physical metallurgy 4e volume3 doc

Phqs e tall IC - Robert W. Cahn and Peter Haasen (-I), editors FOURTH, REVISED AND ENHANCED EDITION .L- A [NORTH-HOLLAND [...]...CHAF'TER 20 DISLOCATIONS J P HIRTH Mechanical and Materials Engineering Department WashingtonState University Pullman, WA 999164-2920, USA R W! Cahn and F! Haasent, eds Physical Metallurgy; fourth, revised and enhanced edition 6 Elsevier Science BY 1996 1832 J l? Hirrh Ch 20, 8 1 I Elementary geometrical properties The concept of crystal dislocations was introduced by POLANYI... radius R and length L ce with u =Poisson’s ratio Differentiation of eq (4) gives: u r n 1 a* 1 dZ* - = -r- ar + -rz=88’ pb sin 6 2741 - v)r’ uee -=urn, us* =a 2 ~ h2 urz= y(a, +urn) This field has the physical features required by fig 2; compression above the glide plane, tension below it, and maximum shear stresses on the glide plane 8 =O The strains are given by Hooke’s Law and their integrals give... analytical result that removes the artificial core divergencies of the Volterra dislocation, eqs (2), (3) and (5) However, as discussed by HrrrTH and LOTHE[1982] and by BULLOUGH TEWARY and [1979], the model is physically unrealistic (compared to a cylindrical atomic model centered on the dislocation) and predicts that symmetry positions are positions of energy maxima instead of minima Nevertheless, atomic calculations... multiple o the interplanar spacing, the extended jog is composed of partial dislocations and stacking faults, as shown For a unit jog with height equal t a single o interplanar spacing, the stair-roddipole $ 4exists only over core dimensions Rather ~ than stair-rods and stacking faults, the jog is then better viewed as a jog-line, equivalent to a row of 1/3 vacancies for the present example (HIRSCH[1962]) . REVISED AND ENHANCED EDITION .L- A [NORTH-HOLLAND