Evolution of stress in individual grains and twins in a magnesium alloy aggregate

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Evolution of stress in individual grains and twins in a magnesium alloy aggregate

C. C. Aydıner, J. V. Bernier, B. Clausen, U. Lienert, C. N. Tomé, and D. W. Brown

Phys. Rev. B 80, 024113 – Published 21 July 2009

Abstract

This is an in situ measurement of the full stress tensor and its evolution in a growing deformation twin and, simultaneously, in the grain where the twin forms. The combined information provides a detailed picture of the grain-twin interaction. The three-dimensional x-ray diffraction method using 80.7 keV synchrotron x rays allows us to in situ investigate a grain within the bulk of a magnesium alloy (AZ31) sample that is compressed to activate the ${10 \bar{1} 2} ⟨ \bar{1} 011 ⟩$ tensile twin system. We observe that the stress state of the twin is drastically different from the one of the grain in which it is embedded. We analyze such result in terms of the shear transformation associated with twinning and the dimensional constraints imposed by the surrounding aggregate.

Received 12 November 2008

DOI:https://doi.org/10.1103/PhysRevB.80.024113

Authors & Affiliations

C. C. Aydıner^1,*, J. V. Bernier², B. Clausen³, U. Lienert⁴, C. N. Tomé¹, and D. W. Brown¹

¹Materials Science & Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Engineering Technologies Division, Lawrence Livermore National Laboratory, Livermore, California 94551, USA
³Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
⁴Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

^*Present address: Mech. Eng. Dept., Bogazici University, Turkey; can.aydiner@boun.edu.tr

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Issue

Vol. 80, Iss. 2 — 1 July 2009

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Images

Figure 1
Schematic of the experimental geometry. The cylindrical compression sample and the associated sample coordinate system.[1, 2, 3] The load is applied along axis 3. The area detector $(40 \times 40 {cm}^{2})$ is 1.8m away from the sample. Targeted grain $(G_{1})$ is centered with respect to the $Ω$ rotation axis as well as the $0.2 \times 0.2 mm$ x-ray beam that engulfs it. The diffraction spots of $G_{1}$ appear on different images that are recorded on the area detector, each corresponding to one-degree $Ω$ sweeps. Also shown is an arbitrary grain $(G_{2})$ in the path of the beam that also contributes spots to the images.Reuse & Permissions
Figure 2
(Color) Orientation of the hexagonal unit cells of the parent grain and the twin variant 2 in the bulk of the sample. The orientation of the common twin plane (green) is also shown. Triads depicting the principal axes of stress and the principal stress components are shown for the parent and variant 2 for an applied stress $(σ_{app})$ of 40 MPa. The length of the arm is proportional to the stress magnitude in that direction. In addition, each arm is color coded for stress values. In the inset on the left, the typical lamellar morphology of the twin is shown in an orientation imaging microscopy (OIM) micrograph of another AZ31 grain with equivalent twin/parent orientation.Reuse & Permissions
Figure 3
(Color online) Predicted regions of interest (ROI) for selected (hkil) spots of twin variant 2. Each column shows the ROI of an (hkil) spot (at the $Ω$ frame that the spot intensity is maximum) as a function of applied load. The appearance of the spot at the originally empty ROI (at 40 MPa) shows the nucleation of the twin, and the spot intensity increasing with load reflects the growth of the variant.Reuse & Permissions
Figure 4
(Color online) Volume fractions of the parent and the twin variants as a function of applied stress. The sum of all volume fractions is also shown for verification.Reuse & Permissions
Figure 5
(Color online) Projections of the stress tensors of the parent and twin variants along selected sample and crystal directions as a function of applied stress: (a) $σ_{33}$ , crystal stress component along the compression axis (sample axis 3), and volume fractions of the twin variants (dashed lines). (b) $σ_{cp}$ , the component of the stress tensor along the $c$ axis of the parent. (c) $τ_{rs}$ , the resolved shear stress on the twin plane along the twin direction. (d) $σ_{n}$ , the stress projected along the twin plane normal of the respective variants.Reuse & Permissions

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