Why Does Stress Decrease in the Necking Region of Copper Wire?

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Stress decreases in the necking region of copper wire due to the transition from engineering stress to true stress, which accounts for the reduction in cross-sectional area as the material deforms. While additional weight is applied, the thinning of the wire leads to a decrease in the effective area, resulting in lower stress readings despite increased force. The Young's Modulus (YM) for copper is determined from the slope of the stress-strain curve in the elastic region, up to the proportional limit, rather than from the ultimate tensile stress values. The observed dip in the stress-strain curve beyond yield is attributed to microscopic slippage within the material's structure. Understanding these concepts clarifies the behavior of materials under stress and the differences between engineering and true stress-strain curves.
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http://www.ami.ac.uk/courses/topics/0123_mpm/images/met_mpm_imgb.gif
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First off I am sorry about the massive size. The top graph is how a stress strain graph of a metal should look. However i can't seem to think why Mpa of stress decreases as it enters the "necking region". My graph is the one below and although it shows simular trend (limit of proportionality, small yeild point and showing it going into plastic deformation)it was uncompleted because the hoop the weight was attached to snaped and was not time to redo ( will be redoin tomorrow) Every point is a 100g weight being added to the experiment. However my logic is this. how can stress decrease when you are adding more weight and force every time? I thought maybe i had done something wrong i measured the diameter of the wire and used that for all calulations, but if it was thinning then the diameter would be smaller and so would the area.

Same big number / Smaller number = bigger number

It is a theory that has hit me for ages now, I am clearly missing something. Also as one additional question Copper wire has a YM of about 110 - 128 Gpa, where was this measured from? Is it using the highest stress and strain vaules? so the tensile stress or something different like the mean of them all?
 
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There is a difference between the 'enginering' stress-strain curcve and the 'true' stress strain curve. The first sketch is the engineering stress strain curve, which does not account for the 'necking down' of the specimen in the plastic region, creating a smaller area. If it were accounted for (true stress), you wouldn't see that dip in the curve as the stress approaches ultimate. I wouldn't worry about that tiny dip beyond yield, that's some slippage in the microscopic structure of the material.
As far as determining YM fior copper, that's the slope of the stress strain curve in the elastic region up to the proportional limit.
 


First off sorry about the werid title i had put a randm bunch of letters in so i could see if the images had worked on preview.

Thanks you so much mate youve helped me understnad it alot, cheers :)
 

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