Issue 43

D. Gentile, Frattura ed Integrità Strutturale, 43 (2018) 155-170; DOI: 10.3221/IGF-ESIS.43.12 157    3 11 2 3 a C P E I (1) while the strain energy release rate for unitary surface crack advance is given by:  2 2 11 I P a G wE I (2) The condition for stable crack growth is given by:    0 I G a (3) That for the DCB configuration is verified only for the imposed displacement conditions:        2 2 11 4 I const G a a C wE I (4) For the imposed load conditions, the DCB configuration is intrinsically unstable since the derivative is always greater than zero:     2 11 2 0 I G P a a wE I (5) The relation given in Eqn. (1) also requires the value of the elastic traction modulus along the fiber direction. This can be a considerable source of error in the estimation of G I due to the uncertainties and accuracy of the Young modulus. For instance, an accuracy of ± 10 GPa results in an uncertainty of ± 7% in the estimation of the value of G. In addition to this, the error due to the fact that the shear compliance is neglected in the beam theory have also to be considered. Alternatively, G I can be expressed in term of quantities directly measurable in the DCB traction test such as the displacement along the load line and the applied load. According to this the resulting expression for G is given by   2 I nP G ba (6) Eqn. (6) is usually indicated as Compliance Calibration Method (CCM) since the coefficient n corrects the beam theory approximated solution. In the case of perfect load fixtures and Modified Beam Theory (MBT), the coefficient n is equal to 3:   3 2 I P G ba (7) The values obtained with Eqn. (7) overestimate the effective G values and can be taken as upper bound limit. The effective n value can be obtained as linear regression of the compliance measurements as a function of the crack advance on a double Ln plane as also described in the ASTM E-5528 prescription. This methodology requires a number of measures of statistical significance and, even not explicitly stated, partial unloading in order to account for possible non-linearities in the specimen compliance. A third expression to calculate the G I value is called Modified Compliance Calibration method (MCC). From the beam theory modified in order to account for large rotation during loading, the following expression can be derived: