Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size

Dunstan, D. J.; Bushby, A. J.

doi:10.1016/j.ijplas.2013.07.004

Cited by 167 publications

(84 citation statements)

References 39 publications

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“…In recent works [53,54], a power-law dependence of yield or flow stress on grain size was expressed as follows…”

Section: Strengthening Due To Grain Refinementmentioning

confidence: 99%

“…where d is the grain size, σ o and k HP are material constant, the exponents are reported to be in the range from 0 to1 for different classes of materials [53,54]. Analysis of data for a number of metals and alloys has revealed that the typical values of exponent x range from 0.6 to 1 for fcc metals, whilst they are around 0.5 or less for bcc metals, and 0.2 or even zero for ceramics [55].…”

Section: Strengthening Due To Grain Refinementmentioning

confidence: 99%

See 1 more Smart Citation

Strengthening of an Al–Cu–Mg alloy processed by high-pressure torsion due to clusters, defects and defect–cluster complexes

Chen

Gao

Sha

et al. 2015

Materials Science and Engineering: A

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A physically-based model is established to predict the strength of cluster strengthened ultrafine-grained ternary alloys processed by severe plastic deformation. The model incorporates strengthening due to dislocations, grain refinement, co-clusters (due to short range order and modulus strengthening) and solute segregation. The model is applied to predict strengthening in an Al-Cu-Mg alloy processed by high-pressure torsion (HPT). The microstructure was investigated using transmission electron microscopy (TEM), atom probe tomography (APT), and X-ray diffraction (XRD). Analysis of XRD line profile broadening shows that the dislocation density increases significantly due to severe plastic deformation, which contributes to the increase of strength. APT reveals the presence of nanoscale coclusters and defect-solute clustering. The concepts of the multiple local interaction energies between solutes and dislocations were used to quantitatively explain the strengthening 2 mechanisms. The model shows a good correspondence with measured microstructure data and measured strength.

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“…In recent works [53,54], a power-law dependence of yield or flow stress on grain size was expressed as follows…”

Section: Strengthening Due To Grain Refinementmentioning

confidence: 99%

Section: Strengthening Due To Grain Refinementmentioning

confidence: 99%

Strengthening of an Al–Cu–Mg alloy processed by high-pressure torsion due to clusters, defects and defect–cluster complexes

Chen

Gao

Sha

et al. 2015

Materials Science and Engineering: A

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“…The index number [3] which has been discussed as a fit parameter in recent years. Korte [4] suggested that the index number of f.c.c.…”

Section: Resultsmentioning

confidence: 99%

The sectional size effect on the deformation behaviour of Inconel 718 at different temperatures

Zhao

Wan²,

Han³

et al. 2015

MATEC Web of Conferences

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Abstract. Inconel 718, as a multiphase super-alloy, is widely used in aeronautics and astronautics industries. In this field, a modified Hall-Petch equation was used to describe the grain size effect on the deformation behaviour of Inconel 718 sheet in uniaxial tension test. There is a piecewise linearity in the -d −1 curve: With the thickness t is a constant, the slope changes obviously after a critical t/d ratio, which increases with strain. Moreover, the influence on sectional curve caused by temperature is also an interesting issue. To address that, the sectionalized curve was fitted at different strains and temperatures, and the phenomena of grain size effect in piecewise curve at different temperatures were further explained. A surface model of Inconel 718 was proposed to explain the intrinsic mechanism of different slopes. The research provided an in-depth understanding of the size effect on the deformation behaviour of Inconel 718 at different hot working temperatures.

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“…It was observed that the microstructures consisted of ferrite and a small amount of pearlite. The classic data in the literature for the grain size dependence of the strength in many metals are reviewed [13]. The ferrite microstructure determination should be done in a magnification suited to the size of the grain so that small grains may not be lost.…”

Section: Methodsmentioning

confidence: 99%

“…The grain size estimation model presented by Umemoto et al, is extended in this research to develop a relationship between ferrite grain size, cooling rate, austeniting time, and temperature. The following Hall-Petch relationship is utilized to relate the yield stress to the ferrite grain size [10][11][12][13][14] where σ y is the yield stress, σ o and K are constants, d α the ferrite grain size. The grain size of a microalloyed steel has an important effect on its properties.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Ferrite Grain Size and Mechanical Properties of a 22MnVNb6 Microalloyed Low Carbon Cast Steel

Pluphrach

Yamsai

2017

Period. Polytech. Mech. Eng.

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Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size

Cited by 167 publications

References 39 publications

Strengthening of an Al–Cu–Mg alloy processed by high-pressure torsion due to clusters, defects and defect–cluster complexes

Strengthening of an Al–Cu–Mg alloy processed by high-pressure torsion due to clusters, defects and defect–cluster complexes

The sectional size effect on the deformation behaviour of Inconel 718 at different temperatures

Estimation of Ferrite Grain Size and Mechanical Properties of a 22MnVNb6 Microalloyed Low Carbon Cast Steel

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