Plastic deformation

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

2. 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

3. B C s sM B C A x d d/2 Slip in metals • 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 a

4. Slip in metals

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

6. Edge dislocation in simple cubic crystal Burger vector ^ dislocation line dislocation line Dislocations:edge 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.

7. 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

8. 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

9. C,N Si Elastic limit Mn Mo Ni 1 2 Concentration of alloyed element % Alloys • 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

10. 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

11. Alloys with Guinier-Prestonzones 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 Cooled by quenching to room temperature Al+ 5% Cu alloy is homogeneous at 550 OC 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

12. –Fe ferrite BCC • –Fe austenite FCC Steel and martensitic transformation 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

13. s U sU work hardening sL L plastic deformation elastic region DL/L Interaction of dislocation with impurities 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