Page 405 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C009.fm Page 385 Monday, May 23, 2005 3:58 PM

9 Application to Structures

Recall Figure 1.7 in Chapter 1, which illustrates the so-called fracture mechanics triangle. When
designing a structure against fracture, there are three critical variables that must be considered:
stress, flaw size, and toughness. Fracture mechanics provides mathematical relationships between
these quantities. Figure 9.1 is an alternative representation of the three key variables of fracture
mechanics. The stress and flaw size provide the driving force for fracture, and the fracture toughness
is a measure of the material’s resistance to crack propagation. Fracture occurs when the driving
force reaches or exceeds the material resistance. Chapter 7 and Chapter 8 describe experimental
methods to measure fracture toughness in metals and nonmetals, respectively. This chapter focuses
on approaches for computing the fracture driving force in structural components that contain cracks.
Several parameters are available for characterizing the fracture driving force. In Chapter 2, the
stress-intensity factor K and the energy release rate G were introduced. These parameters are suitable
when the material is predominately elastic. The J integral and crack-tip-opening displacement
(CTOD) are appropriate driving force parameters in the elastic-plastic regime. Recall from
Chapter 3 that the J integral is a generalized formulation of the energy release rate; in the limit of
linear elastic material behavior, J = G.
Techniques for computing fracture driving force range from very simple to complex. The most
appropriate methodology for a given situation depends on geometry, loading, and material proper-
ties. For example, a three-dimensional finite element analysis (Chapter 12) may be necessary when
both the geometry and loading are sufficiently complicated that a simple hand calculation will not
suffice. When significant yielding precedes fracture, an analysis based on linear elastic fracture
mechanics (LEFM) may not be suitable. 1
This chapter focuses on fracture initiation and instability in structures made from linear elastic
and elastic-plastic materials. A number of engineering approaches are discussed; the basis of these
approaches and their limitations are explored. This chapter covers only quasistatic methodologies,
but such approaches can be applied to rapid loading and crack arrest in certain circumstances (see
Chapter 4). The analyses presented in this chapter do not address time-dependent crack growth.
Chapter 10 and Chapter 11 consider fatigue crack growth and environmental cracking, respectively.

9.1 LINEAR ELASTIC FRACTURE MECHANICS

Analyses based on LEFM apply to structures where crack-tip plasticity is small. Chapter 2 intro-
duced many of the fundamental concepts of LEFM. The fracture behavior of a linear elastic structure
can be inferred by comparing the applied K (the driving force) to a critical K or a K-R curve (the
fracture toughness). The elastic energy release rate G is an alternative measure of driving force,
and a critical value of G quantifies the material toughness.
For Mode I loading (Figure 2.14), the stress-intensity factor can be expressed in the following
form:

K I Y = σπ a (9.1)

1 There are a number of simplified elastic-plastic analysis methods that use LEFM parameters such as K, combined with
an appropriate adjustment for plasticity. Two such methodologies are described in the present chapter: the reference stress
approach and the failure assessment diagram (FAD).

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