International Journal of Fracture 103: 259–277, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. The interaction of a curved crack with a circular elastic inclusion B. A. CHEESEMAN and M. H. SANTARE The Department of Mechanical Engineering and the Center for Composite Materials, University of Delaware, Newark, DE 19716, USA Received 8 January 1999; accepted in revised form 10 November 1999 Abstract. The solution to a curved matrix crack interacting with a circular elastic inclusion is presented. The problem is formulated using the Kolosov–Muskhelishvili complex stress potential technique where the crack is represented by an unknown distribution of dislocations. After an appropriate parameterization, the resulting singular integral equations are solved with the Lobatto-Chebyshev quadrature technique. The accuracy of the current solution is shown by comparing these results to previously published results. A preliminary investigation is conducted to study the effects of crack curvature and inclusion stiffness on the stress intensity factors and it is shown that in certain instances, the effect of the crack curvature and the inclusion stiffness are competing influences. Key words: Curved matrix crack, circular elastic inclusion, crack curvature, inclusion stiffness. 1. Introduction The interaction of a crack with an inclusion is an important problem in a variety of fields on many different scales. From microcracking in composite materials to the mechanical analysis of mining operations, the effect of an inclusion on a crack has been the focus of considerable engineering interest. Though important practically, the crack-inclusion problem has only been examined within the past thirty years due to its inherent complexity. Over this time, a substan- tial body of work on straight crack-inclusion problems was generated; however, until recently, relatively few investigations concerning curved crack-inclusion interactions were conducted. Therefore, the purpose of this paper is to analyze the problem of a curved crack interact- ing with a circular elastic inclusion in an infinite matrix. Before detailing the mathematical approach used in this study, a review of the previous crack-inclusion investigations will be presented. 1.1. PREVIOUS STRAIGHT CRACK- INCLUSION INVESTIGATIONS Perhaps the first investigation of the crack-inclusion problem can be attributed to Tamate (1968). Using complex stress potentials, Tamate investigated the effect of a circular elastic inclusion on an external radial crack. For the case of uniaxial loading, a Laurent series expan- sion was determined for the complex stress potentials required for solving the resulting dual Hilbert problem. It was shown that a relatively rigid inclusion decreases the stress intensity factor of the crack whereas a more compliant inclusion increases the stress intensity factor. Atkinson (1972) noted that this solution was limited due to the form of series expansion and resolved the problem by employing a Chebyshev polynomial expansion to numerically solve the singular integral equations. He gives values of the stress intensity factor for radial cracks under both uniaxial and biaxial tension at different distances from the inclusion for