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SHEAR BEHAVIOR AND RELATED MECHANISMS IN MATERIALS PLASTICITY

Shear on the Flow Surface of Metallic Crystals

[+] Author and Article Information
Michel G. Darrieulat

Ecole Nationale Supérieure des Mines de Saint-Etienne, Centre “Sciences des Matériaux et des Structures,” UMR CNRS No. 5146, 158 cours Fauriel, 42023 Saint-Etienne, Cedex 2, Francedarrieulat@emse.fr

Asdin Aoufi

Ecole Nationale Supérieure des Mines de Saint-Etienne, Centre “Sciences des Matériaux et des Structures,” UMR CNRS No. 5146, 158 cours Fauriel, 42023 Saint-Etienne, Cedex 2, Franceaoufi@emse.fr

J. Eng. Mater. Technol 131(1), 011104 (Dec 19, 2008) (11 pages) doi:10.1115/1.2969258 History: Received February 05, 2008; Revised June 18, 2008; Published December 19, 2008

The present article addresses the following question: How is it that shears are so common in the plastic deformation of metallic alloys? An answer is sought in a geometric description of the shear flow when the deformation is produced by slip systems gliding according to the Schmid law. Such flows are represented schematically by what is called “simple shear” and a kinematic study is done of the way these shears can be produced by the joint activity of various slip systems. This implies specific conditions on the glide rates, which can be known analytically thanks to adequate parametrizations. All the possible shears have been calculated in the case of cubic metals deforming with identical critical resolved shear stresses (Bishop and Hill polyhedron). Three dimensional representations are given in the space of the Bunge angles associated with the principal directions of the shears. A special attention has been given to the number of slip systems involved. Most of the shears are not far from some combination of two or three systems. This is quantified by defining the misorientation ω between a shear taken at random and the set of shears produced by the glide on two or three octahedral slip systems. It is found that in most cases, ω<15deg. The maximum value of ω (30.5 deg) is found for the orientations called Cube and U in rolled metals.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sheared zones at the surface of a test-piece deformed in a channel die

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Figure 2

Geometry of simple shears: (a) effect on an element of matter and (b) elongation (Δa), neutral (Δb), and contraction (Δc) directions

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Figure 3

Section (φ2,φ1) for Φ=34π of the [0,π]3 cube representing all the possible shears; partition of the shears according to the flow cones to which they belong

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Figure 4

Three dimensional representation of the shears produced by the combination of two or three octahedral slip systems; see comments in the text

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Figure 5

Projection of Fig. 4 on (φ2,φ1). The octahedral slip systems are marked by a cross. The bold lines represent the combinations of two slip systems and the thin ones represent the combinations of three slip systems.

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Figure 6

Three dimensional representation of the shears produced by the octahedral slip systems of a given variety of rank 4

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Figure 7

Histograms of the misorientations between the random shear: (a) the octahedral slip systems, (b) the shears of the varieties of rank 2, and (c) the shears of the varieties of rank 3

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Figure 8

{111} Pole figure picturing the misorientations of the random shear to the shears of the varieties of rank 3; contours for ω=15 deg, 20 deg, and 25 deg and fiber {hk0}⟨kh¯0⟩

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