Int J Fract (2007) 148:361–371 DOI 10.1007/s10704-008-9209-3 ORIGINAL PAPER Towards a new model of crack tip stress fields C. J. Christopher · M. N. James · E. A. Patterson · K. F. Tee Received: 14 May 2007 / Accepted: 23 April 2008 / Published online: 16 May 2008 © Springer Science+Business Media B.V. 2008 Abstract This work introduces a novel mathemat- ical model of the stresses around the tip of a fatigue crack, which considers the effects of plasticity through an analysis of their shielding effects on the applied elas- tic field. The ability of the model to characterize plas- ticity-induced effects of cyclic loading on the elastic stress fields is assessed and demonstrated using full- field photoelasticity. The focus is on determining the form of the shielding stress components (induced by compatibility requirements at the elastic–plastic inter- face along the crack flank and via the crack tip plastic zone) and how they influence the crack tip elastic stress fields during a load cycle. The model is successfully applied to the analysis of a fatigue crack growing in a polycarbonate CT specimen. Keywords Crack tip stress · Plasticity · Crack closure · Crack shielding · Full field photoelasticity · Mathematical modelling C. J. Christopher · M. N. James (B ) · K. F. Tee Faculty of Technology, University of Plymouth, Plymouth, UK e-mail: mjames@plymouth.ac.uk E. A. Patterson Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA Present Address: K. F. Tee Department of Aerospace Engineering, University of Bristol, Bristol, UK 1 Introduction Fatigue crack growth generates a plastic zone around the crack tip and along the crack flanks which leads to what is termed plasticity-induced closure (Elber 1970). Its existence complicates fatigue life prediction and because its causative mechanisms are not fully under- stood conservative assumptions are usually made in com- ponent and structural design. Plasticity-induced closure isnowrecognizedasoneofanumberofacracktipshield- ing mechanisms which lead to a reduction in the effec- tive stress intensity range experienced at the crack tip. Crack closure remains controversial in terms of mea- surement, magnitude, origin and interpretation, because there are still some fundamental aspects that are incom- pletely understood (James 1997). A significant contrib- utory factor to this lack of understanding is the fact that experimental measurement of the occurrence of crack closure is generally obtained from indirect means. Photoelastic stress analysis is a technique that poten- tially offers the opportunity for direct visualization of crack tip and crack flank stresses, and of the interaction between these. Analysis of the effects of plasticity- induced crack closure has received little attention in pre- vious photoelastic studies largely because the usual photoelastic resins are too brittle to grow fatigue cracks. Polycarbonate, however, is abirefringent material that is ductile enough to grow fatigue cracks in standard speci- men geometries and is known to exhibit plasticity- induced closure (James et al. 2003). It is possible to further investigate and modify the current photoelastic 123