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Research Papers

Nucleation and Boundary Layer Growth of Shear Bands in Machining

[+] Author and Article Information
Shwetabh Yadav

Department of Industrial and Systems Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: shwetabh@tamu.edu

Dinakar Sagapuram

Department of Industrial and Systems Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: dinakar@tamu.edu

1Corresponding author.

Manuscript received May 7, 2019; final manuscript received June 4, 2019; published online August 1, 2019. Assoc. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 141(10), (Aug 01, 2019) (7 pages) Paper No: MANU-19-1274; doi: 10.1115/1.4044103 History: Received May 07, 2019; Accepted June 06, 2019

We demonstrate a novel approach to study shear banding in machining at low speeds using a low melting point alloy. In situ imaging and an image correlation method, particle image velocimetry (PIV), are used to capture shear band nucleation and quantitatively analyze the temporal evolution of the localized plastic flow around a shear band. The observations show that the shear band onset is governed by a critical shear stress criterion, while the displacement field around a freshly nucleated shear band evolves in a manner resembling the classical boundary layer formation in viscous fluids. The relevant shear band parameters, the stress at band formation, and local shear band viscosity are presented.

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Figures

Grahic Jump Location
Fig. 1

True stress–strain plots for Wood’s metal obtained from uniaxial compression tests at different strain rates

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Fig. 2

Schematic of the experimental setup for in situ imaging of plastic flow and deformation in plane-strain cutting. The high-speed images are analyzed using a PIV image correlation method to obtain quantitative full-field deformation data.

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Fig. 3

High-speed images with superimposed streaklines (from PIV analysis) showing (a) continuous chip formation at V0 = 0.01 mm/s and (b) shear banded chip formation at a higher V0 of 0.6 mm/s. In the latter case, localized shear along periodic bands (see at arrow) can be immediately seen from the streaklines.

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Fig. 4

High-speed image sequence showing shear band formation. Frames (a)–(c) show the development of low-strain chip segment. Frames (d)–(f) show the nucleation phase of shear band formation, where the band front initiates near the tool tip at O (in frame (d)) and then propagates toward the free surface of the workpiece. The nucleation stage is complete when the band front meets the free surface at O′. Frames (g)–(i) show the shear band growth (sliding) phase where the material slides along the plane OO′. (a) t = 0 ms, (b) t = 30 ms, (c) t = 60 ms, (d) t = 110 ms, (e) t = 120 ms, (f) t = 140 ms, (g) t = 170 ms, (h) t = 200 ms, and (i) t = 230 ms.

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Fig. 5

Cyclic force profiles during shear banded chip formation at V0 = 0.6 mm/s (α = 0 deg). Fc is the cutting force (along V0) and Ft is the thrust force (perpendicular to V0). The points marked by a–i show force oscillation during the formation of a single shear band, with the individual points a–i corresponding to the exact time instances in Fig. 4. Shear band nucleation occurs at point d, while the onset of band sliding (growth) coincides with point g.

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Fig. 6

(a) Schematic of a streakline passing through the shear band plane and relevant displacement parameters. Time-evolution of the streakline during shear band growth, captured using the PIV analysis, was used to compute the displacement profiles. U is shear displacement parallel to the shear band plane, whereas y is the perpendicular distance from the band. The evolution of displacement field around the band during different time instances of the growth phase is shown in (b). The distance (y) where UUmax (marked by the dashed line) increases with time, reflecting the lateral growth of shear band width during the sliding phase.

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Fig. 7

Normalized displacement plot showing U/Umax as a function of nondimensional parameter ξ=4νt, where ν is the fitting parameter (kinematic viscosity) and t corresponds to the time interval of sliding. The theoretical displacement curve predicted by the viscous fluid model [Eq. (2)] is shown as a solid black line. The experimental displacement profiles at different time instances of sliding collapse with this normalization and coincides with the theoretical curve when ν = 9.5 × 10−10 m2/s.

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