International Journal of Fracture 125: 51–71, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. Disc analogy for approaching circular arc cracks P.B.N. PRASAD ∗ and K.R.Y. SIMHA Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560012, India Received 11 September 2003; accepted in revised form 18 December 2003 Abstract. The limiting situation of a pair of approaching circular arc crack tips in a homogeneous medium is examined to draw analogies with circular disc problems. As the crack tips approach each other, the narrow material ligament bridging the crack tips controls the stresses, stress intensity factors and energy release rates. In particular, this ligament sets up the length scale for singularity analysis for a given radius of the arc crack. Following a detailed analytical examination of approaching crack tips, a photoelastic visualisation of the stress field is presented. Experimental isochromatics are also compared with theoretical predictions for some specific cases. Finally, based on the ideas developed in this paper, existing notions on interacting cracks and cavities treated in the literature are reinterpreted. Key words: Arc cracks, crack propagation, energetics, isochromatics. 1. Introduction Interesting crack patterns observed in brittle coatings demand a fundamental appreciation of interacting cracks. Conventionally, fracture mechanics ideas have been largely discussed with reference to straight cracks. However, there are many situations promoting curved cracks. Around circular inclusions and holes, concentric circular arc cracks may be initiated and propagated. Another motivation for studying arc cracks has to do with some analytically stim- ulating cases pertaining to the interaction and coalescence of approaching arc cracks which forms the primary focus in this paper. Consider the symmetrical propagation of a circular arc crack under hydrostatic tension, which is a common state of initial stress in thin films and coatings. Assuming the crack to extend uniformly at both ends, inside the disc region defined by the crack circle, the stresses evolve with crack growth. Before the disc breaks free from the surrounding material, a narrow ligament bridging the cracktips connects the disc to the surrounding material. Elastic theory of thin ligaments often leads to unexpected results (Markenscoff and Dundurs, 1992; Ramakrishna, 1995; Wu and Markenscoff, 1996). Stress analysis of ligaments is given a special attention in this paper. With increasing crack extension, the strain energy content inside the disc gets depleted. Calculating the energy for crack growth calls for a whole field analysis of the single arc crack problem. A similar requirement applies to the case of a pair of propagating arc cracks but the analytical complexity increases disproportionately. Further, the evolution of stresses and strain energy content inside the disc differs markedly for single arc crack when compared to a pair of arc cracks. In this paper, explicit expressions for stresses, stress intensity factors and energy released are derived for symmetrically growing single and double arc cracks. The influence of different ∗ Currently at Department of Civil Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Japan 466