Axi-symmetric compression of solid cylinders

Abstract

The analytical and experimental methods of determining the compressive yield stress of materials have been reviewed briefly. Using aluminum, EN 24 steel, lead and a tin-lead eutectic alloy, the areas of applicability of the Cook and Larke method (including its modified form for strain-rate sensitive materials) and the ring compression test have been delineated. Under conditions of sliding friction, both the methods give similar values for the coefficient of friction. Under sticking or near-sticking friction conditions, the modified Cook and Larke method is more accurate, because the interpretation of the ring compression test ignores the strain-rate sensitivity of the flow stress. Within the experimental range, the coefficient of friction and the interface friction factor were unaffected by the changes in the strain level, strain rate, grain size and efficacy of lubrication. Under slow loading conditions, the effect of specimen dimensions on the flow stress could be attributed entirely to a change in the frictional contribution. The strain and/or strain-rate hardening behaviour, as well as the grain size dependence of the flow stress of the different materials, were consistent with earlier wellknown results. Earlier workFor evaluating the true stress-true strain curves of materials, axi-symmetric compression of solid cylinders is often used. In these tests friction is present and this leads to barrelling [1,2]. But the analysis of many metal-forming processes, e.g. extrusion, requires a knowledge of the compressive yield stress of a material, i.e. which is corrected for friction [3,4]. A correction for friction can be effected either analytically or experimentally.For analysing a cold-working process, Coulomb's law 9 = gN, where 9 is the frictional (shear) stress, p is the coefficient of friction and N is the normal stress, is often used. While in most analyses p is treated as constant, in reality it depends on a number of variables in a complicated way, e.g. material properties, efficacy of lubrication, rate of sliding at the interface. In hot working, on the other hand, sticking friction is assumed. Here the frictional stress is taken as equal to the shear yield stress of the material in plane strain, again an idealized picture [5,7].A barrelling correction, which is analogous to necking correction in tension, is often made. But this calculation is influenced by the specimen dimensions and the lubricant used. Additionally, some questionable assumptions are also involved in the analysis [8-113. Slip-line field solutions are often inapplicable for axi-symmetric flow problems [12][13][14][15][16][17].Early experimental methods of Rummel, Meyer and Nehl and Siebel and Pomp are only of historical significance [18][19][20][21][22][23][24]. The methods of Taylor and Quinney [25], Ford [26] and Polakowski [23] are time consuming as they require remachining (which also changes the overall mechanical history of the specimen) and cannot be used when an allotropic transformation is present in the material, e.g. a steel...

Analysis of Compression Behavior of a [011] TA Single Crystal with Orientation Imaging Microscopy and Crystal Plasticity

“…The upturn in the stress-strain diagram above 20% strain is similar to that seen by numerous other investigators [1,[3][4][5][6] during compression testing; however, the effect seems particularly acute. The magnitude of the upturn and its occurrence at relatively low strain suggests that factors other than friction may be significant.…”

“…Tests under these conditions establish a baseline for comparison with the results of more sophisticated, and expensive, experimental techniques such as renewing the solid lubricant at regular intervals during the test and optimizing the type and thickness of lubricant. Ultimately, the minimization of frictional effects will increase the accuracy of extrapolation methods as described by Ray and Mallik [5] and Singh and Padmanabhan [6] for end-effect correction and decrease the effort in their application.…”

Mechanical and rheological testing to develop thermoplastic elastomer-polyborodimethylsiloxane blends for personal impact protection

“…Following Cook and Larke [18] and Singh and Padmanabhan [19], we chose 20 mm diameter and 20 mm height to minimize frictional effects. Specimens were tested between flat PTFE platens lubricated with Super Lube (the usual silicone-based lubricants stick to X3180).…”

The Correlation between Hardness and Yield Strength of Hard Materials

“…To measure the yield strength and the elastic modulus of the polymers, cylindrical samples with a diameter of 15 to 20 mm were tested in uni-axial compression at a nominal strain rate of 8 × 10 -3 s -1 . To correct for errors due to friction, samples with different height to diameter ratio varying from 2 to 0.5 were tested [11]. The elastic modulus was determined from the elastic part of the curve after correction for the stiffness of the machine.…”