Hysteresis energy

Mechanism of the Great Hysteresis Energy of Carbon Black-Filled Rubber... 

It has often been pointed out for a long time that the hysteresis energy given from the hysteresis loop under large extension is too big compared with the viscoelastic dissipation energy. For example, the hysteresis loop given from the stress relaxation is only 20%-30% of that from the stress-strain curve, when both measurements are performed at the same relaxation time and the... 

As is well known, there is a close relation between the input energy at break, Ub and the hysteresis energy at break, Hb, for many kinds of filled and unfilled rubber vulcanizates, given by the following empirical Equation 18.2 ... 

Equation 18.2 reveals the importance of energy dissipation in the fracmre of mbbery materials, that is, the strength of rubbers, whether filled or unfilled, is governed by the hysteresis energy dissipated in deforming the system. 

FIGURE 18.20 Relation between input energy and hysteresis energy at break for HAF carbon-filled and unfilled styrene-butadiene rubber (SBR). (From Payne, A.R., J. Polymer, Sci., 48, 169, 1974.)... 

Hysteresis energy given from the hysteresis loop at break in carbon black-fiUed rubbers includes the apparent hysteresis energy whose fraction is roughly a half of the total one, which results from the buckling of the super-network. 

FIGURE 22.13 Simple analytical model of hysteresis friction of rubber moving over a rough road profile left). Tire on a wet road track, where hysteresis energy losses dominate the traction behavior right). (From Kluppef M. and Heinrich, G., Kautschuk, Gummi, Kunststojfe, 58, 217, 2005. With permission.)... 

FE simulations of the stress-strain properties of fiUer-reinforced elastomers are an important tool for predicting the service live performance of mbber goods. Typical examples are the evaluation of rolling resistance of tires due to hysteresis energy losses, mainly in the tire tread or the adjustment of engine mounts in automotive applications. 

Equation (12.18) establishes that the hysteresis energy, the energy associated with the area in the hysteresis region of an intrusion-extrusion cycle, is given by... 

Thus, the expression for the pore potential is identical to the pressure-volume work differences between intrusion and extrusion and can be expressed as the hysteresis energy, i.e. 

Hysteresis Energy loss, the difference between the work output in a cycle of extension and retraction. 

Hysteresis energy is that energy used per cycle of operation to overcome the effect of hysteresis. 

Because of hysteresis, energy is dissipated as heat in a magnetic material as it is taken round a complete B-H loop, and the hysteresis energy loss Wh per unit volume of material is... 

In Fig. 23a, the hysteresis energies (I/hys) calculated from the cycles in Fig. 22a are plotted against the maximum strain in terms of uniaxial (/Imax) and biaxial (Abiax nax) extension ratios. All C/bys data collapse onto a single curve hence, the hysteresis energy only depends on the maximum extension of the polymer chains. 

Fig. 23 (a) Hysteresis energy i/bys and (b) fraction/y of dissociated cross-links during loadingunloading compression (open symbols) and elongation cycles (filled symbols) of a surfactant-containing HM PDMA hydrogel, shown as a function of the maximum strain -l, ax or ibiax, max, Co = 15 % (w/v), C17.3M = 2 mol%, SDS = 7 % (w/v), NaCl = 0.5 M. From [41] with permission from Elsevier... 

We indicated all relative quantities by asterisks. Thus we defined the relative first cycle residual strain, and relative first cycle hysteresis energy dissipation by... 

With respect to varying PU composition, the dominant result from these tests was the differences between polymers based on the two hard segments. For all combinations of chain extenders and macrodiols, residual strain s and hysteresis energy dissipation E]jj, were highest for hard segments ofDBDI than ofMDI. 

Influence of strain amplitude on Mullins effect and hysteresis energy loss... 

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