Page 31 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

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History and Overview 11

Linear elastic fracture mechanics (LEFM) ceases to be valid when significant plastic deforma-
tion precedes failure. During a relatively short time period (1960–1961) several researchers devel-
oped analyses to correct for yielding at the crack tip, including Irwin [20], Dugdale [21], Barenblatt
[22], and Wells [23]. The Irwin plastic zone correction [20] was a relatively simple extension of
LEFM, while Dugdale [21] and Barenblatt [22] each developed somewhat more elaborate models
based on a narrow strip of yielded material at the crack tip.
Wells [23] proposed the displacement of the crack faces as an alternative fracture criterion
when significant plasticity precedes failure. Previously, Wells had worked with Irwin while on a
sabbatical at the Naval Research Laboratory. When Wells returned to his post at the British Welding
Research Association, he attempted to apply LEFM to low- and medium-strength structural steels.
These materials were too ductile for LEFM to apply, but Wells noticed that the crack faces moved
apart with plastic deformation. This observation led to the development of the parameter now known
as the crack-tip-opening displacement (CTOD).
In 1968, Rice [24] developed another parameter to characterize nonlinear material behavior
ahead of a crack. By idealizing plastic deformation as nonlinear elastic, Rice was able to generalize
the energy release rate to nonlinear materials. He showed that this nonlinear energy release rate
can be expressed as a line integral, which he called the J integral, evaluated along an arbitrary
contour around the crack. At the time his work was being published, Rice discovered that
Eshelby [25] had previously published several so-called conservation integrals, one of which was
equivalent to Rice’s J integral. Eshelby, however, did not apply his integrals to crack problems.
That same year, Hutchinson [26] and Rice and Rosengren [27] related the J integral to crack-
tip stress fields in nonlinear materials. These analyses showed that J can be viewed as a nonlinear,
stress-intensity parameter as well as an energy release rate.
Rice’s work might have been relegated to obscurity had it not been for the active research effort
by the nuclear power industry in the U.S. in the early 1970s. Because of legitimate concerns for
safety, as well as political and public relations considerations, the nuclear power industry endeavored
to apply state-of-the-art technology, including fracture mechanics, to the design and construction
of nuclear power plants. The difficulty with applying fracture mechanics in this instance was that
most nuclear pressure vessel steels were too tough to be characterized with LEFM without resorting
to enormous laboratory specimens. In 1971, Begley and Landes [28], who were research engineers
at Westinghouse, came across Rice’s article and decided, despite skepticism from their co-workers,
to characterize the fracture toughness of these steels with the J integral. Their experiments were
very successful and led to the publication of a standard procedure for J testing of metals 10 years
later [29].
Material toughness characterization is only one aspect of fracture mechanics. In order to apply
fracture mechanics concepts to design, one must have a mathematical relationship between tough-
ness, stress, and flaw size. Although these relationships were well established for linear elastic
problems, a fracture design analysis based on the J integral was not available until Shih and
Hutchinson [30] provided the theoretical framework for such an approach in 1976. A few years
later, the Electric Power Research Institute (EPRI) published a fracture design handbook [31] based
on the Shih and Hutchinson methodology.
In the United Kingdom, Well’s CTOD parameter was applied extensively to fracture analysis
of welded structures, beginning in the late 1960s. While fracture research in the U.S. was driven
primarily by the nuclear power industry during the 1970s, fracture research in the U.K. was
motivated largely by the development of oil resources in the North Sea. In 1971, Burdekin and
Dawes [32] applied several ideas proposed by Wells [33] several years earlier and developed the
CTOD design curve, a semiempirical fracture mechanics methodology for welded steel structures.
The nuclear power industry in the UK developed their own fracture design analysis [34], based on
the strip yield model of Dugdale [21] and Barenblatt [22].
Shih [35] demonstrated a relationship between the J integral and CTOD, implying that both
parameters are equally valid for characterizing fracture. The J-based material testing and structural