The Rheology Handbook. Thomas Mezger

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СКАЧАТЬ He called this behavior to be “plastic”. Ideal-plastic behavior was illustrated using the Saint Venant model (A. J. B. de Saint Venant, 1797 to 1886 [3.29]); see also DIN 1342-1. Drawings of this model are shown in the meanwhile withdrawn DIN 13342 of 1976, and in [3.10] [3.30]. This model consists of a friction element (or “sliding shoe”), which does not begin to move until the shear force overcomes the resistance caused by static friction. Then the structure of the stressed sample yields, showing an increasing deformation (creep or flow), but the motion is still slowed down by the sliding friction of the friction element. In the past, various rheologists designed a lot of different concepts to explain the behavior in the transition range between rest and flow:

      1 Some rheologists assumed that a material remained completely rigid and undeformed under increasing shear load until the yield point was exceeded. This behavior was called “plastic-rigid” or “inelastic” [3.9] [3.24]. Above the yield point the material showed “plastic flow” and finally, under higher shear load, “viscous flow”. This behavior was described in 1919 using the Bingham model [3.4] (see also Chapters 3.3.6.4a and 14.3: 1916). Both steps of this behavior were termed “viscoplastic ” (as in the redrawn DIN 13342) and [3.30], or as “plastic-viscous” [3.10]. After the load is removed, no reformation occurs at all.Other rheologists were convinced that the sample under increasing shear load first showed reversible elastic behavior in a very limited deformation range until the yield point was exceeded. Then an irreversible plastic deformation occurred. This behavior was described in 1924 by the Prandtl model [3.30], or in 1930 by the Prandtl/Reuss model (DIN 1342-3 and [3.10], see also Chapter 14.3: 1924). Both stages of that behavior were termed “elastoplastic” (withdrawn DIN 13342), as “elastic-plastic” [3.10], or as “plastoelastic” [3.31]. The extent of reformation after removing the load represents the elastic portion. Using modern terms, these kinds of materials should be called viscoelastic liquids.Another concept was that under a low shear load below the yield point the sample was deformed reversible-elastically (deformation behavior according to Hooke). After exceeding the yield point, the material showed plastic behavior (slow flow, slowed down by the friction element according to Saint Venant), and finally, under increased shear load it showed viscous flow (flow behavior according to Newton, without any effect of the friction element). This behavior was described using an extended Bingham model [3.30], and all three stages were named “elastico-plastico-viscous” or “elasto-visco-plastic” or similar terms were used [3.32] [3.33]. The extent of reformation after removing the load corresponds to the elastic portion. Using modern terms, these kinds of materials should be called either viscoelastic liquids if there is only partial reformation even after a sufficiently long period of time, or viscoelastic solids if they are recovering completely even if this may take a longer time.

      For people working scientifically, the term “plastic behavior” used in rheology is a synonym for “inhomogeneous behavior”. For practical users performing rheological tests, the following can be stated: Plastic behavior is shown by materials which do not exhibit homogeneous shear behavior, related to the entire shear gap. These kinds of materials often display effects like wall-slip, sliding and plug flow, when forced to move through capillaries, tubes and pipes. Similar effects may also occur in the gap of a rheometer measuring system. For these kinds of samples, rheological behavior is not constant throughout the whole volume of the test material: a part of the sample is flowing, and another one does not [3.34]. Inhomogeneous shear effects should always be expected when testing dispersions showing a high concentration of solid matter since here, phase separation of the sample may occur. Below a critical shear rate value shear banding effects may occur (see Figure 2.9, no. 6 and 7) [3.26].

      3.3.4.2.4Example 1: Plastic behavior of metals for cold forging processes

      Plastic deformation occurs in cold forging processes of metals, or with other crystal-forming materials, if lattice dislocation takes place between the atomic levels or crystals [3.35] [3.36]. Below the yield point, there is elastic and reversible deformation behavior. Above the yield point, however, behavior is irreversible and inelastic and then, deformation is no more homogeneously distributed throughout the entire shear gap [3.22].

      3.3.4.2.5Example 2: Plastic deformation of the landscape and soil flow (solifluction )

      In the Ice Age (which, for example, came to an end in Northern Germany around 14,000 years ago), the shear force of glaciers moved loose layers of soil masses and pieces of solid rock, e. g. boulders, weighing several tons. The so-called “solifluction” of the partially thawed permafrost soil resulted in plastic deformation of the landscape.

      3.3.4.2.6Example 3: Plastic land subsidence caused by mining or dike construction

      As a result of mining, land subsidence may occur when loosened sediment layers meet ground water. Here, and also in the construction of water protection dikes, the soil-mechanical, rheologically plastic behavior is a crucial point (creep, sliding, flow).

      3.3.4.2.7Example 4: Plastic flow of debris and mud avalanches in the mountains

      Debris and mud avalanches are an inhomogeneous mixture of water, fine sediment (max. particle size up to d = 0.1 mm), mud (clay, silt, sand, with 0.1 mm < d < 20 mm), and larger “particles” (granules, gravel, stones, boulders, up to d = 20 cm or even 1 m, – which ideed was a little bit too large for a normal rheometer …). They may show mean velocities of v = 1 to 30 m/s, thus, more than 100 km/h. Considering a longitudinal section, two zones of the velocity distribution occur: In the lower range close to the bottom a shear zone showing clearly increasing velocity values from the bottom upwards (i. e. flowing layers showing a velocity gradient), and above a zone close to the surface of almost constant velocity (i. e. v = const, showing “plug flow”) [3.37]. For corresponding rheological tests of dipersions showing particel size up to 10 mm, a ball measuring system can be used (see Chapter 10.6.5). Shear experiments on bulk solids and powders are described in Chapter 13.

      3.3.4.2.8Illustration, using the Two-Plates model (see Figure 2.9: no. 4)

      In order to illustrate plastic behavior: Not all flowing layers in the Two-Plates model are shifting along one another to the same extent. Therefore across the shear gap, the resulting shear rate (or “velocity gradient“) and shear deformation (or deflection gradient),respectively, are not constant. СКАЧАТЬ