Proc. R. Soc. A (2012) 468, 2399–2415
doi:10.1098/rspa.2011.0682
Published online 14 March 2012
Quantitative measurement of plastic strain field
at a fatigue crack tip
BY Y. YANG
1
, M. CRIMP
1
, R. A. TOMLINSON
2
AND E. A. PATTERSON
1,3,
*
1
Department of Chemical Engineering and Materials Science, Michigan State
University, East Lansing, MI 48824-1044, USA
2
Department of Mechanical Engineering, University of Sheffield,
Sheffield S1 3JD, UK
3
School of Engineering, University of Liverpool, Liverpool L69 3GH, UK
A novel approach is introduced to map the mesoscale plastic strain distribution resulting
from heterogeneous plastic deformation in complex loading and component geometries, by
applying the discrete Fourier transform (DFT) to backscattered electron (BSE) images of
polycrystalline patches. These DFTs are then calibrated against the full width at half the
maximum of the central peak of the DFTs collected from the same material tested under
in situ scanning electron microscopy uniaxial tensile conditions, which indicates a close
relationship with the global tensile strain. In this work, the technique is demonstrated
by measuring the residual strain distribution and plastic zone size around a fatigue
crack tip in a commercially pure titanium compact tension specimen, by collecting BSE
images in a 15 × 15 array of 115 mm square images around the fatigue crack tip. The
measurement results show good agreement with the plastic zone size and shape measured
using thermoelastic stress analysis.
Keywords: strain field; backscattered electron imaging; fatigue; crack; plastic zone;
thermoelastic stress analysis
1. Introduction
The role of the plastic zone surrounding the tip of a fatigue crack has been
recognized for a long time as important in determining crack growth rates,
including the potential retardation of growth via mechanisms associated with
crack closure (Elber 1970), which has been referred to recently, and perhaps
more accurately or descriptively, as plastic shielding (Pacey et al. 2005). The
mechanisms supporting plasticity-induced closure have been the subject of
unresolved debate (James 1997), primarily because it has not been possible
to make direct measurements of the size and shape of the crack tip plastic
zone, much less evaluate the effect of variations in, for instance, loading or
environmental conditions.
The common method of assessing crack closure effects is to use compliance
measurements, which in the frequently used compact tension (CT) specimen are
based on back-face strain gauge data (Pacey et al. 2005). These measurements
*Author for correspondence (eann.patterson@liverpool.ac.uk).
Received 18 November 2011
Accepted 15 February 2012 This journal is
©
2012 The Royal Society 2399