Section 2.2.0. Fracture Mechanics Fundamentals
Fracture Mechanics is that technology concerned with the
modeling of cracking phenomena. Bulk
(smooth specimen) properties are not normally useful in design for determining
a material’s tolerance to cracks or crack-like defects, because material
tolerance to flaws resides in a material’s ability to deform locally. Since the source of fractures can be
identified with the lack of material tolerance to cracks, it seems only natural
that attention should be focused on the crack tip region where the material
must resist crack extension. This
section will introduce the principal features of a mechanical model that
characterizes a crack movement in structural components fabricated from materials
having low tolerance to flaws.
Some basic information that a designer should be familiar with
prior to the utilization of remaining sections of this handbook is
presented. This subsection will define
the meaning and use of the fracture mechanics model for the control of fracture
and sub-critical crack growth processes.
The application of a fracture mechanics model to solve crack
problems came about through the following realization: component fractures that
result from the extension of small crack-like defects are failures that depend
on localized phenomena. Consider the
three independent modes of crack extension that are illustrated in Figure 2.2.1.
The tensile opening mode, Mode 1, represents the principal action
observed and this is the type of separation that we design against. While fractures induced by shear stresses
can occur, these fractures are rather infrequent. There are hypotheses available for describing the combined
influence of two (or three) modes of crack extension but these will not be
discussed until Section 4. In general,
since improvement of a material’s Mode 1 fracture resistance will also improve
the resistance to the combined mode action, the development of concepts
throughout the Handbook will emphasize Mode 1 crack extension behavior.
Figure 2.2.1. The Three Modes of Crack Extension
A linear elastic analysis of a cracked body provides a good
first approximation to the localized stress state in materials that fracture at
gross section stresses below the yield strength. No additional refinements in the analysis are necessary if the
gross section stresses at failure are below 0.7sys. The elastic analysis when modified to
account for restricted amounts of stress relaxation due to crack tip plastic
deformation provides an adequate description of fracture that occurs above 0.7sys.