Lecture_07_Dislocations_and_Strengthening

Lecture_07_Dislocations_and_Strengthening - MECH 340...

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MECH 340 Engineering Material Dislocations and Strengthening Mechanisms Stress % cold work Strain
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Issues to Address Why are dislocations observed primarily in metals and alloys? How are strength and dislocation motion related? How do we increase strength? How can heating change strength and other properties?
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Dislocations in Materials Metals: Disl. motion easier. -non-directional bonding -close-packed directions for slip. + + + + + + + + + + + + + + + + + + + + + + + + electron cloud ion cores Covalent Ceramics (Si, diamond): Motion hard. -directional (angular) bonding Ionic Ceramics (NaCl): Motion hard. -need to avoid ++ and -- neighbors. + + + + + + + + + + + - - - - - - - - - -
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Slip Systems
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Dislocation Motion Produces plastic deformation, Depends on incrementally breaking bonds. Plastically stretched zinc single crystal. If dislocations don't move, deformation doesn't happen!
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Stress and Dislocation Motion • Crystals slip due to a resolved shear stress, τ R . • Applied tension can produce such a stress. τ R = σ cos λ φ Applied tensile stress: σ = F/A F A F slip dir ection Resolved shear stress: τ R = F s /A s A s τ R τ R F s slip plane normal, n s Relation between σ and τ R τ R = F s /A s F cos λ A /cos φ φ n s A A s λ F F s
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Critical Resolved Shear Stress • Condition for dislocation motion: τ R > τ CRSS 10 -4 G to 10 -2 G typically • Crystal orientation can make it easy or hard to move disl. τ R = σ cos λ 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 σ 300 μ m Slip planes & directions ( 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.
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Dislocation Interaction
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Dislocation Interaction
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Strenthening Mechanisms
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1.Reduce Grain Size grain boundary slip plane grain A grain B σ yield = σ o + k y d 1/2 Grain boundaries are barriers to slip. Barrier "strength" increases with misorientation. Smaller grain size:more barriers to slip. Hall-Petch Equation:
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Example 70wt%Cu-30wt%Zn brass alloy σ yield = σ o + k y d 1/2 Data: [grain size (mm)] -0.5 σ yield (MPa) 50 100 150 200 0 4 8 12 16 10 -1 10 -2 5x10 -3 grain size, d (mm) 0 0.75mm
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2. Solid Solutions Impurity atoms distort the lattice & generate stress. Stress can produce a barrier to dislocation motion. Larger substitutional impurity Impurity generates local shear at C and D that opposes disl motion to the right.
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This note was uploaded on 02/07/2011 for the course MECH 340 taught by Professor Marwandarwiche during the Summer '07 term at American University of Beirut.

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Lecture_07_Dislocations_and_Strengthening - MECH 340...

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