PSI - Issue 13

B. Nečemer et al. / Procedia Structural Integrity 13 (2018) 2261 – 2266 Author name / Structural Integrity Procedia 00 (2018) 000–000

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t i p N N N   (1) where is the number of loading cycles required for the fatigue crack initiation and is the number of loading cycles required for the crack propagation from initial to the critical crack length when final failure can be expected to occur (Glodež et all. 2015). Computational analysis of the fatigue crack initiation period ( ) is performed using elastic-plastic stress/strain field previously determined with Abaqus and subsequent fatigue analysis according to the Fe-safe program package. The latter is based on the low-cycle fatigue material parameters which are in this study taken from the professional literature. The performed crack initiation period is separately calculated for each critical cell of treated auxetic structure. The fatigue crack propagation period ( ) is evaluated using Paris equation:   m da C K a DN        (2) where / is the fatigue crack growth rate, is the crack length, is the number of loading cycles and ∆ is the stress intensity factor range (∆ = − ). The constants and are the material parameters, which are determined experimentally according to the appropriate load ratio = / (the value = 0.1 is considered in this study). The number of loading cycles ( ) required for the crack propagation from initial crack length ( ) to the critical crack length ( ) can then be determined as follows:   0 0 1 c N a a da dN C dK a    (3) 2. Computational model In this section, a computational model of the re-entrant and rotated re-entrant auxetic porous structures is presented. As shown in Figs. 1 and 2, a Compact Tensile (CT) specimen with different oriented base unit cells is used for the subsequent numerical analysis. The relative porosity of both structures is approximately 60 %.

Fig. 1. Geometry and dimensions of treated porous structure

Fig. 2 shows the boundary conditions on treated CT-specimens which are applied to two reference points (point A bottom and point B-top). Points A and B are kinematically coupled to the loading holes. Point A is restrained in both translational degrees of freedom, while the other point B is restrained in x-direction and enables movement in the y direction. The rotational degree of freedom of the specimen enables rotation around the longitudinal axis (z- axis). The external load is prescribed in the lateral direction in point B, where the sinusoidal loading pattern ( = 1000 N, = 100 N) is assumed. Fig. 2 also shows the assumed initial macroscopic notch which extends through two (re-entrant structure) or three (rotated re-entrant structure) base cells. Computational models are discretized with 2D plane stress linear finite elements (element type CPS4). The global size of finite elements 0.15 mm was determined with previous convergence analysis. Re-entrant specimen consists of 185709 finite elements while the rotated re-entrant specimen consists of 180927 finite elements, respectively. In the performed numerical simulation it is assumed that the analysed porous structure is made of aluminium alloy 7075 T651 with material properties given in Table 1.