The strongest size in the inverse HallPetch relationship1

1、免费查阅精品论文The strongest size in the inverse Hall-Petch relationship1Pan Yong1， Zhou Yichun1，Sun Changqing 2*1 Key laboratory of low-dimensional materials and application technologies ，XiangtanUniversity，Ministry of Education，Hunan （411105）2 School of Electrical and Electronic Engineering, Nanyang Technological University，Singapore（639798）E-mail：AbstractReproduction of the measured inverse Hall-Petch relation (IHPR) using the currently presentedanalytical solution reveals that: (i) the size induced

2、 energy densitification and cohesive energy loss of nanograins originates the IHPR that could be activated in the contact mode of plastic deformation detection; (ii) the competition between the inhibition of atomic dislocations, via the surface energy density gain and the strain work hardening, and the activation for dislocations through cohesive energy loss determine the entire IHPR profile of a specimen; (iii) the presence of a soft quasisolid phase is responsible for the size-induced softenin

3、g and the superplasticity as well of nanostructures; (iv) the bond nature involved and the T/Tm ratio between the temperature of operating and the temperature of melting dictate the measured strongest sizes of a given specimen.Keywords ： nanostructures ，analytical methods ，plastic deformation ，Hall-Petch relationship ，thermally activated processes1. IntroductionThe mechanically strengthening with grain refinement in the size range of sub-micrometers has traditionally been rationalized with the c

4、onventional temperature-independent Hall-Petch relationship (HPR) 1 that can be simplified in a dimensionless form being normalized by the bulk standard, P(0),measured under the same conditions,- 1 -P(x) P(0) = 1 + Ax(1)the slope A is an adjustable parameter used to fit experimental data. The K = R/d, and x = K-1/2, is the dimensionless form of size, which corresponds to the number of atoms, with mean diameter d, lined along the radius, R, of a spherical-like nanograin, as illustrated in Figure

5、1. Using the dimensionless form of the mechanical strength and the grain size aims to minimize the contribution from artifacts such as the processing conditions and the crystal orientation. The HPR has been well understood in terms of the pile up of dislocations that resist plastic flow from grain refinement 2,3.However, as the crystal is refined from the micrometer regime into the nanometer scale, the HPR process invariably breaks down and the relationship of yield strength versus grain size de

6、parts markedly from that seen at larger grain sizes. With further grain refinement, the yield strength peaks, in many cases, at a mean grain size in the order of 10 nm or so. A further decrease in grain size can cause softening of the solid, instead, and then the HPR slope turns from positive to negative at a critical size, or called the strongest size. The deviation from the HPR is called the inverse Hall-Petch relationship (IHPR)4,5,6,7,8,9.There is a concerted global effort underway towards d

7、eeper insight into the IHPR mechanism with postulated explanations in terms of dislocation-based 10, diffusion-based 11,12, grain- boundary-shearing-based 13, core-shell-role-exchange-based 14, two-phase-based 15, collective- motion-based 16, and dislocation-absorption-based 17 models. It has been suggested that the grainboundaries (GBs) consisting of under-coordinated atoms contribute to the GB performance 18. The1 The project is supported by NNSF of China (Nos. 10772157 and 10525211) and Minis

8、try of Education(RG14/06), Singapore.* Associated at Xiantan University, ecqsunntu.edu.sgstrongest Cu grain size of 10 15 nm, for instance, is attributed to a switch in the microscopic deformation mechanism from dislocation-mediated plasticity in the coarse-grain interior to the GB sliding in the nanocrystalline regime 19. A significant portion of atoms resides in the GB and the plastic flow of the GB region is responsible for the unique characteristics displayed by such materials 20. In the HPR

9、 regime, crystallographic slips in the grain interiors govern the plastic behavior of the polycrystallite; while in the IHPR regime, GB dominates the plastic behavior. During the transition, both grain interior and GB contribute competitively. The slope in the HPR is suggested to be proportional to the work required to eject dislocations from GBs 21. The strongest size is suggested to depend strongly on the stacking-fault energy and the magnitude of the applied stress 22,23.Although there is a growing body of experimental evidence for such unusual deformation in the nanometer regime, the underlying atomistic mechanisms for the IHPR are yet poorly understood. As pointed out by Kumar et al 24 and Mayrhofer et al 25 the physical origin of the IHPR transition and the factors dominating the strongest size have been a long-sta

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