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Research Papers

Measures of Bulk and Grain Strain in Deformation Processes

[+] Author and Article Information
Craig S. Hartley

 El Arroyo Enterprises, 231 Arroyo Sienna Drive, Sedona, AZ 86336

Jonathan E. Spowart

Air Force Materials Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, OH 45433

J. Eng. Mater. Technol 131(1), 011006 (Dec 17, 2008) (8 pages) doi:10.1115/1.3026548 History: Received February 25, 2008; Revised August 13, 2008; Published December 17, 2008

This study illustrates a method of measuring internal total strain based on the observation that networks of internal boundaries within a polycrystalline material deform locally in a manner congruent with the local metal flow. Appropriate measurements of the development of the spatial anisotropy of such networks with increasing deformation provide a basis for defining several measures of the local total strain. These quantities, called “grain strains” when the boundaries observed are grain boundaries, can serve as an experimental measure of the internal total strain at various locations in a specimen for comparison with computations based on finite element models using various constitutive relations or phase field simulations of grain growth or deformation. Experimental measurements of grain strains at the center of a ferritic steel sheet rolled in nominally 10% increments to 50% total reduction in thickness illustrate the method and correlate well with corresponding strains based on measures of the change in thickness of the sheet and the assumption of plane strain.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Specimen location and coordinate system employed for metallographic analysis

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Figure 2

Representative digital micrographs of an ultralow carbon steel sheet, rolled to 31.3% total reduction (three passes); (a) as-etched, RD-LT plane; (b) as-etched, RD-ST plane; (c) as-etched, LT-ST plane; (d) as-binarized, RD-LT plane; (e) as-binarized, RD-ST plane; and (f) as-binarized, LT-ST plane

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Figure 3

Logarithmic grain strain components versus logarithmic bulk strain components

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Figure 4

Conventional grain strain components versus conventional bulk strain components

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Figure 5

Lagrangian grain strain components versus Lagrangian bulk strain components

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Figure 6

Eulerian grain strain components versus Eulerian bulk strain components

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Figure 7

Effective grain strains versus effective bulk strains

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Figure 8

Schematic Illustration of gauge volume for measurements

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Figure 9

Comparison of least-squares MAT and data for 31.3% reduction by rolling

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