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Lecture note 18 (11-03-2011)

# Lecture note 18 (11-03-2011) - MAE 581 Advanced Materials...

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1 MAE 581 Advanced Materials Science Lecture note 18 Line defects Concept of dislocation All crystalline materials usually contain lines of structural discontinuities running throughout each crystal or grain. These line discontinuities are termed dislocations and there is usually about 10 10 to 10 12 m of dislocation line in a meter cube of material. Dislocations enable materials to deform without destroying the basic crystal structure at stresses below that at which the material would break or fracture if they were not present. Figure 3.10 (a) Slip of crystal planes. (b) Shear stress versus displacement curve. A crystal changes its shape during deformation by the slipping of atomic layers over one another. The theoretical shear strength of perfect crystals was first calculated by Frenkel for the simple rectangular-type lattice shown in Figure 3.10 with spacing a between the planes. The shearing force required to move a plane of atoms over the plane below will be periodic, since for displacements x<b/ 2, where b is the spacing of atoms in the shear direction, the lattice resists the applied stress, but for x>b/ 2 the lattice forces assist the applied stress. The simplest function with these properties is a sinusoidal relation of the form:

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2 where is the maximum shear stress at a displacement = b/ 4. For small displacements the elastic shear strain given by x/a is equal to τ / μ
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Lecture note 18 (11-03-2011) - MAE 581 Advanced Materials...

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