Hencky strain

Typically, in compression tests a cylindrical piece of the test sample is compressed between smooth plates using a Material Tester. Assuming constant volume, the stress and strain (Hencky strain) are calculated from the force, displacement data. However,... 

The true strain (Hencky strain) e is also correspondingly different from the nominal or Cauchy or engineering strain e ... 

More recent work by Utracki and Gendron on pressure oscillations in extrusion of poiyethyienes [231] led them to conclude that the pressure oscillation does not seem to be related to elasticity or slip. They conclude that the parameter responsible for pressure oscillations is the critical strain (Hencky) value of the melt. For LLDPE, Sc < 3, for HDPE, s < 2, while for LDPE, s, > 3.5. The instability seems to be based on the inability of the polymer melt to sustain levels of strain larger than the critical strain. 

Fig. 16 Compression stress (a) - Hencky strain (sh) curves for gels of )0-glucan samples from oat oatlOO (2.12) and oat200 (2.13), barley bar 100 (2.80) and bar200 (3.04), wheat whe200 (3.66), and lichenan lie 100 (24.49) with cellotriosyl/cellotetraosyl ratios given in parenthesis. Polymer concentration, 8% w/v and gel curing temperature 25 °C...

Okamoto et al. [48] first conducted an elongation test on PP-based nanocomposites in the molten state at constant Hencky strain rate, so using elongation flow optorheo-metry [49]. They also attempted to control the alignment of the dispersed silicate... 

Fig. 9.12 (A) Time variation of elongational viscosity for PLA-based nanocomposite (MMT = 4wt%) melt at 170°C (B) Strain rate dependence of up-rising Hencky strain. Reprinted from [47], 2003 Wiley-VCH Verlag GmbH Co.

Regarding elongation-induced structure development, Figure 9.12(B) shows the Hencky strain rate dependence of the up-rising Hencky strain (r.t) ) — f.0 x ft) recorded for PLANC at 170 °C. The r.t) increases systematically with the eo- The lower the value of s0, the smaller the value ofs,lE. This tendency probably corresponds to the rheopexy of PLANC under slow shear flow. 

Recently, Muliawan et al. (52), who have been studying melt fracture, and in particular sharkskin extrudate instabilities over the last decade, have presented interesting experimental results relating the extensional stress-Hencky strain behavior of polymer melts to their sharkskin (exit) and gross (capillary entrance) melt fracture behavior. For the purposes of this discussion, results obtained with two Nova Chemicals... 

Fig. 12.26 True tensile stress-Hencky strain curves for resins C and E at Hencky strain rate of 20 s-1 and temperature of 170°C. [Reprinted by permission from E. G. Muliawan, S. G. Hatzikiriakos, and M. Sentmanat, Melt Fracture of Linear Polyethylene, Int. Polym. Process., 20, 60 (2005).]...

As mentioned above, it is far more difficult to measure extensional viscosity than shear viscosity, in particular of mobile liquids. The problem is not only to achieve a constant stretch rate, but also to maintain it for a sufficient time. As shown before, in many cases Hencky strains, e = qet, of at least 7 are needed to reach the equilibrium values of the extensional viscosity and even that is questionable, because it seems that a stress overshoot is reached at those high Hencky strains. Moreover, if one realises that that for a Hencky strain of 7 the length of the original sample has increased 1100 times, whereas the diameter of the sample of 1 mm has decreased at the same time to 33 pm, then it will be clear that the forces involved with those high Hencky strains become extremely small during the experiment. 

Estimate for an extensional viscosity of 105 N s/m2 the force needed to maintain a stretching rate of 1 s 1 of a sample with an original diameter of 1 cm at a Hencky strain of 7. 

FIG. 15.24 Schematic representation of the four roller extensional rheometer, designed by Meissner (1972) to attain high Hencky strains. Two sets of rotary clamps are individually driven by two motors at constant rotation rates. The force in the sample is measured by a transducer F mounted on a leaf spring. From Barnes, Hutton and Walters (Gen Ref 1993). Courtesy Elsevier Science Publishers. 

In the same way, but much more complicated, with a damping function depending on the Hencky strain, it proved to be possible to calculate the transient extensional viscosity as a function of qe. The result is illustrated in Fig. 15.30 for the same polymer. It shows that extensional viscosity remains finite and increases with increasing strain rate up to a maximum at qe = 2 s, after which it decreases again. The calculated lines coincide quite well with the experiments, but the calculated viscosities are somewhat too high. 

FIG. 16.21 Apparent or transient extensional viscosity of the round robin test fluid Ml as a function of Hencky strain, measured in many different devices (lames and Walters, 1993). The various instruments are spin line Binding et al. Ferguson and Hudson Ngyuen et al. horizontal spin line Oliver open siphon Binding et al. stagnation flow. Laun and Hingmann Schweitzer et al. contraction flow. Binding et al. ... 

The validity of this model and its ability to predict the deformability of layered baked foods and polymeric solid foams arrays have been demonstrated by Swyngedau et al. (1991), Swyngedau et al. (1991) and Swyngedau and Peleg (1992). When Hencky s strain is used to characterize the deformation, then (Peleg 1993a) ... 

---