Plane-strain compression test

Plane strain compression tests (Fig. 12.2b) may be also used. One principal dimension remains constant thus a = vo2, where a2 ar d 03 are the principal stresses in the three directions x, y and z. This test has to be performed with care, due to different breadth dies, and friction coefficients, but it is nevertheless used to complete the yielding criteria curves (see below). 

Figure 12.2 Schematic representations of (a) pure shear test (b) plane strain compression test and (c) three-point bending test.

Another alternative is the plane strain compression test, shown in Figure 14.5c. The advantage displayed by this experiment is that the area of the specimen remains constant over the test and therefore = a . This test can be classified as a pure shear test as only two of the three sample dimensions are changed. 

Williams and Ford developed plane-strain compression test which was initially applied to metals (Wilhams and Ford 1964). It was based on the fact that strain is easier to measure in compression test. The same test method may be used for polymer blends to obtain total deformation curves up to high levels of strain that may be encountered in engineering applications. Williams had further explained the application of this technique to polymers (Williams 1964). 

From the early studies of yield behaviour of polymers, one example has been selected the plane-strain compression tests on PMMA, carried out by Bowden and Jukes [22]. The experimental set-up is shown in Figure 11.15. A partioular advantage of this technique is that yield behaviour can be observed in compression for materials that normally fracture in a tensile test. In this case PMMA was... 

Figure 11.15 The plane-strain compression test. (Reproduced with permission from Bowden...

Figure 12.16 The plane-strain compression test. (Reproduced from Bowden, P.B. and Jukes, j.A. (1968) The plastic yield behaviour of polymethylmethacrylate. J. Mater. Sci., 3, 183. Copyright (1968) Springer Science and Business Media.)...

From the early studies of yield behaviour of polymers, one example has been selected the plane-strain compression tests on PMMA, carried out by Bowden and Jukes [28],... 

Figure 14.5 Scheme of tests used for determining yield in polymers (a) Tension (b) uniaxial compression (c) plane strain compression (d) simple shear. 

A standard yield criterion, such as the modified von Mises criterion or the modified Tresca criterion, can be used to predict the yield stress in other modes of testing (such as uniaxial compression, plane strain compression and simple shear), from the value of ay(T) in uniaxial... 

Blazynski and Cole [14] were interested in sflain hardening in tube drawing and tube sinking. Drawn tubes were sectioned and tested in plane strain compression. 

Aki K, Richards PG (1980) Quantitative seismology Theory and methods. Vol. I, WH Freeman and Compaity, San Francisco Dahm T (1996) Relative moment tensor inversion based on ray theory Theory and Synthetic Tests. Geophys. J Int., 124 245-257 Dai ST, Labuz JF, Carvalho F (2000) Softening response of rock observed in plane-strain compression. Trends in Rock Mechanics, Geo SP-102, ASCE, pp 152-163... 

Guzatto R., Da Roza M. B., Denardin E. L. G., Samios D. (2009). Dynamical, morphological and mechanical properties of poly (ethylene terephthalate) deformed by plane strain compression. Polymer Testing, Vol. 28, pp. 24-29, ISSN 0142-9418 Karagiannidis P. G., Stergiou A. C., Karayannidis G. P. (2008). Study of crystallinity and thermomechanical analysis of annealed poly (ethylene terephthalate) films. European Polymer Journal, Vol. 44, pp. 1475-1486, ISSN 0014-3057 Keum J. K, Song H. H. (2005). Thermal deformations of oriented noncrystalline poly(ethylene terephthalate) fibers in the presence of mesophases structure. Polymer, 46, pp. 939-945, ISSN 0032-3861... 

For each material type, four tests including uniaxial tension (UT), uniaxial compression (UC), plane strain compression (PSC) and simple shear (SS) were carried out. All experiments were performed at room temperature and at an initial strain rate of 0.5min on a INSTRON 4467 and a INSTRON 1185 equipped with suitable testing rigs. 

Finally, Figure 14.5d shows a schematic of simple shear deformation. The specimen is clamped between steel blocks. The blocks must move parallel to each other in order to get a shear strain that is uniform along the waisted region. The shear stress is calculated as t = F/A, where F is the force applied to the plane of area A. In this test it is not necessary to distinguish between nominal and true stress because the shear strain does not affect A. The shear strain is defined as y = Ax/y, where Ax is the displacement of planes separated by a distance y. Ax being measured in the direction of the force applied, which is perpendicular to y. As in the case of the compression plane strain test, there is no change in the dimension of the sample along the z axis. 

The failure function can be measured directly in a number of ways. Some are rather complex and still under development, like the new plane strain biaxial tester with flexible boundaries30, but the simplest method so far is the uniaxial compression test. Only the version developed by Williams et al,24 gives results close to those obtained indirectly with the Jenike shear cell, the other versions yield relative measurements only. 

The yield stress, i.e. the 0.2% proof stress of Al3Nb in air, is shown in Fig. 19 as a function of temperature above 850 °C. Between 600°C and 800 °C, Al3Nb fails catastrophically in air tests because of grain boundary oxidation, which is known as a pest phenomenon. Below 500 °C, the fracture strain in compression is smaller than 0.2 %, whereas plastic deformation in bending has only been observed above 1050°C. The plane strain fracture toughness is only about 2 MN/m at room temperature, as was also found by others (Schneibel etal., 1988). 

It is also interesting that in compression tests on oriented polypropylene at low temperatures it is not in general appropriate to describe the deformation in terms of c-slip. Deformation bands in these specimens form in general at approximately 45° to the compression axis, i.e. near to planes of maximum shear stress, independent of specimen orientation. Bands in specimens for 6 < 45° and 0 > 60° are highly localised, indicating considerable strain-softening after yield. By contrast at 0 = 45°, which... 

Gurau ef al. [129] presented another apparatus used to measure the in-plane viscous and inertial permeability coefficients. In their method, an annular DL sample was placed between an upper and lower fixture. The gas entered the upper fixture and was then forced fhrough fhe DL info fhe ouflef porfs (open to the atmosphere). A strain sensor was located in the upper fixture in order to determine the thickness of fhe DL (i.e., deformation) because fhe whole assembly was compressed to a determined pressure. In fhis mefhod, the flow rate, temperatures in both fixtures, and pressures were monitored in each test. Once the data were collected, the in-plane permeability was determined from the Forchheimer equation by application of fhe leasf squares fit analysis method. 

The problem of definition of modulus applies to all tests. However there is a second problem which applies to those tests where the state of stress (or strain) is not uniform across the material cross-section during the test (i.e. to all beam tests and all torsion tests - except those for thin walled cylinders). In the derivation of the equations to determine moduli it is assumed that the relation between stress and strain is the same everywhere, this is no longer true for a non-linear material. In the beam test one half of the beam is in tension and one half in compression with maximum strains on the surfaces, so that there will be different relations between stress and strain depending on the distance from the neutral plane. For the torsion experiments the strain is zero at the centre of the specimen and increases toward the outside, thus there will be different torque-shear modulus relations for each thin cylindrical shell. Unless the precise variation of all the elastic constants with strain is known it will not be possible to obtain reliable values from beam tests or torsion tests (except for thin walled cylinders). 

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