Fatigue crack growth of new FML composites for light ship buildings under predominant mode II loading condition

Abstract

The use of light but strong materials is largely studied in various area of the shipbuilding, this because the need of reducing the weight, and especially the weight of all the structures above the main deck assume primary importance for the stability. Traditionally in fast boats like fast ferries, hydrofoils, patrol boats, the typical materials are Aluminum alloy or composites, both those materials have advantages and disadvantages, but the new development of technologies made possible to combine them, in order to have a new material, combining the advantages of both, in terms of fatigue resistance, firefighting characteristics. In this paper, predominant mode II fatigue delamination tests of fiber metal laminates made of alternating layers of 2024-T3 aluminum alloy sheets and unidirectional E-Glass/epoxy laminates are presented. Several experimental tests are carried out employing the End Notched Flexure fixture and a progressive damage model is used to simulate the damage accumulation in the aluminum-composite interface, in the localized area in front of the crack tip, where micro-cracking or void formation reduce the delamination strength during fatigue tests. In particular, the numerical model is based on the cohesive zone approach and on the analytical definition of a damage parameter, directly related to the fatigue crack growth rate da/dN. The numerical model, implemented in ANSYS environment, uses a fracture mechanics-based criterion in order to determine the damage propagation. In particular, the study has allowed to determine the damage model constants that are used for numerical verification of the experimental results.

Appendix

The coordinates of the point N of Fig. 8 are determined by the intersection of the line $\overline{AB}$ (see Eq. 13) with the line $\overline{OD}$ (see Eq. 14), that can be represented as a function of damage variable D_N.

$$ \frac{{y - \tau_{0} }}{{0 - \tau_{0} }} = \frac{{x - \delta_{0} }}{{\delta_{\hbox{max} } - \delta_{0} }}\,\,\, \Rightarrow \,\,\,y = \tau_{0} \left( {1 - \frac{{x - \delta_{0} }}{{\delta_{\hbox{max} } - \delta_{0} }}} \right) $$

(13)

$$ y = k_{0} \left( {1 - D_{N} } \right)x = \frac{{\tau_{0} }}{{\delta_{0} }}\left( {1 - D_{N} } \right)x $$

(14)

Substituting Eq. 13 into Eq. 14 and solving for x:

$$ \frac{{\tau_{0} }}{{\delta_{0} }}\left( {1 - D_{N} } \right)x = \tau_{0} \left( {1 - \frac{{x - \delta_{0} }}{{\delta_{\hbox{max} } - \delta_{0} }}} \right)\,\, \Rightarrow \,\,x = \frac{{\delta_{0} \cdot \delta_{\hbox{max} } }}{{\left( {1 - D_{N} } \right)\left( {\delta_{\hbox{max} } - \delta_{0} } \right) + \delta_{0} }} $$

(15)

In particular, for $D_{N} = 0\,\,\,\, \Rightarrow \,\,\,x = \delta_{0} \,$; When $D_{N} = 1\,\,\,\, \Rightarrow \,\,\,x = \delta_{\hbox{max} } \,$.

From Eq. 13, it is possible to obtain:

$$ y = \frac{{\tau_{0} \cdot \delta_{\hbox{max} } \left( {1 - D_{N} } \right)}}{{(1 - D_{N} )(\delta_{\hbox{max} } - \delta_{0} ) + \delta_{0} }} $$

(16)

In particular, for $D_{N} = 0\,\,\,\, \Rightarrow \,\,\,y = \tau_{0} \,$; When $D_{N} = 1\,\,\,\, \Rightarrow \,\,\,y = 0\,$.