Materials lecture 2(b)

Materials lecture 2(b)

1. True stress+True strain

   • real stress/strain carried by sample-instantaneous cross sectional area/length
     • strain hardening exponent equation. sigma=K.E^n
       • n= true strain at UTS, K = UTS/n^n
   • fundamental properties of material
   • true stress=increase continuously=no maximum.
     • Theoretical strength, experimental=much less= dislocation(plas def)+crack propgation

2. Poisson's ratio=V

   • +ve longitudinal strain=ln(li/lo)=El
   • -ve traverse strain= Ln(Di/Do)=Et
   • v=-Et/El
   • property of material
     • elas def=v=0.25-0.3
       • volume does change in elastic deformation
     • plas def=v=0.5 for any metal. Volume=not change in plastic deformaiton

3. eng stress/strain= independent of specimen size=comparison. show max UTS=max load specimen can carry.

4. work hardening-strain hardening-cold working

   • true stress/strain graph=continuing slope=more deformation= more stress to continue deformation.
     • Metal=strain/work hardens as it deforms. Work hardening rate= gradient of slope.
     • Even past UTS when load to continue=decreases=still work hardening= true stress=still increasing=cross section A=decreasing=necking
     • Flow stress-stress required to maintain plastic deformation

5. strain rate+temp effects on stress/strain properties

   • strain rate=how fast you deform.
     • small effect on flow stress- strain-rate change of 100X= increase flow stress by only 12%. M increases at higher temp
   • superplasticity-high temps=Al+Ti=Vsmall grain=superplastic= survive strains>100% = Vductile+Vsoft=processed using processes for plastics
   • Temp
     • below 0.3-0.4 Tmelt
       • fcc(Cu, Ni, Al)=insensitive to temp
       • b.c.c=stronger lower temp=sensitive to temp. -200 degree=2X yield stress than RT but more brittle=DBTT
     • above 0.3-0.4 Tmelt
       • all metals=relatively soft

6. Grain size/shape=smaller grain diameter=stronger it is=higher yield stress=Hall-Petch equation

   • HSLA steels-strength from fine grain.

7. Work/strain hardening+cold working

   • forming process=plastic def.
   • below 0.3-0.4Tmelt= plas def= work hardens+strengthens+reduce ductility=cold working-sigman=k epsilon^n
     • Metals=undergo cold-work when deformed at RT
     • Work hardening= due to generation+motion of dislocations

8. Effect of temp on mech+micro during hot working

   • t<0.3tm=recovery=internal stress from cold working=released
   • 0.5tm=recrystallization=new grains
     • Strength/hardness=decrease, ductility=increase=back to pre cold worked levels
   • above 0.5tm=grain growth
     • deleterious effects on formability,strength, toughness

9. cold forming, area under curve=work per unit volume T<0.4Tm-work hardening-flow stress increase with strain

   • Hot forming, recrystallization+plastic def. igor elas def