Plastic deformation Extension of solid under stress becomes permanent when s exceeds elastic limit se L DL s Ductile solids: able for plastic deformation (metals, plastics) Brittle solids: break suddenly without being deformed (ionic and covalent crystals) s elastic region fracture se sM DL/L plastic deformation Ductility grows with temperature: metals can be shaped easily at high temperatures

Ductility Solids change shape without appreciable change in volume The maximum extension can be from a few to 50% Work hardening: elastic limit of metal can be increased by plastic deformation s s1 se new elastic region original elastic region e1 DL/L

Slip in metals to each other, but solid remains crystalline Planes of atom in crystal slip with respect to each other, but solid remains crystalline Slip planes are seen on a surface as slip lines Slip planes are parallel to lattice planes (HCP has 3 slip systems, FCC has 12 slip systems) Al, Ag, Au, Pb, Cu A d B C a s sM x A B C d/2 d

Slip in metals m , dyn/cm2 sM , dyn/cm2 m/ sM Sn Ag Al Duralumin Fe 1.9x1011 1.3x107 15000 Ag 2.8x1011 6x106 45000 Al 2.5x1011 4x106 60000 Duralumin 9.9x108 250 Fe 8x1011 1.5x109 500

Slip in metals: Schmid’s law normal “Slip begins on a given slip system, when the shear stress resolved on that system reaches a critical value” S f F a slip direction Slip lines on Al crystal 50 mm

Dislocations:edge Edge dislocation in simple cubic crystal line Burger vector ^ dislocation Burger circuit- path around dislocation line: 3 steps to->, 3 steps down, 3 steps to <-, 3 steps up. “Failure” to close this circuit is Burger vector b Dislocation may “glide”- little energy should be supply to slip crystal. Elastic limit in real crystal << ideal crystal.

Dislocations: screw dislocation line Atoms/ molecules bond to screw dislocation during crystal growth. Burger vector II dislocation line Density of dislocations: from 102 dislocations/cm2 in the best Ge and Si to 1012 dislocations/cm2 in heavily deformed metals Motion of dislocation can be blocked by: another dislocation, grain boundary, point defect Work-hardening: annealing decrease dislocation density to 106 dislocations/cm2. After plastic deformation density increases to 1012 dislocations/cm2, but motion of the dislocation can be blocked by pinning at other dislocations

Dislocations: grain boundaries grain boundary Dislocations are blocked by grain boundaries -> slip is blocked Smaller grain size-> larger surface of grain boundaries -> larger elastic limit Empirical equation for maximum elastic stress (Petch) sM =A+Bd-1/2, d -grain diameter Elastic limit in cooper doubles when grain size falls from 100 mm to 25 mm dislocations

Alloys Substitutional solution: dissolve atoms replace Alloys contain several mixed constituent metals Substitutional solution: dissolve atoms replace those of basic metal (Cu in Ni ) Interstitual solution: added elements are lodged in in interstitial sites (C in Fe) Motion of dislocations is impeded by irregularities -> elastic limit increases Elastic limit Concentration of alloyed element % C,N Si Mn Mo Ni 1 2

Alloys with precipitates Alloy contains two phases: predominant phase of matrix and precipitated phase is dispersed in form of fine grains. This take place at high concentration of added element Motion of dislocations are blocked by this grains -> larger elastic limit. Dislocation can pass the precipitated grains

Alloys with Guinier-Preston zones Alloy with GP zones is intermediate between homogeneous and precipitated phases: added element is concentrated in ~10nm GP zones. These zones block motion of dislocation Structure hardening Al+ 5% Cu alloy is homogeneous at 550 OC Cooled by quenching to room temperature Alloy with GP zones: high elastic limit Alloy in Concord: Al +2% Cu +1.5% Mg+1% Ni has sM~450Mpa with operation temperature up to 120O C

Steel and martensitic transformation –Fe ferrite BCC –Fe austenite FCC Martensite: needle crystals of a form aligned in g form C is diluted in a form hard but brittle New phase: Fe3C cementit in a-ferrite hard and ductile Fe – 0.5% C alloy at 950OC has g form quench to room temperature annealing T<800OC

Interaction of dislocation with impurities elastic region sL sU DL/L U L plastic deformation work hardening Impurities diffuse to dislocations and form “clouds”-> dislocations are pinned -> higher elastic limit When s exceeds sU dislocations escapes impurities -> stress needed for plastic deformation decreases