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Fracture mechanics concerns the growth of cracks. Fracture mechanics models can provide answer to questions like: If the crack size, specimen geometry and loading are known, what is then the maximum load that the component can carry?
A central concept is the Griffith criterion: Crack growth is energetically favourable when the decrease in the potential energy (during an incremental crack growth) is equal (or exceeds) the energy absorbed by the fracture process. Denote the potential energy release rate G and the fracture energy (the crack growth resistance) of the process zone by GIc (both have the unit energy per unit area, J/m2). The Griffith criterion for crack growth then becomes G=GIc.
The Griffith criterion is valid when the volume in which the material fails (the process zone) is small in comparison with other dimensions (e.g. crack length, specimen width and thickness) and when the crack growth resistance is constant during crack growth. That is usually fulfilled for ceramics and high strength metals. For some materials the crack growth resistance increases with increasing crack extension, because the process zone evolves. This is called rising crack growth resistance or R-curve behaviour.
Some materials, in particular fibre composites, may experience large scale bridging (LSB). Then, the failure process must be characterised by a bridging law (see Basic solid mechanics concepts).
A particular useful tool in fracture mechanics modelling is the J integral. The J integral is path independent and gives the potential energy release rate. It has a very useful application for the measurement of the bridging law in large scale bridging problems (Sørensen and Jacobsen, 1998).
For testing purposes it is advantageous to use specimens for which the energy release rate G decreases during crack growth. Then, crack growth can be stopped and reinitiated, so that the fracture energy can be determined from the growth of a truly sharp crack (in contrast to crack initiation from a machined notch). Also, many tests can be performed for each specimen. Such a specimen is the so-called double cantilever beam (DCB) specimen loaded with pure bending moments (Sørensen et al., 1996).
Selected publications
Sørensen, B. F., Brethe, P. and Skov-Hansen, P., 1996, "Controlled Crack Growth in Ceramics: The DCB-Specimen Loaded with Pure Moments", J. Euro. Ceram. Soc., Vol. 16, pp. 1021-5.
Sørensen, B. F. and Jacobsen, T. K., 1998, "Large Scale Bridging in Composites: R-curve and Bridging Laws", Composites part A, vol. 29A, pp. 1443-51 |