Analytical Modeling of the Mechanics of Nucleation and Growth of Cracks

With the traditional fracture mechanics approaches, an initial crack and self-similar progression of cracks are assumed. In this treatise, theoretical and numerical tools are developed to mathematically describe non-self-similar progression of cracks without specifying an initial crack. A cohesive-decohesive zone model, similar to the cohesive zone model known in fracture mechanics as Dugdale-Barenblatt model, is adopted to represent the degradation of the material ahead of the crack tip. This model unifies strength-based crack initiation and fracturebased crack progression. The cohesive-decohesive zone model is implemented with an interfacial surface material that consists of an upper and lower surface connected by a continuous distribution of normal and tangential nonlinear elastic springs that act to resist either Mode I opening, Mode II sliding, Mode III sliding, or mixed mode. The initiation of fracture is determined by the interfacial strength and the progression of fracture is determined by the critical energy release rate. The material between two adjacent laminae of a laminated composite structure or the material between the adherend and the adhesive is idealized with an interfacial surface material to predict interfacial fracture. The interfacial surface material is positioned within the bulk material to predict discrete cohesive cracks. The proper work-conjugacy relations between the stress and deformation measures are identified for the interfacial surface theory. In the principle of virtual work, the interfacial cohesive-decohesive tractions are conjugate to the displacement jumps across the upper and lower surfaces. A finite deformation kinematics theory is developed for the description of the upper and lower surface such that the deformation measures are invariant with respect to superposed rigid body translation and rotation. Various mechanical softening constitutive laws thermodynamically consistent with damage mechanics are postulated that relate the interfacial tractions to the displacement jump. An

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