Section 126.96.36.199. Crack Initiation J-Integral
The JIc can be used as a toughness value at
the initiation of crack tearing from a sharp fatigue crack in metallic
materials. This toughness value can
serve as a basis for screening tough materials or for evaluating materials
utilized in sub-KIc thicknesses. Requirements for a valid JIc value according to
ASTM E1820 are based on the ratio of the JIc to yield
where B is thickness and b0 is the
initial ligament. The relationship
between the J-integral and the stress-intensity factor was given in Section 11
where E¢ = E, the elastic modulus, for plane stress,
for plane strain, and n = Poisson’s ratio.
Thus, using Equations 7.2.5 evaluated at the critical condition (J =
JIc, K = KJIc) and Equation 7.2.4, the
thickness requirement becomes after some algebra
For the typical condition where the ratio of yield strength to
elastic modulus (sys/E) is below 0.1, JIc
values can be obtained using specimens thinner than that required by the KIc
standard (ASTM E399).
The KJIc value in Equation 7.2.6, however,
does not normally correspond to the KIc value that would be
obtained using the planeain fracture toughness standard. The KJic value based on JIc
measurements is typically lower and thus leads to conservative estimates of
the ASTM E399 KIc value.
The differences in KJIc and KIc
arise as a result of differences in the amount of allowable physical crack
growth associated with the two standards; there is less growth allowed for the JIc
value than for the KIc value.
While the use of a toughness standard for sub-KIc
thickness specimens provides additional opportunities for characterizing
material resistance to fracture, the JIc concept appears
somewhat limited relative to the design of aerospace structures. A single test of a JIc
type specimen might be similar in cost to a KIc type test;
but a number of JIc type specimens must be tested to develop
the required crack resistance data prior to estimating the JIc
value. Through unloading compliance
testing, it is possible to reduce the number of tests.