Andrew Sheng, Giacomo Po, and Nasr M. Ghoniem

A new computational technique: The Discrete Crack Mechanics method (DCM) is introduced in this lecture.  DCM is a dislocation-based crack modeling technique, where cracks are constructed using Volterra dislocation loops.  The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques.  Mesh-dependence in existing comptutational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite-medium solution of discrete dislocations, and an FEM solution of a correction problem that satisfies external boundary conditions.  In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract.  Solving for the equilibrium positions of the inner loops gives the crack shape and stress field.  The equation of motion governing the crack tip is developed for quasi-static growth problems.  Convergence and accuracy of the DCM method is verified with 2D and 3D problems with well-known solutions.  Crack growth is simulated under load and displacement (rotation) control.  In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.  The method is experimentally-verified with a displacement-control diametral compression test of an alumina disk and is shown to give good estimates of its fracture toughness.  An application of the method to complex thermal shock problems will be given, where 3-D crack propagation in the cylindrical liner of a Hall Thruster is accurately modeled.