PSI - Issue 28

11

Author name / Structural Integrity Procedia 00 (2019) 000–000

Rhys Jones et al. / Procedia Structural Integrity 28 (2020) 26–38

36

4. Conclusions In fatigue tests on aircraft components and structures employing carbon-fibre reinforced-plastic (CFRP) composites no, or only little, retardation (i.e. slowing) of the fatigue crack growth (FCG) rate usually occurs as a delamination grows. However, this is not typically the case in laboratory tests where the double-cantilever beam (DCB) test is employed to obtain fracture-mechanics data for the composite under cyclic-fatigue Mode I loading. Indeed, in the DCB test it is extremely difficult to perform fatigue tests without extensive fibre-bridging developing across the crack faces, behind the crack tip. This fibre-bridging leads to a significant retardation of the FCG rate in the DCB test. The results from the DCB tests also invariably exhibit a relatively large degree of inherent scatter. Thus, in the present paper, a novel and simplified methodology is proposed for predicting an ‘upper-bound’, i.e. ‘worst case’, FCG rate curve from the laboratory DCB test data which is truly representative of a composite exhibiting no, or only very little, retardation of the FCG rate under fatigue loading. The proposed methodology also takes into account the inherent scatter of such fatigue tests. To achieve this we have employed a variant of the Hartman-Schijve equation. Also, recommendations are made for undertaking DCB tests such that sufficient, and sound, experimental fatigue data are obtained, which then enables the proposed methodology for calculating the ‘upper-bound’ FCG rate curve to be successfully adopted. The ‘upper-bound’ FCG rate curve, predicted as described in the present paper, encompasses all the experimental results and yields a curve which can be used, with confidence, by industry for (a) material development, characterisation and comparison studies, and (b) design and lifing studies. Acknowledgments Rhys Jones acknowledges support via the Office of Naval Research NICOP Grant N62909-19-1-2011-P00001. Appendix A. The mathematical relationship between ∆� and ∆� The Hartman-Schijve variant of the Nasgro equation used in this paper takes the form: � � � � � � � ∆√���∆�� ��� √������ ��� /√�� � � (A1) It is important to note that the term ∆� ��� differs from the quantity ∆� �� , where the latter term corresponds to the value of ∆√ associated with a delamination growth rate, da/dN , of 10 -10 m/cycle, see ASTM (2014). The use of ∆� �� in equation (A1) is inappropriate. Since, at ∆√ = ∆� �� , equation (A1) would return a value of da/dN that is zero, instead of the required value of da/dN = 10 -10 m/cycle. Therefore, the term ∆� ��� is introduced to ensure that at ∆√ = ∆� �� the value of da/dN is equal to 10 -10 m/cycle. Hence, the values of ∆� ��� and ∆� �� are related by: 10 -10 = � � ∆�� �� ��∆�� ��� √������ ��� /√�� � � (A2) To illustrate the magnitude of the difference, which is generally very small, let us consider, from Yao et al (2018), a predicted upper-bound FCG rate curve where D = 1.73 x 10 -8 , n = 2.22, A = G co = 115 J/m 2 and ∆� ��� = 3.2 √(J/m 2 ). This yields a value of ∆� �� = 3.3 √(J/m 2 ), i.e. a difference of 0.1 √(J/m 2 ) compared to the value of ∆� ��� . Thus, as can be seen, the difference between the values of ∆� ��� and ∆� �� is indeed very small. Nevertheless, from a mathematical and an engineering perspective, it is better to use ∆� ��� , and not ∆� �� , in Equation (2), i.e. Equation (A1), otherwise unnecessary errors can be introduced at low delamination FCG rates.