Randomly distributed interfacial arc cracks within the inclusion-inhomogeneity-matrix system

The theory of eigenstrains is employed to solve the problem of n partial annular cracks along the cemented interface of a pipe or more specifically are oil wellbore casing. This approach provides the possibility to study the interacting effect of two or more arc cracks with different lengths and angles. Partial annular cracks around the casing-cement and/or cement-formation interfaces are considered to experience leaking fluid pressure p, and the matrix is considered to be under the applied stresses σij0,i,j=1,2 at infinity. Although problems dealing with partial arc cracks are limited to bi-materials (a circular inclusion embedded in a matrix) in the presence of one or two symmetric partial cracks, this work provides an analytical solution for the hollow cylindrical casing-cement sheath-formation rock system with randomly distributed partial annular cracks scattered within the above-mentioned interfaces. The proposed solution can be utilized in different engineering problems like fiber corrosion related problems.