Microstructure From Processing: Evaluation and Modelling Grain size control: Lecture 3 Martin Strangwood, Phase Transformations and Microstructural Modelling, School of Metallurgy and Materials

Introduction Thermal exposure generally increases grain size and the control is by (i) transformation, (ii) solute drag or (iii) Zener drag Added deformation leads to an increase in stored energy that can be used to form ‘new’ grains

Starting state Annealing converts a high energy state (deformed) into a lower energy one and so the processes are driven by the energy of the deformed starting state Deformation introduces a number of defects: Point defects - vacancies and interstitials (latter only really for irradiated material); vacancies often arise from dislocation motion, e.g. jogs Vacancies Dislocations Jog

Starting state Annealing converts a high energy state (deformed) into a lower energy one and so the processes are driven by the energy of the deformed starting state Deformation introduces a number of defects: Line defects - dislocations Planar defects - stacking faults and boundaries Defects store excess energy in elastic strain fields around them and annealing removes them at a rate dependent on the type and number of defects

Defect behaviour Energy Number Mobility Overall Vacancies Dislocations Stacking faults Grain boundaries Low High High High Low Low

Defect behaviour Energy Number Mobility Overall Vacancies Small Dislocations Dominant Stacking faults Secondary Grain boundaries Tertiary Low High High High Low Low

Stages in annealing The dominant nature of dislocations means that these determine the stages of annealing Recovery - re-arrangement of dislocations, but little reduction in numbers

Stages in annealing Primary recrystallisation - removal of excess dislocations reducing stored energy as new dislocation-free grains form Uniform grain growth - reduction in grain boundary area Secondary recrystallisation - non-uniform grain growth Tertiary recrystallisation

Deformed structure - Cu FCC structure with high stacking fault energy Structures imaged on normal-transverse plane after cold deformation Rolling direction

Deformed structure - Cu Cells Up to 10 %  ~ 0.5 - 1.0 m diameter {111} Microbands ~ 40 x 0.2 m > 10 % 

Deformed structure - Cu Microbands rotate parallel to rolling plane Increasing  35° Macroscopic shear bands form - thin sheets of elongated narrow cells Higher  These features are associated with nucleation of recrystallised grains

Deformed structure - 70:30 brass FCC structure with low stacking fault energy Initially just a random arrangement of dislocations with no clear defined cell structure 40 - 60 % cold reduction Very thin deformation twins form on planes of high shear stress, ~ 0.02 m thick 50 - 80 % cold reduction Twins rotate to become parallel to sheet surfaces

Deformed structure - 70:30 brass 60 - 90 % cold reduction Macroscopic shear bands form at lower strains than in high SFE materials Random arrangement of dislocations

Recrystallisation and softening High SFE, e.g. Cu Primary recrystallisation Hv Work hardened 50 % softening = 50 % primary recrystallisation Annealing temperature

Recrystallisation and softening Low SFE, e.g. brass Recovery Primary recrystallisation Hv Work hardened Excessive recovery leads to retardation of recrystallisation 50 % softening 50 % primary recrystallisation Annealing temperature

Laws of recrystallisation Minimum deformation needed to initiate recrystallisation Activation barrier Smaller amounts of deformation need higher recrystallisation temperatures Thermally activated Increasing annealing times reduce temperature needed for recrystallisation Diffusional growth

Laws of recrystallisation Recrystallised grain size depends on on degree of deformation (chiefly) and annealing temperature (to a lesser extent); smaller grains result from larger degrees of deformation and lower annealing temperatures Nucleation rate effects As original grain size increases, greater amounts of deformation are required for equivalent recrystallisation time and temperature Driving force and nucleation site reduction The amount of ‘cold’ work needed for equivalent hardening increases as deformation temperature increases Rearrangement of defects during deformation and reduced driving force

Laws of recrystallisation New grains do not grow into deformed grains of similar orientation Texture affects recrystallisation Continued heating can cause the recrystallised grain size to increase (not always the case) Grain boundaries can drive some annealing processes

Dislocation stored energy Dislocations store the greatest amount of excess energy in a cold deformed metallic alloy and primary recrystallisation is driven by the removal of excess dislocations The size of this driving force can be estimated in two ways

Stress-strain curve Hot working? Al-based alloys can have a fairly flat work hardening curve 200 Work done Stress Strain 0.5 ~10 % is stored; P1 ~ 107 J m-3 Hot working?

Dislocation density Excess dislocations store energy is strain energy around the extra half plane Dislocation energy per unit length can be multiplied by dislocation density (length / unit volume) to give total energy  = shear modulus; b = Burger’s vector

Dislocation density in Al For a dislocation density of N dislocations per unit area of slip plane, then: Recovery reduces the value of 

Measuring stored energy?

Measuring stored energy DSC XRD EBSD TEM

SIBM Grains with different Schmid factors will start yielding under different applied stresses During deformation the Schmid factors change as the sample gets longer and thinner so that the slip planes and directions rotate During cold rolling adjacent grains will undergo different levels of strain and so have different stored energies (dislocation densities) B A Dislocation density of A < dislocation density of B

Boundary bulging If the stabler A grain is allowed to grow into the less stable grain B by bulging of the A/B grain boundary then there will be a decrease in free energy (Gv) but an increase in interfacial energy Original A/B boundary Bulged A/B boundary B A L Bulge is stable and can grow if: Schmid factor can give up to 10 % variation, hence viable

Intragranular nucleation Grain refinement would require greater nucleation and the formation of new recrystallised grains within the deformed grains would also block the growth of those from grain boundaries During deformation (depending on SFE) sub-grains can form separated by boundaries (SGB) with a few degrees misorientation Under the correct processing conditions transition bands can form across grains and act as intragranular nucleation sites for recrystallised grains

Transition bands Transition bands consist of a large number density of fine sub-grains, which achieve a large orientation change rapidly {111} Transition bands The high number density of fine sub-grains gives conditions for SIBM with the misorientation established allowing growth into the surrounding sub-grains

Transition band formation As plastic deformation proceeds the slip planes and directions rotate towards the tensile axis (i.e. towards or away from <110> depending on sense of stress and crystal structure) Rotation away from <110> can be either to <100> or <111> so that parts of a grain can rotate one way and other parts the other way; these two parts are separated by a transition band

Transition band formation BCC FCC Tension Transition bands Compression

Dutta-Sellars Equations

Dutta-Sellars Equations The D-S equations have a relatively simple form and are easy to apply with clearly identified parts, that have been shown to fit data well Original fit data

Dutta-Sellars Equations The original fitting data used was limited to 0.3 strain; 0.03 – 0.04 wt % Nb; and a mean prior austenite grain sizes in the range 12 – 100 μm Application of the D-S equations to more recent datasets has revealed less good agreement Improvement of the D-S approach is needed along with expansion to more realistic aspects Subsequent data

Re-crystallisation Ranges Initially a 0.046 wt % Nb steel was used that had been homogenised at 1225 °C for four days Re-heating at 1225 °C for one hour prior to Gleeble testing gave a uni-modal large grain size (250 - 280 μm) for which the original D-S equations should apply

Grain Size Distributions Relationships of the type were replaced by a simple halving of the original grain size size on recrystallisation – this effectively limits each prior austenite grain to the formation of two recrystallised grains This allowed each class in the starting grain size distribution to be treated separately to build up a recrystallised grain size distribution (a similar approach has been used for TSDR material by the CEIT group).

Grain Size Distributions This approach gives good quantification with the percentage recrystallised and for grain size distributions both unimodal and bimodal

Grain Size Distributions

Literature Values A grain class-based approach improves the fit for our experimental data and for literature data. The outliers generally have high (0.09 wt %) and low (0.02 wt %) [Nb] or higher [N]. Birmingham data Literature data The grain-size class approach expand the original D-S equations and should be used as standard for future applications

Segregation Effects during Hot Rolling The presence of solute-rich and solute-depleted regions will alter: Degree of dissolution during re-heating (already mentioned) Driving force for re-precipitation of strain-induced precipitates during deformation and holding Solute drag The differing Nb levels (currently experimental but to be predicted) can be used as input for the D-S equations with the appropriate grain size distribution

Segregation Effects during Hot Rolling For an average grain size this leads to a widening of the partial recrystallisation regime

Segregation Effects during Hot Rolling For the use of a class-based prediction then assumptions need to be made regarding the fraction of the each class in solute-rich and solute-depleted material The D-S equations are then applied for each class and composition

Recrystallisation Prediction The use of different compositions for different regions gives good agreement with Gleeble simulations (single hit)

Grain Size Distributions The class-based segregated approach gives reasonable agreement for grain size distribution 1225/1025 1225/975 The extent of recrystallisation for different grain size classes changes with deformation temperature

Grain size distributions Grain size distributions were evaluated in terms of D5% (grain size class constituting the first 5 area% of the total area measured), Dmode (the mode grain size class) and Dmax (the largest grain size class in the distribution). Dmode Dmax D D5% 5%

Effect of strain and initial grain size on recrystallised grain size The recrystallised grain size decreases with an increase in strain for all initial grain sizes during single hot deformation – shown here for mode grain size: Whilst the mode grain size decreases as the applied strain increases, the rate of refinement decreases and the initially different grain size values converge at high strain.

Predicting the recrystallised grain size distribution The modified equation (exponents derived from the classical theory for rate of nucleation) was used to predict the grain size distributions Grain boundary nucleation is assumed in deriving the equation   Original equation   Modified equation D’ values were fitted to the measured grain size distribution in terms of D5%, Dmode and Dmax for Fe-30Ni using the original equation in order to establish the best fit D’ values

Best fitted D’ values for predicting the D5% Dmode & Dmax D5%, Dmode & Dmax in the 50-60 µm, 110-120 µm & 160-180 µm distributions for different applied strains D’ represents the ‘efficiency’ of nucleation of new grains and is dimensionless. For D5% Dmode & Dmax D’ values increase steadily with increasing strain for the smallest initial grain size distribution A flattish region is observed with low strain for the largest initial grain size distribution A lower D’ value for the Dmode and D5% might suggest that fine grains recrystallise first due to higher stored energy.

Best fitted D’ values for predicting the D5% & Dmax in the 50-60 µm, 110-120 µm & 160-180 µm distributions for different applied strains D5% & Dmax have similar trends to those observed for the Dmode D’ values. D’ values increase steadily with increasing strain for the smallest initial grain size distribution A flattish region is observed with low strain for the largest initial grain size distribution

Variation of stored energy with initial grain size The deformation curves shown are for the 50 - 60 µm,110 -120µm and 160 -180µm samples deformed to a strain of 0.3 cold strain The finest initial grain size distribution (50-60 µm) material shows a greater work hardening rate than the other samples, which is consistent with a higher stored energy for the same plastic strain

Example distribution fit - 110-120 micron mode, 0.7 strain D’ = 0.83 reported in literature for predicting Carbon Manganese (C-Mn) steels does not give a good fit to the measured grain size distribution Carbon Manganese (C-Mn) steels D’ = 1.1 reported in literature for predicting Nb - containing steels was used to show that the literature equations can predict the mode grain size The variable D’ approach gives a good fit to the measured grain size distribution  

Summary of RMS errors for predicted grain size distributions in highly alloyed steels   RMS error Alloy type Initial mode grain size / µm Strain D' variation Constant D’ approach (1.1) Strip steel 0.15 3.14 7.71 160-180 0.3 7.61 16.00 0.45 8.00 21.87 High Aluminium steel 25-30 0.7 27.92 11.70 7.00 9Cr forging steel 170 - 180 10.83 12.50 4.42 18.80 360 - 380 6.90 17.00 The fit between measured and predicted grain size distributions for the variable D’ approach deteriorates as the complexity of the alloy increases and at lower strain values, although in almost all cases the fit is better than for a constant D’ approach

Control of grain size The coverage of distributions has been extended to consider strain and grain size (including the order of recrystallisation) rates of recrystallisation growth rates (and particle distribution)