Axisymmetric Fracture Mechanics Problems

Abstract

Fracture mechanics is the study of strength of materials containing flaws or cracks under the action of externally applied loads. A crack can be defined as a notch with its radius of curvature approaching zero, causing the stresses to become infinite at the crack tip. The theory of fracture has been in constant development since Griffith [73,74] described brittle fracture using energy considerations and the stress solutions of Inglis [75]. The stress intensity factor, K, was defined by Irwin [76] to characterise cracks using the complex variable analysis of Westergaard [77] to derive expressions for the stresses and displacements in the vicinity of the crack tip. Analytical methods, usually involving sophisticated mathematics, were developed for a wide range of crack problems by several researchers, such as Sneddon [78], Lowengrub [79] and Rice [80]. Also, several handbooks of different crack configurations have been compiled [81,82,83], to aid designers to assess the stress state near the crack tip. However, the analytical methods are limited to relatively simple geometries and loading conditions not representative of the majority of complex engineering applications. Experimental techniques, on the other hand, tend to be very costly and time-consuming.KeywordsStress Intensity FactorHollow CylinderDisplacement MethodCrack ProblemStrain Energy Release RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.