Stable crack growth trajectories and fracture due to interacting cracks

Despite impressive progress in the field of fracture in recent years, there are still a number of important practical problems that are not well understood. Amongst these, propagational stability, the direction of crack extension in mixed mode loading, directional stability, alternating crack trajectories, and crack interaction were explored in this thesis.;The conditions leading to the onset of crack growth and the conditions under which a crack will continue to propagate or arrest for mixed mode I and II loading are reviewed. It is shown that the current ASME Section-XI Code rules for treating mixed mode loading can be non-conservative based on the interaction model used. The energy based propagational stability criterion for mode-I loading is discussed for mixed mode I and II loading.;After a detailed review of the literature on the subject of the direction of crack extension, three major approaches to this problem--energy, stress, and stress intensity factor--were explored. Comparison of these theories shows that they predict very similar directions for crack extension. A unifying theory to prove the equivalence or lack of equivalence of existing theories for the direction of crack extension is analytically difficult and could not be obtained. Other criteria based on the maximum hoop strain and the maximum void growth rate and the extension of the maximum hoop stress criterion into the elastic plastic regime were explored. However, these approaches do not provide improvement over the maximum hoop stress criterion which gives reasonable predictions for the direction of crack extension.;The directional instability of cracks in nominal mode I loading has been explained in the literature by examining the role of the second term in the series expansion for the stress field. In the present work, by employing finite element techniques, directional instability is explained by using only the singular terms in the series expansions for the stress fields in mode I and II loading, and small perturbations in the crack direction which arise during numerical computations.;Next, the "sinusoidal" crack trajectories that are observed in fracture problems but have never been explained are examined. First, it is shown that the trajectory of a crack can be estimated by applying the maximum hoop stress criterion incrementally, and it is demonstrated that alternating mode II loading leads to an alternating crack trajectory. By analyzing a specific problem--the crack trajectory in a glass strip with a moving thermal stress field--it is shown that the a crack deviates from its plane due to a biaxial tensile stress state and then is driven back by shear stresses which produce mode-II loading. This provides an explanation for the "sinusoidal" crack pattern.;Finally, the effect of crack interaction is studied. An important practical problem, the cracking in the blade attachment area of turbine rotors, is analyzed and the beneficial impact of crack interaction on the size of the critical crack and the life of this component is demonstrated.