Calculation of the Stress Interaction between Dislocation Pile-Ups in Neighbouring Misoriented Grains

Abstract:

During the early stages of the plastic deformation of a polycrystal, dislocations can pile-up against grain boundaries. Experimental results on large-grained materials have provided excellent verification of this phenomenon. Such a pile-up may activate dislocation slip in the neighbouring grain. Whether this occurs depends on the misorientation between the grains and the resolved shear stresses in the affected grain. Several approximate criteria have been proposed to predict the occurrence of this mechanism. Here, the problem will be assessed directly by calculating the Peach-Köhler force produced by a single dislocation pile-up in one grain on all the possible slip systems in the neighbouring grain, in combination with the effect of the applied external stress as obtained through calculation of the Schmid factor. It will be seen that the problem is significantly more complex than what is generally assumed in basic explanations of the Hall-Petch effect: highly localised stress concentrations are generated for certain misorientations, which are capable of punching out small dislocation loops which may then propagate into the neighbouring grain.

• Periodical: Materials Science Forum (Volume 879)
• Pages: 1731-1736
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.879.1731
• Online since: November 2016
• Authors: R. Schouwenaars*, A. Ortiz, V. H. Jacobo
• Keywords: Dislocations, Hall-Petch Relationship, Misorientation, Peach-Köhler Force, Pile-Up

References

[1] Hall E O 1951 Proc. Phys. Soc. B 64 747.

[2] Petch N J 1953 J. Iron and Steel Inst. 174 25.

[3] W.M. Baldwin, Acta Metall. 6 (1958) 139.

[4] D.J. Bushby, A.J. Dunstan, Int. J. Plast. 40 (2013), 152.

[5] Nazarov A A Romanov A E and Valiev R Z 1990 Scripta Metall. Mater. 24 (1929).

[6] Shen Z Wagoner R H and Clark A T 1988 Acta Metall. 36 3231.

[7] Soer W A and De Hosson J Th M 2005 Mater. Letters 59 3192.

[8] Soer W A Aifantis K E and De Hosson J Th M 2005 Acta Mater. 53 4665.

[9] Meyers M A Mishra A and Benson D J 2006 Prog. Mater. Sci. 51 427.

[10] de Koning M Kurtz R J Bulatov V V Henager C H Hoagland R G Cai W and Nomura M 2003 J. Nucl. Mater. 323 281.

DOI: 10.1016/j.jnucmat.2003.08.008

[11] Liu B Raabe D Eisenlohr P Roters F Arsenlis A and Hommes G 2011 Acta Mater. 59 7125.

DOI: 10.1016/j.actamat.2011.07.067

[12] Liu B Eisenlohr P Roters F and Raabe D 2012 Acta Mater. 60 5380.

[13] Schouwenaars R Seefeldt M and Van Houtte P 2010 Acta Mater. 58 4344.

[14] Baskaran R Akarapu S Mesarovic S D and Zbib H M 2010 Int. J. Solids Struct 47 1144.

[15] Schouwenaars R, Jacobo V H and Ortiz A, 6th International Conference on Nanomaterials by Severe Plastic Deformation, IOP Conf. Series: Materials Science and Engineering 63 (2014) 012132.

DOI: 10.1088/1757-899x/63/1/011001

[16] Hirth J P and Lothe J 1968 Theory of Dislocations (New York: McGraw-Hill).

[17] Shen Z, Wagoner R H and Clark, W A T. Acta metall. 36 (1988), 3231-3242.

[18] Balluffi R W, Komem Y, and Schober T. Surface Science, 31 (1972) 68-103.

[19] Clark W A T, Wagoner R H, Shen Z Y, Lee T C, Robertson I M and Birnbaum H K. Scripta Metall Mater 26 (1992) 203-206.

[20] Lee T C, Robertson I M and Birnbaum H K. Metall Trans A, 21 (1990) 2437-2447.

[21] Tschopp M A and McDowell D L. Scripta Mater 58 (2008) 299-302.

[22] Tschopp M A Tucker G J and McDowell D L. Comput Mater Sci, 44 (2008) 351-362.

[23] Spearot D E, Tschopp M A, Jacob K I and McDowell D L. Acta mater, 55 (2007) 705-714.