PSI - Issue 28

34 Rhys Jones et al. / Procedia Structural Integrity 28 (2020) 26–38 Author name / Structural Integrity Procedia 00 (2019) 000–000 9 occur then the mean value of ∆� ��� will be falsely skewed. Further, considering the general scatter associated with fatigue tests on all types of materials, the minimum number of such replicate DCB test programs for a CFRP composite, whereby the measured values of da/dN and ∆√ are obtained as function of the initial pre-crack extension length, a p - a o , is suggested to be eight in number, see the Composite Materials Handbook (2012). Secondly, the value of the constant, A , in Equation (2) is now taken to be equivalent to the quasi-static value of the Mode I initiation fracture energy, G co , at the onset of crack growth, which has the value of 250±45 J/m 2 for the ‘M30SC/DT120’ CFRP from the work of Yao et al. (2014, 2017, 2017a, 2018, 2018a). Thirdly, the number of standard deviations whereby to reduce the mean values of both the terms ∆� ��� and G co to obtain the ‘upper-bound’ FCG rate curve needs to be considered. Obviously, any number of the standard deviations could be selected, depending upon the industrial application being considered. From the aerospace community, as discussed by Niu (1992) and Rouchon (2009), two obvious options arise which are to subtract either two or three standard deviations from the mean values of ∆� ��� and G co . The former option of taking the mean values of the threshold, ∆� ��� , and of G co , minus two standard deviations will clearly give the less conservative ‘upper-bound’ fatigue growth curves and is termed the ‘B’ basis approach. In this approach, the mechanical property value indicated is the value above which at least 90% of the population of values is expected to fall with the confidence of 95%. This value is used in the design and service-lifing of redundant or fail-safe structural analyses, where the loads may be safely distributed to other members. If a more conservative curve is required, for example in primary aircraft structure, an approach based on taking the mean value of ∆� ��� and of G co minus three standard deviations may be preferred. The is termed the ‘A’ basis approach and, in this case, the mechanical property value indicated is the value above which at least 99% of the population of values is expected to fall with the confidence of 95%. This value is used to design and service-life a single member where the loading is such that its failure would result in a loss of structural integrity. (It should be noted, of course, that any number of values of the standard deviation could be selected to be subtracted from the mean values of the terms ∆� ��� and G co to obtain a given ‘upper-bound’ FCG rate curve. The higher the number that is selected then the more conservative the predicted ‘upper-bound’ FCG rate curve will be and, it is logically assumed, the more demanding would be the intended application for the composite material. Interestingly, if the value of the subtracted standard deviations becomes too high, then the denominator in Equation (2) cannot be mathematically resolved from an engineering standpoint. It is suggested that, if such a situation arises, this indicates that the number of standard deviations being stipulated is too large and/or the measured standard deviation is too high. Therefore, the fatigue behaviour of the composite material will not now meet the stated requirements for the intended application.) Fourthly, for Equation (2), the values of D and n required to obtain the single, linear, ‘master’ Hartman-Schijve relationship were found to be 1.73 x 10 -8 and 2.22 respectively, using units for the y-axis of m/cycle and for the x-axis of  (J/m 2 ), see Fig. 3. Thus, all the values of the parameters needed to compute the ‘upper-bound’ FCG rate curve from the proposed methodology based upon using the Hartman-Schijve approach, see Equation (2), are now known, and are shown in Table 1. The ‘predicted upper-bound’ FCG rate curve from the present approach for the ‘M30SC/DT120’ CFRP using a ‘mean-3sd’ for ∆� ��� , and of G co is shown in Fig. 2. Now, as may be seen, this ‘upper-bound’ FCG rate curve predicted from the present methodology does indeed encompass, and bounds, all the experimental data. Fig. 2 also reveals that the exponent of the power-law relationship that is associated with the approximately linear region between log da/dN versus log ∆√ of the ‘upper-bound’ FCG curve is relatively low in value. Thus, this ‘upper-bound’ FCG curve represents the ‘worst-case’ for the FCG rate data; and no, or very little, retardation of the growth of the delamination is present in this predicted curve. In Fig. 2 the ‘upper-bound’ curve from the prior methodology discussed in Yao et al. (2018) is also shown. Here a ‘mean-3sd’ value for ∆� ��� was also employed but the methodology used in this previous work involved a rather extensive extrapolation of the measured data, which is not always feasible and is somewhat cumbersome. The route proposed in the present paper is considered to be a far more simple, robust and straightforward methodology, without the need to undertake often difficult extrapolations to access the mean and standard deviation of the value of ∆� ��� . However, the two ‘upper-bound’ FCG rate curves are very similar in nature, as would be expected since the values of ‘ ∆� ��� - 3sds’ are very similar, and therefore the new route described in the present paper is the methodology proposed for future use in ascertaining the predicted ‘upper-bound’ FCG rate curve.