Materials and Manufacturing
Polymer matrices used in this work were EPON™ 862 (Diglycidyl Ether of Bisphenol F)/Epikure W (purchased from Miller Stephenson), CYCOM® 977–3, and CYCOM® 5250–4 (supplied by Solvay). Epon 862 (Epoxy) was mixed at a mass ratio of 100:26.4 with Epikure W curing agent, while 977–3 (Tough Epoxy) and 5250–4 (BMI) were provided premixed and stored in the freezer under 0°F. The reinforcement used was 2-ply CNT yarn (supplied by Nanocomp Technologies).
A manufacturing process from previous work [23] was performed to prepare pullout samples. The pullout test is known to have a higher variance in results [24] than other testing methods due to uncontrollable factors such as fiber defects, surface, and circumference [23], [25]. However, controllable factors such as the fiber's embedded length into the matrix and fabrication methods [23] help reduce this variation if these are kept constant as much as possible. The horizontal mold used in this study, shown in Fig. 1, helps to keep an embedded length between 2.5 and 3.5 mm.
Pullout Test and IFSS Calculation
The ARES-G2, which can be utilized as a rheometer or DMA, was used in the orthogonal position to perform the testing. This equipment has tension clamps that allow testing on miniature samples in an enclosed environment. A custom fixture that accommodates the sample's geometry was used to complete the testing. This custom testing setup and the horizontal mold allow pullout tests on microscale samples multiple times using the same fixture. This custom testing setup can be seen in Fig. 2.
The process of manufacturing and testing nano-interfaces is challenging and slowly emerging for the development of high-performance components used in aircraft. The specialized equipment used in this study utilizes precise load readings, increasing the accuracy of the data. The custom testing fixture was manufactured via micromachining to achieve high geometrical precision.
To perform the pullout test, each sample was exposed to the desired temperature for 5 minutes before starting the test to ensure a constant equilibrium temperature. Then, the load was applied at the respective strain rate, and the force-displacement curves were recorded. The maximum force (Fmax), along with the measured fiber perimeter (p) and embedded length (l), was used to calculate the apparent IFSS using Eq. 1:
$$\tau IFSS= \frac{Fmax}{pl}$$
1
The fiber perimeter was determined from the hole left in the resin. This hole was measured with a Dino-Lite digital microscope.
Design of Experiments
To systematically study the correlation between multiple variables, a full factorial design was adopted to test various combinations using minimal materials quickly. The main factors to be studied are polymer resin (3 levels: Epoxy, Tough Epoxy, and BMI), strain rate (3 levels: 1.5, 2.5, 3.5 mm/min), and testing temperature (6 levels: different for each polymer resin, summarized in Table 1). This gives a total of 54 unique combinations. A power curve analysis determined the number of experimental runs to include in the design. To ensure a 90% power to detect a difference of 0.6 between each pair of temperature settings, the procedure requires 2 replicates, as shown in Fig. 3. This gives 108 experimental runs tested in a completely random order.
Thermal Analysis
The values of testing temperature are dependent on the resin's Tg. Dynamic mechanical analysis (DMA) was performed using an ARES-G2 (TA Instruments, New Castle, DE, USA) in tension to evaluate the thermomechanical properties of the resins. A gripping gap of 30 mm was used with a frequency of 1 Hz with an oscillation amplitude of 0.01% in the temperature range of -90°C to 425°C, depending on the resin decomposition temperature, with a ramp rate of 5°C/min. The Tg for Epoxy, Tough Epoxy, and BMI are 149, 237, and 295°C, as illustrated in Fig. 4 and calculated from the peak of the Tan(delta) curve.
Regression Spline Modeling of Interfacial Strength
The interfacial strength exhibits highly nonlinear behavior as a function of temperature. This behavior is expected to show differences with different substrate materials. To accurately delineate the different regimes of temperature behavior, the experiments tested the IFSS under 6 different temperatures, and the data is modeled using regression splines. Regression splines are a non-parametric regression modeling technique to closely model local non-linearities of the response function [26]. The approach divides the response range into equal-length segments specified by knots. It models each of these segments with cubic spline functions as the predictor of the model as a flexible representation to capture local non-linearities. The number and location of the knots are selected based on model selection criteria such as cross-validated mean square prediction error, Akaike Information Criterion (AIC), or adjusted R squared [26].
Testing temperature ranges from − 90°C to resin's Tg + 50°C, each representing temperature extremes (temperatures 1 and 6). To calculate temperatures 2 to 5, the temperature range was calculated by subtracting the temperature extremes; this value was divided into six equal parts to maintain the same temperature increment for each resin. The summary temperatures for each resin are summarized in Table 1.
Table 1
Testing temperatures for each resin
| Temperature (°C) |
1 | 2 | 3 | 4 | 5 | 6 |
Polymer Matrix | Epoxy | -90 | -32.2 | 25.6 | 83.4 | 141.2 | 199 |
Tough Epoxy | -90 | -14.6 | 60.8 | 136.2 | 211.6 | 287 |
BMI | -90 | -3 | 84 | 171 | 258 | 345 |