Abstract
The current work presents a novel methodology for the experimental quantification of the crack tip plastic zone during fatigue crack growth. This methodology is based on the application of yield criteria to estimate the area and the shape of the plastic zone at the crack tip. The implementation of the proposed methodology requires the use of strain maps calculated from the differentiation of the displacement fields obtained by digital image correlation (DIC). Stress maps can subsequently be inferred from both von Mises and Tresca yield criteria. Fatigue tests and associated measurements of plastic zone size and shape were conducted on a compacttension specimen made from commercially pure titanium at R ratio of 0.6. In addition, the ability to predict the shape and size of the experimentally observed crack tip plastic zone has been explored using three different analytical elastic crack tip models [Westergaard, Williams and Christopher- James-Patterson (CJP)]. This analysis indicated that the CJP model provided the most accurate prediction of the plastic zone and shape.
Highlights
I t has long been recognised in the fracture mechanics community that identifying plastic zone shape and size, and any influences of the plastic zone on a growing fatigue crack is relatively complex whether attempted by simulation or experiment
It is clear that the plastic zone size and shape predicted by the CJP model is an excellent fit to the experimental data, while the Westergaard and Williams models predict somewhat larger dimensions
The experimental data is in close agreement with the plastic zone area calculated from the CJP model at all crack lengths, while the predicted area using the Westergaard and Williams models is higher than the experimental results
Summary
I t has long been recognised in the fracture mechanics community that identifying plastic zone shape and size, and any influences of the plastic zone on a growing fatigue crack is relatively complex whether attempted by simulation or experiment. Most of the reported works to predict plastic zone size and shape at the crack tip employ approaches based on Linear Elastic Fracture Mechanics (LEFM), such as Irwin’ [6] or Dugdale’s [7] estimates, or the model based on Westergaard equations [8], among others These are simplistic approaches and, there is a clear application field consisting in combining full field measurement techniques with an improved model of the crack tip stress field that attempts to better incorporate the influence on the elastic stress field driving growth, of any stresses induced by the plastically deformed region that surrounds a growing fatigue crack. The three models considered in this work are the Westergaard crack tip stress equations, Williams’ expansion series for crack tip stresses and the recently developed CJP model [9] for crack tip displacement fields
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