An accurate and fast analysis for strongly interacting multiple crack configurations including kinked (V) and branched (Y) cracks

In this study, multiple interacting cracks in an infinite plate are analyzed to determine the overall stress field as well as stress intensity factors for crack tips and singular wedges at crack kinks. The problem is formulated using integral equations expressed in terms of unknown edge dislocation distributions along crack lines. These distributions derive from an accurate representation of the crack opening displacements using power series basis terms obtained through wedge eigenvalue analysis, which leads to both polynomial and non-polynomial power series. The process is to choose terms of the series and their exponents such that the tractions on the crack faces are virtually zero compared to the far field loading. Applying the method leads to a set of linear algebraic equations to solve for the unknown weighting coefficients for the power series basis terms. Since no numerical integration is required unlike in other methods, in most cases, solution takes just a few seconds on a PC. The accuracy and efficiency of the method are first demonstrated with a simple example of three aligned cracks with small ligaments between their tips under tensile loading. The results are compared to exact results as well as to those of other numerical methods, including recent FIE, FEM and BEM approaches said to have fast computation times. Thereafter, some new and challenging crack interaction problems including branched Y-cracks, two kinked V-cracks are solved. From a parametric study of the various crack configurations, stress intensity factors are graphed and tabulated to demonstrate subtleties in the magnitudes of the crack interactions.