There has been a lot of research interest in the manufacture of ultra-fine grained (UFG) metals for their enhanced strength and hardness by employing severe plastic deformation (SPD) processing techniques.
Plane-strain orthogonal cutting has recently been exploited as a means to refine the microstructure of metallic materials from tens of micrometers or greater to a few hundred nanometers, e.g., aluminum alloys , copper [2-4], nickel-based superalloys , steels  and titanium .
Machining only needs a single pass to create large enough strains required for the creation of sub-micron grain sizes in the chips. The plastic strain imposed can be modulated by an appropriate choice of the rake angle of the cutting tool. The material processing rate can also be easily controlled by regulating the cutting speed and/or depth of cut.
No physics-based model, analytical or empirical, available to quantitatively predict the change of grain sizes during machining.
The large-strain in the chip formation has been used as a qualitative measure for the grain size change. The effects of cutting speed and workpiece temperature are also very qualitative.
A predictive model based on the grain refinement mechanism in machining is critically needed to better design and optimize the process parameters, such as the cutting speed, temperature, depth of cut and tool geometry, etc., for producing the desirable microstructures by machining.
Dislocation Density-Based Material Model (1) 5 Dislocation density-based material models are useful tools to capture grain size evolution during complex dynamic processes like machining involving multi-process variables Estrinand other researchers [6-9] developed a dislocation density evolution model for equal channel angular processing (ECAP).Their dislocation density-based material model was compatible with the material constitutive models developed under varying conditions of strains, strain rates and temperatures . In the model, a dislocation cell structure is assumed to form during deformation, which consists of two parts, dislocation cell walls and cell interiors, and obeys a rule of mixtures.
Dislocation Density-Based Material Model (2) Fig. 1 A typical TEM microstructure of cold rolled nickel with dislocation boundaries .
A new, refined grain structure emerges as the misorientation between cells in the dislocation cell structure increases with strain. The cell structure can be considered as a ‘precursor’ of the eventually developing grain structure.
Thus, in this modeling approach, the theoretically calculated cell size is identified with the grain size.
Dislocation Density-based Material Model (5) 9 Table 1. Dislocation density-based model parameters Fig. 2 Dislocation density-based plasticity model predictions for CP Ti
CEL Modeling of Steady-State Orthogonal Cutting A novel coupled Eulerian-Lagrangian (CEL) model is developed to simulate steady-state chip formation and grain refinement in orthogonal cutting. 10 Fig. 3 CEL model setup using ABAQUS/Explicit
CEL Model Validation 11 Table 2. CEL model validation test conditions Fig. 5Comparison of predicted cutting force with experiments Fig. 4 Comparison of predicted temperature
Material Dislocation Subroutine in CEL model 12
Cutting and Dislocation Evolution Simulations 13 Table 3. Orthogonal cutting experiments of CP Ti 
Video: Cutting and Dislocation Evolution Simulation 14
Dislocation Evolution Simulation 15 Fig. 6 Schematic illustration of microstructural evolution during machining. Predicted total dislocation density (1/mm2) Homogeneous, loosely distribution of dislocations in the bulk material Elongated dislocation cell in the chip primary shear zone, with dense dislocations on the cell walls and blocked dislocations by subgrain boundaries Well developed sub-micron grains in the chip, by break up and reorientation of subgrains. TEM micrographs taken in cutting of copper 
Simulation Result: Strain Rate 16 Measured Predicted Fig. 7 Strain rate for orthogonal cutting of CP Ti with a rake angle of 20°
The strain rate prediction matched well with the measurement
The predicted chip morphology was nearly identical to the actual chip
Simulation Result: Strain 17 Fig. 8 Effective strain predictions for orthogonal cutting of CP Ti with a rake angle of 20°
The average effective strain in the chip was predicted to be about 1.5 and 3.8 for the rake angle of 20° and -20°, respectively, while the measured strains were 1.4 and 3.5 for the rake angle of 20° and -20°, respectively.
Largest strains were predicted in the secondary shear zone along the tool-chip contact and on the machined surface.
Simulation Result: Temperature 18 Fig. 9 Temperature (°C) predictions for orthogonal cutting of CP Ti Rake angle 20° Rake angle -20°
The predicted average cutting temperature in the shear zone was increased from ambient to 70 °C and 150 °C for the rake angle of 20° and -20°, respectively.
Simulation Result: Grain Size 19 Fig. 10 Predictions of the grain size d (nm) distribution for orthogonal cutting of CP Ti Rake angle 20° Rake angle -20° Table 4. Grain refinement predictions
The histograms of predicted grain sizes in the chips show a further reduction of grain size by about 20 nm when the rake angle is changed from 20° to -20°.
By using the -20° rake angle tool, the induced average shear strain in the chip was more than doubled from the case of 20° rake angle tool. But the average temperature in the chip also increased by about 80-100 °C, which adversely affected the grain refinement due to the increase of dislocations annihilations at a higher temperature.
The sum of the effects of the strain and temperature increases contributed to the shift of 20 nm in average grain size from the 20° to -20° rake angle tool.
Summary A dislocation density-based numerical framework was developed to simulate grain refinement in orthogonal cutting. The CEL model predictions of steady-state chip formation, strain and strain rate distributions in the chip all matched well with the actual measurements. The grain size was predicted to be refined to a minimum of about 100 nm not only in the chip but also near the machined surface for cutting of CP Ti, which match well with the measured values. The numerical framework developed in this study has been shown to be a useful tool to predict grain refinement in cutting and other SPD processes. 21
References M.R. Shankar, S. Chandrasekar, A.H. King, W.D. Compton, Microstructure and stability of nanocrystalline aluminum 6061 created by large strain machining, ActaMaterialia, 53 (2005) 4781-4793. H. Ni, A.T. Alpas, Sub-micrometer structures generated during dry machining of copper, Materials Science and Engineering A, 361 (2003) 338-349. S. Shekhar, J. Cai, J. Wang, M.R. Shankar, Multimodal ultrafine grain size distributions from severe plastic deformation at high strain rates, Materials Science and Engineering: A, 527 (2009) 187-191. S. Swaminathan, M.R. Shankar, S. Lee, J. Hwang, A.H. King, R.F. Kezar, B.C. Rao, T.L. Brown, S. Chandrasekar, W.D. Compton, K.P. Trumble, Large strain deformation and ultra-fine grained materials by machining, Materials Science and Engineering: A, 410-411 (2005) 358-363. M.R. Shankar, B.C. Rao, S. Lee, S. Chandrasekar, A.H. King, W.D. Compton, Severe plastic deformation (SPD) of titanium at near-ambient temperature, ActaMaterialia, 54 (2006) 3691-3700. S.C. Baik, Y. Estrin, H.S. Kim, R.J. Hellmig, Dislocation density-based modeling of deformation behavior of aluminium under equal channel angular pressing, Materials Science and Engineering A, 351 (2003) 86-97. S.C. Baik, R.J. Hellmig, Y. Estrin, H.S. Kim, Modeling of deformation behavior of copper under equal channel angular pressing, Zeitschrift fur Metallkunde, 94 (2003) 754-760. S.C. Baik, Y. Estrin, H.S. Kim, H.-T. Jeong, R.J. Hellmig, Calculation of deformation behavior and texture evolution during equal channel angular pressing of IF steel using dislocation based modeling of strain hardening, Materials Science Forum, 408-412 (2002) 697-702. V. Lemiale, Y. Estrin, H.S. Kim, R. O'Donnell, Grain refinement under high strain rate impact: A numerical approach, Computational Materials Science, 48 (2010) 124-132. Hansen, N., Huang, X., and Winther, G., Grain orientation, deformation microstructure and flow stress, Materials Science and Engineering: A, 494 (2008) 61-67. 37