The app does virtual experiments and derives G*, G', G'' (relative to some arbitrary maximum value=1) and tanδ.Īlthough this is an artificial graph with an arbitrary definition of the modulus, because you now understand G', G'' and tanδ a lot of things about your sample will start to make more sense. tanδ=G''/G' - a measure of how elastic (tanδ1).G''=G*sin(δ) - this is the "loss" or "plastic" modulus. G'=G*cos(δ) - this is the "storage" or "elastic" modulus.This can be done by splitting G* (the "complex" modulus) into two components, plus a useful third value: What it doesn't seem to tell us is how "elastic" or "plastic" the sample is. Our thought experiment therefore gives us two bits of information: the "phase" angle difference δ between the stimulus (stress) and response (strain) and the modulus, G* from Maximum_Stress/Maximum_Strain. Why the two "Maximums"? Well for the plastic case at maximum stress the strain is zero so a "modulus" based on Stress/Strain would be infinite at that point. So in this test set-up we can always measure "modulus" as Maximum_Stress/Maximum_Strain. Near the cross-over points, the angular velocity is maximum so the stress is maximum: the responses are exactly 90° out of phase.Īs we all know, modulus is Stress/Strain. At the top and bottom of the sine curve, the oscillation velocity is near-zero so the rate is zero so the stress is zero. To understand the pure plastic deformation remember that viscous stress is proportional to strain rate. Going back to our thought experiment, the strain response of a pure elastic is instantaneous - as the stress increases so does the strain. That's why we need G' (which measures the elastic component) and G'' (which measures the plastic component). In reality, most solid samples are a mixture of both. In other words, at one extreme we talk about "elastic" deformations that return to their original position and "plastic" deformations that are permanent. Or imagine instead that it was a "pure liquid" so that on release of any stress the sample would not return at all to its original state. The material is, then, a purely elastic solid. Imagine that the sample was a "pure solid" so that on release of any stress the sample would spring (literally) back to its original position. You can equally apply an oscillating strain and measure the stress, the two modes are equivalent in theory (though there are practical reasons for choosing one or the other). Measure the strain (% stretch) induced in the sample via that stress, noting that the strain varies sinusoidally with time. Apply a stress (force) that twists the top disc back and forth in a sinusoidal motion. Imagine a sample trapped between two discs.
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