For slip to occur in polycrystalline materials 5 independent slip systems are

For slip to occur in polycrystalline materials 5

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For slip to occur in polycrystalline materials, 5 independent slip systems are required (von Mises criterion). Hence, materials which are ductile in single crystalline form, may not be as ductile in polycrystalline form. FCC crystals (Cu, Al, Au) have excellent ductility. At higher temperatures more slip systems may become active and hence polycrystalline materials which are brittle at low temperature, may become ductile at high temperature. 12/1/2015 31 ǀ Middle East Technical University ǀ Çağla Meral ǀ [email protected] ǀ Plastic deformation by slip For a material, which crystalline structure is more ductile (deform more readily under load before breaking): HCP, BCC or FCC? 12/1/2015 32 Q
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12/1/2015 17 ǀ Middle East Technical University ǀ Çağla Meral ǀ [email protected] ǀ Single Crystal Slip 12/1/2015 33 Unslipped single crystal Slip plane Direction of force Zinc crystal ǀ Middle East Technical University ǀ Çağla Meral ǀ [email protected] ǀ Crystals slip due to a resolved shear stress, τ R . Applied tension can produce such a stress. Resolved shear stress Tuesday, December 01, 2015 34 normal to slip plane, n s Resolved shear stress τ R = F S / A S Shear area A S τ R τ R F S Relation between s and τ R F cos λ A / cos φ λ F F S φ n S A S A Applied tensile stress s = F / A F Area A Force F τ R = F S / A S 𝜏 𝑅 = 𝜎 cos 𝜆 cos 𝜙
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12/1/2015 18 ǀ Middle East Technical University ǀ Çağla Meral ǀ [email protected] ǀ Critical resolved shear stress 12/1/2015 35 critical resolved shear stress = minimum stress that initiates slip Ø : Angle between the normal to the slip plane and the applied stress directions. λ: Angle between the slip and stress directions. τ CR = σ . cos λ . cos Ø ǀ Middle East Technical University ǀ Çağla Meral ǀ [email protected] ǀ Angle between two directions Sometimes the angle between two directions may be necessary. Vector A: [h 1 k 1 l 1 ] Vector B: [h 2 k 2 l 2 ] α : angle between A and B Tuesday, December 01, 2015 36 cos a = (h 1 2 +k 1 2 +l 1 2 ) (h 2 2 +k 2 2 +l 2 2 ) h 1 h 2 + k 1 k 2 + l 1 l 2 A . B=|A| |B| cos a
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