I was going through this website :https://www.tf.uni-kiel.de/matwis/amat/iss/index.html where it answered a question: Why is the maximum of the (nominal) stress-strain curve and the beginning of necking related? So for explaining the relation it stated that curves taken at different strain rates may not be very different, you always need somewhat larger stresses at higher strain rates to achieve the same strain. Why do you need somewhat larger stresses at higher strain rates to achieve the same strain achieved in lower strain rate?. Can someone give an explanation for such behaviour?
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$\begingroup$ Can you give some more details about exactly what sort of system you are considering. Both viscous and inertial forces could be the cause, but as it is you haven't given enough information for us to be able to answer. $\endgroup$– John RennieCommented Nov 22, 2018 at 6:58
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$\begingroup$ I'm talking about stress strain curve for a specimen(steel) generated using Universal testing machine. $\endgroup$– hr08Commented Nov 22, 2018 at 7:55
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2 Answers
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Dislocations have limited velocities. At slow rates of strain, materials can flow and creep and achieve large deformations without great force. Think of geology, glaciers, salt crystals, etcetera.
And it may be better to think of the forces and stresses as the independent variable, as the cause of the deformation. The convention of putting the strain on the horizontal axis may cause misunderstandings.
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It is a common situation in many materials that are strain rate dependent (viscoelasticity, viscoplasticity). Since there is always a "delay" between applied force and observed deformation, it is necessary to apply a certain extra level of force so that the same strain is reached at equal times in both cases. This is easy to see in a concrete example, for example in a linear Kelvin-Voigt viscoelastic model the stress $\sigma$, strain $\varepsilon$, and strain rate $\dot{\varepsilon}$ are related by means:
$$\varepsilon(t) = \frac{\sigma(t)-\eta \dot{\varepsilon}(t)}{E} $$
being $E > 0$ the Young's modulus, and $\eta > 0$ the visicocity parameter. For each time $t$ we need greater stress $\sigma$ due to the subtractive effect of $\dot{\varepsilon}$.
