MAT_101_Winter08_Lecture_10

MAT_101_Winter08_Lecture_10 - Energy of a Dislocation The...

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Energy of a Dislocation The Line Tension “T” – Broken and stretched bonds around the dislocation There is EXTRA energy associated with the Defect = m J b 2 G T 2 r G = “Shear Modulus” – Total Extra Energy in the Crystal Due to the Dislocation d long: (J) d b 2 G Td Energy 2 r = = – Dislocations like to be straight (minimize d) – Dislocations like to have SMALL |b| (minimize |b| 2 )
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Geometry and Nomenclature of Dislocation Glide: Glide Planes Glide Plane Definition: a plane on which a specific dislocation can glide Physically: the glide plane must contain b and t Mathematically: n = b x t (note b = Burgers vector and t = dislocation line tangent vector ) Screw Dislocation b || t MANY Glide Planes! Edge Dislocation b t Only ONE Glide Plane! BUT. ..
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Concept of Cross Slip Cross Slip Screw-component dislocations can lie on many slip plans (b // t) Example on the right shows an expanding dislocation loop and cross slip
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Slip Systems ( Red arrow indicates most common slip systems)
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Dislocation Geometry in Deformation
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Even More on Shear Stress • Crystals slip due to a resolved shear stress, τ R . • Applied tension can produce such a stress. τ R = σ cos λ cos φ Relation between σ and τ R τ R = F s /A s F cos λ A /cos φ φ n s A A s Applied tensile stress: σ = F/A F A F s l i p di r ec t o n Resolved shear stress: τ R = F s /A s A s τ R τ R F s slip plane normal, n s λ F F s
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Critical Resolved Shear Stress • Condition for dislocation motion: τ R > τ CRSS • Crystal orientation can make it easy or hard to move disl. 10 -4 G to 10 -2 G typically τ R cos λ cos φ τ R = 0 φ =90° σ τ R = σ /2 λ =45° φ =45° σ τ R = 0 λ =90° σ
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Dislocation Motion in Polycrystals ( λ , φ ) change from one crystal to another. τ R will vary from one crystal to another. • The crystal with the largest τ R yields first. • Other (less favorably oriented) crystals yield later. σ Adapted from Fig. 7.10, Callister 6e. (Fig. 7.10 is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) 300 µ m
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4 Strategies for Strengthening: 1: Reduce Grain Size • Grain boundaries are barriers to slip. • Barrier "strength" increases with misorientation. • Smaller grain size: more barriers to slip. • Hall-Petch Equation: g r a i n b o u d y slip plane grain A B σ yield o + k y d 1/2 Adapted from Fig. 7.12, Callister 6e. (Fig. 7.12 is from A Textbook of Materials Technology , by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.)
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Grain Size Strengthening: An Example • 70wt%Cu-30wt%Zn brass alloy 0.75mm σ yield o + k y d 1/2 • Data: Adapted from Fig. 7.13, Callister 6e. (Fig. 7.13 is adapted
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MAT_101_Winter08_Lecture_10 - Energy of a Dislocation The...

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