Interactions of morphologically complex cracks under tension and compression

Morphologically complex cracks, e.g., kinked, branched and zigzag cracks, are frequently present in brittle materials subjected to remote tension and compression at both the microscopic and macroscopic scales. The nucleation and interaction of such cracks can control the fracture of the materials. Analysis of morphologically complex cracks is thus of fundamental importance for understanding the fracture process. In this research, a theoretical model is developed for computing (i) the stress intensity factors of strongly interacting morphologically complex cracks, and (ii) the overall strains of a solid containing such cracks. The cracks can be arbitrarily distributed and randomly oriented. The model development is essentially based on the satisfaction of the crack boundary conditions in a two-dimensional solid. The techniques used include: (i) superposition of Hilbert problems, (ii) dislocation modeling of the crack deviations, i.e., kinks, branches and zigzags, and (iii) piecewise quadratic polynomial method for solving the integral equations resulting from satisfying the boundary conditions on the crack deviations. The stress intensity factor at a crack tip is determined from the parameter characterizing the dislocation density at the tip. The overall strains are computed directly by summing the predicted crack opening displacements. Extensive numerical results under the plane strain conditions are presented. The predictions are also compared to those of a model that neglects crack interaction. The following scientific issues are addressed: (i) effect of crack morphology: asymmetry or antiasymmetry of the individual crack, a crack with multiple kinks, (ii) effect of crack configuration: collinear and stacked parallel cracks under remote tension, a column or multiple columns of kinked cracks under remote compression, (iii) effect of loading and physical parameters: stress biaxiality, frictional sliding of closed cracks under remote compression, and (iv) differences in the solutions of the overall strains between periodically distributed and randomly distributed cracks. Interpretation of the numerical results suggests that crack morphology and crack configuration play a major role in fracture. The effects of these geometrical parameters are further complicated by the physical parameters and the presence of strong crack interactions. The major contribution of this research is the development of a capability to quantitatively predict such effects for an arbitrary distribution of cracks