Modeling the Mechanical Properties of Clay Powder Filled Recycled Low Density Polyethylene Composites

This study modeled some mechanical properties of clay powder filled recycled low-density polyethylene, rLDPE (rLDPE composite). The rLDPE is commonly referred to as used sachet water bags. The clay powder (filler) was obtained by sun-drying, grinding, and sieving. Two particle sizes of clay powder were used: −90 μm and −425 μm to represent the passing sizes at different clay powder contents of 5, 10, 15 and 20 wt% which were thoroughly mixed with the recycled low-density polyethylene in an injection molding machine at 173°C. The results showed that the tensile strength, tensile modulus, hardness, flexural strength, fatigue strength and hardness increased with increase in clay powder contents. However, there were decreases in strain-at-breakage and shear strength as clay powder content increased. Model equations showed that smaller particle size enhanced the mechanical properties and equations generated can be used to predict the properties of composites at predetermined clay contents. Standard deviations obtained for the various mechanical properties show that the model, in most cases had the lowest degree of scatter (dispersion) than those of −90 μm and −425 μm. Hence, these models are suitable to predict outcomes of the properties of the clay filled recycled low-density polyethylene composites.

Polymer composites consist of the primary phase known as the matrix phase and the secondary phase referred to as the reinforcement. The matrix is ductile and it binds the reinforcing agent in a composite while the reinforcing agent is strong and it enhances the mechanical properties of the polymer composite. The composite that is well formulated possesses a better property than the individual component [2]. The most popularly used thermoplastic is polyethylene (PE) because it is tough, chemically inert, unable to absorb moisture, exhibits low coefficient of friction, easy to process, unable to conduct electricity. Polyethylene is used in making pipes, containers and other products. The composite of polyethylene is widely used in many fields due to its improvement in mechanical and physical properties unlike the pure polyethylene. Polyethylene composites are used in packaging, electrical component, storage of thermal energy, automotive, biomedical and aerospace [3].
Clay which is made up of inorganic and organic materials can be found locally within the environment and has been applied in the production of various composites. It has been classified as being a very good and distinct organic reinforcing filler. The use of clay as a reinforcing agent in the production of composite products has a good reinforcing effect over the polymer matrix as a result of its inherent properties such as layered structure, high stiffness about 150 -250 GPa, high strength and surface area about 700 -800 m 2 . Physicochemical conditions, processing method and high surface area of clay, are the factors that can lead to increase in interfacial interactions between the polymer and the reinforcing phases. Clay powder can improve the mechanical properties of composites more than the composites prepared from mineral/inorganic fillers such as glass fiber, talc, metal oxides and others [4].
Many researchers have used clay in the filling polymers, for instance Longanathan et al., (2011) used nanofibers and montmorillonite based organo-clay to fill polypropylene by melt-spinning and it was observed that their structures and mechanical properties were enhanced [5] [6]. It was observed that mechanical properties and free vibration characteristics were improved. Different weight percentages of fibers, 5%, 10%, 20%, 25%, and 30% were also used to fill the composites. The results showed that 5% addition of nano clay and 15% jute fibers yielded the best tensile strength, impact strength and vibration behavior of the composites whereas 5% nano clay and 25% jute produced composite with best flexural strength. Increase of nano clay or jute beyond these values reduced the respective properties.
In recent years, the application of nano clay in bio-degradable polymers also attracts more and more interest, which aims to enhance the tensile modulus, tensile strength and the interfacial interaction of bio-resin [7]. Better properties of nanocomposites are believed to be achieved even at a small amount of clays when clays are fully exfoliated [8] [9] [10] [11]. Different models have been used to predict various characteristics and mechanical properties of composites. The models predicted results which conformed with the experimental results [12] [13] [14].
Recently, the clay powder filled recycled low density polyethylene composites were prepared using filler loadings of 0%, 5%, 10%, 15% and 20% with particle sizes of 90 µm and 425 µm passing sizes. The result showed improved mechanical properties [15]. In this work, the model predicted the effects of clay powder and particle sizes on some mechanical properties of recycled low-density polyethylene (rLDPE) composites that were determined in [15].

Materials and Methods
The clay used was obtained from Awo-Omamma village in Imo state, Nigeria. The recycled low density polyethylene used was picked from Federal University of Technology, Owerri, Imo State, Nigeria. rLDPE were sorted, washed, sun-dried and ground to powder form.

Composites Preparation
The clay (filler) was sun-dried, ground to fine particles and sieved into two mesh size ranges, namely: -90 µm (particles passing through 90 µm sieve down to submicron or nanoparticles) and -425 to +90 µm (particles passing through 425 µm sieve but retained on 90 µm sieve) respectively. For the sake of simplicity, these size ranges are subsequently referred to as 90 and 420 µm respectively. That is, 90 µm filler particles are the undersize of 90 µm sieve while 425 µm particles are the oversize of 90 µm sieve plus the undersize of 425 µm sieve. In other words, all the oversize of 425 µm sieve were rejected while the undersize were used as filler in polypropylene matrix. Different clay powder contents; 5, 10, 15, and 20 wt% were homogenously mixed with recycled low-density polyethylene at the two particle sizes studied.

Tensile Properties
In the determination of tensile properties of the prepared rLDPE composites, the injection molded sheet was cut into dumb bell shape of specimen dimensions 160 mm × 20 mm × 3 mm and placed on Universal Testing machine at a head speed of 5 mm/min according to ASTM standard. The tensile strength, tensile modulus and strain-at-breakage of the composites were calculated using Equations

Strain-at-Breakage
The strain-at-breakage was determined using Equation (2) Strain-at-Breakage 100 where, L i = initial length of specimen L f = final length of specimen

Tensile Modulus
The tensile modulus of the composites were calculated using the formula in 3

Flexural Strength
For the flexural strength the specimen was cut to 300.0 mm length, 19 mm breadth and 3.3 mm thick. It was performed according to ASTM. D790 using Universal Testing Machine at a constant rate of 2 mm/min. Test specimen was cut to 300 mm length, 19 mm breadth and 3.3 mm thick.
The flexural strength was calculated using Equation (4)

Shear Strength
In the determination of shear strength, the specimen was inserted into the shear test box, a continuous steady load was added till it pierced through the specimen. The force used for piercing the sample was measured (shearing force). The shear strength is given in Equation (5).

Fatigue Strength
Fatigue strength was tested by determining the number of cycles needed to crack the material when stress was applied below its tensile strength (n i ) and the number of cycles needed to enlarge the crack to a yield point before failure occurred, Journal of Materials Science and Chemical Engineering (n p ), as given in Equation (6).

Hardness Test (Brinnel Hardness)
Hardness test was carried out using a tensiometer UTM (Model No.8889 made in England by Tensiometer Ltd.). A steel ball of diameter of 10 mm was forced into the material under a load, F. After removal of the load, the two diagonals X and Y of the indentation left on the surface of each sample was measured and the arithmetic mean (d) was calculated. The Brinnel hardness was computed using the relationship in Equation (7) ( ) The modeling was based on comparison between equations for 90 µm and 425 µm passing sizes and choosing the one that has R 2 nearer to 1 because it is more useful for prediction. With these respective model equations, the properties can be predicted for clay powder contents that were not experimented on. The model curves were observed to align closely with the curve of the particle size that gave the model equations. The model curves were plotted alongside with experimental curves for the purpose of comparison. Figure 1 shows the effect of clay powder contents on the modeled and unmodeled tensile strength of recycled low-density polyethylene composites at 90 µm and 425 µm passing particle sizes respectively. From Figure 1, the modeled and unmodeled tensile strength of recycled low-density polyethylene composites increased alongside with clay powder content at the two particle sizes studied, these were due to the high strength of the clay. Figure 1 also shows that 90 µm passing particle size yielded higher tensile strength (For both modeled and

Tensile Strength
where T.S 90 µm is the tensile strength at −90 µm clay particle size and x is the filler content.
The model curve was found to align closely with the curve of the clay particle size that gave the model curve. From the model equation generated, it was possible to predict the tensile strength of any clay powder content even the values that were not experimented on.
Furthermore, standard deviations for the series of data obtained for each particle size range and the model as indicated in Figure 1 (SD −90 µm , SD −425 µm and SD model ) show that the model has the lowest value implying that it has the lowest degree of scatter from the mean value. This attests to the fact that the model is best suited for prediction. Figure 2 shows the effect of clay powder contents on the modeled and unmodeled strain-at-breakage of rLDPE composites. It was shown that strain-at-breakage decreased as clay powder content increased. This is as result of inert and hard nature of the clay which decreased the plasticity of the rLDPE thereby decreasing its ductility. This is in agreement with the work of Onuegbu and Madufor [12] who found that the strain-at-breakage decreased with increase in clay powder contents. Model equation for strain-at-breakage is given in Equation (9): Also, the model shows that it is possible to predict the value of strain-at-breakage for any clay powder content. It also shows that smaller particle sizes yield better results.

Strain-at-Breakage
The standard deviations as shown in Figure 2 also show that the model has the lowest standard deviation, an indication that its degree of scatter is least, hence suitable for prediction.

Tensile Modulus
The data on the model and un-model modulus of filled rLDPE are illustrated in The model equation also shows that smaller particle sizes yield better results.
Tensile modulus can also be predicted at any chosen clay powder content with the aid of the model equation generated.
The values of standard deviation obtained for tensile modulus also showed that the model has the least value, meaning that it has the least degree of scatter.

Flexural Strength
which also shows that the smaller the particle size, the better the mechanical property [16].
The standard deviations however show that the model has a value of standard deviation between those of −90 µm and −425 µm. This implies that its degree of scatter is a compromise between the two particle size ranges.

Shear Strength
The shear strength of the rLDPE composites of clay powder at the particle sizes of 90 µm and 42 µm were observed to decrease with increase in powder contents. Moreover, at 90 µm, the shear strength was higher than that of 425 µm particle size. The reason is that more stress was required to cut across a given area of composites with 90 µm clay particle size than with that with 425 µm clay particle size. The model equation for shear strength is given in Equation (12).
This also confirmed that the composite with 90 µm clay particle size improved the properties better than the 425 µm clay particle size. From the model equation generated, values of shear strength can be predicted at any clay powder content.
The least value of standard deviation, as shown in Figure 5, was obtained for −425 µm followed by the model and finally the −90 µm. It is obvious from the values that the model has a standard deviation (6.117) very close to that of −425 µm (6.107) meaning that there is a low degree of scatter. Figure 6 shows that the fatigue strength for clay powder rLDPE composites Model and un-model fatigue increases with increase in clay powder content at both 90 µm and 425 µm particle sizes considered. This is as a result of the improved stiffness of the material.

Fatigue Strength
Model equation,   The standard deviations as shown in Figure 6 also show that the model has the lowest standard deviation, an indication that its degree of scatter is least, hence suitable for prediction.

Hardness (Brinell Hardness)
The hardness of the rLDPE composite with the 90 µm and 425 µm clay particle passing sizes were observed to increase with increase in the clay powder content. This is due to enhancements of the abrasion and impact strength by finer particle size of the 90 µm clay particle size than the rLDPE composite with 425 µm clay particle passing size.
The model equation generated for prediction purposes is given in Equation Hence, with the model equations generated, the values of hardness can be predicted at any clay powder content.
The standard deviations as shown in Figure 7 again show that the model has the lowest standard deviation, an indication that its degree of scatter is least, hence suitable for prediction.

Conclusion
From the study, the models for the mechanical properties of clay powder filled rLDPE composite at two different clay particle size ranges have been determined. The tensile strength, tensile modulus, flexural strength, fatigue strength and hardness of the clay filled rLDPE were observed to increase with increase in clay powder content for the model and un-model. An improved property was obtained at clay particle passing size of 90 µm than at 425 µm. Strain-at-break and shear strength decreased with increase in clay content. Model equations generated Journal of Materials Science and Chemical Engineering from the results showed that decrease in particle size enhanced most of the mechanical properties. These equations can also be useful for predicting the tested properties at predetermined clay powder contents. Standard deviations obtained for the various mechanical properties show that the model, in most cases had the lowest degree of scatter (dispersion) than those of −90 µm and −425 µm. It is therefore recommended that these models be used to predict outcomes of clay filled recycled low-density polyethylene composite for laboratory and industrial production of the composite.