Theory of the tensile test

Hart, Edward W.

doi:10.1016/0001-6160(67)90211-8

Cited by 950 publications

(283 citation statements)

References 3 publications

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“…ʈ ⌰ is important because it directly governs the ductility of most nanocrystalline metals, which fail by severe plastic strain localization (5,37). The higher the ⌸ and therefore ⌰, the better the ductility and the larger the range of uniform elongation, because according to Hart's criterion (38), ⌰ Ͻ (1 Ϫ m) for the initiation of plastic strain localization (5,39).…”

Section: Resultsmentioning

confidence: 99%

Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals

Zhu

Li²,

Samanta³

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

538

263

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Nano-twinned copper exhibits an unusual combination of ultrahigh strength and high ductility, along with increased strain-rate sensitivity. We develop a mechanistic framework for predicting the rate sensitivity and elucidating the origin of ductility in terms of the interactions of dislocations with interfaces. Using atomistic reaction pathway calculations, we show that slip transfer reactions mediated by twin boundary are the rate-controlling mechanisms of plastic flow. We attribute the relatively high ductility of nanotwinned copper to the hardening of twin boundaries as they gradually lose coherency during plastic deformation. These findings provide insights into the possible means of optimizing strength and ductility through interfacial engineering.activation volume ͉ interfacial hardening ͉ nanoscale twins ͉ slip transfer reaction N anocrystalline metals with grain size finer than 100 nm routinely exhibit up to five times higher strength than their coarse-grained counterparts but suffer from greatly diminished ductility (1-3). showed that introduction of coherent nano-twins, typically tens of nanometers in thickness, in ultrafine-grained copper (with grain size of several hundred nanometers) leads to an unusual combination of ultrahigh strength (Ϸ1 GPa) and high ductility (14% elongation to failure). The plastic deformation characteristics of nanocrystalline metals have previously been rationalized on the basis of a number of mechanisms (7), including grain boundary (GB) sliding (8, 9), grain rotation (10), and diffusional creep (11). An effective experimental technique to probe the active deformation mechanism is to measure the sensitivity of flow stress to the rate of loading, ʈ because both the sensitivity index m and the associated activation volume v* can vary by orders of magnitude for different rate-limiting processes. For face-centered cubic metals such as copper, grain refinement into the nanocrystalline regime leads to an increase in m by up to an order of magnitude relative to microcrystalline metals with grain size in the micrometer range, and a concomitant decrease in the activation volume v* by two orders of magnitude (14,15). Nano-twinned copper shows the same characteristics of increased rate sensitivity and reduced activation volume as nanocrystalline copper without twins (4, 5, 12, 13) even when the average grain size is several hundred nanometers. However, it achieves very high strength without severely compromising ductility (4, 5).The commonly used strengthening model for nanocrystalline metals is the Hall-Petch relation (7, 16), which is a scaling function relating strength to grain size. The Hall-Petch relation is derived based on strengthening mechanisms (17) at internal interfaces, which proliferate in nanocrystals. However, it says nothing about ductility. To model ductility, it is necessary to revisit detailed physical processes at materials interfaces, in particular those involving dislocations, which are the carriers of plastic strain. Dislocation processes at internal interfac...

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Section: Resultsmentioning

confidence: 99%

Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals

Zhu

Li²,

Samanta³

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

538

263

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“…As mentioned above, the pearlitic matrix is able to transform easily without diffusion of carbon from graphite in contrast with the ferritic matrix. A distinctive feature of superplasticity is a marked dependency of the flow stress on the strain rate(7) (13). The value of the strain rate sensitivity exponent, m, close to unity in the equation, (1) stress was used as the flow stress; 2) the strain rate was formed by dividing the strain per thermal cycling by the time span of that cycle; and 3) any temperature dependence of the constant, k, was disregarded.…”

Section: Methodsmentioning

confidence: 99%

Transformation Superplasticity in Ductile Cast Iron

Tanaka

Ikawa

1976

Trans. JIM

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The influence of the concurrent phase transformation on the deformation of ferritic and pearlitic ductile cast irons was studied under tensile stresses at high and low thermal cycling rates. Transformation plasticity, characterized by the linear relationship between the transformation strain per cycle and the externally applied stress (i.e., strain rate sensitivity exponent, m is 0.8), was observed under all conditions. The transformation strain is greater on heating from pearlite to austenite than on cooling from austenite to pearlite. The transformation strain at the high heating and cooling rate results in a smaller transformation strain. Large uniform elongations (above 200%) can be obtained by repeated thermal cycling under a constant stress. It is suggested that the plasticity is due to the creep enhanced by excess vacancies generated during the volume change. In the early thermal cycling, the voids are formed at both sides of the spheroidal graphite. In the later stage, the voids are filled up with the matrix strnchire snrressively.

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“…[36] From a mechanistic point of view, all these factors help to attain a large uniform elongation via delaying necking instabilities. Hart's instability criterion [80] suggests that a high strain hardening rate and strain rate sensitivity is essential for delaying necking instabilities. [70,81] Accordingly, necking instability sets when the condition given by the following relation is reached.…”

Section: Mechanical Behaviormentioning

confidence: 99%

Nanostructured Ti Consolidated via Spark Plasma Sintering

Ertörer

Topping

et al. 2010

Metall Mater Trans A

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Cryomilled nanocrystalline commercially pure (CP)-Ti powders were spark plasma sintered (SPS) using different process parameters (heating rate, temperature, pressure, and dwell time) to study densification, microstructure, and mechanical behavior. The results were rationalized on the basis of the relevant literature and experimental results, and they reveal a strong dependence on SPS parameters. An interesting finding was that the measured high ductility was accompanied by a moderate strength (yield strength [YS] = 770 MPa, ultimate tensile strength [UTS] = 840 MPa with~27 pct elongation to failure). The combinations of microstructure and mechanical response were attributed to the multistep processing at different temperature ranges as well as to the presence of interstitial solutes.

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Theory of the tensile test

Cited by 950 publications

References 3 publications

Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals

Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals

Transformation Superplasticity in Ductile Cast Iron

Nanostructured Ti Consolidated via Spark Plasma Sintering

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