@article{eprints1945,
           pages = {535--547},
         journal = {International Journal of Fracture},
          volume = {141},
          author = {Alberto Carpinteri and Marco Paggi and Nicola Pugno},
            year = {2006},
          number = {3-4},
           title = {An analytical approach for fracture and fatigue in functionally graded materials},
       publisher = {Springer-Verlag},
        keywords = {Functionally graded materials; Multi-layered elements; Brittle crack propagation; Fatigue crack growth},
        abstract = {The problem of brittle crack propagation and fatigue crack growth in functionally graded materials (FGMs) is addressed. The proposed analytical approach can be used to estimate the variation of the stress-intensity factor as a function of the crack length in FGMs. Furthermore, according to the Paris? law, the fatigue life and the crack-tip velocity of crack propagation can be predicted in the case of fatigue crack growth. A comparison with numerical results obtained according to the Finite Element method will show the effectiveness of the proposed approach. Detailed examples are provided in the case of three-point bending beam problems with either a FGM interlayer, or a FGM external coating. A comparison is presented between two types of grading in the elastic modulus: a continuous linear variation in the FGM layer and a discrete approximation with a multi-layered beam and a constant Young?s modulus in each layer.},
             url = {http://eprints.imtlucca.it/1945/}
}