The Application of Statistical Design of Experiments to Study the In-Plane Shear Behaviour of Hybrid Composite Sandwich Panel

: This paper presents a statistical aspect of experimental study on the in-plane shear behaviour of hybrid composite sandwich panel with intermediate layer. The study was aimed at providing information of how significant the contribution of intermediate layer to the in-plane shear behaviour of new developed sandwich panel. The investigation was designed as a single factor experimental design and the results were throughly analysed with statistics software; Minitab 15. The panels were tested by applying a tensile force along the diagonal of the test frame simulating pure shear using a 100 kN MTS servo-hydraulic UTM. The result shows that the incorporation of intermediate layer has sinificantly enhanced the in-plane shear behaviour of hybrid composite sandwich panel. The statistical analysis shows that the value of F 0 is much higher than the value of F table , which has a meaning that the improvement provided by the incorporation of intermediate layer is statistically significant.


Introduction
A hybrid sandwich panel that is formed by inserting intermediate layer between skins and core has shown excellent performance under flexural loading as reported by Fajrin et al. [1,2]. The concept of hybrid sandwich panel with intermediate layer itself was first developed by Mamalis et al. [3]. However, flexural behaviour is not of considerable importance when applying sandwich panel as a wall of building structure. In-plane shear behaviour is the most critical behaviour that needs to be carefully understood when using sandwich panel for a wall especially when the wall is considered as a structural component. It was expected that employing intermediate layer could enhance the in-plane shear behaviour of sandwich panels. The stress discontinuity along the cross section of the panel is believed as a prime contributor for failure in sandwich panel. The idea of adding intermediate layer, which has intermediate properties between the skins and core, is to reduce the problem. The abrupt step between the high and low stresses within the skins and core might be reduced when the intermediate layers are incorporated.
Theoretically, as stated in reference [3], the existence of intermediate layers generates sandwich panel with higher load carrying capacity due to its ability to prevent early failure modes such as face wrinkling or indentation. Further theoretical analysis reported by Fajrin [4] also shows a significant contribution of intermediate layer to increase the flexural rigidity of a sandwich panel.
The term of "statistical experimental design" was introduced by Montgomery [5]. Other terms are used by statisticians such as "designed experiments" or "design of experiments" to describe the same process. In a designed experiment, the researchers make deliberate or purposeful changes in the controllable variables of the system or process, observe the resulting system output data, and then make an inference or decision about which variables are responsible for the observed changes in output performance. While all experiments may be considered to be designed experiments, some are poorly designed that may result in ineffectively uses of valuable resources. Statistically designed experiments allow efficiency and economy in the experimental process and also obtain scientific objectivity conclusions [6].
Although the experimental results can be simply analysed with descriptive statistics, involving inferential statistics may enrich the value of findings. In this study, a specific hypothesis was tested using significance analysis which is a mathematical tool that is commonly used to determine whether the outcome of an experiment is the result of a relation-ship between specific factors or solely the result of chance [7]. Commonly, experimental researches in civil engineering field are conducted according to a standardized procedure which only involving descriptive statistics in the analysis. It rarely found a report that uses inferential statistics analysis for making conclusions [8]. The descriptive statistics only presents an immediate result without proper analysis how significant the differences between the conditions under investigation and those are kept constant. The significance analysis, which is a part of inferential statistics, is commonly performed by examining the variation in a set of responses and assign portions of this variation to each variable in a set of independent variables. This analysis is also known as the analysis of variance (ANOVA) with the aims to identify important independent variables and determine how they affect the response [5]. As in the experiment only one variable was investigated, the analysis employed was called as the one-way or single factor ANOVA. This paper presents a statistical aspect of the experimental study on the inplane shear behaviour of hybrid composite sandwich panel with intermediate layer.

The Application of Statistical Analysis in Composite Research
Statistical aspects, especially inferential statistics, often ignored in structural researches due to time and cost constraint. However, it has been extensively used in the broad field of composite material research. Some case studies are provided as follow. Phoenix et al. [9] used Weibul statistics to establish theoretical model for predicting the strength and lifetime in creep rupture of carbon-epoxy composites. Also, Phoenix [10] presented statistics aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. In other study, Bayerlein and Phoenix [11] used statistics analysis to study the effect of size to the strength of composites prepared with carbon fibers and epoxy resin. Toutanji et al. [12] employed Weibull statistics analysis to investigate the effect of adding carbon fibers on the mechanical properties of cement paste composites. Alhozaimy et al. [13] performed statistical significance analysis to study the effect of adding polypropylene fibers on the compressive, flexural and impact properties of concrete materials with different binder compositions.
More recent studies in this research area also involve statistics analysis. Balzer and McNabb [14] employed a two-way ANOVA to study the effect of microwave curing on tensile strength of carbon fibre composites. Jun et al. [15] used response surface method to determine the significant factors that affected the properties of the wood-rubber composite.
The similar method was employed by Mathivanan et al. [16] in observing the factors influencing deflection in sandwich panels subjected to low-velocity impact. A full factorial design, which is a branch of design of experiments, was employed by Shahdin et al. [17] to study the significance of low energy impact on modal parameters for composite beams. Also, Dwivedi et al. [18] used a two-level full factorial design of experiment to study the abrasive wear behaviour of bamboo powder filled polyester composites. Satapathy and Patnaik [19] used Taguchi method in designing their experiment to investigate the dry sliding wear behaviour of red mud filled polyester composites. Furthermore, Davim and Reis [20] used the same method in designing experiment for establishing the correlation between cutting velocity and feed rate with the delamination in carbon fiber reinforced epoxy composites.
Although statistical analysis is hardly found as a primary approach in earlier green composite research, few studies dealing with natural fibers composites have recently been designed and analysed using statistical frameworks. Prasad et al. [21] conducted optimization of design parameters using ANOVA to study the performance of jute and banana fibers reinforced polymer matrix. The same method also employed by Venkateshwaran et al. [22] to study the effect of layering pattern to the mechanical properties of woven jute/banana hybrid composites. More recently, El-Shekeil et al. [23] designed their experiment to study the significance of different parameter to the tensile strength of kenaf fibers reinforced polyurethane composites using Taguchi model and analysed the results using ANOVA. Clearly, a few different statistic methods have been extensively used in fiber composite researches.

Experimental Design and Testing Program
The experiment was designed as a single factor experiment in which 3 levels of a factor had been examined. The factor refers to the type of intermediate layer used in the sandwich panel. Level 1 and 2 refer to as jute fibre composite (JFC) and medium density fibre (MDF) while level 0 was a reference or control level (CTR) which was sandwich panels without intermediate layer. The specimens had overall dimensions of 380 x 380 mm providing a clear internal dimension of 300 x 300 mm between frame boundaries. The overall thickness was maintained at 26 mm for all specimens. The aluminium sheet with the thickness of 0.5 mm was used as the skins and expanded polystyrene (EPS) for the core. The thickness of EPS core for the control specimens was 25 mm and 19 mm for the specimens with intermediate layer. Each specimen group was replicated 5 times with a total of 15 samples tested. The sample arrangement for the in-plane shear specimens and the schematic testing program are presented in Table 1 and Figure 1, respectively.  A tensile force was applied along the diagonal of the test frame simulating pure shear and the testing rig was enabled to freely rotate by placing a pin bolt at each corner. This ensured that the frame did not contribute to the load carrying capacity of the whole system. The corners of the panel were cut to enable the connector plate to go through to the frame while minimizing stress concentration at the corners.

Results and Discussions
The failure loads of specimens tested under in-plane shear testing are listed in  As previously mentioned, the experiment was designed as a single factor experiment in which 3 levels of a factor had been observed. The factor refers to the type of intermediate layer incorporated within the hybrid sandwich panel. For the analysis purpose, the data for ANOVA are tabulated as shown in Table 3.  As it can be seen in Table 3, some important parameters for theoretical calculations can be determined such as replications (n = 5), total number of samples (N = 15), and number of levels or treatments (a = 3). The theoretical results of the ANOVA are summarized in Table 4 while such analysis obtained by statistical software Minitab 15 is presented in Table  5. The inference statement suggests that the in-plane shear load carrying capacity of hybrid sandwich panels with JFC and MDF intermediate layer was significantly higher than the conventional sandwich panels. This statement has a 95% chance of being true, or 5% of not being true, as the significance level used for the analysis was 95%. Based upon the P value, which was much less than 0.005, it can also be concluded that there has factor levels or treatments that have different means. The P-value for this experiment, as presented in the Table 5, was approximately 0.000. A pairwise comparisons were also conducted in this in-plane shear test results to confirm the decisions drawn from the analysis of variance. The results of Tukey"s, Dunnet"s, and Fisher"s test are presented in Table 6, 7, and 8, respectively. Table 6 shows the result of Tukey"s test conducted for the data of in-plane shear test. The comparison of level 0 to level 1 has the confident interval of 36336 for the lower value and 42790 for the upper value, and the critical value of 39563. For level 0 to level 2, the lower and the upper value was 8890 and 15344, respectively. In contrast, the analysis showed negative confident values when the level 2 was compared to the level 0. The lower and upper value was -30673 and -24219, respectively with the centre or critical value of -27446. Although all the confident values were negative, it has a similar meaning with the previous all positive values because they are not containing zero number. The rule for concluding that all levels are different was that whenever the Tukey"s confidence intervals contain zero number, it indicates that the means are not different. In short, it can be concluded that all the treatment means differ as none of confident levels contains zero. The Tukey"s test also suggests that there is a significant different between level 1 and level 2, as they contain only negative numbers or none of confident levels contains zero.    Both tables showed that the mean square between treatments was many times larger than    The result of Fisher"s test is given in Table 8 which shows a similar configuration with the Tukey"s test. The comparison of level 0 to level 1 and level 2 has all positive confident intervals while the comparison of level 1 to level 2 has all negative numbers. The configuration of the confident values, that only contain positive or negative numbers, indicate that the means are different as they are not including zero number.