Steady crack growth in a thin, ductile plate under small-scale yieldingconditions: Three-dimensional modeling

摘要

This work employs high resolution, finite element computations to investigate key features of the elastic-plastic fields near a steadily advancing crack at quasi-static rates under three-dimensional, small-scale yielding conditions. The model represents a structurally thin component constructed of a material (e.g., Al and Ti alloys) with flow stress and fracture toughness properties that together limit the size of the in-plane plastic zone during steady-growth to no more than several multiples of the plate thickness. The computational approach generalizes the streamline integration procedure used previously for two-dimensional studies into three dimensions to represent steady-state growth on a fixed mesh in a boundary-layer framework. The plate thickness provides the only geometrical length scale. Crack extension occurs at the remotely applied, fixed loading without the need for a local growth criterion. In the first computations of this type, the present work considers a straight crack front advancing under local and global mode I loading with zero T-stress in a moderately hardening material. Applied remote loads at steady growth generate plastic zone sizes ahead of the advancing crack front ranging from 0.25 to 6.4 times the thickness. Key results include: (1) the crack-front fields exhibit a self-similar scaling characterized by a non-dimensional loading parameter; (2) three-dimensional effects extend to distances of approximately 1.5-2.5 times the thickness ahead of the advancing crack front for key values of this loading parameter, beyond which the fields (elastic-plastic then linear-elastic at greater distances) become uniform over the thickness; and (3) crack opening profiles on the outside surface reveal a "wedge-like", opening shape which simplifies the definition of a crack-tip opening angle.