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For the following stress-strain curves we have to choose which one corresponds to aluminium and which one to carbon fiber, a composite: enter image description here enter image description here

We think the carbon fiber should be the one with the higher modulus of elasticity and the lower strain (the first figure) because of its ceramic composition, but we are not really sure about it. What really concerns us is the peak created at the second curve; if it were a metal it would not make sense for the material to create a neck, right? Furthermore, can a metal bear that much strain (10%)?

Patricia GC
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  • You can calculate the modulus of elasticity in the elastic region. For the upper curve, this is about 54 GPa, and for the lower, about 6.25 GPa. Young's modulus for pure aluminum 70 GPa. Therefore, the upper curve corresponds to aluminum. – Alex Trounev Nov 11 '19 at 12:44
  • But carbon fiber usually has a greater experimental Young's modulus, so wouldn't it be the other way around ( the upper curve corresponding to carbon fiber) ? – Patricia GC Nov 12 '19 at 14:55
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    See the curve for aluminum in Fig. 4 in the article https://www.researchgate.net/publication/257757496_A_novel_technique_to_increase_strain_distribution_homogeneity_for_ECAPed_materials – Alex Trounev Nov 12 '19 at 16:19

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The carbon fiber composite should indeed have a higher stiffness (modulus of elasticity) and lower strain (because it is brittle). The first curve is also a typical curve for a composite: the stress increases until a critical point. At this point, there arises a crack that will propagate and cut the sample very fast. This causes an abrupt drop in the curve.

The second figure looks more like a curve for aluminium. It has a lower stiffness and a higher maximal strain (it can indeed reach up to 10 %). This higher strain is achieved because the metal is more ductile than a carbon composite. The peak is indeed originating from the necking. It is possible to form necking in a metal because the metal is ductile and can deform.

Frederic
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  • You obviously did not look at the scale of the applied force up to 600MPa for a second figure. Aluminum does not withstand more than 100MPa - see the curve for aluminum in Fig. 4 in the article https://www.researchgate.net/publication/257757496_A_novel_technique_to_increase_strain_distribution_homogeneity_for_ECAPed_materials – Alex Trounev Nov 13 '19 at 16:20
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The first curve is Al. This curve acts like a common metal, which has a single modulus in the elastic region, and shows brief necking before failure. The failure is abrupt breaking the entire specimen at once. The modulus of Al is roughly 65 GPa, which corresponds closely to the top graph in the region from 0 to 0.02% strain.

The second curve is the fiber composite, which shows two distinctly different moduli. There are multiple instances of failure, where load is reduced abruptly without a full break in the sample.

You cannot use the modulus of carbon fiber itself to determine which curve here is the composite because the global modulus of the composite is determined by the cross sectional area of the full specimen (not just the fiber), and is a mixture of the moduli of both the fiber and the matrix.

Lastly, a quick google image search of Al and carbon fiber composite stress vs. strain diagrams should give a good indication of which of these is correct.

Michael
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