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**HELP!! Stress Strain Question**

**1. Homework Statement**

In part (a) of the problem, we found that due to a certain stress, the amount of

elastic strain that a material undergoes is

[itex]\epsilon_E=.0087[/itex]

and the amount of plastic strain is

[itex]\epsilon_{pl}=.0113[/itex].

The total strain is therefore

[itex]\epsilon_T=.02[/itex]

We are then told that a sample of this material with original length

[itex]l_o=610 \ mm[/itex] undergoes that same stress involved in part (a).

What is the new length [itex]l_f[/itex]after the stress is removed ?

So I believe the idea behind this is that we gain the elastic portion of the strain back, but the plastic elongation should be added onto the original length.

I wrote this quantitatively as:

[tex]l_f=l_0+\epsilon_{pl}\Delta l[/tex] (1)

To find the change in length we have:

[tex]\epsilon_T=\frac{\Delta l}{l_0} \Rightarrow \Delta l=\epsilon_Tl_0[/tex] (2)

Therefore (1) becomes:

[tex]l_f=l_0+\epsilon_{pl}(\epsilon_Tl_0)[/tex]

[tex]\Rightarrow l_f=l_0(1+\epsilon_T\epsilon_{pl})[/tex]

Plugging in numbers we have l

_{f}=.6101 mm

but the correct answer is .6167 which is waayyy off.

What am I missing here?

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