Transient creep compliance function

Chapters 5 and 6 discuss how the mechanical characteristics of a material (solid, liquid, or viscoelastic) can be defined by comparing the mean relaxation time and the time scale of both creep and relaxation experiments, in which the transient creep compliance function and the transient relaxation modulus for viscoelastic materials can be determined. These chapters explain how the Boltzmann superposition principle can be applied to predict the evolution of either the deformation or the stress for continuous and discontinuous mechanical histories in linear viscoelasticity. Mathematical relationships between transient compliance functions and transient relaxation moduli are obtained, and interrelations between viscoelastic functions in the time and frequency domains are given. 

The first two terms on the right-hand side of equation [12.6] are viscoelastic terms proposed by Schapery, where e represents uniaxial kinematic (or total) strain at time t, o is the Cauchy stress at time t, is the instantaneous compliance and AD(r[i ) is a transient creep compliance function. The factor g defines stress and temperature effects on the instantaneous elastic compliance and is a measure of state dependent reduction (or increase) in stiffness. Transient compliance factor gi has a similar meaning, operating on the creep compliance component. The factor gj accounts for the influence of loading rate on creep. The function i ) represents a reduced timescale parameter defined by ... 

In the transient compliance function, J(t), the retardation spectrum L(x) is modulated by the function 1 — exp(—t/x) [see Eq. (9.15)]. Plotting this function against In t/x gives the sigmoidal curve shown in Figure 9.6. We should note that the time of observation ( ) in the first quadrant is greater than the retardation times, and as a result x varies between zero and t. Then the creep compliance function for viscoelastic liquids is approximately given by (1,2)... 

Oscillatory studies are useful for materials with short relaxation times, comparable to the period of oscillation. For long relaxation times, however, transient methods are used. The creep test subjects the material to constant stress, and follows the strain as a function of time. Creep compliance J(t) is the ratio of strain to stress, and is a function of elapsed time from the instant of application of the stress ... 

We will now consider another type of transient response. Let a shear stress a be applied at the viscoelastic solution at = 0. In a general case, a time-dependent shear strain is developed that can be measured to get the creep comphance J(t). The creep compliance has the dimensions of a reciprocal modulus, and it is therefore an increasing function of time. From theories of viscoelasticity, it is possible to calcrflate the creep compliance from the relaxation modrflus and inverse ... 

The creep function J(t) is the transient strain per unit stress in a step-stress experiment. The resolution at short times is also limited from instrument response and sensitivity. J(t) at short times may also be derived from the high frequency complex compliance data. 

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