. In the case of the third sample, my modulus is far below what I would expect (22.5 GPa). I am however, convinced it is cast iron due to a number of factors; the shape of the load/extension diagram, the uts/fracture stress and above all the fact that it smelled like cast iron. :biggrin:

    2. Relevant equations

    σ=F/A, ε=ΔL/L0, E=σ/ε

    3. The attempt at a solution

    My successful attempt at calculating the modulus for samples A and B was to take an average (mean) across the entire elastic region for both stress and strain, and using these values to calculate. Essentially creating a best fit line, which made sense given E is actually the gradient. It worked superbly for the first two samples; 206.6 GPa for the steel sample, and 68 GPa for the Aluminium.

    The problem with the 'Cast Iron' sample, is that it doesn't have any apparent linear portion; it curves from the origin to the fracture point. I was hoping someone could provide some ideas what to do. Perhaps there is a special technique for materials of this type?

    I have included a picture of the stress/strain diagram of sample B (Al) and Sample C ('cast iron') to illustrate what I mean.

    FYI, the dotted lines represent 0.2% offset, as you can see, it is particularly accurate for Sample B.

    Many, many thanks for any help.

  2. jcsd
  3. Nov 26, 2012 #2
    sample B has a well-defined yield, compared with sample C. It is quite common, in non-linear cases like C to take an equivalent linear case, using the 0.002 strain as a reference point.
  4. Nov 28, 2012 #3
    Hi, thanks for the reply, although I don't quite follow.

    I'm aware that using 0.2% proof stress is the done thing unless the material shows yield point behaviour. What I'm having difficulty with is calculating the Young's Modulus. As I state above, my figure of 22.5 GPa is more inline with Graphite than Cast Iron which is in the region of 170 GPa.

    Unless I'm misinterpreting your answer somehow?

  5. Nov 28, 2012 #4
    FYI, I've solved the problem.

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