PSI - Issue 32

S.A. Bochkareva et al. / Procedia Structural Integrity 32 (2021) 334–339 Author name / Structural Integrity Procedia 00 (2019) 000–000

338

5

2.2. Effective properties of composites under bending Further, the obtained properties were used to simulate the stress-strain state of composites during bending as effective characteristics of layers reinforced with carbon fibers (besides the shear modulus). When modeling bending, the delamination was not introduced. Therefore, it was taken into account only through the calculated effective properties of monolayers. Various lay-outing patterns were investigated: [0°/0°], [90°/90°], [0°/90°] as well as layers of biaxial (weaving) fabric. In the case of [0°/0°] layout the polymer layers alternated with carbon fiber layers directed along the x -axis (Fig. 1); in the case of [90°/90°] the fibers were directed along the z -axis; in the case of [0°/90°] – carbon fiber layers alternated: ones being oriented along the x -axis; then a polymer layer; then a fiber layer oriented along the z -axis. Then the sequence was repeated. In the case of [biaxial] fabric, the polymer alternated with layers of carbon fibers directed along the x - and the z -axis, which imitated the fabric. Then the sequence was repeated. The component ratio (carbon fibers and binder) in the composite was: 40 vol. % for the fiber, 60 vol. % for the– the matrix. When calculating the effective properties of a layer with carbon fibers, the polymer filled the free space between unidirectional fibers (it was 20% in one layer, while it was 40% for the fabric). Thus, the ratio of carbon fiber and polymer layers in a specimen would be approximately 50 ÷ 50 vol. % (in the case of fabric it was 60 ÷ 40 vol.%). In doing so, 11 layers of carbon fibers would contain about 10 % of the total amount of polymer (in the case of fabric it was 20 %). The flexural stress and the relative bending deformation of the composites were determined by the formulas: , where F – applied force, b – specimen width y – deflection of the neutral axis, h – specimen height, L – distance between supports (span). The force was calculated by summing over the obtained stresses multiplied by the load application area. Reaching of yield stress (strength) within 10 % of the specimen was taken as a fracture criterion (to terminate the calculation). Modeling of three-point bending was carried out according to the scheme in Fig. 7 (ISO 14125: 1998). 2 bh LF = σ 2 3 , 2 L hy = ε 6

b

σ b (Pа)

1,00E+009

8,00E+008

a

PEEK 90°/90°_100% 0°/90°_100% 0°/90°_20% biaxial_100% biaxial_20% 0°/0°_100% 0°/0°_20%

6,00E+008

4,00E+008

2,00E+008

ε b

0,00E+000

0,00 0,01 0,02 0,03 0,04 0,05

Fig. 7. Computational domain diagram for modeling of 3P-bending

Fig. 8. Dependences of flexural stress vs relative bending deformation corresponding to different CF layouts and adhesion level (100% and 20 %)

The boundary conditions were set as follows: for the corner points A and B at the bottom: displacements along the y ( v ) axis were zero, i.e. the sample support condition: ν =0 At the point C, displacements along the x axis (u) were zero, which enabled to maintain symmetry: U=0