Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

These numerical and experimental studies provide a better understanding of the behaviour of
debond damaged sandwich composites under static or fatigue loading. Moreover, they develop
reliable analysis tools for assessing the damage tolerance and fatigue lifetime of debonded
sandwich composites.
Since Linear Elastic Fracture Mechanics (LEFM) for the interfaces is the main theoretical
foundation of this thesis, it will be presented in the next section of the Introduction. Finally, a
brief history of fatigue analysis in sandwich composites will be presented in the last section of
the Introduction.
1.3 Linear Elastic Fracture Mechanics
Griffith in 1920 established the foundations of fracture mechanics. He applied a stress analysis of
an elliptical hole from Inglis (1913) to the unstable crack propagation problem. Based on the
principle of energy conservation of thermodynamics, Griffith proposed the energy balance
concept for fracture. According to Griffith’s theory, a crack may be formed or propagate if the
potential energy change provided by strain energy and external forces, resulting from crack
growth, is enough to overcome the surface energy and generate new surfaces. In 1948 Irwin
extended Griffith’s concept to metals by including plastic energy dissipation at the crack tip. In
1956 Irwin proposed the Griffith energy or energy release rate G as a measure of available
energy for crack growth as
where is the potential energy and dA is the crack area increment. According to Equation (1.1)
the critical energy release rate Gc or fracture toughness can be defined as
where Ws is the required energy for creation of new surfaces.
Generally, a crack may experience three types of loading, see Figure 1.3. Mode I loading where
the applied load tends to open the crack, mode II loading where the in-plane shear loading tends
to slide one crack face against the other and mode III corresponding to the out-of-plane shear and
sliding of the crack flanks. A crack may be loaded in any of these three modes or in a mixedmode
combination of them. In 2D modelling of a crack problem, only the first two modes are
typically used.
5
(1.1)
(1.2)