Issue 31

J. Lopes et alii, Frattura ed Integrità Strutturale, 31 (2015) 67-79; DOI: 10.3221/IGF-ESIS.31.06 73 Figure 6 : Model of the unit width hybrid beam Loading member and support modelled as rigid bodies. The cohesive elements use the Quadratic Nominal Stress Criterion (QUADS) shown in Eq. 1. 2 2 2 0 0 0 1 n s t n s s t t t t t t                      (1) The variables n t , s t , t t are the normal stress and the shear tensions on both directions respectively of the cohesive models. The variables 0 n t , 0 s t , 0 t t are the damage threshold values of the cohesive elements. The Macaulay operator in the normal stress n t is used to ensure that the damage does not occur when 0 n t  . The damage evolution of the cohesive elements uses the mixed mode criterion proposed by Benzeggagh and Kenane, the B-K criterion [23]. This criterion accounts for the variation of fracture toughness as function of the mode ratio. In order to match the experimental result with the numerical simulation several values of G IIC were tested as the dominant failure mode in this test is Mode II (Tab. 3). In order to replicate the actual test, the numerical model has to include the contact interaction between the beam and the loading member and the beam and the support. A penalty formulation was established for the contact properties and interaction definition was set to surface to surface interaction. Simulations with contact formulation are prone to severe discontinuous nonlinearities. Therefore the entire displacement was divided by 10 equal steps of 0.1mm to reduce severe discontinuities in the solver. The accumulated effect of cohesive elements with damage model and damage evolution, and the contact formulation causes a very intense computational effort. Some initial settings of the steps module, namely the tolerances of the Line Search control parameters and the Time Incrementation parameters had to be increased from their initial settings in order to enable the solver to reach a solution. R ESULTS AND ANALYSIS Experimental results he apparent inter-laminar shear strength for the reference beam (monolithic CFRP) was calculated based on the load measured by the testing machine using Eq. (2) [12]: 3 4 F b h     (2) where: F is the load in (N), b and h are the width and thickness of the specimens respectively (mm),  is the apparent inter-laminar shear strength (MPa). T