Spring relaxation, shear stress

Figure 10. Plot of logJ0 shear stress vs. time for spring relaxation experiment.

One feature of the Maxwell model is that it allows the complete relaxation of any applied strain, i.e. we do not observe any energy stored in the sample, and all the energy stored in the springs is dissipated in flow. Such a material is termed a viscoelastic fluid or viscoelastic liquid. However, it is feasible for a material to show an apparent yield stress at low shear rates or stresses (Section 6.2). We can think of this as an elastic response at low stresses or strains regardless of the application time (over all practical timescales). We can only obtain such a response by removing one of the dashpots from the viscoelastic model in Figure 4.8. When a... 

The ratio shear viscosity to shear modulus is often symbolised by the time x = ti / G. For the Maxwell model, x is called the stress relaxation time. In the Kelvin model x is a measure of the time required for the extension of the spring to its equilibrium length under a constant stress. X is called the retardation time. 

Figure 3-1 represents a Maxwell element. If the spring corresponds to a shear rigidity G, = 1 /Jj (we choose shear as the type of deformation to be worked out in detail, though any other deformation would do as well) and the dashpot to a viscosity 77, then the relaxation time of the element is defined as t, = and is a measure of the time required for stress relaxation. If jj/ is in poises and G,- in dynes/cm, t,- is in seconds. 

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