PSI - Issue 32

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

336

3

components was taken. Criterion of maximum deformations was also checked (strain intensities corresponding to the yield stress were taken as limiting ones). If the criterion in an element was met, the elastic modulus decreased there by a factor of 100 relative to the elastic modulus of the polymer. In doing so, the stresses were zeroed that corresponded to the failure of the appropriate element. If the element in which the criterion was met contained a contact node, the delamination between the fiber and the binder was realized (i.e. the corresponding mesh points were no longer connected). The fracture limit of the composite as a whole was determined based on the fulfillment of one of two conditions. I) the number of failed elements has reached 10 % of the corresponding material area (usually a binder); II) the number of detached nodes of one layer has reached 50 % of the number of nodes in this layer. If this took place the composite was considered as failed.

y

σ (Ра)

1,00E+008

8,00E+007

6,00E+007

4,00E+007

2,00E+007

ε

x

0,00E+000

0,00 0,01 0,02 0,03 0,04 0,05 0,06

z

Fig. 1. Computational domain with applied finite element mesh; tension across fibers; there is no detachment of contacting nodes

Fig. 2. Engineering stress-strain of neat PEEK

When stretched along the fibers, the displacements along the x ( u ) axis were set stepwise on the right and left at the boundaries of the computational domain (Fig. 1). Displacements along the y ( u ) axis at these boundaries were equal to zero, while the lower and upper boundaries remained free. In addition, when stretching along the fibers, the conditions for displacement equality were set along the y -axis at intermediate points between the main contact nodes (before delamination between the binder and the fibers took place). This was motivated by avoiding intersection of fibers and the binder within the finite element mesh during compression in the transverse direction due to Poisson effect. The conditions were similar to those described in Bochkareva et. al. (2020). After the delamination, only the y -axis alignment conditions were employed. Since delaminated fibers moved along the y -axis in the opposite direction and pressed the delaminated binder, then the conditions at the lower edge of the fibers in the lower half of the computational domain were set. In the upper half of the computational domain they were specified at the upper edge of the fibers. When stretching across the fibers (Fig. 1), stepwise displacements along the y ( v ) axis were set at the upper and lower boundaries of the computational domain. Displacements along the x axis at these boundaries were equal to zero, while the right and left boundaries remained free. The effective tensile modulus was determined as the ratio of area-averaged effective stresses over deformations. Figure 3 shows the displacement surfaces along the y ( v i ) axis where delamination take place. One can see tension along the fibers (a) and across ones (b). One i -th step is depicted. Failure is taken into account. Fibers/polymer ratio was equal to 60 – 40 vol. %. When stretched along the reinforcement direction the polymer matrix is firstly deformed and failed (Fig. 3, a). Since the fibers are stronger, they are fractured last. Therefore, imperfect contact (the number of contact points and the level of delamination stresses) did not affect the elastic modulus. The latter is determined by the percentage of fibers. Since failure took place when 50 % delamination of one carbon fiber layer occurred, the level of delamination stresses would affect the strength properties of the composite that resulted from delamination (Fig. 4). The maximum adhesion level was taken to be the tensile stress corresponding to the yield point. Therefore, the change in the adhesion level was determined by the ratio of the delamination stress ( σ a ) over the yield point ( σ Y ). Figure 5 shows the dependences obtained when stretching across the fibers, while the level of adhesion was equal to the yield stress of the matrix. With decreasing the level of adhesion the dependences remained the same, but the limiting stresses decreased proportionally. An increase in the number of contacting nodes gave rise to the same results as in the case of ideal adhesion. With the number of contacts above 130 the curves coincided. It is seen that with decreasing the number of contact points the tensile strength decreased.