PSI - Issue 57

J. Torggler et al. / Procedia Structural Integrity 57 (2024) 152–160 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

158

7

4.2. Local analysis based on fiber strain

As seen in the previous section, the applied lateral displacement amplitude U has a varying degree of effect on the service life of the considered fabrications at different fibre angles. Subsequently, the fibre strain is to be calculated by means of an analytical approach and considered as relevant for the fatigue damage of the composite material. Figure 6 shows the principle procedure described before for a single fibre of a fibre ply in detail. Based on the geometric relationships, the fibre strain is determined in the further course. In step 0, the longitudinal prestress is applied, and the fibre is preloaded. This state is defined as the reference state, as the strain amplitude is to be calculated. In this state the reference length l 0 can be defined as 0 =√ 0 2 + 02 (1) with y 0 from measurement and x 0 = x s . x s results from y s = 60 mm and = tan ( ) (2) where φ f is the present fibre angle specification of the sample. In step 1 the lateral displacement amplitude U is applied in lateral direction X . At the same time, a displacement V in longitudinal direction happens to keep the longitudinal prestress F y constant. Therefore, the deformed length of the fibre results to: 1 =√( 0 − ) 2 +( 0 + ) 2 (3) Based on that, the difference in length can be directly calculated as = 1 − 0 (4) Since the requirement of low strains is not fulfilled, with the help of the difference in length, the logarithmic strain ε log can be calculated as = ln (1 + 0 ) (5)

x 0

U

x s

V

y 0

l 0

l

1

y s φ f

Sample geometry

Step 0 Preload

Step 1 Displacement

Figure 6: Geometrical relationships on a fibre in the sample