The Pareto chart obtained from Minitab shows the absolute significance of the standardized effects from the biggest to the smallest. The reference line shows the effects which are statistically significant. Statistical software Minitab 18 yields the Pareto charts as shown in

Figure 12a which indicates that face sheet thickness is the most significant factor that governs the flexural peak force, followed by pre-bend impact energy and temperature. Earlier observation in

Figure 8 and

Figure 9 showed similar observations that these three factors were the prominent factors controlling flexural performance for the composite sandwich panel. Bending configuration had a much smaller effect than the other three.

The main effects plots, given in

Figure 12b, which identified the influence of individual factors further validated the findings from the Pareto charts. The main effects plot provides the average data at the low and high factors. The gradient of the straight line corresponds to the significance of the factor directly. It is evident that the flexural peak force increases with increase in face sheet thickness (Th) whereas it decreases with increase in impact energy (Energ) and temperature. Inward bending shows inferior flexural performance compared to outward bending configurations. The flexural peak force is mainly influenced by face sheet thickness and impact energy whereas temperature and configuration (Conf) both have mild influences.

Figure 13 portrays the interaction plot, which interprets the two-way interaction of the factors. If the slope of the two lines is not the same, there exists some interaction. It is concluded that apart from face sheet thickness and impact energy, which both are strong independent factors, all the other factors have interactions with each other.

Contour plots are obtained by the constant response line projections from the response surface into the two-dimensional factor plane. Thus, the contour plot gives the prediction of impact energy and temperature on the x- and y-axes, respectively, along with contour lines for the peak load. At a specific impact energy, the contour plot can be used to graphically predict the flexural force for a particular temperature.

Figure 14a shows that increasing impact energy will significantly reduce peak force for a given temperature for the bending inward case, whereas for the outward case, impact energy has a gentler influence (

Figure 14b). This substantiates the experimental observation in

Figure 9, as discussed earlier. Analysis of variance (ANOVA) is a statistical tool that calculates data based on the difference between two or more means. The variance within the groups and variances between the groups are compared. Subsequently, a regression equation can be obtained to describe the relationship between the response and the variables or factors. The algebraic representation of the regression equation for a linear model can be represented as:

where

$Y$ is the response variable,

$c$ is the constant or intercept of y-axis,

${m}_{1}$ is the slope of the line and

${x}_{1}$ is the value of the factor. The regression equation with more than one factor can be represented as:

where

${m}_{1}$,

${m}_{2}$,…,

${m}_{n}$ are the coefficients of the

${x}_{1}$,

${x}_{2}$, …,

${x}_{n}$ factors. From ANOVA, considering the factors having

p-values less than 0.05 only, the regression equation for the bending peak force, P is as follows:

here,

t is the face sheet thickness,

IE is the impact energy,

T is the temperature and

C is the bending configuration. Graphical prediction based on contour plot and statistical prediction based on regression Equation (3) are further compared with experimental results for flexural peak force for 4 J pre-bend impact energy at 23, −30 and −70 °C, as shown in

Figure 15. Excellent agreement between experimental data and statistical prediction was observed. The greatest differences were for the −70 °C cases, where the statistical predictions deviate from experimental data. In reality, the impacted front face sheet matrix which was in compression during inward bending was severely embrittled at −70 °C [

22,

23] that led to flexural failure of the specimen at a much lower force. However, for the outward case, linear assumptions made by the statistical analysis underpredicted the experimental peak load, whereby the undamaged front face sheet compressive properties were enhanced at low temperature (−70 °C) and bottom face sheet tensile properties were uncompromised due to little or no damage during impact.