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10 Fracture Mechanics: Fundamentals and Applications

1.2.3 POST-WAR FRACTURE MECHANICS RESEARCH 1

The fracture mechanics research group at the Naval Research Laboratory was led by Dr. G.R. Irwin.
After studying the early work of Inglis, Griffith, and others, Irwin concluded that the basic tools
needed to analyze fracture were already available. Irwin’s first major contribution was to extend
the Griffith approach to metals by including the energy dissipated by local plastic flow [10]. Orowan
independently proposed a similar modification to the Griffith theory [11]. During this same period,
Mott [12] extended the Griffith theory to a rapidly propagating crack.
In 1956, Irwin [13] developed the energy release rate concept, which was derived from the
Griffith theory but in a form that was more useful for solving engineering problems. Shortly
afterward, several of Irwin’s colleagues brought to his attention a paper by Westergaard [14] that
was published in 1938. Westergaard had developed a semi-inverse technique for analyzing stresses
and displacements ahead of a sharp crack. Irwin [15] used the Westergaard approach to show that
the stresses and displacements near the crack-tip could be described by a single constant that was
related to the energy release rate. This crack-tip characterizing parameter later became known as
the ‘‘stress-intensity factor.” During this same period of time, Williams [16] applied a somewhat
different technique to derive crack tip solutions that were essentially identical to Irwin’s results.
A number of successful early applications of fracture mechanics bolstered the standing of this
new field in the engineering community. In 1956, Wells [17] used fracture mechanics to show that
the fuselage failures in several Comet jet aircraft resulted from fatigue cracks reaching a critical
size. These cracks initiated at windows and were caused by insufficient reinforcement locally,
combined with square corners that produced a severe stress concentration. (Recall the unfortunate
hatch design in the Liberty ships.) A second early application of fracture mechanics occurred at
General Electric in 1957. Winne and Wundt [18] applied Irwin’s energy release rate approach to
the failure of large rotors from steam turbines. They were able to predict the bursting behavior of
large disks extracted from rotor forgings, and applied this knowledge to the prevention of fracture
in actual rotors.
It seems that all great ideas encounter stiff opposition initially, and fracture mechanics is no
exception. Although the U.S. military and the electric power generating industry were very sup-
portive of the early work in this field, such was not the case in all provinces of government and
industry. Several government agencies openly discouraged research in this area.
In 1960, Paris and his coworkers [19] failed to find a receptive audience for their ideas on
applying fracture mechanics principles to fatigue crack growth. Although Paris et al. provided
convincing experimental and theoretical arguments for their approach, it seems that design engineers
were not yet ready to abandon their S-N curves in favor of a more rigorous approach to fatigue
design. The resistance to this work was so intense that Paris and his colleagues were unable to find
a peer-reviewed technical journal that was willing to publish their manuscript. They finally opted
to publish their work in a University of Washington periodical entitled The Trend in Engineering.

1.2.4 FRACTURE MECHANICS FROM 1960 TO 1980

The Second World War obviously separates two distinct eras in the history of fracture mechanics.
There is, however, some ambiguity as to how the period between the end of the war and the present
should be divided. One possible historical boundary occursed around 1960, when the fundamentals
of linear elastic fracture mechanics were fairly well established, and researchers turned their
attention to crack-tip plasticity.

1 For an excellent summary of early fracture mechanics research, refer to Fracture Mechanics Retrospective: Early Classic
Papers (1913–1965), John M. Barsom, ed., American Society of Testing and Materials (RPS 1), Philadelphia, PA, 1987.
This volume contains reprints of 17 classic papers, as well as a complete bibliography of fracture mechanics papers published
up to 1965.