AN ANALYTICAL CRACK-TIP ELEMENT FOR LAYERED ELASTIC STRUCTURES

A previously developed linear elastic crack-tip element analysis is re viewed briefly, and then extended rand refined for practical applicati ons. The element provides analytical expressions for total energy rele ase rate and mode mix in terms of plate theory force and moment result ants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for de lamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a ''m ode mit parameter,'' Omega, as obtained from a separate continuum anal ysis is necessary to complete the mode mix decomposition. This paramet er depends upon the elastic and geometrical properties of the material s above and below the crack plane, but not on the loading A relatively simple finite element technique for determining the mode-mix paramete r is presented and convergence in terms of mesh refinement is studied. Specific values of Omega are also presented for a large number of cas es. For those interfaces where a linear elastic solution predicts an o scillatory singularity, an approach is described which allows a unique physically meaningful value of fracture mode ratio to be defined. Thi s approach is shown to provide predictions of crack growth between dis similar homogeneous materials that are equivalent to those obtained fr ont the oscillatory field solution. Application of the approach to del amination in fiber-reinforced laminated composites is also discussed