Stress concentration of terminating twins
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finite crystalline volumes of a parent phase are realigned into new positions in a twin and the parent and product phases meet the following requirements: the crystal structure is unaltered, the product and the parent phase remain in contact and the orientation of the product is different than the orientation of the parent phase.' Such rearrangement of atoms is frequently observed in solids formed f r o m a gaseous, liquid or another solid phase. Twins are also observed when defects in a material are removed in thermal annealing process. Twins are formed when a crystalline solid is deformed, especially when slip is very difficult under the conditions of deformation. The m a n y different circumstances under which one observes the presence of twins in a solid has p r o m p t e d its study by a number of workers. 2 The coordinated m o v e m e n t of atoms to produce a twin may be thought to have arisen as a result of macroscopic deformation. In such a deformation, the coordinates of the lattice points of the parent phase are related to the coordinates of the lattice points in the twin by a linear function. When the a t o m positions do not coincide with the lattice points, shuffles of atoms around each lattice point will be necessary to restore the structure of the parent after homogeneous deformation. Since the product and the parent are in contact, the f o r m a t i o n of a twin leaves one plane unaltered in its dimensions as well as unrotated, and this plane is known as the twinning plane. Since the twin has the same structure as the parent, there cannot be a volume change and the deformation is said to be a simple shear, so that both the direction in which the shear acts and the magnitude of the shear are important in the description of twin. The formation of a twin by a homogeneous deformation process leads therefore to a change in shape of the crystal without altering its structure. Whenever a twin forms within a crystal, its natural change of shape is restrained by the surroundings, and as a consequence, the material is left in a state of internal stress. The determination of this stress is important for several reasons. The nature of shear stresses present in the vicinity of a twin contributes to our understanding of the interactions beK. S. SREE HARSHA is Professor and Chairman, Department of Materials Engineering, San Jose State University, San Jose, CA 95195. This paper is based on a presentation made at a symposium on "The Role of Twinning in Fracture of Metals and Alloys" held at the annual meeting of the AIME, St. Louis, Missouri, October 15-19, 1978, under the sponsorship of the Mechanical Metallurgy Committee of The Metallurgical Society of AIME. METALLURGICAL TRANSACTIONS A
tween twins and dislocations. The presence of tensile stresses in the vicinity of a twin can result in the nucleation of a crack, so that these stresses are important in studying twin-induced fracture phenomenon. The motion of atoms, particularly those in interstitial positions, ought to be influenced because of the
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