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Research Papers

Formation of a Prismatic Dislocation Loop in the Interface of a Circular Cylindrical Inclusion Embedded in a Thin Slab

[+] Author and Article Information
Jérôme Colin

Institut P’,
Université de Poitiers,
SP2MI-Téléport 2,
Futuroscope F86962, Chasseneuil Cedex, France
e-mail: jerome.colin@univ-poitiers.fr

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 31, 2015; final manuscript received October 19, 2015; published online November 13, 2015. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 83(2), 021006 (Nov 13, 2015) (7 pages) Paper No: JAM-15-1458; doi: 10.1115/1.4031895 History: Received August 31, 2015; Revised October 19, 2015

The introduction of a prismatic dislocation loop in the interface of an axisymmetric precipitate embedded in a thin slab of infinite lateral extension has been theoretically investigated. The critical misfit strain resulting from the lattice mismatch between the inclusion and the slab has been characterized for the loop formation versus the thickness of the slab and the radius of the inclusion. The case where the precipitate is embedded in a semi-infinite matrix is also discussed and a stability diagram of the structure is displayed with respect to the loop introduction versus the geometric and misfit parameters.

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Topics: Slabs , Dislocations
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References

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Figures

Grahic Jump Location
Fig. 1

An axisymmetric precipitate of radius R is embedded in a thin slab of thickness h. The elastic coefficients of both phases are equal. A prismatic dislocation loop of Burgers vector (0, 0, b) is located in the interface between the inclusion and the slab at a distance d from the upper free-surface.

Grahic Jump Location
Fig. 2

Total energy variation ΔẼtot versus the loop distance from the upper free-surface d̃ for different values of the misfit strain parameter ε*ν. For ε*ν=0.001, ΔẼtot is positive for all d̃ values. A minimum in energy is observed when the loop is emitted in the interface at d = h/2 for ε*ν=0.006. ΔẼtot cancels at d = h/2 when the misfit parameter reaches a critical value ε*ν,c=0.01196. For ε*ν=0.015 > ε*ν,c, the formation of the interface dislocation loop should occur in the horizontal plane of symmetry of the structure.

Grahic Jump Location
Fig. 3

Critical misfit strain parameter ε*ν,c versus the slab thickness h̃, for different values of the inclusion radius R̃

Grahic Jump Location
Fig. 4

Total energy variation ΔẼtot versus the distance d̃ between the loop and the free-surface in the case of a semi-infinite matrix and for different values of the misfit parameter ε*ν. For ε*ν=0.002, ΔẼtot is positive. For ε*ν=0.008, ΔẼtot is negative for d̃ > 92 and the introduction of the loop is favorable.

Grahic Jump Location
Fig. 5

Critical distance from the free-surface d̃c versus the misfit strain parameter ε*ν, for different values of the inclusion radius R̃

Grahic Jump Location
Fig. 6

Critical misfit strain parameter ε*ν,c versus the distance of the loop from the free-surface d̃ for different values of the radius R̃

Grahic Jump Location
Fig. 7

Three-dimensional contourplot of ΔẼtot energy versus (R̃,d̃,ε*ν), the surface of energy corresponding to ΔẼtot=0. Region 1 is dislocation-free, the dislocation formation is favorable in region 2.

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