Crack unloading is 15% of collapse load. Compliance is

Crack length measurement using unloading
compliance technique consists of calculation of crack length from the
compliance value measured during fracture test of a specimen/component.  

 

2.1
Theory

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Compliance
refers to the property of a material undergoing elastic deformation when
subjected to an applied force. It is equal to the reciprocal of stiffness. The
presence of crack in a structure leads to an increase in the compliance of the
structure. The change in compliance leads to a decrease in resonant frequencies
and load redistribution in a statically indeterminate structure (Fleck 1991). The
compliance measured in a cracked geometry is related to the crack length.

Saxena and Hudak (1978) developed the analytical
expressions correlating crack growth and compliance for standard specimens. Elastic
compliance correlations were formulated for a wide range of crack lengths using
results from Newman’s modified boundary collocation techniques and Wilson’s
deep crack analysis. ASTM E647 specifies the guidelines for determination of
crack size using compliance technique. Compliance is measured from the
force-displacement plot obtained during the fracture test where the specimen is
unloaded partially at different points as shown in Fig. 1. The amount of
unloading is 15% of collapse load. Compliance is calculated
by fitting a straight line to the upper linear part of the force-displacement
curve. Compliance in such analytical models is expressed in terms of a dimensionless
quantity normalized for elastic modulus and specimen thickness.

ASTM E647 mentions that all
compliance-crack size relationships are applicable only for the measurement
locations on the specimen for which they were developed. In lieu of an
analytically derived compliance relationship, it is possible to empirically develop
a compliance curve for any type of specimen used in fatigue crack growth rate
testing.

  

Fig.
1 Force-displacement plot in a fracture test showing partial unloading

 

2.2
Normalised compliance equations

 

The compliance correlations developed for
standard specimens mentioned in the previous section are not suitable for crack
growth measurement in components like pipes. Studies carried out by Chattopadhyay
et al. (2006) had shown that the deformation of the pipe component affects the
compliance. Hence the unloading compliance of a Throughwall Circumferentially Cracked
pipe (TCC) depends on crack length as well as the deformation level. This is
due to the fact that the stiffness of the specimen changes as the deformation
increases which in turn changes the basic geometry. A non-linear finite element
analysis was carried out by Chattopadhyay et al. (2014) considering both
geometric and material non-linearity for TCC pipes of different R/t ratio
(R=mean radius, t=thickness).