PSI - Issue 42

T. Vandellos et al. / Procedia Structural Integrity 42 (2022) 50–57

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C2 - Restricted

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Author name / Structural Integrity Procedia 00 (2019) 000 – 000 The scalar yarn failure variables df1t , df2t (respectively in warp and weft directions in tension), df1c and df2c (respectively in warp and weft directions in compression) are defined by = ( 〈√ −√ 0 〉 + √ ) with i=1,2 , ̇ ≥ 0 and = 1 2 ( : : ) (4) Where 0 are the onsets of yarn failure, and parameters which are linked to the progressive laws and the driving forces. Finally, in the general framework of the ODM-OxOx formulation, the specific strain tensor accounts for the residual strains after unloading, due to the evolution of the different damages. Nevertheless, this term was not used in the present work because the effects of unloading were not studied. 3.3. Description of the cohesive zone model To model the interface damage between the bond and the CMC substrate, a cohesive zone model was used. This kind of model permits to describe the onset of a delamination and the progressive crack growth at the interface using a traction-separation law. Several shapes are available in the literature for the cohesive law, as reported by Alfano (2006) and Campilho (2017). In this study, a triangular law was used. This law relate the force and the displacement separation vectors considering firstly an elastic behavior and secondly a progressive degradation of the interface properties until its failure. Three parameters are required : the initial stiffness K , the cohesive tensile strength ( σ C ) and the critical energy release rate ( G C ). The same properties were considered for each loading direction. 4. Numerical results and discussions 4.1. Modeling with the CMC damage behavior The Fig. 6-a compares the experimental curve (blue solid line) with two numerical curves obtained respectively with an elastic behavior model (red dash-dot line) and the damage behavior using ODM (purple dashed line). It appears that the simulation with the continuum damage model describes perfectly the first and the second phases of the experimental response described in the Fig. 2-a. As illustrated in Fig. 6-b, the non-linearity, which occurs at 0.5mm, is explained by the matrix damage, associated with the scalar dm1 , in the longer CMC substrate. This kind of damage increases with the imposed displacement until the failure of the sample. When the load attains its maximum, the scalar df1t , corresponding to the yarn failure under tension in warp direction, activates in the CMC substrate, near the corner of the bonded joint. This location correlates with the experimental failure of the sample.