Research Papers

A Rate-Sensitive Plasticity-Based Model for Machining of fcc Single-Crystals—Part II: Model Calibration and Validation

[+] Author and Article Information
Nithyanand Kota

Department of Mechanical Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213

Anthony D. Rollett

Department of Materials Science and Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213

O. Burak Ozdoganlar1

 Department of Mechanical Engineering, Department of Materials Science and Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213; e-mail: Ozdoganlar@cmu.edu

The simplified version closely mimics the behavior of results from force model in Refs. [15-16] (also shown in Figs.  77). The small difference between the two stems from the rounding of the yield vertex when the rate-sensitive constitutive equations are used.

The orientation angles about [0 0 1], [1 1 1], [1 0 1], [1 1 2], [2 1 2], [2 1 3],[2 1 6] and [1 0 2] zone axes were measured clockwise from [0 1 0], [1 1 −2],[0 1 0], [−1 1 0], [−1 0 1], [−1 −1 1], [1 4 −1] and [0 1 0] directions, respectively.


Corresponding author.

J. Manuf. Sci. Eng 133(3), 031018 (Jul 01, 2011) (9 pages) doi:10.1115/1.4004135 History: Received March 17, 2010; Revised March 29, 2011; Published July 01, 2011; Online July 01, 2011

For a range of precision machining and micromachining operations, the crystallographic anisotropy plays a critical role in determining the machining forces. Part II of this work presents the calibration and validation of the rate-sensitive plasticity-based machining (RSPM) model developed in Part I. The five material parameters, including four hardening parameters and the exponent of rate sensitivity, for both single-crystal aluminum and single-crystal copper are calibrated from the single-crystal plunge-turning data using a Kriging-based minimization approach. Subsequently, the RSPM model is validated by comparing the specific energies obtained from the model to those from a single-crystal cutting test. The RSPM model is seen to capture the experimentally observed variation of specific energies with crystallographic anisotropy (orientation), including the mean value, symmetry, specific trend, amplitude, and phase of the peak specific energy. The effects of lattice rotation, hardening, and material-parameter variations on the predicted specific energies is then analyzed, revealing the importance of both lattice rotation and hardening in accurately capturing the specific energies when cutting single-crystals. Using the RSPM model, the effects of crystallographic orientation, rake angle and friction angle on specific energies are also analyzed. Lastly, a simplified model that uses Merchant’s shear angle, thereby circumventing the minimization procedure, is constructed and evaluated.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic representations of (a) the planing operation and (b) the plunge-turning operation on single-crystal workpieces

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Figure 2

(a) Typical specific energy data from experiments as it varies with the orientation angle θ of the cutting plane and (b) the definition of the zone axis, cutting direction, and cutting plane orientation

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Figure 3

Typical iterations during the Kriging-based calibration procedure: (a) iteration points for the material parameters and (b) the root-mean squared error between the experimental data and the model with specified parameters. The first 60 steps involve a space-filling design-of-experiments

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Figure 4

Comparison of experimental and predicted specific cutting energy for (a) aluminum and (b) copper for the calibration cases

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Figure 5

Choice of incremental strain Δγ through convergence: Variation of plastic power for cutting direction [hkl] = [1 0 0], cutting plane normal [uvw] = [0 1 0], and zone axis [abc] =  [0 0 1] (see Fig. 1) (the candidate shear angle for the graph shown is 39 deg); and percentage variation from limiting value with decreasing Δγ. The selected Δγ value is identified in the figures with dashed vertical line.

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Figure 6

Validation case: comparison of the specific energies from the model and from experiments for single-crystal aluminum for the zone axis of [0 0 1]

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Figure 7

The effects of hardening and lattice rotation on specific energy: (a) and (b) no hardening and no lattice rotation; (c) and (d) hardening without lattice rotation; (d) and (f) lattice rotation without hardening cases. The former of each pair is for [0 0 1] zone axis, and the latter is for [1 0 1] zone axis. The full RSPM model (hardening and lattice rotation) is used as the reference for each case.

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Figure 8

Definition of the metrics used for analyzing the effect of different parameters: M is the mean value, and Ω is the amplitude (about the mean) of the specific energy as it varies with the orientation angle

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Figure 9

Effect of material parameters on mean M and amplitude Ω of specific energies for aluminum: (a)–(f) The exponent of the power law a; (b)–(g) the initial reference stress τo; (c)–(h) the saturation stress τv; (d)–(i) the initial hardening slope Θo; and (e)–(j) the exponent of rate sensitivity n

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Figure 10

(a) The material model (plastic stress versus cumulative slip) with the hardening effect; and the effects of (b) the initial reference stress, (c) the saturation stress, (d) the initial hardening slope, and (e) the exponent of the power law on the material model

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Figure 11

The selected zone axes in the basic stereographic triangle

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Figure 12

The effect of zone axis on specific cutting energy for aluminum for zone axes (a) [0 0 1], (b) [1 0 1], (c) [1 0 2], (d) [1 1 1], (e) [1 1 2], (f) [2 1 2], (g) [2 1 3], and (h) [2 1 6]

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Figure 13

The effect of zone axis on (a) the mean and (b) the deviation of specific cutting energy for aluminum

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Figure 14

The effect of zone axis on (a) the average cumulative slip and (b) the average lattice rotation for aluminum

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Figure 15

Variation of (a) the mean and (b) the amplitude with the rake and friction angles for aluminum

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Figure 16

(a) The proportion of (average) power spent in plastic deformation (to total power) and (b) the actual power spent in plastic deformation for aluminum across the range of rake and friction angles

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Figure 17

Comparison between the specific cutting energy obtained using the Merchant’s shear angle and that from the complete model including minimization of total work for (a) [0 0 1], (b) [1 0 1], (c) [1 1 1], and (d) [2 1 2] zone axes



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