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Journal of Engineering Materials and Technology | Volume 129 | Issue 1 | TECHNICAL PAPERS
TECHNICAL PAPERS

Effect of Strain Gage Length When Determining Residual Stress by Slitting

[+] Author and Article Information
Matthew J. Lee

Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, CA 95616

Michael R. Hill1

Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, CA 95616mrhill@ucdavis.edu

1

Corresponding author.

J. Eng. Mater. Technol 129(1), 143-150 (Jul 12, 2006) (8 pages) doi:10.1115/1.2400263 History: Received May 12, 2005; Revised July 12, 2006
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This paper investigates the effect of strain gage length on residual stress estimated by the slitting (or crack compliance) method. This effect is quantified for a range of gage length normalized by sample thickness, l∕t, between 0.005 and 0.100. For specific l∕t values, compliance matrix elements are determined by finite element methods for a range of crack depth and polynomial basis functions for residual stress. Resulting compliance matrices are shown and used to determine error in residual stress that may arise due to differences in l∕t assumed in data reduction and existing in the slitting experiment. Errors increase monotonically with increasing difference between assumed and actual l∕t and reach a root-mean-square error of 14% of peak stress. In order to avoid such errors, a scheme is presented that allows compliance matrices to be computed for 0.005⩽l∕t⩽0.100 from tabulated coefficients and limits root-mean-square error to <2% of peak stress. An example is provided to illustrate the application of the data reduction scheme to laboratory data.
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Copyright © 2007 by American Society of Mechanical Engineers
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References

1
Vaidyanathan, S., and Finnie, I., 1971, “Determination of Residual Stress From Stress Intensity Factor Measurements,” Appl. Mech. Rev., 52 (2), pp. 75–96.
2
Finnie, I., and Cheng, W., 2002, “A Summary of Past Contributions on Residual Stresses,” Mater. Sci. Forum, 404–407 , pp. 509–514.
3
Finnie, I., and Cheng, W., 1996, “Residual Stress Measurement by the Introduction of Slots or Cracks,” "Localized Damage IV Computer Aided Assessment and Control of Localized Damage—Proc. of the International Conference 1996", Computational Mechanics, Billerica, MA, pp. 37–51.
4
Cheng, W., and Finnie, I., 1985, “A Method for Measurement of Axisymmetric Axial Residual Stress in Circumferentially Welded Thin Walled Cylinders,” ASME J. Eng. Mater. Technol., 107 (3), pp. 181–185.
5
Cheng, W., Finnie, I., and Vardar, O., 1991, “Measurement of Residual Stresses Near the Surface Using the Crack Compliance Method,” ASME J. Eng. Mater. Technol., 113 (2), pp. 199–204.
6
Prime, M., 1999, “Residual Stress Measurement by Successive Extension of a Slot: The Crack Compliance Method,” Appl. Mech. Rev., 52 (2), pp. 75–96.
7
Cheng, W., Finnie, I., Gremaud, M., and Prime, M. B., 1994, “Measurement of Near Surface Residual Stresses Using Electric Discharge Wire Machining,” ASME J. Eng. Mater. Technol., 116 (1), pp. 1–7.
8
Rankin, J. E., and Hill, M. R., 2003, “Measurement of Thickness-Average Residual Stress Near the Edge of a Thin Laser Peened Strip,” ASME J. Eng. Mater. Technol.  [CrossRef], 125 (7), pp. 283–293.
9
Rankin, J. E., Hill, M. R., and Hackel, L. A., 2003, “The Effects of Process Variations on Residual Stress in Laser Peened 7049 T73 Aluminum Alloy,” Mater. Sci. Eng., A  [CrossRef], 349 (1–2), pp. 279–291.
10
Hill, M. R., and Lin, W. Y., 2002, “Residual Stress Measurement in a Ceramic-Metallic Graded Material,” ASME J. Eng. Mater. Technol.  [CrossRef], 124 (2), pp. 185–191.
11
Prime, M. B., and Hill, M. R., 2002, “Residual Stress, Stress Relief, and Inhomogeneity in Aluminum Plate,” Scr. Mater.  [CrossRef], 46 (1), pp. 77–82.
12
Dewald, A. T., Rankin, J. E., Hill, M. R., Lee, M. J., and Chen, H.-L., 2004, “Assessment of Tensile Residual Stress Mititagion in Alloy Welds Due to Laser Peening,” ASME J. Eng. Mater. Technol.  [CrossRef], 126 (4), pp. 465–473.

Figures

Grahic Jump Location
+Full block geometry model. Variables are thickness of the part in the slitting direction t, the slit depth a, the slit width w, the length L, the gage length l, the depth B, and the distance between the center of the gage and the center of the slit s.
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Full block geometry model. Variables are thickness of the part in the slitting direction t, the slit depth a, the slit width w, the length L, the gage length l, the depth B, and the distance between the center of the gage and the center of the slit s.
Figure 1

Full block geometry model. Variables are thickness of the part in the slitting direction t, the slit depth a, the slit width w, the length L, the gage length l, the depth B, and the distance between the center of the gage and the center of the slit s.

Grahic Jump Location
+Finite element model used in analysis
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Finite element model used in analysis
Figure 2

Finite element model used in analysis

Grahic Jump Location
+Compliances for l∕t=0.005 and various input stress order
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Compliances for l∕t=0.005 and various input stress order
Figure 3

Compliances for l∕t=0.005 and various input stress order

Grahic Jump Location
+Compliances for a range of l∕t and input stress order, (a) j=2, (b) j=5, (c) j=9, and (d) j=12
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Compliances for a range of l∕t and input stress order, (a) j=2, (b) j=5, (c) j=9, and (d) j=12
Figure 4

Compliances for a range of l∕t and input stress order, (a) j=2, (b) j=5, (c) j=9, and (d) j=12

Grahic Jump Location
+Computed residual stress for σinp(x)=P5 and varying l∕t, computed using reference l∕t=0.005
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Computed residual stress for σinp(x)=P5 and varying l∕t, computed using reference l∕t=0.005
Figure 5

Computed residual stress for σinp(x)=P5 and varying l∕t, computed using reference l∕t=0.005

Grahic Jump Location
+Normalized RMS stress error for varying l∕t, over a range of reference l∕t and input stress order (a) j=2, (b) j=5, (c) j=9, and (d) j=12
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Normalized RMS stress error for varying l∕t, over a range of reference l∕t and input stress order (a) j=2, (b) j=5, (c) j=9, and (d) j=12
Figure 6

Normalized RMS stress error for varying l∕t, over a range of reference l∕t and input stress order (a) j=2, (b) j=5, (c) j=9, and (d) j=12

Grahic Jump Location
+Normalized RMS stress change due to mesh refinement
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Normalized RMS stress change due to mesh refinement
Figure 7

Normalized RMS stress change due to mesh refinement

Grahic Jump Location
+g(l∕t) for input stress order j=2, 5, 9, and 12, and g¯(l∕t)
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g(l∕t) for input stress order j=2, 5, 9, and 12, and g¯(l∕t)
Figure 8

g(l∕t) for input stress order j=2, 5, 9, and 12, and g¯(l∕t)

Grahic Jump Location
+Normalized rms difference in compliance matrix elements from geometry-specific FEM and from the compact representation using Eq. 10
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Normalized rms difference in compliance matrix elements from geometry-specific FEM and from the compact representation using Eq. 10
Figure 9

Normalized rms difference in compliance matrix elements from geometry-specific FEM and from the compact representation using Eq. 10

Grahic Jump Location
+Normalized rms difference in stress computed using compliance matrices from geometry-specific FEM and from the compact representation using Eq. 10
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Normalized rms difference in stress computed using compliance matrices from geometry-specific FEM and from the compact representation using Eq. 10
Figure 10

Normalized rms difference in stress computed using compliance matrices from geometry-specific FEM and from the compact representation using Eq. 10

Grahic Jump Location
+C(ai∕t,P12,l∕t=0.060) for geometry-specific FEM and for the compact representation using Eq. 10
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C(ai∕t,P12,l∕t=0.060) for geometry-specific FEM and for the compact representation using Eq. 10
Figure 11

C(ai∕t,P12,l∕t=0.060) for geometry-specific FEM and for the compact representation using Eq. 10

Grahic Jump Location
+Computed stress for input stress order=12 and l∕t=0.060 using compliance matrices from geometry-specific FEM and for the compact representation using Eq. 10
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Computed stress for input stress order=12 and l∕t=0.060 using compliance matrices from geometry-specific FEM and for the compact representation using Eq. 10
Figure 12

Computed stress for input stress order=12 and l∕t=0.060 using compliance matrices from geometry-specific FEM and for the compact representation using Eq. 10

Grahic Jump Location
+Residual stress in laser peened 316L stainless steel computed using a compact representation compliance matrix (left axis), and difference between stress computed using compact representation and geometry-specific FEM compliance matrices
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Residual stress in laser peened 316L stainless steel computed using a compact representation compliance matrix (left axis), and difference between stress computed using compact representation and geometry-specific FEM compliance matrices
Figure 13

Residual stress in laser peened 316L stainless steel computed using a compact representation compliance matrix (left axis), and difference between stress computed using compact representation and geometry-specific FEM compliance matrices

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