Creep curves approach

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

Once the limiting strain is known, design methods based on the creep curves are quite straightforward and the approach is illustrated in the following... 

If creep curves are available at only one temperature then the situation is a little more difficult. It is known that properties such as modulus will decrease with temperature, but by how much Fortunately it is possible to use a time-temperature superposition approach as follows ... 

Note that this question involved a biaxial state of stress in the material and hence, strictly speaking, the creep curves used are not appropriate. However, creep curves for biaxial states of stress are rarely available, and one possible approach is to calculate an equivalent stress, a , using a van Mises type criterion... 

For the past century one successful approach is to plot a secant modulus that is at 1% strain or 0.85% of the initial tangent modulus and noting where they intersect the stress-strain curve (Fig. 2-2). However for many plastics, particularly the crystalline thermoplastics, this method is too restrictive. So in most practical applications the limiting strain is decided based on experience and/or in consultation between the designer and the plastic material manufacturer. Once the limiting strain is known, design methods based on its creep curves become rather straightforward (additional information to follow). 

Solids of different classes, including polymers, are characterized typically with a complex non-uniform structure on various morphological levels and the presence of different local defects. The theoretical approaches describe the deformation of solid polymers via local defects in the form of dislocations (or dislocation analogies ) and disclinations, or in terms of dislocation-disclination models even for non-crystalline polymers [271-275, 292]. In principle, this presumes the localized character and jump-like evolution of polymer deformation at various levels. Meantime, the structural heterogeneity and localized microdeformation processes revealed in solids by microscopic or diffraction methods, could not be discerned typically in the mechanical (stress-strain or creep) curves obtained by the traditional techniques. This supports the idea of deformation as a monotonic process with a smoothly varying rate. Creep process has been investigated in the numerous studies in terms of average rates (steady-state creep). For polymers, as the exclusion. 

Figure 15.7 gives a typical creep curve for bovine serum albumin films, showing an initial, instantaneous, deformation, characteristic of an elastic body, followed by a non-linear flow that gradually declines and approaches the steady flow behaviour of a viscous body. 

Empirical approaches to represent the creep curves of materials by mathematical functions have been known for more than 60 years. One of the first is the Andrade equation... 

As shown by Fig. 3.11 for an applied force, the creep strain is increasing at a decreasing rate with time because the elongation of the spring is approaching the force produced by the stress. The shape of the curve up to the maximum strain is due to the interaction of the viscosity and modulus. When the stress is removed at the maximum strain, the strain decreases exponentially until at an infinite time it will again be zero. The second half of this process is often modeled as creep recovery in extruded or injection-molded parts after they cool. The creep recovery usually results in undesirable dimensional changes observed in the cooled solid with time. 

Figure 11.8 shows typical curves for Re/Rex as functions of t and M, calculated from Eqs. (11-31) to (11-36) for 7 = 2.65. Even for low Rex (curve 2), the velocity approaches the terminal value more rapidly than predicted by the creeping flow solution. At higher Rex the steady terminal velocity is approached more rapidly, but the value required to achieve a given fraction of Rcx increases with Rex- The trajectory is generally more sensitive to Rex than to 7 as shown by Fig. 11.9, where we have plotted the t and required to... 

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