Serrated Stress-Strain Curves

Serrated stress-strain curves, similar to those occurring in metals, have also been observed in ceramics. Such stress-strain curves are shown in schematic Fig. 4.47 and experimentally observed serrated curves in alumina are illustrated in Figs. 4.48 and 4.49, formed during deformation at two temperatures and at the 

The serration curves in ceramics are analogous with those observed in HCP and BCC metals during low-temperature deformation. Serration is formed by the movement of partial dislocations this motion converts part of a crystal to a twin orientation. It is believed that dislocations are involved in twinning, but the mechanism is not yet clear. 

In this section, the formation of deformation and annealing twins were discussed with the resulting stress-strain relation characterized by serrated curves. As indicated here, there is no basic difference in twin formation between ceramics and metals. 

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Figure 3, which is a replot of the data of Fig. 1, was included to focus attention on the deformational behavior of these steels as measured by elongation. At 70 F, these steels deform by localized necking and extensive reduction of area, followed by fracture in the necked area (see Fig. 10). At -320 and -423°F, these same steels deform by a much more uniform elongation and reduction of area over the entire reduced section (see Fig. 10). This condition is most pronounced in the 62 cold-worked samples. At low temperature, the increase in strength in the reduced section due to plastic strain and associated martensite formation more than offsets the increase in stress due to the reduction in cross-sectional area (i.e., necking down) hence, the sample elongates over the entire reduced section prior to failure. At -423 F this elongation frequently occurs in a discontinuous manner, accompanied by audible clicks, serrations in the stress—strain curve, and striations in the sample, whose appearance is not unlike Luder s bands. The cross section of such a striation is shown in Fig. 12. These striations have been observed in other alloys by other investigators, and have been variously attributed to catastrophic twinning, thermal instability, and the burst-type formation of dislocations [1]. In this material another possibility exists, namely, the formation of martensite. This transformation is known to occur by an instantaneous shear mechanism and yields a volume increase which could account for the serrated stress—strain curve [5]. These effects demonstrate again that the...

A 10 /i. The Liiders bands seen in Fig. 4.79 are parallel to the 001 slip planes. The large yield drop corresponds to the first Liiders band formation while the formation of additional Liiders band is associated with the serration of the stress-strain curve. Many specimens tested gave the same stress-strain curves with Liiders bands formation. 

Tensile stress-strain curves below 319 F and in some cases above -319°F are marked with load serrations. The reasons advanced for these serrations are many and varied [3-6],... 

At low temperatures, titanium alloys generally exhibit serrated yielding in their stress-strain curves. This is true of both a-phase- and near-a-phase alloys (see Fig. 8.7 for commercial-purity titanium [Con84] and Ti-6Al-3Nb-2Zr [Lav82]) as well as of metastable p-phase alloys (see Fig. 8.8). The mechanisms of serrated yielding are different in the two cases the a-phase alloys seem to undergo... 

Fig. 4.56 Serrated stress versus strain curves in a 24 mol% YzOs-ZrOz specimen, com nessed at an imposed strain-rate of = 1.6x10 s between 1310 and 1450 °C. All the tests are performed in easy glide conditions [21]. With kind permission of Elsevier...

A clue to the reason for this behavior can be found from the load-diameter-extension data. At temperatures above which load serrations do not occur, the load increases uniformly as the diameter decreases until maximum load occurs, and further deformation is restricted to one neck. At the lower temperatures a different behavior occurs and the load extension curve is serrated. Each load drop corresponds to a diameter decrease at one or several necks, which have formed before "maximum load." Further, it must be realized that the rising load portion of each serration corresponds to an essentially elastic extension, whereas plastic deformation occurs during the rapidly decreasing load portions. During this decreasing load, at about constant strain, elastic strains are relieved and "exchanged" for an equivalent amount of plastic strain. Finally, consideration must be given to the fact that in these steels austenite is metastable and transforms under stress to yield martensite. 

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