Eco-friendly green composites reinforced with recycled polyethylene for engineering applications

Polyethylene (PE) and cement are industrial products that promote environmental pollution. These products when exposed on the landfill have tremendous effects on the lives of humanity and other living creatures, including animals. Therefore, this research presents the results of experimental and theoretical modeling of green composites (without the inclusion of cement) reinforced with recycled polyethylene waste for applications in the Mechanical and Civil Engineering industry. The composites are produced using different weight fractions of laterite and molten PE mixed homogeneously to produce unique green composites with excellent mechanical properties. The green composite with 40 wt.% laterites and 60 wt.% PE exhibited the highest compressive strength, flexural strength and fracture toughness of 25 MPa, 7.3 MPa and 0.6MPam\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.6 MPa\sqrt{m}$$\end{document}, respectively. Additionally, the green composite recorded maximum yield stress of ∼2MP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 2 MP$$\end{document}. The maximum yield stress of the green composites falls under the minimum range of yield stress for traditional concrete structures. The SEM images reveal evidence of bonding and ligament bridging in the green composites reinforced with 40 wt.% laterites and 60 wt.% PE. The probability distribution plots show that the polyethylene in the green composites follows the Weibull distribution with low Anderson Darling Statics and p-values greater than significance level of 5%. Composites are produced with laterite and molten PE without the inclusion of cement to produce unique green composites with excellent mechanical properties. The green composite exhibited excellent compressive strength, flexural strength and fracture toughness of 25 MPa, 7.3 MPa and 0.6 MPa√m, respectively. A maximum yield stress of ~ 2 MPa was recorded for the green composite. The SEM images reveal evidence of bonding and ligament bridging. The green composite is well characterized by the Weibull distribution. Composites are produced with laterite and molten PE without the inclusion of cement to produce unique green composites with excellent mechanical properties. The green composite exhibited excellent compressive strength, flexural strength and fracture toughness of 25 MPa, 7.3 MPa and 0.6 MPa√m, respectively. A maximum yield stress of ~ 2 MPa was recorded for the green composite. The SEM images reveal evidence of bonding and ligament bridging. The green composite is well characterized by the Weibull distribution.


Introduction
Nowadays, the use of plastics such as polyethylene (PE) has become very necessary for the livelihood of humanity. Due to its high demand across the world, the different types of PE including low-density polyethylene (LDPE), medium-density polyethylene (MDPE), and high-density polyethylene (HDPE) among others are becoming a nuisance to the environment [1,2]. The generation of these wastes has become very common in Africa and the world at large. These polymers are now in high demand, and it is not surprising seeing several of them disposed of the environment, causing an accumulation of waste in the landfills and this limits the usage of the land for agricultural and other developmental activities [3,4]. Moreover, PE wastes take a longer time (not less than fifty years) to degrade under natural environment settings [5] with further research [6,7] even suggesting that the average complete degradation of these wastes can exceed hundred years.
In trying to eliminate or reduce the pile-up of PE wastes on the environment, few researchers have capitalized on the need to re-use these polymers/plastics by incorporating them into cement-based structures for sustainable building applications [1,2,[8][9][10][11][12] and other applications in the composite industry [13][14][15]. The problem associated with these cement-based structures is that the cement itself is a pollutant and contributes to overall global carbon dioxide emission; otherwise, cement-based structures are durable and possess excellent mechanical [16][17][18] and physical properties [19,20]. However, these cement-based structures used in most construction works are expensive and not environmentally friendly. Therefore, to achieve the United Nations Sustainable Development Goal 11 [21], there is a need to produce cost-effective and environmentally friendly composite materials for sustainable and affordable construction applications by applying basic mechanical and civil engineering principles.
Laterite, formed as a result of the chemical weathering of rocks is a type of soil that is often red due to the availability of iron oxides [1,8]. This type of soil is predominantly found in tropical regions, with Ghana, not an exception. Laterite is abundantly available in Africa with well-graded particle sizes that are uniformly distributed. They can be easily compressed and moulded into earth-based bricks for sustainable building and construction applications. However, earth bricks manufactured with 100% laterite produce weak mechanical properties such as compressive and flexural strengths for load-bearing structures due to cracking [8]. Also, earth-based has limited-service life, thereby making it less durable. Because of this, their mechanical properties can be improved by mixing them with cement or lime, and other recycled materials.
Although few researchers tried to incorporate recycled PE [1,2,[8][9][10][11][12], fibers and crop residue [22][23][24][25][26], and other wastes including leather tannery and crumb rubber [27][28][29][30][31] into cement-based structures for sustainable construction applications in the mechanical and civil engineering industries, they failed to address the cement issue being a pollutant critically. Therefore, this work produces eco-friendly green composite materials reinforced with recycled PE without the inclusion of cement, an industrial pollutant. The composites are prepared by mixing different weight percentages of laterite and PE to produce unique laterite/PE composites with excellent mechanical properties comparable to cement-based structures [32,33].

Shear lag theory
The shear lag theory is considered one of the important theories in composite materials as far as ductile and/or unidirectional fiber/melted fiber reinforcements are concerned [34]. This theory can model composite materials such as cementbased structures reinforced with whiskers or fibers/melted fibers [34,35]. In the application of this model, the applied load is assumed to be transferred from the matrix material to the fibers/melted fibers through the mechanism of shearing.
The Cox model assumes that the displacement gradient in the fiber/melted fiber is proportional to the difference between the displacement in the fiber and the matrix [35] expressed as: where d f dt is the displacement gradient in the fiber/melted fiber, u and v are the axial fiber/melted fiber and axial matrix displacements, while h is a proportionality constant.
Applying simple force balance for matrix-fiber interaction, we obtain: where, f is the stress of the fiber, d is the fiber diameter, and m is the shear stress of the matrix.
By simplifying, we obtain; By substituting Eq. (3) into Eq. (1), we have: The strain in the fiber is expressed as: (2) where, f is the strain of the fiber, E f is the elastic modulus of the fiber and the rest have their usual meanings. Similarly, the strain in the matrix is given as: where, m is the strain in the matrix. Differentiating Eq. (4) with respect to z yields: The solution to Eq. (7) is: where, istheshearlagparameter, C 1 andC 2 are constants, Cosh(βz) is the hyperbolic cosine function of βz, sinh (βz) is the hyperbolic sine function of βz and the rest have their usual meanings.
where G m is the matrix shear modulus,E f is the fiber Young's/elastic modulus, d is the fiber diameter, D is the diameter of the unit cell. At the end of the fibers/melted fibers, some boundary conditions are applicable. Assuming f = 0 , and in the middle of the agglomerated fiber, d f ∕dz = 0. We can then substitute this into Eq. (8) to determine the values for C 1 and C 2 as follows [34,35]: where all the symbols have their usual meanings as shown previously.
A modified version from Cox (1952) model was done and that for strongly bonded fiber ends, 0 ≠ 0 . For this, mean fiber stress ( f ) could then be determined from [35]: Applying the simple rule of the mixtures model, we can express the mean composite stress as: where, c is the mean composite stress, ̃m denote the mean stress of the matrix, ̃f is the mean stress of the fiber and V f represents the weight fraction of the fiber.

Statistical analysis
Gaussian and Weibull distributions are widely applied in the strength analysis of ceramic-matrix composites. The Weibull distribution with two parameters can be described by the following equation [36]: where F u represents the material failure probability under uniaxial tensile stress, m denotes the Weibull modulus/shape parameter, whiles o represents the scale parameter and m relates to the scatter in the data. The Weibull modulus/shape parameter, m represents a measure of how homogeneous the strength data are. This parameter has an influence on the probability value (p-value) which depicts how the data are strongly distribution.

Processing and characterisation of polyethylene-laterite composite
Discarded 'pure water sachets', a loose term used in Africa, were collected at the Tamale Technical University in Northern Ghana. These discarded 'pure water sachets' were classified as pollutants that were washed with detergents (such as sodium dodecyl sulphate or laundry detergents) and water and air dried for six (6) hours. The microbes on the discarded pollutants pose fewer environmental concerns after washing with sodium dodecyl sulphate or laundry detergents. The dried 'pure water sachets' classified as low-density polyethylene (LDPE) were measured in different weight fractions of LDPE filler (40, 50, 60, and 70 wt.%). These LDPEs were melted above 130 • C in a fume hood and homogeneously mixed (without water but molten PE) to include the weight fraction of LDPE filler (40, 50, 60, 70 wt.%) for 5 min using the rule of mixture strength model. The laterite (containing Iron oxide and Titanium in large quantities as well as Aluminum and Silicon in moderate quantities) with a grain size of 900 m after sieving was obtained from Tamale Technical University, Tamale, Ghana. The laterite has grain size distribution as shown in Fig. 1. The resulting polyethylene-laterite composites were then poured into a mould with dimensions of 20 × 20 × 20 mm for compression testing and 50 × 13 × 6.5 mm for flexural and fracture toughness testing. Each of these samples was then allowed to air dry at room temperature (30 • C ) for 24 h. The as-ready samples were prepared for mechanical testing using the Universal Testing Machine to determine several mechanical properties, including compressive strength, flexural strength, and fracture toughness. A total of ninety (90) samples were produced for compression, flexural, and fracture toughness testing, thus, making thirty (30) samples for each sample composition.

Compression and flexural testing
The compressive and flexural strength measurements were performed under displacement control with a displacement rate of 0.03 mm/s and a strain rate of 0.02/s. The loading was carried out monotonically for all the samples until failure occurred and the samples were separated into two or more pieces. Before carrying out the actual testing, the accurate dimensions of the samples were measured using a pair of digital vernier calipers.

Fracture toughness testing
The thirty (30) samples prepared for fracture toughness measurement were measured using the Universal Mechanical Testing Machine (TIRAtest Model 2810, Schalkau, Thuringia, Germany). These tests were carried out using Single Edge Notch (SEN) specimens with dimensions of 50 × 13 × 6.5 mm and a notch width of ∼ 3mm . The fracture toughness experiment was carried out under load control with a stress intensity factor increase rate (K) of 0.01 MPa √ ms −1 . These samples were loaded monotonically until fracture occurred by separation of the samples into two or more pieces.

Microstructure
The microstructural results for the green composite are illustrated in Fig. 2 (a-c). The SEM images were prepared on braked surfaces and then polished with P120 SiC abrasive papers (CarbiMet, Buehler, Uzwil, Switzerland), with an rpm of 130. The polished samples for the different weight fractions of LDPE were viewed with the SEM. From the images, several phenomena occur including matrix-polyethylene bonding, matrix-polyethylene debonding, and the appearance of micro-cracks and secondary/multi-cracks. The green polyethylene composite with 40 wt.% laterites and 60 wt.% PE (Fig. 2c) has excellent bonding between the matrix and PE reinforcement, although some visibility of gully erosions can be seen in the middle of the SEM images. From the gully erosion, there are pieces of evidence of ligament bridging at specific locations, thus, serving as an impediment for crack propagation. However, Figs. 2 (a-b) behave differently with the visibility of micro-cracks and secondary/multi-cracks in most surface areas. This is due to the inability of the PE reinforcement to bond firmly with the laterite matrix. When PE reinforcement is too tiny in the mixture, the PE binder/glue cannot effectively arrest all micro-cracks in the composite, leaving excess laterite that is forced to interact with each other. The interaction of this laterite-laterite produces several micro-cracks in the composite. This laterite-laterite interactions form weak linkage within themselves, thereby creating weak bonding in the composite. Also, the presence of these micro-cracks with time grows and propagates to other sections in the composite, resulting in weaker strengths in the overall composites.

Compressive strength
The results for the compressive strength of the green composite are illustrated in Figs. 3 (a-d). Critically examining  Figure 2d recorded the lowest compressive strength of 7.5 MPa. The scientific reason behind this lower strength is that once the composite (with 30 wt.% laterites plus 70 wt.% polyethylene) reached its ultimate compressive strength, multiple voids occur leading to very weak interactions between the polyethylene-polyethylene interphases instead of the polyethylene-laterite interphases. Polyethylene-polyethylene interaction then causes the composite to be weak, thereby reducing the overall compressive strength of the composite. The composite in Fig. 3c had the highest compressive strength of 25 MPa, which is higher than previous work on polyethylene-cement composites [1, 2, 8, 9, 10, 11, 12 and Table 1. The reason behind this tremendous jump is that the melted polyethylene served as an effective glue/binder, due to proper binding and interactions of polyethylene-laterite interphase. Polyethylene-laterite interactions form stronger bonds between them and this reinforces the composite after the melted polyethylene molded in all the laterite into one constituent during curing. This, therefore, increases the overall compressive strength of the composite. The hypothesis is that large volumes of PE not exceeding 60% have maximum compressive strength and large elongation.

Fracture toughness
The result for the fracture toughness of the green composite is illustrated in Fig. 5. It is shown that the green composite with 60 wt.% PE and 40 wt.% laterite recorded the highest fracture toughness of ∼ 0.6MPa √ m , with the least fracture toughness being the composite with 30 wt.% laterites and 70%PE ( ∼ 0.1MPa √ m ). The increased in fracture toughness of ∼ 0.6MPa √ m for the green composite with 60 wt.% PE and 40 wt.% laterite was as a result of the PE serving as an impediment for dislocation and propagation of cracks and filling voids in cracks and micro-cracks. In this case, cracks are initiated by accumulated stress concentration around the tip of the notch. This stress concentration is responsible for the propagation of cracks in the composite due to constant stress pile-ups. However, since the PE binder firmly bonds the particles together, when cracks begin to propagate, they come in contact with the PE obstacle within the shortest possible time. This barrier created by the PE obstacle causes excessive stress concentration around the cracks, thereby allowing the cracks to gather excess energy for them to overcome the PE obstacle. This excess energy needed by the cracks to overcome the obstacle takes a lot of time. The longer the cracks take to overcome the obstacle, the more stress is concentrated, and the better the overall strength of the composite. The decreased in fracture toughness of ( ∼ 0.1MPa √ m ) for 70 wt.% PE was as a result of less filling of voids of the PE in the composite. This implies that the PE will not be able to bind all the laterite particles together, leading to lesser

Shear lag analysis
The shear lag analysis of the cementless polyethylene-laterite composite (also known as the green composite) is illustrated in Fig. 6. It is seen that the green composite recorded a maximum shear lag young's modulus of approximately 8 MPa for the different weight fractions of PE (40, 50, 60, and 70 wt.%). The value of young's modulus suggests minimal disconnection in the fibers of the green composite. Furthermore, the value of 8 MPa also suggests that most of the composite's fibers were correctly connected, thus increasing the strength and stiffness of the cementless polyethylene-laterite composite as seen in the strength analysis.

Statistical analysis of polyethylene in the green composite
The results of the statistical analysis of dislocated polyethylene in the green composites are shown in Fig. 7. The probability plots show that the Weibull distribution well characterizes the green composites' grain diameter and yield stress. This is evident as the probability distribution plots have low (but more than 5%) Anderson Darling Statics values and p-values greater than the significance level of 5%. This means the dislocated polyethylene in the green composites follows the Weibull distribution. This means that the polyethylene serving as a binder in the composite is reliable and can adapt to different situations as far as it is following the Weibull distribution. The Weibull distribution is one of the reliability analyses for life and experimental data.

Conclusion
This study shows that polyethylene in its molten state when mixed with laterite without the inclusion of cement can be used as a sustainable material for Mechanical and Civil Engineering applications. The green composite with 40 wt.% laterites and 60 wt.% PE exhibited the highest compressive strength, flexural strength, and fracture toughness of 25 MPa, 7.3 MPa, and 0.6MPa √ m , respectively. Additionally, a maximum yield stress of ∼ 2MPa was recorded for the green composite with 40 wt.% laterites and 60 wt.% PE. This maximum yield stress ( ∼ 2MPa) of the PElaterite composites falls under the minimum range of yield stress for traditional concrete structures ( ∼ 2MPa − 5MPa) . The SEM images reveal evidence of bonding and ligament bridging in the green composite reinforced with 40 wt.% laterites and 60 wt.% PE. The probability distribution plots show that the dislocated polyethylene in the green composites follows the Weibull distribution since the Anderson Darling Statics values are low (but more than 5%) and the p-values are greater than the significance level of 5%.
The results show that the green composite with 40 wt.% laterites and 60 wt.% PE can have applications in the Mechanical and Civil Engineering industry for the production of building blocks/bricks and pavement.