Confalonieri, F.

Perego, U.

F. Confalonieri

U. Perego

Archivio istituzionale della ricerca - Politecnico di Milano

YIC 2017IV ECCOMAS YOUNG INVESTIGATOR CONFERENCE13-15 September 2017, Milano, ItalyA smooth cohesive law for mixed-mode delaminationFederica Confalonieri∗ and Umberto Perego∗∗ Department of Civil and Environmental EngineeringPolitecnico di MilanoPiazza Leonardo da Vinci, 32, 20133 Milano, Italye-mail: federica.confalonieri@polimi.it; umberto.perego@polimi.itKEYWORDS: Delamination; Cohesive Model; Interface Elements; Mixed-Mode.ABSTRACTDelamination, i.e. the decohesion between layers, is one of the main failure modes in com-posite materials. Making use of robust and accurate numerical tools is fundamental toreliably predict the delamination growth. The finite element simulation of these problemsis often dealt with by the insertion between adjacent layers of interface elements, whoseconstitutive behavior is described by a cohesive model in terms of a traction-opening dis-placement law. In the literature, there exists a variety of works devoted to the formulationof cohesive laws (see [1] for a comparative review of some models), although many of themexhibit a number of shortcomings, such as the need of strong assumptions on the loadingpath and on the mixed-mode failure properties, or the lack of thermodynamic consistency.Real-life delamination processes are indeed often characterized by mixed-mode loadingconditions with varying mode ratio. In addition, several experimental results show thatthe fracture energy significantly grows in passing from pure Mode I to pure Mode II [2].Figure 1: Three-surface activation domain.This work presents a new cohesive model, specifically conceived for mixed-mode delami-nation. The model is based on an isotropic damage formulation, that ensures its thermo-dynamic consistency for any loading path. The interaction between normal and tangentialopenings is modeled by introducing a three-modes activation surface, of the type shownin Fig. 1, defined in the plane of dimensionless cohesive tractions. Each normal defines adistinct damage mode, namely one opening and two shear-dominated modes. The shapeof the domain depends only on the angle of inclination of the two shear dominated modes,which acts as a parameter of internal friction in the presence of positive normal tractions.The projection of the cohesive tractions onto the three normals allows for a decompositionof the strain energy release rate in terms of the contributions of the three damage modes.The overall fracture energy is an outcome of the interaction between damage modes, with-out the need of introducing any empirical law. As an example, Fig. 2 shows the growthof fracture energy as a function of the mode-mixity ratio for a AS4/PEEK carbon-fiber-reinforced composite (see [3]). The light dashed curve reports the numerical result of thepresent model, the dark one the widely used empirical Benzeggagh-Kenane (BK) law [2],while the square dots are experimental points resulting from Mixed-Mode Bending tests[4]. It can be noted that the proposed model is able to adequately reproduce the transitionfrom pure Mode I to Mode II in terms of dissipated energy at complete decohesion.Figure 2: Mixed-mode fracture energy vs mode-mixity parameter.An exponential softening branch, deriving from the inelastic potential proposed in [5], isintroduced in order to allow for a more accurate fitting of experimental data and to reducethe oscillatory response in the case of explicit dynamic analyses.The proposed cohesive model has been validated on several benchmark tests available inthe literature, mainly focusing on Mixed-Mode Bending (MMB) tests [4].REFERENCES[1] R. Dimitri, M. Trullo, L. De Lorenzis, G. Zavarise. Coupled cohesive zone mod-els for mixed-mode fracture: A comparative study. Engineering Fracture Mechanics,148:145-179, 2015.[2] M.L. Benzeggagh, J.H. Crews. Measurement of mixed-mode delamination fracturetoughness of unidirectional glass/epoxy composites with mixed-mode bending appa-ratus. Composites Science and Technology, 56:439-449,1996.[3] P.P. Camanho, C.G. Davila, M.F. de Moura. Numerical Simulation of Mixed-modeProgressive Delamination in Composite Materials. Journal of Composite Materials,37:1415-1438,2003.[4] J.R. Reeder, J.H. Crews. Mixed-mode bending method for delamination testing.AIAA Journal, 28:1270-1276,1990.[5] C. Comi, U. Perego. Criteria for mesh refinement in nonlocal damage finite elementanalyses. European Journal of Mechanics A/Solids, 23:615-632,2004.

A smooth cohesive law for mixed-mode delamination

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A smooth cohesive law for mixed-mode delamination

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Archivio istituzionale della ricerca - Politecnico di Milano