Page 29 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C01.fm Page 9 Tuesday, April 12, 2005 5:55 PM

History and Overview 9

a longer wire corresponded to a larger sample volume, and a higher probability of sampling a
region containing a flaw. These results were only qualitative, however.
A quantitative connection between fracture stress and flaw size came from the work of Griffith,
which was published in 1920 [7]. He applied a stress analysis of an elliptical hole (performed by
Inglis [8] seven years earlier) to the unstable propagation of a crack. Griffith invoked the first law of
thermodynamics to formulate a fracture theory based on a simple energy balance. According to this
theory, a flaw becomes unstable, and thus fracture occurs, when the strain-energy change that results
from an increment of crack growth is sufficient to overcome the surface energy of the material
(see Section 2.3). Griffith’s model correctly predicted the relationship between strength and flaw
size in glass specimens. Subsequent efforts to apply the Griffith model to metals were unsuccessful.
Since this model assumes that the work of fracture comes exclusively from the surface energy of
the material, the Griffith approach applies only to ideally brittle solids. A modification to Griffith’s
model, that made it applicable to metals, did not come until 1948.

1.2.2 THE LIBERTY SHIPS
The mechanics of fracture progressed from being a scientific curiosity to an engineering discipline,
primarily because of what happened to the Liberty ships during World War II [9].
In the early days of World War II, the U.S. was supplying ships and planes to Great Britain
under the Lend-Lease Act. Britain’s greatest need at the time was for cargo ships to carry supplies.
The German navy was sinking cargo ships at three times the rate at which they could be replaced
with existing ship-building procedures.
Under the guidance of Henry Kaiser, a famous construction engineer whose previous projects
included the Hoover Dam, the U.S. developed a revolutionary procedure for fabricating ships
quickly. These new vessels, which became known as the Liberty ships, had an all-welded hull, as
opposed to the riveted construction of traditional ship designs.
The Liberty ship program was a resounding success, until one day in 1943, when one of the
vessels broke completely in two while sailing between Siberia and Alaska. Subsequent fractures
occurred in other Liberty ships. Of the roughly 2700 Liberty ships built during World War II,
approximately 400 sustained fractures, of which 90 were considered serious. In 20 ships the failure
was essentially total, and about half of these broke completely in two.
Investigations revealed that the Liberty ship failures were caused by a combination of three factors:

• The welds, which were produced by a semi-skilled work force, contained crack-like flaws.
• Most of the fractures initiated on the deck at square hatch corners, where there was a
local stress concentration.
• The steel from which the Liberty ships were made had poor toughness, as measured by
Charpy impact tests.

The steel in question had always been adequate for riveted ships because fracture could not
propagate across panels that were joined by rivets. A welded structure, however, is essentially a
single piece of metal; propagating cracks in the Liberty ships encountered no significant barriers,
and were sometimes able to traverse the entire hull.
Once the causes of failure were identified, the remaining Liberty ships were retrofitted with
rounded reinforcements at the hatch corners. In addition, high toughness steel crack-arrester plates
were riveted to the deck at strategic locations. These corrections prevented further serious fractures.
In the longer term, structural steels were developed with vastly improved toughness, and weld
quality control standards were developed. Also, a group of researchers at the Naval Research
Laboratory in Washington, DC. studied the fracture problem in detail. The field we now know as
fracture mechanics was born in this lab during the decade following the war.