Quantitative measurement of plastic strain field at a fatigue crack tip

by Y. Yang, M. Crimp, R. A. Tomlinson, and E. A. Patterson

Proceedings AVolume ():rspa20110682

March 14, 2012

©2012 by The Royal Society

A schematic of the array of images around the crack tip consisting of a 15×15 (225 in total) grid of tiles which were 115 μm square with a centre-to-centre spacing of 187 μm.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

Phase difference (red line) and magnitude of the thermoelastic stress analysis (TSA) signal (blue line) as a function of distance along a line through the tip of the fatigue crack in the direction of

crack growth.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

Upper half of the array shown in figure 1 of backscattered electron images around the crack tip at a centre-to-centre spacing of 187 μm.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

(a) Backscattered electron images h5, h8, h11 and h14 from figure 3; (b) their corresponding discrete Fourier transforms (DFTs) and (c) a horizontal line profile across the centre of each DFT

and showing a decrease in the centre peak width with increasing d...

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

A schematic showing the process of fitting line profiles and measuring the full width at half the maximum of the profile.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

The full width at half the maximum of the discrete Fourier transform profiles plotted as a function distance from the crack tip for the images along the line ahead of the crack.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

Engineering stress–strain curve obtained for the commercially pure titanium; the arrows indicate the strain increments at which the in situ uniaxial tensile test was interrupted to collect

backscattered electron images.

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

The full width of half the maximum (FWHM) of the discrete Fourier transform (DFT) as a function of the engineering strain based on images recorded at increments of plastic strain during an in

situ tensile test; note that the elastic strain of 0.6% has been ...

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society

Map of plastic strain around the crack tip (0, 0) based on the full width of half the maximum of the discrete Fourier transforms of images obtained for the tiles shown in figure 2, together with the

thermoelastic stress analysis data (white line) and estima...

Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.0682

©2012 by The Royal Society