Europhys. Lett.
Volume 63, Number 5, September 2003
Page(s) 708 - 714
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00591-8
Europhys. Lett., 63 (5) , pp. 708-714 (2003)

Conformal dynamics of precursors to fracture

F. Barra1, 2, M. Herrera1 and I. Procaccia1

1  Department of Chemical Physics, The Weizmann Institute of Science Rehovot 76100, Israel
2  Departamento de Física, Facultad de Ciencias Físicas y Matemáticas Universidad de Chile - Casilla 487-3, Santiago, Chile

(Received 8 April 2003; accepted in final form 27 June 2003)

An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and the stability of a circular cavity under biaxial stress, including the effects of surface stress.

46.50.+a - Fracture mechanics, fatigue and cracks.
62.20.Mk - Fatigue, brittleness, fracture, and cracks.
81.40.Np - Fatigue, corrosion fatigue, embrittlement, cracking, fracture and failure.

© EDP Sciences 2003