The data from the mechanical testing was analysed within a statistical analysis software, Minitab v19 (Minitab LLC, USA). An Analysis of Variance was performed to provide the size of each parameter effect (F-Value) and the significance of each parameter effect (P-Value). The results of the statistical analysis for the UTS and E are given in Table 4 and 5 respectively.
Table 4 ANOVA Results for Main Parameters and All Interactions for UTS.
ANOVA Analysis Results for UTS
|
Parameter
|
F-Value
|
P-Value
|
|
Parameter
|
F-Value
|
P-Value
|
Main Parameters
|
|
|
|
3-Way Interactions
|
|
|
Matrix Material (M)
|
169.89
|
0.000
|
|
M*R*L
|
9.30
|
0.000
|
Reinforcement Material (R)
|
855.22
|
0.000
|
|
M*R*O
|
3.86
|
0.024
|
Number of Fibre Layers (L)
|
11,483
|
0.000
|
|
M*L*O
|
19.00
|
0.000
|
Fibre Orientation (O)
|
8.25
|
0.005
|
|
R*L*O
|
0.75
|
0.473
|
2-Way Interactions
|
|
|
|
4-Way Interaction
|
|
|
M*R
|
9.42
|
0.000
|
|
M*R*L*O
|
10.90
|
0.000
|
M*L
|
6.87
|
0.010
|
|
|
|
|
M*O
|
12.56
|
0.001
|
|
|
|
|
R*L
|
297.61
|
0.000
|
|
|
|
|
R*O
|
1.52
|
0.223
|
|
|
|
|
L*O
|
2.60
|
0.110
|
|
|
|
|
Table 5 ANOVA Results for Main Parameters and All Interactions for E.
ANOVA Analysis Results for E
|
Parameter
|
F-Value
|
P-Value
|
|
Parameter
|
F-Value
|
P-Value
|
Main Parameters
|
|
|
|
3-Way Interactions
|
|
|
Matrix Material (M)
|
6.90
|
0.010
|
|
M*R*L
|
33.30
|
0.000
|
Reinforcement Material (R)
|
1,338
|
0.000
|
|
M*R*O
|
137.46
|
0.000
|
Number of Fibre Layers (L)
|
2,733
|
0.000
|
|
M*L*O
|
55.09
|
0.000
|
Fibre Orientation (O)
|
96.83
|
0.000
|
|
R*L*O
|
8.66
|
0.000
|
2-Way Interactions
|
|
|
|
4-Way Interaction
|
|
|
M*R
|
114.25
|
0.000
|
|
M*R*L*O
|
99.16
|
0.000
|
M*L
|
17.63
|
0.000
|
|
|
|
|
M*O
|
68.73
|
0.000
|
|
|
|
|
R*L
|
76.28
|
0.000
|
|
|
|
|
R*O
|
64.96
|
0.000
|
|
|
|
|
L*O
|
37.52
|
0.000
|
|
|
|
|
The Pareto charts for the standardised parameter effects for UTS and E are given in Figures 3 and 4.
As can be seen from Tables 4 and 5, and Figures 3 and 4, for both UTS and E, all four main parameters are statistically significant (Standard Effect is higher than the significance line for 95% significance) and can control the mechanical response of the material, although the number of layers exerts the greatest influence on both UTS and E, and is significantly more important than any other parameter. This is as expected since the UTS and E of the reinforcement fibres (Table 1) are at least an order of magnitude greater than those of the polymer matrix materials, and, via the Rules of Mixtures (Equations 1 and 2), have increased effect in increasing the mechanical properties as their volume fraction (f), e.g number of layers, is increased.
It is surprising that the type of reinforcement has such a small effect on the mechanical response, with the Standardised Effect on UTS for ‘reinforcement’ being only 27% of that for ‘layers’ (Figure 3), although for E, the effect of reinforcement type is more significant, being 70% of that for ‘layers’ (Figure 4).
The type of matrix material has been shown to have very little effect on the mechanical response, with the Standardised Effect for ‘matrix’ being only 12% of that for ‘layers’ for UTS (Figure 3) and only 5% of that for ‘layers’ for E (Figure 4). Also, for E, the ‘matrix’ parameter is only just significant (2.63) compared to the significance limit of 1.98. This is also in agreement with the mechanical performance of the elements forming the composite. UTS for Nylon and Onyx are similar (36 and 51 MPa), with Onyx only 42% higher than Nylon; whereas for E, there is a 157% increase for Onxy over Nylon (3.4 vs 1.6GPa), hence, the smaller statistical effect on UTS, and larger effect on E, of selecting Onyx over Nylon as the matrix material. Thus, lower-cost, and more abundant Nylon matrix material offers similar performance to the more expensive Onyx.
Fibre orientation, within the bounds of these trials (0,45 and 0,90 bi-directional orientations) has very little impact on either UTS (2.87 at significance limit of 2.0) (Figure 3) or E (9.84 at significance limit of 1.98), being only 3% (UTS) and 19% (E) of the standardized effect of ‘layers’.
Table 6 below shows the results for the mechanical performance of the highest strength / highest stiffness samples (using 12 layers of reinforcement and (0,90) reinforcement deposition). These are compared to the theoretical values obtained using the Rule of Mixtures (ROM) as given in Equations 1 and 2.
Where f is the fibre volume fraction in the composite, UTSf and UTSm are the UTS of the fibre and matrix respectively, and Ef and Em are the flexural moduli of the fibre and matrix respectively.
Table 6 Comparison of Experimental Values for UTS and E Against Calculated Values. Δ is UTS (Experimental) as a % of UTS (ROM).
Composite
|
UTS (MPa) Experimental
|
UTS (MPa)
ROM
|
Δ(%)
|
E (GPa) Experimental
|
E (GPa) ROM
|
Δ(%)
|
Nylon-GF-12-90
|
220 ± 4
|
273
|
81
|
6.4 ±0.1
|
8.3
|
77
|
Nylon-CF-12-90
|
249 ± 13
|
429
|
58
|
13.02 ± 0.06
|
21.24
|
61
|
Nylon-KF-12-90
|
158 ± 8
|
282
|
56
|
7.52 ± 0.07
|
10.26
|
73
|
Onyx-GF-12-90
|
212 ± 5
|
267
|
79
|
7.3 ± 0.1
|
9.3
|
78
|
Onyx-CF-12-90
|
278 ± 8
|
387
|
72
|
15.5 ± 0.3
|
21.6
|
72
|
Onyx-KF-12-90
|
161 ± 4
|
276
|
58
|
8.00 ± 0.07
|
10.99
|
73
|
The selection of parameter levels for main parameters can be informed from the Main Effects Plots (Figures 5 and 6). These indicate the change in observed average (over all samples) mechanical response as a result in change in parameter level. Tables 7 and 8 show the change in average UTS (as a % of the global average UTS) and change in average E (as a % of the global average E for each of the parameter levels. From Figures 5 and 6 and Tables 7 and 8, it is clearly evident that the results for UTS and E follow similar, but not identical, trends.
For ‘matrix’ parameter, selecting Onxy over Nylon does provide a small increase in both UTS and E, but this is only from 5.58% below global mean to 11.66% above (UTS) (Table 7) and from -1.55% below global mean to 1.55% above (E) (Table 8). This is due to the higher UTS and E values for Onyx over Nylon (Table 1). Thus, optimal properties are achieved by selecting Onyx over Nylon as matrix material, although, as discussed later, the improvements in mechanical response may not outweigh the extra cost incurred.
For ‘reinforcement’ parameter, there is a large effect in moving from GF to CF, with large increases in both UTS (from 0.14% below global mean to 22.06% above – Figure 4 and Table 7) and E (from 0.12% below global mean to 42.75% above – Figure 5 and Table 8). There is a nearly equally sized decrease in properties for both UTS and E when selecting KF, shifting to 22.94% below global mean (UTS) and 16.98% below global mean (E). The increase in properties in selecting CF over both GF and KF is due to CF having the highest performance of any of the reinforcement materials (Table 1). None of the composites performed to the predicted level (Table 6), with UTS being 58-81% of predicted and E being 61-78% of predicted. The lower performance agrees with previous work by Dickson et al [12], where the reduced performance was concluded to be due to failure of the bond between the fibre and matrix, leading to fibre pull-out. The poor performance of KF over GF, despite its higher mechanical properties over GF (Table 1), also agrees with the findings of Dickson et al [12], where fibre pull-out was more prevalent for KF, and, due to the pulled fibres being residue free, are thought to be weaker bonded to the matrix than CF or GF, which both left residue bonded to the fibres. Thus, optimal properties are obtained by selecting CF as reinforcement material.
The ‘layers’ parameter has the largest influence over the mechanical properties. From the Main Effect plots for UTS and E (Figures 5 and 6), moving from 4 layers to 12 layers provides an improvement in UTS from 46.52% below global mean to 46.56% above global mean; the same change results in raising E from 30.76% below global mean to 30.76% above global mean. The inability to attain the predicted performance values (Table 6), may also be due to increasing porosity levels observed between fibre and matrix for increasing fibre fraction [12], thus limiting the effectiveness of increasing fibre content (number of layers). Thus, optimal properties are obtained by using a higher number of reinforcement layers, and, as we see later, is an affordable choice.
The Main Effect plots also show a marginal improvement in moving from a (0,45) pattern to a (0,90) pattern, with UTS increasing from 1.23% below global mean to 1.27% above global mean (Table 7), and E increasing from 5.78% below global mean to 5.80% above global mean (Table 8). This small effect may be due to the similarity between the two lay-up patterns. Higher performance was achieved by Klift et al [23], achieving 400 MPa (σ=20.35) UTS for Nylon-Carbon samples, using a concentric ring lay-up, with our Nylon-CF only achieving 249±6 MPa. Although the results are not directly comparable as Klift et al [23] used an increased number of reinforcement layers of 16, compared to 12 in our research. It is clear though from this research that a (0,90) pattern does help to optimise the UTS and E and has no significant effect on the cost (as we see later).
Table 7 The differential mean UTS values (as a % of the global average UTS - dotted line on Figure 5)
|
Parameter
|
Level
|
Matrix
|
Reinforcement
|
Layers
|
Orientation
|
1
|
-5.68%
|
-0.14%
|
-46.52%
|
-1.23%
|
2
|
11.66%
|
22.06%
|
46.56%
|
1.27%
|
3
|
|
-22.94%
|
|
|
Table 8 The differential mean E values (as a % of the global average E - dotted line on Figure 6).
|
Parameter
|
Level
|
Matrix
|
Reinforcement
|
Layers
|
Orientation
|
1
|
-1.55%
|
-0.12%
|
-30.76%
|
-5.78%
|
2
|
1.55%
|
42.75%
|
30.76%
|
5.80%
|
3
|
|
-16.98%
|
|
|
The tensile and flexural stress-strain behaviour for the six composite material combinations (for the highest UTS samples (12 layers and 0,90 lay-up orientation) are given in Figures 7 and 8. It can be seen that the tensile and flexural properties are determined primarily from the reinforcement type. The failure behaviour under tensile load is similar for all material combinations, with fairly constant modulus up to the failure point and then rapid failure. This is due to the UTS of the fibres being significantly higher than that of the matrix materials (Table 1), so once fibre failure occurs, the matrix fails very rapidly. Both the CF and GF failure occurs at around the nominal strain (1.5 and 2.1% respectively), but the KF samples fail below their nominal value (2.7%), failing at 1.9%, supporting further that the failure mechanism is a combination of fibre breakage and fibre pull-out as described earlier. This is further supported by the behaviour of the KF reinforced samples under compressive load (Figure 8), having a lower flexural modulus than GF samples at higher strain, despite the nominally higher modulus (Table 1).
The Cost to Strength Ratio ($/MPa) for UTS, and UTS values for each of the 24 composites and for the un-reinforced Nylon and Onyx (average of 5 samples for each) is given in Figure 9. The Cost Ratio ($/GPa) for E, and E values for each of the 24 composites and for the un-reinforced Nylon and Onyx (average of 5 samples for each) is given in Figure 10. The cost for manufacture used to calculate the Cost Ratio values was calculated using the material usage (matrix and reinforcement) recorded from the Mark Two printer after each build (and divided by 5 to obtain cost / part).
It can be deduced from the analysis of cost verses strength (Figure 9) and stiffness (Figure 10) that the lowest cost to strength ratio (most desirable) is achieved using a GF reinforced Nylon with 12 layers and (0,90) lay-up, at 0.0221±0.0002 $MPa-1, and achieving 220±2 MPa UTS (79±1 % of highest UTS, achieved using CF reinforced Onyx with 12 layers and (0,90) lay-up. The equivalent material using (0,45) only achieves a UTS of 187±4 MPa (67±1 % of highest UTS) at a cost to strength ratio of 0.0261±0.0005 $MPa-1. The highest performing composite, 278±4 MPa (CF reinforced Onyx with 12 layers and (0,90) lay-up) has a cost to strength ratio of 0.0303±0.0004 $MPa-1, 37±2 % higher cost than the optimum cost to strength ratio material. Thus, for a 21±1 % increase in strength, a 37±2 % increase in cost is incurred, making the most cost-effective material option highly attractive for all but the most demanding applications.
The stiffest material is CF reinforced Onyx with 12 layers and (0,90) (15.5±0.3 GPa), and is 2nd most cost-effective material (0.49±0.06 $GPa-1) (Figure 10). The most cost-effective material is GF reinforced Nylon with 12 layers and (0,45) (0.40±0.02 $GPa-1), which is 20±3 % lower cost but only retains 39±2 % of the stiffness of the stiffest material. It is therefore only practical to use this most cost-effective material where high stiffness is not a design requirement. Only three materials have E>10 GPa, and these are all CF reinforced with 12 layers. It is therefore practical to use the stiffest material (CF reinforced Onyx with 12 layers and (0,90)) for all but the most cost-sensitive applications. KF does not provide any technical advantage over CF and is also not competitive economically.