PSI - Issue 39

Branko Nečemer et al. / Procedia Structural Integrity 39 (2022) 34 – 40 Author name / Structural Integrity Procedia 00 (2019) 000–000

37

4

_ = 4071.5 −0 . 326

0 100 200 300 400 500 600 700

_ = 3625.7 −0 . 316

Re-entrant structure Rotated re-entrant structure

Am plitude force [N]

100

1000

10000

Fig. 4. − fatigue life curves

Number of load cycles to failure - log (N) [Cycle]

3. Computational modelling In this section, a computational model for the fatigue analyses of the re-entrant and rotated re-entrant auxetic specimens are presented. The boundary conditions of the analysed auxetic specimens are presented in Fig. 5 . The restraints were prescribed in reference points A and B which represent the centre of the clamping holes. In the computational models, point A was tied in both translational degrees of freedom, while the other point B was restrained in the x-direction and enables movement in the y-direction. The rotational degree of freedom of the specimen enabled the rotation around the longitudinal axis (z-axis). The external load was prescribed in the lateral direction in point B. The external force was defined as one closed sinusoidal loading cycle between the minimum and maximum force. The computational analyses were performed at load control at load ratio 0.1, where five loading levels were selected.

(a)

(b)

Point B

Point B

Point A

Point A

Fig. 5. Boundary conditions: (a) Re-entrant auxetic structure; (b) Rotated re-entrant auxetic structure

In the computational model, the geometries were discretized with 2D plane stress linear finite elements with a global size of 0.3 mm. The re-entrant auxetic specimen consists of 50,231 finite elements while the rotated re-entrant auxetic specimen consists of 48,755 finite elements, respectively. In the computational model, the nonlinear kinematic material model was applied. In the proposed material model, the material behaviour was modelled by defining the data pairs obtained from the cyclic stress-strain curve (Tomažinčič et al (2019)) . In the performed computational analyses, the fatigue life of the analysed auxetic specimens was determined using the strain-life approach with consideration of a Morrow mean stress correction. In the framework of the ANSYS software, the strain-life parameters σ f ', b , ε f ', c , K ' and n ' were integrated into the material model. The strain-life parameters were obtained previously from the low cycle fatigue tests of the based material (AA 7075-T651); see Tomažinčič et al (2019) . The total fatigue life of the analysed auxetic specimen represents the sum of the number of cycles to failure for the first three cells ( = 1 + 2 + 3 ). Fig. 6 shows the schematic procedure of the computational determination of the total fatigue life.