Page 406 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C009.fm Page 386 Monday, May 23, 2005 3:58 PM

386 Fracture Mechanics: Fundamentals and Applications

FIGURE 9.1 Relationship between the three critical variables in fracture mechanics. The stress and flaw size
contribute to the driving force, and the fracture toughness is a measure of the material resistance.

where
Y = dimensionless geometry correction factor
s = characteristic stress
a = characteristic crack dimension

If the geometry factor is known, the applied K can be computed for any combination of s and a.
I
The applied stress intensity can then be compared to the appropriate material property, which may
be a K value, a K-R curve, environment-assisted cracking data, or, in the case of cyclic loading,
Ic
fatigue crack growth data (see Chapter 10).
Fracture analysis of a linear elastic structure becomes relatively straightforward once a K
solution is obtained for the geometry of interest. Stress-intensity solutions can come from a number
of sources, including handbooks, the published literature, experiments, and numerical analysis.
A large number of stress-intensity solutions have been published over the past 50 years. Several
handbooks [1–3] contain compilations of solutions for a wide variety of configurations. The published
literature contains many more solutions. It is often possible to find a K solution for a geometry that
is similar to the structure of interest.
When a published K solution is not available, or the accuracy of such a solution is in doubt, one
can obtain the solution experimentally or numerically. Deriving a closed-form solution is probably
not a viable alternative, since this is possible only with simple geometries and loading, and nearly all
such solutions have already been published. Experimental measurement of K is possible through
optical techniques, such as photoelasticity [4, 5] and the method of caustics [6], or by determining G
from the rate of change in compliance with crack length (Equation (2.30)) and computing K from G
(Equation (2.58)). However, these experimental methods for determining fracture driving force param-
eters have been rendered virtually obsolete by advances in computer technology. Today, nearly all
new K solutions are obtained numerically. Chapter 12 describes a number of computational techniques
for deriving stress intensity and energy release rate.
An alternative to finite element analysis and other computational techniques is to utilize the
principle of elastic superposition, which enables new K solutions to be constructed from known
cases. Section 2.6.4 outlined this approach, and demonstrated that the effect of a far-field stress on
K can be represented by an appropriate crack-face pressure. Influence coefficients [7], described
below, are an application of the superposition principle. Section 2.6.5 introduced the concept of
weight functions [8, 9], from which K solutions can be obtained for arbitrary loading. Examples
of the application of the weight function approach are presented in Section 9.1.3.