Quantitative measurement of plastic strain field at a fatigue crack tip by Y. Yang, M. Crimp, R. A. Tomlinson, and E. A. Patterson Proceedings A Volume

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  • Quantitative measurement of plastic strain field at a fatigue crack tipby Y. Yang, M. Crimp, R. A. Tomlinson, and E. A. PattersonProceedings AVolume ():rspa20110682March 14, 20122012 by The Royal Society

  • A schematic of the array of images around the crack tip consisting of a 1515 (225 in total) grid of tiles which were 115m square with a centre-to-centre spacing of 187m.Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.06822012 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.2011.06822012 by The Royal Society

  • Upper half of the array shown in figure1 of backscattered electron images around the crack tip at a centre-to-centre spacing of 187m. Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.06822012 by The Royal Society

  • (a) Backscattered electron images h5, h8, h11 and h14 from figure3; (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.2011.06822012 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.2011.06822012 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.2011.06822012 by The Royal Society

  • Engineering stressstrain 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.2011.06822012 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.2011.06822012 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 figure2, together with the thermoelastic stress analysis data (white line) and estima...Y. Yang et al. Proc. R. Soc. A doi:10.1098/rspa.2011.06822012 by The Royal Society

    A schematic of the array of images around the crack tip consisting of a 1515 (225 in total) grid of tiles which were 115m square with a centre-to-centre spacing of 187m.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. The extent of the plastic zone found from the phase difference map is superimposed as a black area.Upper half of the array shown in figure1 of backscattered electron images around the crack tip at a centre-to-centre spacing of 187m. The images in the near-crack tip region show more lattice rotation and contrast variation, indicating more residual plastic deformation.(a) Backscattered electron images h5, h8, h11 and h14 from figure3; (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 distance from the crack tip to the image location.A schematic showing the process of fitting line profiles and measuring the full width at half the maximum of the profile. Line profiles were first smoothed using an adjacent-averaging five-point window. The left half of a smoothed profile was then fitted to an exponential curve.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.Engineering stressstrain 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.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 subtracted from the data and that error bars represent 2s.d.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 figure2, together with the thermoelastic stress analysis data (white line) and estimates of the plastic zone size based on approaches of Dugdale's (green line) and Irwin's (blue line; dimensions in millimetres).