1. Cold Working is Actually Strain Hardening Basic equation relating flow stress (strain hardening) to structure is:  o =  i +  Gb  1/2 Yield stress increases as  increases: large hardening small hardening    y0y0  y1y1   o is the yield stress   i is the “friction stress” – overall resistance of lattice to dislocation motion   is numerical constant 0.3 – 0.6  G shear modulus  b is the burger’s vector   is the dislocation density

2. Effects of Cold Work Yield strength (  y ) increases Tensile strength (TS) increases Ductility (%EL or %AR) decreases As cold work is increased

3. Other Cold Work Effects Usually a small decrease in density (few 10 ths of a percent) An appreciable decrease in electrical conductivity (increased number of scattering centers) Small increase in the thermal coefficient of expansion Because of increased internal energy – chemical reactivity is increased (decreased resistance to corrosion)

4. Results for polycrystalline iron:  y and TS decrease with increasing test temperature. %EL increases with increasing test temperature. Why? Vacancies help dislocations move past obstacles. Climb of Edge Dislocations Never Screw  -  Behavior vs. Temperature -200  C -100  C 25  C 800 600 400 200 0 Strain Stress (MPa) 00.10.20.30.40.5 2. vacancies replace atoms on the disl. half plane 3. disl. glides past obstacle 1. disl. trapped by obstacle obstacle Positive Climb

5. Strain Energy Related to Cold Work Mentioned that ~10% of the energy imparted during cold working is stored as strain energy Amount of strain energy is increased by increasing the severity of deformation, lowering the deformation temperature, and by impurity additions The strain energy increase is stored in the highly deformed microstructure – dislocation tangles Metastable microstructure! Figure: Stored energy of cold work and fraction of the total work of deformation remaining as stored energy for high purity copper Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3 rd Edition, PWS Publishing Company, 1994.

6. Annealing Can we release the stored strain energy? YES! The material is in an unstable state – but there is an activation energy barrier to releasing that energy By heating the material and adding energy to the system we can increase the probability of moving past the activation barrier Heat treating cold worked material is called Annealing

7. Release of Stored Energy What happens as we heat up cold worked material? Curve to the left is an anisothermal anneal curve Two samples – one cold worked and the other not Samples are heated continuously from low temperature to a higher temperature Energy release is determined as a function of temperature Difference in power to heat the specimens at same rate Figure: Anisothermal anneal curve for electrolytic copper Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

8. Annealing Stages 1.Recovery 2.Recrystallization 3.Grain Growth The cold worked state is thermodynamically unstable. With increasing temperature it becomes more and more unstable Eventually the metal softens and returns to a strain-free condition Complete process is known as Annealing Annealing is easily divided into 3 distinct processes: tensile strength (MPa) ductility (%EL) tensile strength ductility Recovery Recrystallization Grain Growth 600 300 400 500 60 50 40 30 20 Annealing Temperature (ºC) 20 0 100300400500600700

9. Recovery Defined as: Restoration of physical properties of a cold worked metal without any observable change in microstructure –Electrical conductivity increases and lattice strain is reduced –Strength properties are not affected Involves: –Dislocation Annihilation –Polygonization: Removal of grain curvature created during deformation Regrouping of edge dislocations into low angle boundaries within grains Reduces the energy of system by creating reduced energy subgrains Source 2: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3 rd Edition, PWS Publishing Company, 1994. Source 1: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

10. Recrystallization Recrystallization is: The replacement of the cold worked structure by the nucleation and growth of a new set of strain free grains –Density of dislocations is reduced –Strain hardening is eliminated –The hardness and strength is reduced and the ductility is increased –Driving force for recrystallization is the release of stored strain energy  Note this is also the driving force for recovery and therefore they are sometimes competing processes Source 1: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

11. How does it work? Nucleation of strain free grains occurs at points of high lattice curvature –Slip line intersections –Deformation twin intersections –Areas close to grain boundaries Several models (unproven) that propose mechanisms for nucleation: –Grain boundary bulging due to a local variance in strain energy –Sub-boundary rotation and coalescence Source 2: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3 rd Edition, PWS Publishing Company, 1994.

12. New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains. 33% cold worked brass New crystals nucleate after 3 sec. at 580  C. 0.6 mm Recrystallization

13. All cold-worked grains are consumed. After 4 seconds After 8 seconds 0.6 mm Further Recrystallization

14. TRTR º º T R = recrystallization temperature

15. Variables for Recrystallization Six main variables influence recrystallization behavior: 1.The amount of prior deformation 2.Temperature 3.Time 4.Initial grain size 5.Composition 6.Amount of recovery or polygonization prior to the start of recrystallization Because the temperature at which recrystallization occurs depends  Recrystallization temperature is not a fixed temperature like melting point The practical definition for recrystallization temperature is: The temperature at which a given alloy in a highly cold worked state completely recrystallizes in 1 hour. Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

16. Affect of Variables on Recrystallization 1.Minimum amount of deformation is required 2.The smaller the deformation, the higher the temperature required for recrystallization 3.Increasing annealing time decreases required recrystallization temperature. Temperature is more important than time. Doubling annealing time is approximately equivalent to increasing annealing temperature 10 o C 4.Final grain size depends most on the degree of deformation and to lesser extent on the annealing temperature. The greater the deformation & the lower the annealing temp., the smaller the recrystallized grain size. 5.The larger the original grain size, the greater the amount of cold work required to produce same recrystallization temp. Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.

17. Affect of Variables on Recrystallization 6.The recrystallization temperature decreases with increasing purity of the metal. Solid solution alloying additions ALWAYS raise the recrystallization temperature. 7.The amount of deformation required to produce equivalent recrystallization behavior increases with increased working temperature 8.For a given reduction in cross-section – different metal working processes produce different effective deformations. Therefore, identical recrystallization behavior may not be obtained. Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.