plastic deformation permanent, unrecovered mechanical deformation  = f/a stress deformation by...

Download Plastic Deformation Permanent, unrecovered mechanical deformation  = F/A stress Deformation by dislocation motion, “glide” or “slip” Dislocations –Edge,

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  • Plastic DeformationPermanent, unrecovered mechanical deformations = F/A stressDeformation by dislocation motion, glide or slipDislocationsEdge, screw, mixedDefined by Burgers vectorForm loops, cant terminate except at crystal surfaceSlip systemGlide plane + Burgers vector

    maximum shear stress

  • Slip system = glide plane + burgers vectorCorrespond to close-packed planes + directionsWhy?Fewest number of broken bondsCubic close-packedClosest packed planes {1 1 1} 4 independent planesClosest packed directionsFace diagonals

    3 per plane (only positive)12 independent slip systemsCrystallography of Slip

  • HCPBCCPlanes {0 0 1} 1 independent planeDirections 3 per plane (only positive)3 independent slip systemsPlanes {1 1 0} 6 independent planesDirections 2 per plane (only positive)12 independent slip systemsOccasionally also {1 1 2} planes in BCC are slip planes Diamond structure type: {1 1 1} and --- same as CCP, but slip less uncommon

  • Why does the number of independent slip systems matter?s = F/AAre any or all or some of the grains in the proper orientation for slip to occur?HCPCCP Large # of independent slip systems in CCP at least one will be active for any particular grain True also for BCC Polycrystalline HCP materials require more stress to induce deformation by dislocation motionmaximum shear stress

  • Dislocations in Ionic Crystalslike charges touchlike charges do not touchlong burgers vector compared to metals12(1) slip brings like charges in contact(2) does not bring like charges in contactcompare possible slip planesviewing edge dislocations as the termination defect of extra half-planes

  • Energy Penalty of Dislocationsbonds are compressedbonds are under tensionR0tensionREcompressionEnergy / length |b|2Thermodynamically unfavorable Strong interactionsattraction annihilationrepulsion pinningToo many dislocations become immobile

  • SummaryMaterials often deform by dislocation glideDeforming may be better than breakingMetalsCCP and BCC have 12 indep slip systemsHCP has only 3, less ductile|bBCC| > |bCCP| higher energy, lower mobilityCCP metals are the most ductileIonic materials/CeramicsDislocations have very high electrostatic energyDeformation by dislocation glide atypicalCovalent materials/SemiconductorsDislocations extremely rare

  • Elastic DeformationConnected to chemical bondingStretch bonds and then relax backRecall bond-energy curveDifficulty of moving from R0Curvature at R0Elastic constants(stress) = (elastic constant) * (strain)stress and strain are tensors directionalthe elastic constant being measured depends on which component of stress and of strain

  • Elastic ConstantsY: Youngs modulus (sometimes E)l0Fstress = uniaxial, normal stressmaterial elongates: l0 lstrain = elongation along force directionobservation:s (stress)e (strain)Ymaterial thins/necks: A0 Ai elongates: l0 litrue stress: use Ai; nominal (engineering) stress: use A0true strain: use li; nominal (engineering) stress: use l0

  • Elastic ConstantsConnecting Youngs Modulus to Chemical BondingCoulombic attractionF = k DRstress*areastrain*lengthR0 k / length = Ywant k in terms of E, R0observed within some classes of compoundsHooks Law

  • Elastic ConstantsBulk Modulus, Kapply hydrostatic pressures = -Pmeasure change in volumeP = F/Alinear responseUseful relationship:Can show:analogous to Youngs modulusCoulombic:hydrostatic stress

  • Elastic ConstantsPoissons ratio, napply uniaxial stresss = F/Ameasure e|| - elongation parallel to forceFRigidity (Shear) Modulus, Gyxmeasure e - thinning normal to forcel0DlFFapply shear stresst = F/Ameasure shear strain= tanf ff e|| eA

  • Elastic ConstantsGeneral Considerations 6 parametersStress, s: 3 3 symmetric tensorIn principle, each and every strain parameter depends on each and every stress parameterStrain, e: 3 3 symmetric tensor 6 parameters 36 elastic constants 21 independent elastic constants in the most general caseSome are redundantMaterial symmetry some are zero, some are inter-relatedIsotropic material only 2 independent elastic constantsnormal stress only normal deformationshear stress only shear deformationCubic material G, Y and n are independent

    k = (stress*area)/(strain*length) = Y * length*K = Vo*(Vo^-7/3) = Vo^-4/3*