Does flute angle influence box performance?

In the production of boxes, it is customary to align the flutes vertically, corresponding to a 0° flute angle. This configuration is widely believed to yield optimal compressive strength, despite existing evidence from corrugated flute boards and boxes that challenge this assumption. The present study investigates the hypothesis that non-vertical flute angles do not significantly compromise box compression strength and may potentially offer enhancements in other performance characteristics. Regular slotted container boxes (385 × 238 ×  300 mm) constructed from single wall C-flute board were used in this study. Ten flute angles were selected for box level testing: 0°, 5°, 7.5°, 10°, 12.5°, 15°, 20°, 30°, 45° and 60°. Samples of converted board were subjected to edge crush testing (ECT) following TAPPI T-811 and four-point-bending following TAPPI T-820. Box crush testing (BCT) followed NZS 1301.800 2006 (New Zealand Standard). Component testing results were consistent with previous studies. Outcomes showed a general linear reduction in ECT with increasing flute angle, and nonlinear relationships between flute angle and bending force and stiffness. At the box level, peak load did not decline significantly between 0° and 45°, however 60° flute angles had significantly lower peak loads (α = 0.05). At certain angles, notably 10° and 30°, less variation in peak load was observed. BCT force and stiffness of the box significantly improved in terms of median and variation at 10° and 30°. Therefore, a flute angle of less than 45° does not significantly reduce compression strength.


Introduction
Box production typically involves aligning flutes vertically with respect to the applied load, which is intuitively thought to offer maximum compressive strength.This is supported by experimental studies showing that boxes with vertically aligned flutes have 20% higher compression strength than horizontally aligned flutes [1] and corrugated board edge crush strength and bending force are generally highest in this direction [2][3][4].Since boxes are themselves a hierarchical structure, the performance of Recent investigations reveal further insights into component, board, and box behaviour.While McKee's approach is widely used industrially as it gives a simple, reasonable estimate of box, modern, more advanced techniques which account for aspect ratio and component properties give more accurate results.Such approaches have been reported as reducing error from between 8-15%, to around 6% [9].This requires more detailed quantification of the orthotrophic strain in a material, as recently shown, an elegant method to achieve this involves use of ECT in both standard CD, but also at 45° in order to determine all strains for the material while monitoring with DIC (digital image correlation) and video extensometry [10].A similar approach by the same authors involved creating a model to evaluate the compressive strength and stiffness of board in the CD, and validated this with experimental testing, monitored with DIC.This showed good agreement and that it was possible to use this to estimate the effects of changing different layers within the board.It also showed the importance of using optical strain measurement given the inherent compliance in test machine crossheads [11].An analytical study of bending stiffness of five-layer corrugated board based on paper properties and board geometry showed that liners contributed almost all the bending stiffness of the board, at least in MD, where the fluting medium contributed less than 1% to the overall bending stiffness of the board.For asymmetric board, the orientation of the board during testing influenced the bending stiffness, as would be expected.Similarly, alterations to liner thickness or defects greatly influenced the board performance [12].A modelling and numerical homogenisation approach exploring effects of grammage on ECT and BCT showed paper configuration is important.The influence of grammage changes depends on board asymmetry; changing the heaviest liner had the largest effect, and increasing fluting weight reduces the sensitivity to liner variation [13].A simplified modelling approach for ECT of multi-layered board, included tensile testing of paper at 45° to generate validation data for the analytical models [14].A machine learning approach to estimate ECT based on paper and board characteristics appeared promising and included training data which accounted for loading at different angles.Interestingly, the different flute profiles in the training data had different proportional changes in ECT as flute angle changed [15].Other recent studies emphasise the importance of reducing variability in the data any the corrugated board will also depend on orientation of its component papers.In most vertical flute boxes, practical considerations dictate that the fibres of the component papers run perpendicular to the flutes due to the corrugating process.Therefore, the component papers are arranged directly opposite to the direction that they should be to provide maximum compressive strength in line with the flutes.Rotating the liners and medium by 90°, placing the fibres of the paper in line with the flutes (termed linear corrugating) improves both short and long-term box performance as the paper is better able to resist top-to-bottom loading and suffers less from hygroexpansivity [5].
While box performance is often quantified in terms of top-to-bottom crushing resistance, boxes experience multi-axial loading in service due to interactions with other boxes when palletised, interactions with the box contents and general shock and vibration through the supply chain.Both machine and cross direction properties of the component boards and papers have also been shown to play an important role in box performance [5][6][7].The concept of optimising geometric means of the component paper performance has also been suggested as an avenue to maximise board performance [6].
Limited box-level studies have explored the performance of boxes whose components are not oriented either vertically or horizontally.Maltenfort examined the performance of fruit trays which were cut at a 45° angle in order to reduce wastage of board for the design in question.The fruit trays were unexpectedly found to have superior compression test performance compared to standard trays with vertically oriented flutes [8].Curatalo examined the compressive strength of boxes for which flute angle ranged from 0° to 90° in 15° increments.Compression strength was found to increase nonlinearly as corrugations approached the vertical (i.e.closer to 0°) and parallel to the applied force, and concluded that end-to-end compression strength could be increased in a greater proportion than the corresponding reduction in top-to-bottom compression strength [7].At the board level, Jamsari tested board samples (with angles 0°, 30°, 45°, 60°, 90°) in 4-point bending tests and found that the 30° and 45° samples improved bending stiffness compared to 0° without significantly affecting the maximum bending force [4].As box performance is substantially influenced by panel bending, this finding suggests that angled flutes could bring performance benefits.estimates of box and board performance are based on, be this paper properties, ECT or BCT [16,17].
Considering the practical difficulties of rotating paper components at industrial scale, this investigation will explore possible strategies to improve box performance within the constraints of standard corrugated board as a source material.One option is to rotate the board itself during die cutting and create boxes with angled flutes.Vertical flutes were defined as 0° flute angle and horizontal flutes as 90° flute angle.We tested the hypothesis that non-vertical flute angles do not significantly reduce box compression strength and may in fact confer advantages in other aspects of performance.Our goal was to confirm these phenomena at the box level using mechanical testing in order to provide data to inform subsequent modelling or experimental investigations.Considering that the studies referenced above use relatively large incremental angles (i.e.15°, or 30°), we evaluated 10 flute angles that ranged from 0° to 60°, mainly concentrated within 0 to 20° in order to gain insights which may not have been captured previously.We conducted box crush testing (BCT) at each flute angle, along with edge crush testing (ECT), and four-point bending of the component board.

Materials and methods
R e g u l a r s l o t t e d c o n t a i n e r ( R S C ) b o x e s (385 × 238 × 300 mm) were used in this study, constructed from single wall C-flute board (200 gsm Kraft linerboards with 150 gsm semi-chemical medium) supplied by a New Zealand papermaker.The geometric characteristics of the board are given in Table 1 and the details of each paper component are listed in Table 2.
Ten flute angles were selected for box level testing: 0°, 5°, 7.5°, 10°, 12.5°, 15°, 20°, 30°, 45° and 60°.These boxes were created using a cutting table (Zünd) and were stored in a dry environment in a flat packed state to prevent damage prior to testing.They were assembled using standard brown packing tape to hold top and bottom flaps in place.
Component testing was conducted in parallel with the box crush testing in order to enable comparison of predicted BCT via the McKee equation (Eq. 1) [18] with experimentally measured BCT.This testing followed the procedure described by Jamsari [4] involving edge crush testing (ECT) and four-point bending testing in the machine direction (MD) and cross direction (CD).Three box blanks of each angle were reserved for ECT and four-point-bending, and broadly equal numbers of samples were cut from these to distribute variation equally during testing.Samples were cut from box blanks in order to test material most representative of the boxes themselves; sampling locations were chosen to exclude any of the creased or regions close to the creased areas.Following cutting, samples were stored in controlled conditions at 23 °C at 11% RH for at least 48 h and then 50% RH for at least 24 h prior to testing in accordance with the TAPPI T-402 standard.At least ten ECT, vertical, and horizonal four-point bending samples were tested at each flute angle.

Theoretical BCT calculation
The component property results were also used in the McKee equation [18] as a comparison with experimental data.
where BCT and ECT are the box and edge crush forces (in N), D MD and D CD are, respectively, the machine direction and cross direction stiffnesses (N m), and Z is the perimeter of the box which is 1.24 m in the current study.

Edge crush test (ECT)
Samples for ECT were cut from converted board panels using an Epilog Fusion M2 laser cutter into  38.1 × 50.8 mm rectangles following the TAPPI T-811 standard (Fig. 1).Samples were cut at each flute angle (relative to the vertical edges of the box) referred to above.Approximately 6 mm from each end of the sample was reinforced with paraffin wax prior to conditioning to prevent failure in these regions during testing.
The experiment was run using a texture analyser (TA.XT Plus, Texture Technologies Corp.) with a constant displacement speed of 12.5 mm min −1 .At the start of each test, two metal blocks were used as guides to ensure that the sample was held vertically.These were manually removed when the force was between 22 and 67 N as indicated in TAPPI T-811 standard.ECT force was calculated by dividing maximum force by sample width, (50.8 mm).Typical force-displacement curves for ECT are shown above in Fig. 2.

Four-point bending
Samples for four-point bending (260 × 50.8 mm samples in accordance with TAPPI T-820) were cut from converted box panels using the laser cutter.Samples for bending tests were cut relative to the vertical and horizontal edges of the box for each of the 10 flute angles, Fig. 1.As with ECT, the texture analyser was used to apply a constant displacement speed of 12.5 mm min −1 to the samples.The centre deflection of the sample during the test was measured using a laser displacement sensor.Following testing, a graph of force against centre deflection was plotted for each trial and the bending stiffness calculated using Eq.2:  where D is the flexural stiffness (N m), Δ is the slope of the force against centre deflection graph (N m −1 ), L bottom is the distance between both the bottom anvils (m), w is the width of the sample (m) and a is the distance between the bottom and upper anvil (m) at either end.
Sample performance was assessed in terms of peak bending force and bending stiffness.Typical force-displacement curves for bending stiffness tests are shown above in Fig. 3.

Box crush testing (BCT)
Boxes were tested according to NZS 1301.8002006 (New Zealand Standard) [19].Ten boxes (the recommended minimum number of samples for this standard) of each flute angle were used in the present study to maximise the number of flute angles that could be tested.The boxes were conditioned for 48 h at 23 °C and 50% RH to ensure consistent equilibrium moisture content prior to testing.A Wiedemann 60CS universal tester fitted with fixed platens was used to compress boxes at a crosshead speed of 10 mm min −1 until failure.
As shown in Fig. 4, the highest load prior to failure was recorded as the BCT load (also known as the load  to failure-LTF).Displacement was measured from a preload of 220 N as specified in the standard.The boxes exhibited a discontinuity in their load displacement curve at approximately 1.8 kN of loading.Our observation from testing of similar boxes indicated this was due to crushing of the flap creases, in addition to the preliminary low stiffness region where the flaps themselves are compressed as noted in previous studies [20,21].Garbowski et al. have reported that this discontinuity is a consequence of offset between the horizontal crease lines causing the upper part of the creased material to contact the platen first [22].This discontinuity was not related to buckling of the box panels themselves.In the present study, we focussed on analysing the stiffness of the first linear region after compression of the flaps as the magnitude of loading in this region is closest to the loading the boxes would experience in service.

Statistical analysis
All analyses were conducted using R Version 4.2.1 [23], supplemented by packages 'plyr' [24], and 'PMC-MRPlus' [25].To determine if flute angle significantly affected the response variables (Force, or Stiffness) the Kruskal-Wallis rank sum test was applied [26].This nonparametric test was used in favour of parametric models and ANOVA analyses, following Lantz [27], because sample distributions were not normally distributed.Normality was tested using the Shapiro-Wilk test [28] and homogeneity of variances was tested using the Fligner-Killeen test [29].Therefore, the Kruskal-Wallis test, which makes no assumptions about the underlying distributions was appropriate.When the Kruskal-Wallis rank sum test indicated significant differences (α = 0.05), post-hoc testing via Dunn's many-to-one comparison test (i.e.pairwise comparisons of flute angles with the 0° control) [30] was invoked, using a two-sided alternative hypothesis, to determine which flute angles differed significantly to the control.Though our focus was on those comparisons for which p < 0.05, we note that p-values represent only an index to evidence [31] and do not imply practical significance [32].Therefore, we also considered results for which p exceeded 0.05 but was less than 0.10.Statistical comparisons were supplemented with visual analyses using box-and-whisker plots (see Figs. 3 and 5 for details).
To examine overall trends in relationships between flute angle and maximum force (for both ECT and BCT trials), linear and second-order polynomial models were evaluated with flute angle as the explanatory variable and force as the response.The best models were selected following comparisons using ANOVA, and 95% confidence and prediction intervals calculated over the range of flute angles.
In addition to testing for statistically significant differences between flute angles and force, or stiffness, a system was developed to determine which angle performed best overall in terms of having both the greatest values (on average) and the least variation.Average was assessed in terms of median values and variation assessed using median absolute deviation (MAD).Median and MAD statistics were chosen in favour of mean and standard deviation, primarily due to nonnormality and small sample sizes.Following concepts derived from data envelopment analyses [33][34][35], to essentially rank what are known as "decision making units" (our DMUs here are the flute angles), we plotted median and MAD values at each angle, then calculated the Euclidean distance from each point to an "ideal" point having maximum magnitude (i.e. the greatest median) and no variation (i.e.MAD is equivalent to zero).Following López-Espín et al. [36] who argued that "the distance to the efficient projection point should be minimised", we determined the angle of best performance.

Results
The principal discovery of this study was that the box crush testing (BCT) performance, or load-bearing capacity, exhibited relative consistency when the flute angle ranged from 0° to approximately 30°.This observation is evident in the summary statistics of the trials, as presented in Table 3.A noticeable decline in performance at a 60° flute angle is apparent across all trials and both measured attributes (force and stiffness).Nevertheless, the variation at 60°, as evaluated by the standard deviation (sd), was generally smaller than the variation associated with other flute angles.

Component testing
The component test results and their relationship to BCT performance are summarised in Fig. 5. Figure 5a shows a general linear reduction in ECT strength with increasing flute angle, consistent with other studies of how ECT relates to flute angle [2,4].The linear model had an intercept of 424.6 N, and gradient of − 2.7 N degree −1 (Table 4) indicating that for each unit increase in flute angle, estimated force declined by 2.7 N. The model explained about 63% of the variance (R 2 adj = 0.63).
Four point bending results, summarised in Fig. 5(b,  c) were also consistent with the literature [4], showing a nonlinear change in terms of force or bending stiffness with flute angle, and a crossover in properties at 45° as would be expected.Note that the 0° to 10° MD  results showed more variation than the other angles.At these angles, it is important to ensure that the flute tips meet the point on both bottom anvils before conducting the test as explained in TAPPI T 820.However, for some samples, as the loading started, the samples slightly moved as a result of inertia, hence the larger deviation seen in these angles as opposed to others.Overall bending stiffness of the panel from the combined vertical and horizontal bending tests is shown by the black line in Fig. 5c.This shows that there was a localised peak in bending properties at 10° and combined properties appeared to maximise at 45° but was also higher than 0° at 30° and 60°.In particular, as shown in Fig. 5c, there was a clear local peak of combined bending stiffness at 10°.

Experimental and theoretical BCT results
Figure 5d shows both the experimental BCT results and theoretical values calculated based on component testing results.There was no significant difference in experimentally measured BCT from 0° to 30° and the predicted BCT followed a similar trend.While experimental values were higher than those estimated using McKee's equation, the difference between the two was also not significant.This could be a consequence of the McKee equation coefficients not matching this situation perfectly.

Box failure morphologies
There were clear differences in the failure morphologies of each box.The linerboards appeared to cockle (or wrinkle), until the panel buckled at peak load and creases travelled across the box panel with subsequent compression.As shown in Fig. 6, the creases followed the flutes once the box buckled, although in most cases these creases travelled inwards from the corners of each box to a central parallelogram panel as observed in previous studies.An exception was the 60° box group, in which creases travelled across the whole panel and the failure load was significantly lower (p < 0.001).Most of the boxes (all but 60°) exhibited the typical loading curve expected for RSC boxes (Fig. 2) with a discontinuity at approximately 2.3 kN.As mentioned in the Methods, this was related to compression adjacent to the flap creases for boxes made on the cutting table, not due to failure of the panels themselves.No significant relationships were observed in terms of whether flute angle could have influenced the point at which these creases compressed or the behaviour of the box before or after the discontinuity.Consequently, analysis focussed on the maximum force, and the stiffness of the loading curve prior to the discontinuity (hence simply referred to as stiffness), as these properties are relevant to loading of the box and all showed significant variation as the flute angle was changed.

Influence of flute angle on box stiffness and displacement at failure
As can be seen in the summary of BCT results in Fig. 7, there were no significant differences in peak forces between vertical flutes or any of the flute angles from 5° to 45°.Force was greatest at 5° followed closely by 30° and 7.5°.Only 60° boxes were significantly lower (as shown in Table 5, p < 0.001).In terms of stiffness, both 30° and 10° boxes exhibited significantly higher values (p < 0.001) than the other groups, including the 0° boxes.Again, 60° boxes had a significantly lower stiffness than vertical flute boxes.There were significant differences in displacement at failure between the 0° boxes and the 7.5°, 10°, 12.5°, 15°, 20° and 60° boxes.In all these cases, the displacement at failure was significantly lower than for the vertical flute boxes.As shown in Fig. 7, the magnitude of this difference was around 2 mm.
In terms of both magnitude and variation as summarised by the MAD diagrams in Fig. 8, 5° demonstrated the best performance for force, followed by 10° and 30°.For stiffness the best performance was for 30°, followed by 10° and 45°.60° boxes had the poorest performance in terms of both parameters.

Discussion
In general, these findings are consistent with previous experimental studies at both the board and box levels, which have indicated that compressive performance should not decrease rapidly or linearly with variations in flute angle [4,7,8].By testing a close range of angles between 0° and 20°, the present study provides experimental data not available previously.In contrast to the maximum load-bearing capacity of the box, the stiffness of the box did show significant variation across the tested range of flute angles.The local peaks for combined MD and CD stiffness at 10° and higher values at 30° (Fig. 5c) are consistent with the peaks in overall box stiffness measured experimentally (Fig. 7b) and the concept of the MD and CD stiffness of the board governing panel buckling and playing an important role in the overall performance of the box [4,6,18,37].While the geometric mean of the board stiffness (Fig. 5c, black line) was highest at 45°, this does not correspond to the box level results.This is likely a consequence of the box geometry: at 45° the short side panels no longer contain complete flutes from corner to corner, and these panels buckled readily with creases spanning the whole panel as can be seen in the examples in Fig. 6.Thus, it is reasonable to conclude that these panels were unable to contribute fully to the overall box stiffness.Likewise, in the case of the 60° scenario, where this behaviour was observed for all panels, both the failure load and the stiffness were significantly lower.
There were also significant differences in displacement at failure (Fig. 7c).Since the present study measured the overall displacement of the box, it was not possible to distinguish whether this difference was due to differences in behaviour of the panels or the creases.This could be a topic for subsequent studies, given that it has been shown that a substantial portion (approximately half) of box vertical displacement is related to displacement of the creases [21].The magnitude of this difference was approximately 2 mm which, though not substantial in terms of the overall height of the box, could be relevant to the end use of the box; these boxes had a typical headspace of 10 mm.As above, this behaviour depends on both panel and crease properties.The distance between flutes will increase as flute angle increases and this may influence the way the crease behaves under compression.
This raises the question: Why might these improvements and differences in performance occur at certain angles?Natural hierarchical structures including wood, bone and connective tissues contain numerous examples of anisotropy.Subsequent to conducting the experimental work for the present study we became aware of the concept of the magic angle.This describes the maximum enclosed volume for a helical reinforcing fibre of fixed length in a cylinder, but is also valid for a flat sheet reinforced by fibres in the plane.This angle, 35.26° and its complement, 54.74° was initially identified in nemertean worms [38], but as the name suggests, appears as if by magic in numerous diverse settings [39,40].It is similar to the fibre angle of the intervertebral disc [41], arteries [42], and the spiral angle observed in certain trees [43].Industrially, it is known to reduce the tendency of hoses to distort when pressurised [44].If the flutes of a box are arranged at one of these angles (35.26° or 54.74°), the component papers in that board will be at the other.Considering this, the increase in stiffness observed in the 30° boxes could be a consequence of their constituent papers and flutes approaching this angle.Note also that the S2 layer of the plant cell wall which plays an important role in the stiffness of wood typically varies between 5° and 20° [45][46][47][48], although other angles are possible [49].While generally a steeper angle is considered to result in a stiffer structure, intuitively situation specific differences in aspect ratio and material properties would be expected to influence this, which could explain the finding of the present study that 10° appears to result in optimal stiffness.
These observations could have implications for how such boxes would perform in service.Since variability in BCT is considered to be linked to variability in creep performance [50], the potential of angle flutes to reduce variability in lifetime should also be considered.Similarly, while links between BCT performance and lifetime are well established, the influence of box stiffness on creep performance could also be worthy of consideration.Increased stiffness due to variation in microfibril angle has been linked to reduction in creep rate for wood samples [51][52][53] which could be analogous to the component orientation in this situation.The increased stiffness observed for angle flutes boxes at 10° and 30° would be relevant to the loading levels the boxes would be subjected to in service, and the corresponding reduction in deflection for a given load would intuitively appear to be likely to reduce susceptibility to creep.Given the role of hygroexpansive stress in accelerated creep performance of boxes [5,50], it could be speculated that angle flute boxes may deform preferentially (in a direction governed by the flute angle) as a result of creep.If true, this could prove advantageous in palletization-boxes could be arranged to form pallets which self-reinforce as a consequence of creep loading.Altering the flute angle of the box panels may also improve the response of the box as it interacts with its contents, known to play a substantial role in long-term storage performance of the box [54]; this is also a factor that should be considered in future investigations.
Creating boxes with 30° angled flutes is likely impractical for the regular slotted containers used in the present study, which are cut as vertical strips.Nonetheless, as mentioned in the Introduction, the performance gains related to increased stiffness and reduced variability may prove to outweigh the proportion of board that is wasted.For more irregular shapes such as fruit trays, cutting boxes at an angle has been shown to be a strategy to save board as it is possible to interlock the blanks and reduce board use [8].The potential to cut angled flute inserts to strategically reinforce boxes may also be worth considering.
Another motivation behind this study was to investigate the possibility of cutting blanks at an angle to reduce die shock during cutting.This occurs when a cutter blade strikes parallel to a glue line, resulting in increased tool wear and energy use.Intuitively, this is much less likely to occur if blanks are being cut at an angle.While assembling the boxes, it was notable that folding the angle creases required more care than for vertical boxes to avoid unintended folding of the blank parallel to the flute.Although this was a qualitative observation, it is a factor that would require consideration if this strategy were to be implemented.
While not considered in the present study, board crushing due to printing and conversion could potentially influence performance of angle flute boxes.It is known that this can influence the performance of single and double-walled board, with lower levels, below 30% being approximately linear [55,56].More severe crushing can cause delamination of the flute [4].Conversely a study on board post conversion indicated that differences pre-and post-conversion were insignificant [57].Given that crushing influences the medium and glue joints, it is likely that this could act at a different magnitude to that observed in vertical flute boxes, but this would need to be confirmed experimentally.For example, during printing using rotary dies the forces would be balanced across larger distances (flute tip to flute tip) in angle flute boxes.
The present results clearly show that altering the flute angle does not significantly reduce the short-term load bearing ability of the box over a wide range of angles, between 0 and 45° from vertical.As could be surmised from relationships such as the McKee equation, this is likely a result of synergy between crush strength and bending stiffness.There were significant effects on the stiffness of the box, particularly at 10° and 30°, and in the case of stiffness, there is reason to hypothesise that this could improve the long-term stacking (creep) performance of the box.Another potential benefit is that increased stiffness in the horizontal direction will assist preventing bowing of the panel associated with hydrostatic loading imposed by the product in the box.

Conclusions
This study investigated the influence of flute angle on box compression strength and response to loading.Box crush test performance in terms of force alone did not significantly reduce when flute angle was varied between 0° and 45°.Some angles had higher mean forces, and many angles tested (notably 10° and 30°) showed substantially less variation in peak load.Stiffness showed substantial and significant improvements at certain flute angles compared to 0°.Both 10° and 30° had significantly higher stiffness and lower variation in their performance.Component board properties were also tested and indicate that while ECT reduces almost linearly with flute angle, bending performance does not, consistent with literature and the concept that overall box performance depends on these component properties.These results suggest that varying flute angles of boxes to reduce die shock and/or to optimise board use is unlikely to significantly reduce box performance, at least for the RSC boxes used in the present study.Conversely, varying the flute angle may bring performance benefits by increasing box stiffness and reducing variation in performance.

Figure 1
Figure 1 Example box panels showing how flute angle is defined relative to the box edges in this investigation and how this relates to the ECT and vertical or horizontal four-point bending samples.

Figure 2
Figure 2 Typical forcedisplacement curves for ECT of board at a 0° flute angle.Maximum load was determined for each curve as indicated by the green line.

Figure 3
Figure 3Typical force-displacement curves for four point bending of board at a 0° flute angle in the CD (blue) and MD (red).Slope and maximum load was determined for each curve as indicated by the red and green lines, respectively.

Figure 4 A
Figure 4 A typical loaddisplacement curve (shown in blue) for boxes similar to those used in the present study.Maximum load (green dashed line), displacement at maximum load and stiffness (red line) were determined from these curves, along with the preload of 220 N (region covered by green arrow).

Figure 5
Figure 5 Box and whisker plots depicting maximum force for: ECT trials (a) and vertical and horizontal trials (b), bending stiffness for vertical and horizontal trials (c), and maximum force for BCT trials (d).Flute angles that do not differ significantly to 0° are shown in green, those for which p < 0.05 in red, and those for which 0.05 < p < 0.10 in orange.Vertical and horizontal bending test results are shown in red and blue, respectively, and combined results in black.Shaded areas depict 95% confidence intervals (inner regions) and 95% prediction intervals (outer regions).Estimated mean BCT force values using McKee's equation are shown as asterisks, with line segments representing one standard deviation.

Figure 6
Figure 6 Failure morphologies of boxes following BCT testing.Creasing of each panel is clearly visible.Note that the creases travel across the whole panel in the cases where no complete flutes connect the upper and lower panel edges (short end of 45° and both the long and short faces of the 60° box).

Figure 7 Table 5
Figure 7 Data distributions of BCT trials: force (top panel), work (middle panel), stiffness, and deflection (bottom panel).Boxes shown in green are not significantly different to the 0-degree distributions, red indicates significant difference at α = 0.05.Median values are indicated by horizontal lines, means by black dots, and outliers by asterisks.

Figure 8
Figure 8 Performance of angles in BCT trials assessed using mean force (a), or median stiffness (b), and variation (MAD) to determine distance (shown in green font) from a hypothetical 'ideal' point (green point at top left).Flute angles with the best

Table 2
Properties of the constituent paper that made up the board

Table 3
Summary statistics (mean ± sd) for the box crush and bending test trials

Table 4
Results of the regression analysis for estimating ECT Force from flute angle