PSI - Issue 38

S. Spanke et al. / Procedia Structural Integrity 38 (2022) 220–229

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Author name / Structural Integrity Procedia 00 (2021) 000±000

For the determination of the sti ff ness material parameters equation (17) of the unidirectional layer 6 load steps are needed. Load step 1: ε 1 = 0 . 01 → C i 1 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) i V ( n ) Gp , i = 1 , 2 , 3 Load step 2: ε 2 = 0 . 01 → C i 2 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) i V ( n ) Gp , i = 1 , 2 , 3 Load step 3: ε 3 = 0 . 01 → C i 3 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) i V ( n ) Gp , i = 1 , 2 , 3 Load step 4: ε 4 = 0 . 01 → C 44 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) 4 V ( n ) Gp Load step 5: ε 5 = 0 . 01 → C 55 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) 5 V ( n ) Gp Load step 6: ε 6 = 0 . 01 → C 66 = 1 0 . 01 · N n = 1 V ( n ) Gp N n = 1 σ ( n ) 6 V ( n ) Gp (18) With an inversion of the sti ff ness matrix equation (17) and a coe ffi cient comparison of the compliance matrix, the e ff ective homogenized material parameters of the unidirectional layer are as follows.

2.4. Geometry structure RVE

The geometry of the RVE structure must satisfy equation (13). This means that at opposite edges the material structure must be continued so that no material sti ff ness jumps occur during fluctuation over the edge γ RVE . The fiber distribution in the RVE space is constructed symmetrically on the one hand and with fiber distribution algorithms on the other hand. The fiber distribution algorithms implemented are the Random Microstructure Generator (RMG) of Melro et al. (2008) and the Random Distribution Generator (RDG) of Ge et al. (2019).

(a) RVE57 SYM M1

(b) RVE57 RMG 2

Fig. 3. (a) Symmetrical RVE system fiber volume fraction: 57.02%, (b) RMG RVE system fiber volume fraction: 56.69%

3. Numerical calculation and validation

First, the stress paths of the larger symmetric system and the RMG 57 system from Figure 3 are analyzed. In a second step, the e ff ective homogenized material parameters between symmetrically designed RVE systems and RVE fiber distributions are compared and validated by means of a 4-point bending test.

3.1. Stress paths

Figure 4 and 5 shows von Mises stresses for the RVE systems from Figure 3 for the load steps from Equation (18).