Page 328 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C007.fm Page 308 Monday, May 23, 2005 5:54 PM

308 Fracture Mechanics: Fundamentals and Applications

FIGURE 7.12 Side grooves in a fracture mechanics test specimen.

Typical side-grooved fracture toughness specimens have a net thickness that is approximately 80%
of the gross thickness. If the side grooves are too deep, they produce lateral singularities, which cause
the crack to grow more rapidly at the outer edges.

7.2 K TESTING
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When a material behaves in a linear elastic manner prior to failure, such that the plastic zone is
small compared to the specimen dimensions, a critical value of the Mode I stress-intensity factor
K may be an appropriate fracture parameter. The first standardized test method for K testing,
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ASTM E 399 [8], was originally published in 1970. This standard has undergone a number of
revisions over the years, but the key provisions have remained largely unchanged. Other K testing
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standards have been published throughout the world, including the British Standard 5447 [9], but
are generally based on ASTM E 399.
In ASTM E 399 and similar test methods, K is referred to as ‘‘plane strain fracture toughness.’’
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This phrase actually appears in the title of ASTM E 399. In the 1960s, it was postulated that small
specimens or thin sections fail under plane stress conditions, and that ‘‘plane strain fracture’’ occurs
in thick sections. The ASTM E 399 test method reflects this viewpoint. Over the years, it has been
taken as an indisputable fact that toughness decreases with increasing specimen size until a plateau
is reached. Specimen size requirements in ASTM E 399 are intended to ensure that K measurements
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correspond to the supposed plane strain plateau.
There are a number of serious problems with ASTM E 399 and its underlying assumptions.
Section 2.10 in Chapter 2 reexamines the conventional wisdom with respect to so-called ‘‘plane
stress fracture’’ and ‘‘plane strain fracture.’’ Three-dimensional finite element analysis of the stress
state at the tip of a crack has revealed that the traditional view of the effect of specimen size on
fracture toughness is simplistic and misleading. In addition, it can be shown that the E 399 test
method results in a size dependence in the apparent K that is the opposite of what conventional
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wisdom suggests.