*2.4. Statistical Analysis*

Numerous techniques exist for statistical assessment of experiments. For this paper, two types of evaluation were used: (1) T-test for the test method effect where a single factor for two sets is assessed by evaluation of the *p*-value, which is compared to significance level α = 0.05; where for a *p*-value lower than α, the effect is statistically significant; and where the data sets have different mean values and (2) the Taguchi technique of design of experiments (DOE). DOE is the experimental strategy that facilitates the study of multiple factors at different levels. Questions concerning the influence of these factors on the variation of results can only be obtained by performing an analysis of variance (ANOVA).

In this ANOVA design, 2 factors representing both the materials and test temperature were chosen. Three qualitative levels were set for thermoplastic type (A), and two levels were set for the temperature (B). The full factorial experiment made it possible to also investigate the interactions AB of these two factors.

The full model was

$$Y\_{\rm ijk} = \mu\_{\mathcal{S}} + \kappa\_i + \beta\_{\bar{\jmath}} + (\mathfrak{a}\beta)\_{\bar{\jmath}\bar{\jmath}} + \varepsilon\_{i\bar{\jmath}k} \tag{5}$$

$$
\varepsilon\_{ijk} \sim N\left(0, \sigma^2\right) i = 1, 2, 3; \; j = 1, 2; \; k = 1, 2, \dots, 6. \tag{6}
$$

where *μ<sup>g</sup>* represents a grand mean term common to all observations, *α<sup>i</sup>* is the effect of the *i*th level of A, *β<sup>j</sup>* is the effect of the *j*th level of B, and (*αβ*)*ij* is the interaction effect of level *i* of A and level *j* of B combined. Also, a test for normality of residuals *ε* needs to be done.

#### **3. Results and Discussion**

#### *3.1. Test Method Evaluation*

A comparison of the methods was performed on the PPS material; see Table 4 and Figure 6. The statistical analysis of data using multiple t-tests showed that the AITM test method has a statistically significant effect (*p*-value = 0.011) when compared to pooled values of the two ASTM methods. It means that the AITM data were different from the other two sets. The results of the ASTM and ASTM mod procedures were not statistically different due to scatter of the data. The results confirmed the general rule that, with shorter distances (span lengths), greater forces are required for samples to fail. In general, it is not always possible to have one geometry available. Dimensions may be based on the actual design of the construction and simulation of a real loading.


**Table 4.** Comparison test method influence on interlaminar strength, σ<sup>r</sup> (MPa).

**Figure 6.** Measured interlaminar strength, σ<sup>r</sup> (MPa): the test method comparison using statistic evaluation showed a significant difference of the AITM method.

For the following experiments, the AITM test method was chosen. The main reason was to take sample geometry into account when setting the test fixture (span length).

#### *3.2. Thermoplastic Type and Temperature Evaluation*

The highest interlaminar strength was achieved on the set with the PAEK thermoplastic; see Table 5 and Figure 7.

For room temperature (RT), the average interlaminar strength of the PAEK set was to 18% higher than that for PPS and 16% higher than that for the PEEK set. The PAEK set also showed the smallest variance in measured values. Coefficient of variation (CV) for both test temperatures was less than 3%. The greatest variance of the measured values was evaluated on the PPS set (11%).

For cold temperatures (CT), compared to RT, the strength increased by approx. 10% for PPS, by 8% for PEEK and by 6% for PAEK. The values measured on the PAEK sets showed a very small coefficient of variation (less than 3%). For the PPS and PEEK sets, CV was about 10 %.


**Table 5.** Measured interlaminar strength, *σ*r (MPa).

**Figure 7.** Comparison of the interlaminar strength for 6 data sets, *p*-value 0.05.

A series of statistical analyses to compare the sets was performed. First, all measured data were analysed by ANOVA using DOE++ ReliaSoft (Version 1.0.7; ReliaSoft Corporation, MI, USA). The purpose was to evaluate the main factors and their effects on the results using a general full factorial design with multiple level factors—temperature and thermoplastic type. The Anderson–Darling test of residuals for model (5) proved the normality. The results of analysis for each factor in model (5) are shown in Table 6 in following order: A: thermoplastic type, B: temperature and AB: interaction interactions between both factors. Statistically significant effects of both testing temperature (B) and thermoplastic type (A) on measured strength values were found (*p*-values < 0.05). The interaction of effects (AB) was not proven. In a graphical form, the results are illustrated in Figure 8.

A complete evaluation of the differences for each parameter is shown in Table 7. *t*-tests applied for individual sets revealed that the PAEK interlaminar strength was higher than that for both the PEEK and PPS sets for both temperatures. No difference was proven between the PPS and PEEK sets. Cold conditions at −55 ◦C increased interlaminar strength in all investigated cases compared with RT conditions.


**Table 6.** ANOVA analysis of thermoplastic type and temperature influence on data results.

**Figure 8.** Graphical comparison of the interlaminar strength results: temperature and thermoplastictype influence.

**Table 7.** Statistical comparison of individual files using *t*-tests. D, files are different; ND, files are not different.


For better failure identification, the edges of the sample were painted in white colour. Valid failure occurred for all samples: a delamination in curvature occurred. Figure 9 shows the PPS-CT set failure modes. This set has a relatively high coefficient of variation (<10%). It can be seen from the figure that, at the lowest values, the failure occurred locally, and, in this set, specifically in the middle (sample 9) or at the outer radius (sample 10). For the other samples (6–8), the failure was over the entire thickness of the test sample. Figure 10 shows the PAEK-CT set samples. This set had a small coefficient of variation (2.8%), and similar failures were noted. Localization of the failures could be caused by clustering of the porosity in one place, by a manufacturing defect, or as a natural property of the material.

**Figure 9.** Examples of a typical failure mode for set PPS-CT: the set with the highest coefficient of variation, with the values given in the figure being strengths in MPa.

**Figure 10.** Examples of a typical failure mode for set PAEK-CT: the set with the lowest coefficient of variation, with the values given in the figure being strengths in MPa.
