1. Introduction

2. Climbing Drum Peel Test

3. Materials and Methods

4. Numerical Model

5. Results and Discussion

5.1. Experimental Results

Before the experiments were performed, the specimens were weighed to calculate their water uptake in mass percent. These results are given in Table 6.

It can be seen that an increase of humidity from the room climate (RC) conditioning to a moist conditioning doubled the moisture content, while the immersion in water again more than tripled the water content in comparison to the moist conditioning.

Experimental force-displacement curves are given in Figure 9a, while the averaged result is given in Figure 9b. Here, the arc-length parametrization introduced in [31] was used, which has the advantage of preserving certain characteristics in the force-displacement signal, e.g. magnitude and position of oscillations, and the ability to work on hysteretic data, as is the case for the loading-unloading experiment.

Figure 9. Experimental results of CDP test. (a) shows the individual results and (b) is the averaged result for each conditioning class using an arc-length based averaging scheme (cf. [31]) where the envelopes indicate statistical response corridors.

Figure 9. Experimental results of CDP test. (a) shows the individual results and (b) is the averaged result for each conditioning class using an arc-length based averaging scheme (cf. [31]) where the envelopes indicate statistical response corridors.

Based on the kinematics of the test set-up, the initial rise of the force signal ends after a specimen displacement of about 2 mm, once the drum is fully lifted, at a constant $F_w$ of 120 N. The force signal is unaltered until a specimen displacement of about 20 mm is reached, indicating a crack position right at the end of the PTFE foil. After the PTFE foil, the CoDico interface is yet fully intact, requiring an increase in the force signal to propagate the crack. All conditioning states show an initial incline zone, where the force has not reached a stable value. Reasons for this are boundary effects from the cooled down plastificate in the vicinity of the PTFE inlay, which are also visible in the later discussed optical analysis in Sec. 5.1.1. After about 32 mm of displacement a maximum, stable (on average) force level is reached with periodic force oscillations. These oscillations are caused by a stick-slip crack propagation, indicating that the crack front is not on par with the exact position of the center of the drum.

Significant differences in the force signal between the four conditioning states are evident. Dried specimens exhibit the lowest maximum force with an average $F_d$ of about 220 N, but have the strongest fluctuations in force signal, indicating pronounced erratic crack propagation, which could also be heard during the experiment. As moisture content increases, the maximum force initially increases, i.e. a $F_d$ of about $320$N for RC and 400 N for moist specimens, with fluctuations increasingly weakening. For the specimens immersed in water, however, the maximum force drops again to a lower value slightly above the RC value at around 340 N.

When the maximum displacement of 50 mm is reached the traverse reverts to its initial position, decreasing the force signal slightly below the initial $F_w$ value. Based on the procedure indicated in Figure 2, the enveloped area of the force-displacement diagram was determined numerically for all curves. The newly formed fracture area was measured, so that the critical energy release rate ${\mathcal{G}}_c$, or CERR, could be calculated by using Eq. 5. A statistical box plot for all conditioning states is given in Figure 10.

It can be seen that the lowest mean CERR was achieved by the dried samples with ${\mathcal{G}}_c=1.07·{10}^3\mathrm{J}/{\mathrm{m}}^2$, followed by RC with ${\mathcal{G}}_c=2.07·{10}^3\mathrm{J}/{\mathrm{m}}^2$ and the moist conditioning with ${\mathcal{G}}_c=2.40·{10}^3\mathrm{J}/{\mathrm{m}}^2$, indicating a better energy absorption for an increase in moisture. While the variation in experimental results is low for the dried and RC conditioning, an increased variation is observed for the moist conditioning. Contrary to the upward trend in CERR with increasing moisture content, a further increase of humidity in the case of the immersed samples weakens CERR with ${\mathcal{G}}_c=1.91·{10}^3\mathrm{J}/{\mathrm{m}}^2$. Possible reasons for this are discussed in the following sections.

5.1.1. Fractography

The images of the fracture surfaces are displayed in Figure 11.

A clear distinction between the four different conditioning states can be observed in the fracture surfaces. Most dominantly, the fracture surface of the dried specimen (cf. Figure 11a) shows an alternating fracture pattern with bright and dark regions, which repeats itself through all specimens. Here, the bright regions increase in size for an increased crack propagation (away from the PTFE foil). The number of oscillations correlate with the force drops in the force-displacement curve for dried specimens. This pattern is also visible in some of the fracture surfaces of the conditioned specimens at room temperature in isolated regions, as can be seen in Figure 11b. For elevated humidity levels (cf. moist and wet), the fracture surface does not show this pattern but instead consists of a homogeneous bright area. For all conditioning states, the first few centimeters after the PTFE foil reveal an altered fracture surface with a darker tint, indicating an initial influence zone in the vicinity of the PTFE foil. The length of the influence zone in the vicinity of the PTFE foil correlates with the region in the force-displacement diagram before a stable force value $F_d$ is reached, causing the force to steadily increases instead of suddenly reaching a stable value (cf. Figure 9). The interpretation is that in the vicinity of the PTFE foil a weaker consolidation occurs during the molding process due to the positioning of the LFT-D plastificate (cf. Figure 4). Since the outer surface of the plastificate already cooled down, a weaker consolidation is achieved between the Dico plastificate and the Co tapes. Once the plastificate fills the mold, still warmer material from the inside of the plastificate gets into contact with the areas further away from the PTFE foil, creating a better bond. Thus less energy is required in the area close to the plastificate position to propagate the crack, which explains the gradual increase in force further away from the PTFE foil until a uniform consolidation quality and consequently a stable energy rate is achieved.

Taking a closer look at the alternation pattern in the SEM in Figure 12 shows a good visibility of the alternating fracture pattern. It becomes clear that the alternating pattern is a repetitive switch between a brittle and ductile crack propagation.

In the SEM, the ductile fracture zone (cf. the magenta box or Figure 12d) is characterized by diffuse, fringed edges caused by excessive plastic deformation of the matrix material. Next to the polymer fringes, many fibers from the Co FRTP are visible. The upper sides of the fibers towards the detector are mostly blank with minor polymer residues, indicating a crack propagation along the fiber-matrix interface of the Co tape. The ductile areas in the fracture zone correlate with the bright sections in the images in Figure 11. This can be explained by a high degree of light dispersion due to the rough surface caused by the polymer fringes, so that light entering from the sides directs more light onto the camera’s sensor and creates a brighter surface. Consequently, the only bright fracture surfaces for the moist and wet specimens must be ductile.

The brittle fracture zone in the yellow box or Figure 12c is characterized by a flat and dull surface with slightly elevated plateaus with sharp edges. Contrary to the ductile fracture zone, blank fiber surfaces are not visible. Instead, fiber groves are visible, indicating that the fibers of the Co tape stuck to the Dico side when the crack propagated.

In the transitioning zone (cf. Figure 12b) it can be seen that the transition from ductile to brittle fracture occurs gradually, but over a short distance of a few microns. The fringes decrease in size until the flat and dull characteristics of the brittle zone are reached.

A direct comparison with the complementary fracture surface of the Dico face is made in Figure 13.

Similarly, to the discussed fracture surface on the Co side, a clear distinction between a brittle and ductile fracture zone is visible in the Dico side, indicated by diffuse, fringed edges for the ductile zone and a flat and dull surface for the brittle zone, respectively. Again, grooves of pulled out fibers are visible throughout the fracture zone. The remaining fibers in the brittle fracture zone seem to be surrounded by matrix material, indicating a good interface bonding (cf. Figure 13c). The fibers in the ductile fracture zone appear to have suffered more interface damage, while some of the matrix material remains on the fiber surface (cf. Figure 13d).

A comparison with the ductile fracture pattern within the Co tape in the RC, moist and wet specimens is shown in Figure 14, Figure 15 and Figure 16. Apart from the aforementioned finding that the specimens conditioned at room climate occasionally show brittle fracture zones (cf. Figure 14a), no systematic deviation in the fracture pattern within the ductile zones could be found. All conditioning states show continuous fibers with a debonded interface, with polymer residues dispersed along the fiber length. It can be seen that the connecting matrix material between two adjacent fibers shows pronounced plastic deformation in the form of polymer fringes or wrinkles.

Alternation between ductile and brittle fracture pattern is the reason for pronounced stick-slip crack propagation for dried specimens and for the large force oscillations. Brittle fracture is only rarely seen for specimens conditioned at room temperature and never for moist and wet cases. The explanation is that water absorption within PA 6 leads to a plasticization of the polymer, enhancing the chain mobility within the thermoplastic. Thus, plastic deformation is enhanced. Owing to the more brittle material behavior in dried specimens, crack propagation is hindered and an offset occurs between the crack tip and drum position. This offset increases normal stresses near the crack tip, which, at a critical value causes unstable crack growth so that the crack catches up with the current drum position, preventing crack propagation again. When the drum advances further, stable crack growth initially occurs until the difference between the positions is again large enough to cause a critical stress value and thus unstable crack growth. This behavior explains the stick-slip behavior and the alternation pattern in the fracture surface. In case of moisture plasticized polymer, such stress peaks can be relieved by plastic deformation, resulting in gradual stable crack growth and no stick-slip behavior. Owing to higher deformation energy in highly plastically deformed polymer, the fracture work performed increases, which is confirmed in experiments as moisture content increases. Exceptions are specimens with maximum moisture, which were immersed in water.

One possible cause of this could be hydrolytic processes that take place in contact with water at temperatures above $T_g$. During the hydrolysis process, water reactions break amide groups in polyamide molecules, which leads to a gradual degradation of the polymer structure. This leads to a reduction in molecular mass and viscosity, which has a negative effect on mechanical properties such as tensile strength and hardness. Since $T_g$ is decreasing due to absorbed water and the aging has been going on for a longer time at 50 °C, it can be assumed that such effects are occurring. To verify this, it would be useful to store samples in water at lower temperatures and compare the results. There also is a potential for hydrolysis occurring at the interface between the fibers and the matrix. Reinforcing fibers are commonly treated with sizing to enhance this interface, typically composed of silane or epoxy resin. However, it’s worth noting that both silane and epoxy resin are susceptible to hydrolysis.

5.2. Numerical results

General numerical studies:

The first generic study was the mesh sensitivity study for which the recorded simulation times are given in Table 7.

While the medium mesh density takes less than twice the computational effort of the coarse mesh, the fine mesh takes almost eight times as much run time to complete. Force-displacement plots are given in Figure 17.

Figure 17. Force-displacement curves for mesh study. The force signals were multiplied by 2 to account for the symmetry condition.

Figure 17. Force-displacement curves for mesh study. The force signals were multiplied by 2 to account for the symmetry condition.

Oscillations magnitudes decrease for a finer mesh. Specifically the coarse mesh overestimates these magnitudes significantly in contrast to the fine mesh, while the results of the medium mesh density are close to the fine mesh, indicating a mesh convergence. Qualitatively, the initial force rise shortly before $t=30$s is matched well between medium and fine mesh. The results for coarse mesh differ here. Considering run time increasing by a factor of 4 from medium to fine mesh, a medium mesh density is deemed sufficient for the following studies.

Mass scaling:

To find a suitable mass scaling factor, the ratio between kinetic energy per internal energy was evaluated in Figure 18.

It can be seen that the ratio reduces up to a factor of almost ten for a reduction of mass scaling for a factor of four. Interestingly, a mass scaling factor of 64 results in a great magnitude of oscillation in the interface separation section, which is not seen for the other cases. The simulation with a mass scaling factor of 256 took roughly $10000$s and the run time is about doubled for each reduction by a factor of 4, with a maximum run time of $160000$s for a mass scaling factor 1. The exact run times are given in Table 8.

To avoid large oscillations, while still reducing the run time, a mass scaling of 16 was chosen for the final simulations.

Material properties of Co and Dico:

Resulting force-displacement curves for different combinations of material properties for Co and Dico (cf. Table 4) are given in Figure 19, where Figure 19a represents the simulation with cohesive surfaces intact and Figure 19b represents the simulation without cohesive effects (no crack propagation, i.e. initially completely detached interface).

From Figure 19b, i.e. simulation results without cohesive effects, numerical oscillations can be seen which vary in magnitude depending on the material combination. Since no gravitational effects are considered, the oscillations must result from the reaction forces from the bending resistance of the deformed Co tape and subsequently from the induced vibrations in the explicit model. The force-displacment curves can be separated in two groups. The first group consists of cases in which the Co FRTP stiffness is unchanged at $25$GPa, while the other group is formed by the remaining complement with a Co FRTP stiffness of $50$GPa. The first group shows magnitudes of less than half the magnitudes of the second group, while these magnitudes do not vary significantly within each group, indicating that the stiffness properties of the bulk material (i.e. Dico) from which the flexible structure (i.e. Co) is ought to be peeled off are of secondary importance for the resulting reaction forces. Consequently, while it is important to model all material properties as accurately as possible and necessary, the primary focus should be on modeling the properties of the flexible Co-layer, as the CDP test simulation is particularly sensitive to these parameters. The same picture emerges when cohesive effects are considered, as is the case for Figure 19a. Here, the magnitudes of oscillations in the interface separation section ($>20$mm) is again significantly increased for a stiffer Co material, reinforcing the recommendation to be careful when modeling the flexible structure. The sensitivity on the chosen Co parameters may be reduced for a lower mass scaling factor (here a constant factor of 64 was used), which should be investigated in future studies.

Cohesive parameters:

The results for the numerical study on the influence of cohesive parameters are given in Figure 20.

It can be clearly seen that, in general, an increase in fracture toughness in the cohesive formulation results in an increase in the work required to propagate the crack, while an increase in damage initiation traction/stress results in slightly increased oscillations in the measured reaction force and a steeper increase at initial debonding without changing the area under the force-displacement curve. If the damage initiation traction/stress value is high enough, an increase in fracture toughness linearly increases the measured work. It is of interest that if the damage initiation value is too low, the work required to propagate the crack is reduced, which is evident in the curve for the combination of $\mathcal{G}=4·{10}^3$J/${\mathrm{m}}^2$ and $T=0.1$MPa. The reason for this can be explained by looking at the damage propagation at a displacement of $u=23$mm on the right side of Figure 20. It can be seen that for both fracture toughness values, the lowest damage initiation value of $T=0.1$MPa results in an advancement of the crack tip relative to the drum position, separating the Co tape from the Dico bulk material at an early stage of the simulation. Reasons could be either oscillations in the explicit simulations leading to stress peaks that advance the damage initiation value, or early failure in the shear mode due to in-plane stresses in the interface as the Co tape is pulled down.

During testing, the crack propagation is at the same level as the drum position, necessitating the selection of a sufficiently high value for the damage initiation parameter to prevent the crack from running ahead of the drum position. The numerical results show that a higher damage initiation value means that the crack tip is coherent with the drum position, which is confirmed by comparing the damage initiation stresses of $1.0$MPa and $4.0$MPa. Although the shape of the force-displacement curve at low damage initiation values appears to be more in agreement with the experimental result (cf. Figure 9), which is due to the structure consisting of an influence zone with reduced interfacial toughness leading to a smooth increase of the reaction force over a certain length, the reason is not accelerated crack propagation. Therefore, this effect must not be modeled by artificially reducing the damage initiation value.

Final simulation:

Based on the preliminary studies, the final simulations were run with a given set of cohesive parameters, while leaving the material properties of the Co tape and the Dico bulk material unchanged. In the previous studies it could be observed, that a single cohesive property assignment over the whole interface leads to a sudden jump in the force-displacement signal (cf. Figure 17 and Figure 19a), which is in contrast to the gradual incline as seen in the experimental results (cf. Figure 9b) between the displacement values of $d=20$mm and $d=32$mm. Consequently, the approach of a piecewise constant assignment over 21 segments was chosen, as illustrated in Figure 8. The final value of the fracture energy for each conditioning scenario was calculated only from the stable section between a displacement of $32$mm and $50$mm from the averaged curves to not include the initial incline zone, using the method depicted in Figure 3 and Eq. 4, respectively, with $\Delta u_0=18$mm. The CERR were determined to be $\mathcal{G}=1.0·{10}^3$J/${\mathrm{m}}^2$ for dried samples, $\mathcal{G}=2.0·{10}^3$J/${\mathrm{m}}^2$ for samples at room climate, $\mathcal{G}=2.7·{10}^3$J/${\mathrm{m}}^2$ for moist samples and $\mathcal{G}=2.07·{10}^3$J/${\mathrm{m}}^2$ for immersed samples, while the damage initiation stress was set to $T=1.0$MPa for all cases. Results of the final simulations are given in Figure 21.

In the initial force signal increased oscillations are observed that cannot be seen during the experiments. The reason for this is that at the beginning of the explicit simulation, oscillations build up that are not damped due to the lack of viscous properties in the material model. During interface formation, the oscillations continue with a slightly increased amplitude. The maximum separation force and energetic properties of the experiments are well captured for all conditioning states, indicating a high sensitivity to the cohesive parameter, especially to the separation energy. Only the moist condition simulation shows a slightly reduced rate of increase in the force signal (cf. Figure ??), which results in a later average stabilization of the force signal. A necessary requirement of the given modeling approach was to divide the influence zone after the PTFE foil into smaller segments with piecewise constant cohesive properties in order to achieve a steady slope of the force signal, as could be seen in the experiments. When the drum reaches the last segment, the force signal remains constant in an average sense. In general, it needs to be pointed out that the chosen approach of using cohesive surfaces without having a model for processes in the microstructure (e.g. humidity controlled plasticization) can only capture the overall shape of the force-displacement curves, while concurring oscillations, as it is the case in Figure ?? cannot be explained by the model. To enhance the modeling capabilities and deepen the understanding of aforementioned processes in the microstructure, such as the alternating ductile/brittle crack propagation or hydrolitic effects, a more complicated material model would need to be developed.

6. Conclusions

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