Hall-Petch relationship in a nanotwinned nickel alloy

Hall–Petch relationship in a nanotwinned nickel alloy

Leon L.Shaw,a,*Angel L.Ortiz b and Juan C.Villegas c

a

Department of Chemical,Materials and Biomolecular Engineering,University of Connecticut,Storrs,CT 06269,USA

b

Departamento de Ingenierı

´a Meca ´nica,Energe ´tica y de los Materiales Universidad de Extremadura,06071Badajoz,Spain c

Intel Corporation,Chandler,AZ 85226,USA

Received 5November 2007;revised 4January 2008;accepted 14January 2008

Available online 26January 2008

The Hall–Petch relationship in a nanotwinned alloy with absence of dislocation pile-ups is investigated for the first time.It is shown that,when the twin spacing is large (d >150nm),the hardness exhibits a d À1/2dependence.However,when the twin spacing is small (d <100nm),a d À1dependence results.These phenomena are interpreted based on dislocation-mediated mechanisms corroborated by the analysis of electron microscopy and X-ray diffractometry.Ó2008Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

Keywords:Hardness;Plastic deformation;Twinning;Nanocrystalline microstructure;Hall–Petch relation

Grain refinement has been a topic of intensive re-search for several decades.The driving force behind these enduring efforts is the enhancement of strength as the grain size decreases,as described by the empirical Hall–Petch (H–P)relationship [1,2]r y ¼r i þk y D À1=2

ð1Þ

where r y is the yield strength of a polycrystalline mate-rial,D is the average grain diameter,r i is the overall resistance of lattice to dislocation movement and k y is the H–P slope measuring the relative strengthening con-tribution of grain boundaries (GBs).Eq.(1)has been found to be applicable to a wide range of coarse-grained materials (D P $1l m),including applications to the flow stress at a given strain and the hardness of the material [3],the dislocation cells of heavily deformed materials [4],the materials with several levels of sub-structures,e.g.the co-presence of low-angle cell bound-aries and high-angle cell block boundaries [5],and materials with microsized twins [6,7].

Recently,the applicability of the H–P relation to ultrafine-grained materials (100nm

[13],where a comprehensive list of references can be found.However,studies on the H–P relation in nano-twinned materials are extremely scarce,with only one investigation on single-phase nanotwinned materials re-ported in the open literature [14].In that study,Eq.(1)is found to be valid for electrodeposited Cu with twin thickness as small as 13nm.Furthermore,the Hall–Petch slope is nearly the same as that determined from coarse-grained Cu,suggesting that the strengthening ef-fect of twin boundaries (TBs)is analogous to that of conventional GBs even in the nanometer scale [14].The applicability of the H–P relation to the nanotwin-ned Cu has been explained by dislocation pile-ups against TBs [14].However,it is well known that many materials do not exhibit dislocation pile-ups [15],and their H–P relations have been explained by the activa-tion of GB dislocation sources [16]or other alternative mechanisms [17–19].In this study we have investigated,for the first time,the dependence of the hardness of nanotwinned materials on the twin spacing with absence of dislocation pile-ups.The absence of dislocation pile-ups can be attained from low stacking fault energy materials when the twin thickness is too small to support dislocation pile-ups,as revealed in this study.

A nickel-base HASTELLOY C-2000Òalloy 1with a low stacking fault energy (1.22mJ m À2)[20]was chosen for this study in order to produce a gradient of

1359-6462/$-see front matter Ó2008Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.doi:10.1016/j.scriptamat.2008.01.025

*Corresponding author.Tel.:+18604862592;fax:+18604864745;e-mail:leon.shaw@

1

HASTELLOY and C-2000are registered trademarks of Haynes International,Inc.

Available online at

Scripta Materialia 58(2008)

951–954

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