PSI - Issue 28

Rhys Jones et al. / Procedia Structural Integrity 28 (2020) 26–38 Author name / Structural Integrity Procedia 00 (2019) 000–000 against which to plot the measured rate of the FCG, da/dN , for composites is the range of the applied energy release rate, ∆ G . Also, the use of the maximum value of the energy release-rate, ��� , has been quite widely employed as the x-axis parameter in the FCG plots. However, recent work, for example by Jones et al. (2015, 2016, 2017), Pascoe et al. (2013), Rans et al. (2011), Simon et al. (2017) and Yao et al. (2014, 2017a, 2018), has revealed that the logical extension of the Paris FCG equation for metals to delamination growth in CFRPs is, in fact, to express da/dN as a function of ∆√ , or � ��� , rather than ∆ G , or ��� . Where ∆√ is given by: ∆√ � � ��� - � ��� (1) Following these ideas, a novel empirical methodology based on using a variant of the Hartman and Schijve (1970) equation has been proposed to access the ‘upper-bound’ FCG rate curve, which may be thought of as a material allowable property. The form proposed for the Hartman and Schijve equation, which is a variant of the Nasgro equation, by Jones et al. (2015, 2016, 2017, 2020) and Yao et al. (2018), in terms of ∆√ is: � � � � � � � ∆√�� ∆�� ��� √��� �� ��� /√�� � � (2) where D , n and A are constants. The term ∆� ��� is defined by: ∆� ��� � � ������� � � ������� (3) and the subscript ‘ thr ’ in Equations (2) and (3) refers to the values at threshold, below which no significant FCG occurs. It should be noted that the term ∆� ��� differs from ∆� �� , where ∆� �� is the value of ∆√ corresponding to a crack growth rate, da/dN = 10 -10 m/cycle. (The mathematical relationship between these two terms is discussed in Appendix A.) Further, CFRPs may undergo delamination under Mode I (opening tensile) and under Mode II (in plane shear) loading but, in the present paper, only Mode I loading is considered in detail. However, similar arguments may be advanced for Mode II and Mixed Mode I/II loading, as discussed by Jones et. al. (2015, 2020). Now, the values of ∆� ��� are best chosen so as to ensure that Equation (2) fits the experimental data over the entire range of crack growth rates. Therefore, the measured experimental results may be replotted according to the Hartman Schijve Equation (2) and it has been found by Jones et al. (2015, 2017, 2020) and Yao et al. (2018) that a single, linear, ‘master’ representation may be observed for various CFRP composites, and various structural adhesives, by allowing for relatively small changes in the value of ∆� ��� . A key question that now arises is whether, by using the Hartman-Schijve equation to obtain the single, linear, ‘master’ relationship, a methodology can be developed which allows the calculation of a corresponding valid, ‘upper-bound’ curve for the FCG rate for a delamination. Such an ‘upper-bound’, i.e. ‘worst case’, FCG rate curve should exclude any retardation effects on the FCG rate, e.g. from fibre bridging effects in the DCB test, and also take into account the inherent experimental scatter observed in the fatigue tests. In the present paper, compared to previous work by Yao et al. (2018), a very much simplified methodology to determine the ‘upper-bound’ FCG rate curve is proposed and validated. 3. Results for the ‘M30SC/DT120’ CFRP 3.1 Introduction In a previous papers by Yao (e.g. 2014, 2017, 2017a, 2018) delamination fatigue growth in a range of tests using the ‘M30SC/DT120’ CFRP, which was supplied by Delta-Tech S.p.A., Italy, has been reported. A large number of tests have been conducted but the vast majority of these tests were undertaken using unidirectional laminates and were mainly Mode I tests using the DCB test geometry. As usual, a 12.7 μm thick and 60 mm long ‘Teflon’ film was inserted in the mid-plane of the laminate during fabrication of the DCB test specimens. The role of this ‘Teflon’ film is to act as an initial delamination, or ‘starter crack’, of length, a o , of typically 60 mm. In these tests, prior to fatigue 29 4