Issue 44

P.S. Valvo, Frattura ed Integrità Strutturale, 44 (2018) 123-139; DOI: 10.3221/IGF-ESIS.44.10

First, attention has been devoted to the analysis of the ENF test as the prototype of symmetrically delaminated laminates subjected to pure mode II fracture conditions. Comparison of the available models reveals that shear deformation as accounted for at first order by the Timoshenko beam theory affects the specimen compliance, but not the mode II energy release rate. The shear-deformation correction terms given in Ref. [53] and used in much of the later literature turned out to be incorrect. Hence, their use for experimental test interpretation and comparison of models should be avoided in the future. Indeed, three-dimensional finite element analyses of the ENF test show a dependence of the energy release rate on the shear modulus of the material. This behaviour may be related to local deformation occurring at the delamination crack tip because of high stress concentration, e.g. strain in the laminate thickness direction, Poisson’s effect, and root rotations. Such effects can be captured also with beam theory models, however based on higher-order shear-deformation theories or through the introduction of deformable interfaces connecting the delaminated sublaminates. Similar considerations hold in general for laminates with symmetric, i.e. mid-plane, delamination. Next, a general delaminated beam has been considered with an arbitrarily located through-the-width delamination. In this case, mixed-mode fracture conditions generally occur and G II is only a part of the total energy release rate. In the paper, several mixed-mode partition methods of the literature have been reviewed with specific attention on the effects of shear forces and shear deformation on G II . Lastly, a quantitative comparison has been made between the predictions of the rigid connection model [24], elastic-interface model [37], and local method [21] for a homogeneous and orthotropic laminate with shear forces applied at the crack tip. The results show a quite limited influence of the shear forces on the mode II contribution to the energy release rate, except for nearly symmetric delamination and antisymmetric shear forces. For the sake of simplicity, in the paper, attention has been limited to homogeneous and orthotropic beams. Further studies will be necessary to extend the above considerations to more complex structural elements, such as bi-material and multidirectional laminated beams and plates. [1] Garg, A.C., (1988). Delamination-a damage mode in composite structures, Eng. Fract. Mech., 29, pp. 557–584. DOI: 10.1016/0013-7944(88)90181-6. [2] Sela, N. and Ishai, O., (1989). Interlaminar fracture toughness and toughening of laminated composite materials: a review, Composites, 20, pp. 423–435. DOI: 10.1016/0010-4361(89)90211-5. [3] Bolotin, V.V., (1996). Delaminations in composite structures: its origin, buckling, growth and stability, Compos. Part B-Eng., 27, pp. 129–145. DOI: 10.1016/1359-8368(95)00035-6. [4] Tay, T.E., (2003). Characterization and analysis of delamination fracture in composites: An overview of developments from 1990 to 2001, Appl. Mech. Rev., 56 1–31. DOI: 10.1115/1.1504848. [5] Senthil, K., Arockiarajan, A., Palaninathan, R., Santhosh, B., Usha, K.M., (2013). Defects in composite structures: Its effects and prediction methods – A comprehensive review, Compos. Struct., 106, pp. 139–149. DOI: 10.1016/j.compstruct.2013.06.008. [6] Chatterjee, S.N. and Ramnath, V., (1988). Modeling laminated composite structures as assemblage of sublaminates, Int. J. Solids Struct., 24, pp. 439–458. DOI: 10.1016/0020-7683(88)90001-7. [7] Reid, S.R., Zou, Z., Soden, P.D. and Li, S., (2001). Mode separation of energy release rate for delamination in composite laminates using sublaminates, Int. J. Solids Struct., 38, pp. 2597–2613. DOI: 10.1016/S0020-7683(00)00172-4. [8] Jones, R.M., (1999). Mechanics of composite materials, second ed., Taylor & Francis, Philadelphia. [9] Timoshenko, S.P., (1955).Strength of Materials, Vol. 1: Elementary Theory and Problems, third ed., D. Van Nostrand, New York. [10] Timoshenko, S.P. and Woinowsky-Krieger, S., (1959). Theory of Plates and Shells, second ed., McGraw-Hill, New York. [11] Reddy, J.N., (1984). A Simple Higher-Order Theory for Laminated Composite Plates, J. Appl. Mech., 51, pp. 745–752. DOI: 10.1115/1.3167719. [12] Adim, B., Daouadji, T.H. and Rabahi, (2016). A simple higher order shear deformation theory for mechanical behavior of laminated composite plates, Int. J. Adv. Struct. Eng., 8, pp. 103–117. DOI: 10.1007/s40091-016-0109-x. [13] Barbero, E.J. and Reddy, J.N., (1991). Modeling of delamination in composite laminates using a layer-wise plate theory, Int. J. Solids Struct., 28, pp. 373–388. DOI: 10.1016/0020-7683(91)90200-Y. [14] Williams, T.O. and Addessio, F.L., (1997). A general theory for laminated plates with delaminations, Int. J. Solids Struct., 34, pp. 2003–2024. DOI: 10.1016/S0020-7683(96)00131-X. R EFERENCES

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