Improvement of crack-tip stress series with Pade approximants

摘要

The most favored description of bi-dimensional crack-tip stress fields relies on Williams expansion. In this framework, each stress component is defined as a series which has a certain convergence behavior. Generally, the series is truncated after its first term since it is the most influential one at the vicinity of the crack-tip because of its well-known singularity. However, for some applications, the need for higher order terms arises and the study of truncation influence becomes important. The investigations performed by the authors for a specific fracture configuration have shown the existence of a convergence disk and of rather low convergence rates far from the crack-tip. In this communication, we propose to transform truncated stress series into Pade Approximants (PA) in order to improve both convergence domains and convergence rates. These approximants are rational functions whose coefficients are defined so as to fit the prescribed truncated series. The PA may be obtained following two different procedures. In practical tests, PA stemming from crack-tip stress series exhibit wider convergence domains and higher convergence rates.