0
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

## Abstract

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.

<>

## Figures

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.

Figure 2

Finite element model used in analysis

Figure 3

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

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

Figure 5

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

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

Figure 7

Normalized RMS stress change due to mesh refinement

Figure 8

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

Figure 9

Normalized rms difference in compliance matrix elements 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

Figure 11

C(ai∕t,P12,l∕t=0.060) for 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

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

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections