Physical Metallurgy Principles Fourth Edition SI Version Chapter Eight: Annealing 8-1 8.1 Stored Energy of Cold Work Strain hardening (work hardening) is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed. The temp. at which deformation takes place is cold relative to the melting temp. of the metal. Cold working 2 Energy put into cold work Most of the energy expended in cold work appears in heat. A finite fraction is stored as strain energy associated with various lattice defects created by the deformation (ex. dislocations, point defects) rate (%): decreasing with deformation (6 calories, or 25 J/mole) (strain) (5%) (amount due to deformation) 3 The nature of stored energy of plastic deformation 1. cold working is able to increase the number of dislocations significantly (~ 1016 m-2) (annealed sample ~ 1010-1012 m-2) 2. point defects: another source of retained energy => one mechanism has been described (dislocation intersection: jogs: either vacancies and interstitials as it glides) 4 (Edge with a jog) (screw with a jog) Jogs extra plane Chap. 4 mn, no, and op move (extra plane) b over a stepped surface (not gliding along a plane) 5 Supplement (the principles of engineering materials, p. 294) The overall elastic strain energy or free energy of the material increases with increasing plastic strain (increasing dislocation density). As the temp. is increased, thermal energy aids dislocation movement (both glide and climb) so that dislocations may begin to move in response to the stress fields of surrounding dislocations. 6 8.2 The Relationship of Free Energy to Strain Energy The free energy of deformed metal is greater than that of an annealed metal by an amount approximately equal to the stored strain energy. => minimize dislocations for annealed metal. => G = H (H = U + PV @ constant P and V) G: free energy associated with the cold work H: the enthalpy (or the stored strain energy) S: the entropy increase due to the cold work The free energy increase equated directly to the stored energy 7 High free energy for the cold worked materials => soften (less dislocations, deformation) spontaneously. A metal does not usually return to the annealed condition by a single simple reaction because of the complexity of the cold-worked state. Heating a deformed metal, greatly speeds up its return to the softened state. 8 8.3 The Release of Stored Energy Valuable info about the nature of the reactions that occur as a cold-worked metal returns to its original state may be obtained through a study of the release of its stored energy. There are two important methods of accomplishing this: 1. Anisothermal anneal: sample is heated from low to high temperature; the energy release is determined as a function of temperature. 9 Energy release recrystallization recovery grain growth II I III 2. Isothermal anneal: the free energy is measured while the specimen is maintained at a constant temp. Energy release recrystallization recovery grain growth III III 10 These large energy releases appear simultaneously with the growth of an entirely new set of essentially strain-free grains, which grow at the expense of the original badly deformed grains. May be understood as a realignment of the atoms into crystals with a lower free energy The three stages of releasing stored energy: recovery, recrystallization, and grain growth. 11 Cold-worked 300C 370C 410C 460C 650C 12 8.4 Recovery: Working increases strength, hardness, and electrical resistance, and it decreases ductility. Laue patterns of deformed single crystals show pronounced asterism corresponding to lattice curvatures. Debye-Scherrer (powder): broaden diffraction lines In the recovery stage of annealing, the cold-worked crystal will tend to restore its original physical and mechanical properties. The various physical and mechanical properties do not recover their values at the same rate, indicating the complicated nature of the recovery process. Some properties are more effectively restored at different stages of annealing; e.g. hardness is insensitive to recovery but sensitive to recrystallization. 1 Another anisothermal anneal curve Almost no recovery Recover a lot recrystallization recovery grain growth I II III The fraction of the energy released during recovery is much larger than Fig. 8.2. 2 8.5 Recovery in Single Crystals (simple form of plastic deformation) The complexity of the cold-worked state is directly related to the complexity of the deformation that produces it. For a single crystal: lattice distortions are simpler by easy glide (slip on a single plane) than by multiple glide (simultaneous slip on several systems). Recovery associated with a simple form of plastic deformation: the simple recovery process involves the annihilation of excess dislocations. (positive and negative edge, left and right screw annihilation). it is probable that both slip and climb mechanism are involved. For a polycrystalline metal: lattice distortion may be more severe. 3 if the deformation does not involve bending for a single crystal (easy glide) => it is quite possible to completely recover its hardness without recrystallization. => however, in generally, deformation by easy glide could not be removed even at temperatures close to melting point. Max. compressive Shear stress Zero Neutral axis Max. tensile Slip planes 4 Without loss of time 2nd load Recovery begins very 1st load rapidly. 3rd load The rate at which a property recovers isothermally is a Completely recovery decreasing function of the time. 5 Zn single crystal: deformed by easy glide at 223K quicker Shows the time required to recovery for different temp. The rate of recovery is much faster at 283K. The temp. dependence of recovery time is a Arrhenius-type behavior (easy glide). : the time required to recover a R given fraction of the total yield point 6 Q 1 1 Q / RT2 ( ) 1 e R T T e 2 1 Q: 83140 J/mole for Zn Q / RT1 2 e If for recovery of ¼ of its original yield point in 5 min at 273K (0C) T2 = 273 K 2 = 5 min 83140 1 1 ( ) 8.314 273 300 1 5e 0.185min At 300K (27C) 83140 1 1 ( ) 8.314 273 223 1 5e 18000 min(12.5days) At 223K (-50C) 7 8.6 Polygonization: much more complicated process Another recovery process is called polygonization => in its simplest form, it is associated with crystals that have been plastically bent. => one of the most important recovery processes. Polygonization 1 Driving force for recovery: the reduction in cold worked strain energy. Relieving the strain energy. Rearranging these dislocations to produce a subgrain structure. The development of this configuration which is decidedly of lower energy is known as polygonization. 2 In a Laue photograph, for a single crystal: A finite number of spots is obtained. Each of the elongated, or asterated spots of the deformed crystal is observed before anneal. Crystals with nearly identical orientations (low-angle boundary, low-energy dislocation structure), their patterns will almost coincide. 3 Strain field: additive Strain field: partially Active planes cancel each other A plastically bent crystal must contain an excess of positive edge dislocations that lie along active planes (additive). => high strain energy 4 Strain field: partially cancel each other Strain field: additive In addition to lowering the strain energy, the regrouping of edge dislocations into low-angle boundaries has a second important effect. => removal of general lattice curvature. 5 It is customary to call low-angle boundaries, such as develop in polygonization, subboundaries. The dislocation introduced during working are arranged into more stable configurations (lower strain energy). (the principles of engineering materials, p. 296) 6 8.7 Dislocation Movements in Polygonization An edge dislocation: vertical movement: climb; horizontal movement: slip Both are required in polygonization 7 Various stages of polygonization Y- junction Coalescence of subboundaries Further coalescence the low-angle boundaries Dots: dislocations Associated with slip planes All the dislocations lie in the sub- Combine the boundaries pairs of branches (low angle into single boundaries, or polygon walls. polygon walls) Polygonization process by a simple bending and annealed for 1 hr for iron- silicon single crystals. 8 BCC previous photographs. Photograph of the front surface 9 More complicated case: polycrystalline slip occurs on a number of intersecting slip planes, and lattice curvatures are more complex and vary with position in the crystal. Such complex deformation even happens for single crystals. 10 Typical substructure by TEM 400C 600C 800C (A) high density of dislocations , with no well defined cell boundaries. (B) dislocation density , and random arrays of dislocations are visible (1280 min). 11 The formation of these dislocation arrangements produces only a slight decrease in hardness, since the dislocation density changes very little. Electrical properties are recovered. (the principles of engineering materials, p. 296) 12 8.8 Recovery Processes at High and Low Temperatures Polygonization is too complicated a process to be expressed in terms of a simple rate equation (slide 18). (not as easy as slip). Polygonization involves both slip and climb. Relatively high temp. (because of climb) is required for rapid polygonization. 13 8.9 Recrystallization Energy release recrystallization Energy detected by a recovery grain growth microcalorimeter (13mJ/hr) III III 14 Recovery competes with recrystallization, as both are driven by the stored energy. also thought to be a necessary prerequisite for the nucleation of recrystallized grains. 15 8.10 The Effect of Time and Temp. on Recryslallization One way to study the recrystallization process is to plot isothermal recrystallization curves like The temp. , the time needed to finish the recrystallization. 16 (1/T) Empirical equation: 1/T = K Log + C K: slope, C: intercept, 1/: the rate at which 50% of the structure recrystallized 17 QR for activation enthalpy for the motion of vacancies: a simple physical properties: barrier height.