Page 415 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C009.fm Page 395 Monday, May 23, 2005 3:58 PM

Application to Structures 395

stress of a ductile material in the absence of significant crack-like flaws. When a crack is present,
however, residual stresses do contribute to the fracture driving force and must be included in the
analysis.
In linear elastic analyses, primary, secondary, and residual stresses are treated in an identical
fashion. The total stress intensity is simply the sum of the primary and secondary components:

K I total K I P K = I S + K + I R (9.21)

where the superscripts P, S, and R denote primary, secondary, and residual stress quantities,
respectively.
The distinction between primary and secondary stresses is important only in elastic-plastic and
fully plastic analyses. Section 9.2 and Section 9.4 describe the treatment of primary, secondary,
and residual stresses in such cases.

9.1.5 A WARNING ABOUT LEFM

Performing a purely linear elastic fracture analysis and assuming that LEFM is valid is potentially
dangerous, because the analysis gives no warning when it becomes invalid. The user must rely on
experience to know whether or not plasticity effects need to be considered. A general rule of thumb
is that plasticity becomes important at around 50% of the yield, but this is by no means a universal rule.
The safest approach is to adopt an analysis that spans the entire range from linear elastic to
fully plastic behavior. Such an analysis accounts for the two extremes of brittle fracture and plastic
collapse. At low stresses, the analysis reduces to LEFM, but predicts collapse if the stresses are
sufficiently high. At intermediate stresses, the analysis automatically applies a plasticity correction
when necessary; the user does not have to decide whether or not such a correction is needed. The
failure assessment diagram (FAD) approach, described in Section 9.4, is an example of a general
methodology that spans the range from linear elastic to fully plastic material behavior.

9.2 THE CTOD DESIGN CURVE

The CTOD concept was applied to structural steels beginning in the late 1960s. The British Welding
Research Association, now known as The Welding Institute (TWI), and other laboratories performed
CTOD tests on structural steels and welds. At that time there was no way to apply these results to
welded structures because CTOD driving force equations did not exist. Burdekin and Stone [16]
developed the CTOD equivalent of the strip-yield model in 1966. Although their model provides
a basis for a CTOD driving force relationship, they were unable to modify the strip-yield model
to account for residual stresses and stress concentrations. (These difficulties were later overcome
when a strip-yield approach became the basis of the R6 fracture analysis method, as discussed in
Section 9.4).
In 1971, Burdekin and Dawes [17] developed the CTOD design curve, a semiempirical driving
force relationship, which was based on an idea that Wells [18] originally proposed. For linear elastic
conditions, fracture mechanics theory was reasonably well developed, but the theoretical framework
required to estimate the driving force under elastic-plastic and fully plastic conditions did not exist
until the late 1970s. Wells, however, suggested that global strain should scale linearly with CTOD
under large-scale yielding conditions. Burdekin and Dawes based their elastic-plastic driving force
relationship on Wells’ suggestion and an empirical correlation between small-scale CTOD tests
and wide double-edge-notched tension panels made from the same material. The wide plate
specimens were loaded to failure, and the failure strain and crack size of a given large-scale specimen
were correlated with the critical CTOD in the corresponding small-scale test.