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Research Papers

# Stress Gradient Induced Strain Localization in Metals: High Resolution Strain Cross Sectioning via Synchrotron X-Ray Diffraction

[+] Author and Article Information
M. Croft

Department of Physics Astronomy, Rutgers University, Piscataway, NJ 08854; National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973

N. Jisrawi

Materials Science and Engineering Department, Rutgers University, Piscataway, NJ 08854; Department of Basic Sciences, University of Sharjah, P.O. Box. 27272, Sharjah, United Arab Emirates

Z. Zhong, J. Skaritka

National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973

K. Horvath

Department of Physics Astronomy, Rutgers University, Piscataway, NJ 08854

R. L. Holtz

Materials Science & Technology Division, Naval Research Laboratory, 4555 Overlook Avenue, SW, Washington, DC 20375

M. Shepard

Materials and Manufacturing Directorate, Air Force Research Laboratory, WPAFB, OH 45433-7817

M. Lakshmipathy

Zygo Corporation, Laurel Brook Road, Middlefield, CT 06455

Technical Data Analysis, Inc., Falls Church, VA 22046

V. Shukla, R. K. Sadangi, T. Tsakalakos

Materials Science and Engineering Department, Rutgers University, Piscataway, NJ 08854

J. Eng. Mater. Technol 130(2), 021005 (Mar 12, 2008) (10 pages) doi:10.1115/1.2840962 History: Received July 20, 2007; Revised November 14, 2007; Published March 12, 2008

## Abstract

Strain localization in the presence of a stress gradient is a phenomenon common to many systems described by continuum mechanics. Variations of this complex phenomenon lead to interesting nonlinear effects in materials/engineering science as well as in other fields. Here, the synchrotron based energy dispersive x-ray diffraction (EDXRD) technique is used for high spatial resolution profiling of both compression and tension induced strain localization in important materials/engineering problems. Specifically, compression induced strain localization in shot peened materials and tension induced strain localization in the plastic zones adjoining the faces of a fatigue crack are profiled. The utility of the EDXRD synchrotron technique for nondestructively cross-sectioning strain variations on small length scales (down to $10–20μm$) is described. While the strain field profiling relies on the shift of the Bragg lines, the data show that plastic deformation regions can also consistently be seen in the broadening of the Bragg peaks through the full width at half maximum parameter. Quantitative correlations between the synchrotron based x-ray determined deformations and surface deformations, as measured by optical surface height profiling, are also made.

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## Figures

Figure 2

(a) The strain profiles of ε33 and ε11 in the vicinity of the peened surface layer and the underlying bulk material of the Ti-6Al-4V specimen. The insets illustrate the X-ray scattering geometries for the ε33 (top) and ε11 (bottom) measurements. Note the stress scale (lower right) uses E=118GPa and ν=0.33 (see text) and σ1=175×103ε11 (MPa). (b) The Bragg line FWHM profile (for the ε11 analysis above) illustrating a strong enhancement in the peening deformed region.

Figure 3

(a) Schematic of placket bending with convex peened surface up. (b) Scattering geometries for the ε11 measurement case 2θ=12deg and di=ds=40μm. For the ε33 case, 2θ=6deg and di=30μm and ds=200μm.

Figure 4

(a) The strain profiles of ε33 and ε11 across the entire thickness of a heavily peened 1070 spring steel specimen. Note the stress variation on the right and scale corresponds to the ε11 (blue) curve with and σ1=286×103ε11 (MPa). (b) The Bragg line FWHM profile (for the ε11 analysis above) across the heavily peened 1070 spring steel specimen.

Figure 5

(a) Strain profiles along the y direction (crossing the crack perpendicularly) at a coordinate x=−2mm (i.e., 2mm behind the tip) for a fatigued 4140 specimen. The residual εyy (solid black line) and εxx (dashed blue line) strain components are shown. Note the sharp anomalies (see Label 1 in figure) located at the crack, and the plastic wake zone shaded. The broader background variation (see Labels 2 and 3 in figure) farther from the crack. (b) The Bragg line FWHM profile (for the εyy analysis above) across the wake region of the fatigue crack.

Figure 6

Micrographs related to 1070-steel shot peened specimen illustrating the qualitative peening induced surface deformations. (a) The shot peened surface (x1-x2) surface showing the x1-x2 surface craters caused by the ballistic impacts of shot incident from the x3 direction. (b) The r=3mm radius shot used in the peening process with a millimeter scale included for reference. (c) An edge view of the 1070-steel peened specimen showing the bulging of the peened layer forming a protruding lip (at top of figure) at the edge.

Figure 7

Surface height mapping results providing quantitative surface deformation results for the shot peened 1070-steel specimen. (a) 3D surface height topographic map (tilted for perspective) of the peened x1-x2 surface (see also Fig. 6). (b) A selected line profile from the data set from the previous figure with the appropriate vertical and horizontal length scales provided. A plot (dotted line) of a circle of radius r=3mm equal to that of the peening shot is shown (see also Fig. 6). (c) A surface map of the edge specimen illustrating the bulging of the peened layer to form a lip (see also Fig. 6) at the edge.

Figure 8

Surface map of the edge of the Ti-6Al-4V peened specimen showing the bulging of the plastic peened layer at the edge. Note that the spatial scale of the peening effect is dramatically smaller than that illustrated in the previous figure.

Figure 9

3D perspective surface topographic map of the surface height in the vicinity of a fatigue crack in a 4140-steel specimen. Note the transverse “necking,” inward plastic flow, on the flanks of the crack due to the localized material yielding in tension.

Figure 1

Strain profile of ε33 across the entire thickness of a Ti-6A1-4V double-sided shot peened specimen. The inset shows schematic of the X-ray scattering geometry along with the definition of the coordinate directions. Note the schematic representation of the lip, which was optically profiled and is shown in Figs.  78.

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