PSI - Issue 32

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

337

4

a

b

v i (m)

v i (m)

x (м)

x (m)

y (м)

x (m)

y (m)

y (m)

Fig. 3. Т he surfaces of displacements along the y ( v i ) axis where delamination take place; tension along the fibers (a) and (b) across them; one i -th step with taking failure into account; fibers/polymer ratio of 60 – 40 vol. %

PEEK+C( 80%)

σ p (Pа)

4,00E+009

PEEK+C( 60%)

σ i (Pа)

50000000

3,00E+009

40000000

30000000

12 24 48 96 130

PEEK+C(60%) PEEK+C(80%)

2,00E+009

20000000

1,00E+009

10000000

ε i

σ a /σ t

0

0,00E+000

0,000

0,002

0,004

0,006

0,008

0,0

0,2

0,4

0,6

0,8

1,0

Fig. 5. Dependences of stress over the strain intensity; tension of composites along the y -axis (across the fibers); the number of contact points is varied (with a ratio of carbon fibers to PEEK 80 ÷ 20 vol. % and 60 ÷ 40 vol. %)

Fig. 4. Variation of tensile strength ( σ p ) of composites under tension along the x -axis (along the fibers) as a function of delamination stress level; ratios of carbon fibers and PEEK was equal to 80 ÷ 20 vol. % and 60 ÷ 40 vol. %

a

b

c

τ (Pа)

u (m)

40000000

30000000

12 24 48 96 130 ε τ

20000000

x (m)

y (m)

10000000

0

0,000

0,005

0,010

0,015

0,020

Fig. 6. Results obtained at shear along the fibers y -axis: (a) – stress-strain diagram with a various number of contacting nodes; (b) – computational domain with finite element mesh; (c) – displacement surfaces along the x -axis

The effective shear modulus along the fibers was determined as the ratio of the total shear stresses at the upper boundary of the computational domain over the shear strains. The results for the carbon fiber/polymer ratio 60 ÷ 40 vol. % obtained under shearing are shown in Fig. 6. The number of contact points affected both the shear modulus and the strength (Fig. 6, a). With decreasing the number of contact points the shear modulus of the composites decreased by about 6 times, while the shear strength decreased accordingly (Fig. 6, a). Figure 6 (a) shows the dependences obtained when the adhesion level was equal to the yield stress of the polymer. With decreasing the adhesion level the limiting stresses decreased proportionally. It can be seen in fig. 6 (b, c) that fracture initiated from the side surfaces. In the problem under consideration a discontinuity model was introduced through the number of contacting point. This substantially affected the effective properties of the composites (as was shown above).