The compliance measurement test is based on the relationship between compliance (C), which is a measure of stored energy in the structure, and the strain energy release rate (G).  The relationship as discussed in Section 1.3 is:

where P is the applied load, B is the structural thickness, and a is a measure of crack length.  The compliance in Equation 7.4.1 is associated with the displacement of the load points along the axis of loading.  It should be noted that displacements not along the axis of loading cannot be used in the calculation of the strain energy release rate (G).  Once the relationship between G and C has been established the stress-intensity factor (K) is calculated using:

where E¢ = E, the elastic modulus, for plane stress problems and E¢ = E/(1-n 2) for plane strain problems, n is Poisson’s ratio.  Since the bulk of the material in any given structure is subject to plane stress conditions, the better correlations are obtained between analytically determined K solutions and compliance determined K solutions based on the plane stress formulation of Equation 7.4.2.