Influence of temperature on the creep behaviour by macroindentation of Cocos nucifera shells and Canarium schweinfurthii cores (bio-shellnut wastes in Cameroon)

The aim of this study was to show how temperature modifies the mechanical characteristics of the Cocos nucifera (CN) shells and the Canarium schweinfurthii (CS) cores. The test consisted in performing an instrumented macroindentation on prismatic specimens in an adiabatic chamber; the indentation carried out according to four temperature ranges (30 °C, 50 °C, 70 °C, 90 °C). The Oliver and Pharr method is used for the analysis of mechanical parameters in indentation: reduced Young’s modulus, hardness, creep coefficient. These parameters have enabled to estimate indirect characteristics such as toughness and ultimate mechanical stress to be obtained. The creep data are simulated to have the rheological model to these materials by considering the statistical criteria. As a global observation, when the temperature increases, the mechanical parameters decrease; although CN is more sensitive to the temperature gradient than CS, these 2 materials show performances that allow them to be classified as engineering polymer materials according to the Ashby diagram.


Introduction
Biomaterials are a class of materials comprising biofibres, biopolymers and bio-composites, the main components of which come from agriculture or the plant world, as products or wastes [1][2][3][4][5]. These materials have experienced a boom in recent years, regarding many issues such as reduction of plastic pollution, recycling, stiffness, lightweight, low cost, etc. People are seeking to replace synthetic materials that have a negative impact on the environment and life, causing harmful effects on land, sea and air [1,2,6], by natural materials that are biodegradable [2,6,7].
The development of new materials [18][19][20] requires the determination of their mechanical properties [21,22] when considering various scales starting from the macro to nano scale. Natural biomaterials are among these new materials [23,24], and due to their availability they are increasingly used in industry as secondary resources that can replace or supplement primary resources [25][26][27]: Cocos nucifera (CN) shells and Canarium schweinfurthii (CS) cores are among these bioresources which are available as waste in Cameroon, with an estimated volume around 2,000 tons [28].
When these natural materials are in the form of fibres, surface preparation [1,6,7,9,12,14,34,36] and/or physical or chemical pre-treatments [8-10, 16, 17, 34] are needed in order to achieve the best interface with the matrix and/or an improvement within the strength of the fibres.
In the case of CS, technical applications as a composite material lead to characterization approaches that are similar to those already mentioned for CN, with the enhancement of the effect of density, the water absorption rate, and friction properties [29,35]. Recent work has focused on producing brake linings by combining CS fillers and palm kernel fiber with urea formaldehyde resin. He was interested in the effect of input size and proportions on composite density and dynamic friction coefficient [39]. Standard mechanical characterization can also be carried out for parts of CS when they are in their natural state, such as strength and stiffness [32] or strength and mobility for nuts, the humidity level being an important parameter in the latter case [40].
However, characterization is necessary to better understand the material's behaviour, so as to be to identify or to extend the field of applications, which choice is set depending on the achieved properties. Such an approach is highlighted by works from Schmier et al [41] and Gludovatz et al [38], who both succeed in identifying the mechanisms of crack initiation and toughening related to the anisotropic channel structure, by establishing the morphological parameters of the hierarchical structure of the CN endocarp. Such results can lay the basis for transferring those properties into biomimetic technical applications [41]. Similarly, a very recent study [42] allows establishing a 3D model of the natural and structured composite material constituted by coconut, in the form of a flat structure with coconut-inspired microchannels. This new approach of numerical simulation allows understanding the crashworthiness of coconuts.
For natural materials, the most common mechanical tests are done under static (traction, compression, flexural, etc) or dynamic modes (toughness fracture), either on a single fiber or set of fibers, or on the shell [1,6,7,11,13,30,31,38,43], all these features being prompt to exhibit different orientations and a variable age [38]. Thermophysical properties, density as well as water absorption of the fibers or aggregates can also be determined [13,30,31,35,43].
Several characterization techniques exist [44,45], including indentation [46] which presents an ideal compromise in relation to the stresses that are applied to the studied material.
Characterization by indentation allows several parameters to be determined at the same time: hardness, Young's modulus, and creep [6,7,11,12]. However, as reported by Flores-Johnson et al [3], who determine the hardness of acrocomia mexicana fruit shell, such a technique is seldom used for biomaterials characterization. The same observation can be made for creep, which is not often considered for such materials.
The use of these materials is carried out under various conditions, taking into account environmental criteria such as temperature, humidity or acidity, which strongly influence the parameters of the exposed materials [47,48].
In what follows, the indentation technique will be used to determine the hardness and Young's modulus on both CN and CS biomaterials. In addition, the creep behavior of both materials will be discussed as a function of temperature set at 30, 50, 70 and 90°C respectively, based on the same indentation tests.

Materials
CS and CN are collected as waste in the public squares of the city of Douala in Cameroon. The cleaning by washing with water of the internal and external surfaces has made it possible to eliminate impurities of the following types: pulp, sludge, sand and fibers. The 10×20×3 mm 3 for CS and 10×10×3 mm 3 for CN [49] samples (figure 1) were obtained by sawing the shell portions and polishing the faces of this portion.

2.2 Methods
The mechanical characterization in this case is carried out at variable temperature but using an adiabatic heating module to maintain a given temperature value around the test sample.
The equipment used by Njeugna, et al [49] was modified by adapting the heating module (figure 2). The experiments are carried out at four temperatures (30°C, 50°C, 70°C, 90°C) while using a spherical indenter of diameter Φ6 mm.
These temperatures are chosen to remain below the glass temperature (Tg) of polymer materials [50][51][52] (Tg ò [100-130]°C). At a given isotherm and for a progressive increase of the load (from 0 up to the maximum load of 500N over a constant incremental step of 50 N), the displacement of the indenter penetrating the specimen is recorded by a 1/1000 e precision digital sensor. The load-displacement characteristic graph (figure 3(a)) is obtained by combined reading of the sensor displacement display and the corresponding load value. The test is quasi-static but fast enough to avoid creep effects during loading.
When the maximum load is reached and maintained, creep data is recorded over a period of one hour. After creep (figure 3(b)), this is followed by a progressive unloading of each placed mass, during which the data corresponding to the removal of the indenter are also recorded.
The analysis of the indentation tests is based on the hypothesis of an elastoplastic load rise, followed by a purely elastic unloading (figure 4) As far as the analysis and evaluation of the load-unloading curves resulting from the collection of our data is concerned, it has been carried out in several clearly defined steps using the method of Oliver and Pharr [53] expressed by the equation (1).

= -
Where P is the force; P m is the maximum force applied; h is the indentation depth at any time; h f is the final indentation depth at discharge; h m is the maximum indentation depth at P m ; m is a constant determined by means of a least squares method and is a function of the geometry of the indenter: for a spherical indenter such as in this study m=1 [54][55][56].

Reduced young's modulus
The determination of Young's modulus is based on the assumption that during the unloading curve the removal of the tip is accompanied by a spring back due to the elasticity of the material. Thus the slope of the unloading curve provides a measure Young's modulus [57][58][59]. The method is based on the recovery theory of Hertz [60]. It provides for the modelling of the unloading slope with a function that relates the contact area to the reduced Young's modulus according to the equation (2):

Hardness
Once the method for the calculation of the contact area is available, it is possible to calculate hardness contact H [58,61]. This is done using the formula from equation (3) and the contact area A c .
Creep ratio C IT denoted indentation creep ratio is defined by the relative change in depth of corresponding penetration, according to equation (4).

Creep parameters
With regard to the determination of the rheological model, several models are proposed in the literature. These models are based on the combination of springs and dampers to represent the viscoelastic behavior of a material by its total deformation ε(t) (equation (5)): The Boltzmann's superposition principle, applied in the case of linear viscoelasticity, states that the sum of the deformations resulting from each component of the stress input is the same as the deformation resulting from the combined stress input, the total deformation can be expressed (equation (6)) by an integral representation such as: With D(t) and ΔD(t−τ) being respectively the creep compliance at the time t and in the transient phase and σ 0 the constant stress. For non-linear viscoelasticity, the Schapery model is expressed at constant stress using the description of the irreversibility of thermodynamics for the viscoelastic materials subjected to the external loading in single integral [62,63].
The total deformation (equation (7)) is expressed by: The parameters to be determined in the case of the study in only case of creep of nonlinear viscoelasticity are: g 0 (equation (8)), D 0 (equation (9)). The other g 1 , g 2 , and a σ are function of recovery and this study is focused only on the creep. During the various tests considering every isotherm.  The usual models (figure 5) [64] are listed in table 1. These expressions will be used to test the numerical data obtained during creep acquisition. This in order to know the model that best describes the phenomenon of indentation creep for CN and CS materials.

Models
Mathematics

Density
The test sample is introduced into the cell of the helium pycnometer (Micrometrics 1305). This equipment uses a gas at 140-170 kPa (helium, nitrogen). It is preferably Helium for a best performance, as Helium is stable with all materials. Density was numerically evaluated by (equation (13)).

Toughness
Toughness is assessed by analytical calculation (equation (14)). In general, the mechanical stress of a material can be correlated to the hardness of a material. The relationship between the average pressure under the indenter, the modulus, the yield strength of Young and the hardening behaviors were established. The toughness T of sufficiently hard materials can be obtained using equation (14) as described by Chai, et al [65]. ( ) The parameter a can easily be identified in figure (3). It is calculated knowing the depth h. c .

Ultimate strength
Since 1945, Bishop, et al [8] have suggested that the pressure distribution under an indenter can be approximated by that of a spherical or cylindrical cavity. Relationships between mean pressure under the indenter, yield strength, Young's modulus and strain-hardening behaviour have been established. For plastic solids with perfect elasticity, the pressure (P) at which the cavity extension depends on the ratio between Young's modulus (E) and yield strength (σ y ) and the Poisson's ratio (ν) according to (equation (15)) Following this idea, an extension of the spherical cavity was carried out by Johnson in the early 1970s [66]. He stressed that the radial placement of the material at the elastoplastic limit must take into account the volume of material displaced by the indenter during indentation. Recently, besides these theoretical analyses, an empirical equation is widely used since 1997, the relation between the hardness H and the elastic limit (equation (16)).
It is therefore proven that hardness and ultimate stress are linked by an approximately linear relationship with factors that would depend on the nature of the material.
Thus, considering the data in the literature for materials (acrocomia [3] and macadamia [67]) of the same nature as those under study (CN and CS), a proportionality factor of 2.73 was correlated linking ultimate stress to hardness to obtain (equation (17)

Results and discussion
3.1. Hardness, young's modulus, creep coefficient and toughness Figure 6 shows the results of macroindentation with a maximum applied normal load of 500 N for temperature isotherms of 30, 50, 70 and 90°C on CN and CS samples. A significant variation is observed on the measured mechanical properties (reduced modulus of elasticity, hardness and indentation toughness) as a function of temperature. The general trend is the reduction of the above parameters.
There is a higher hardness value for CN and CS than for palm nut shells, hazelnut, and brazil nut (table 2) a reduced young modulus value almost twice as high. On the other hand, for materials of the same type such as acrocomia and macadamia, the values for hardness and young modulus are much higher than those for CN and CS. For the Scheelea sp, when the hardness is higher than the hardness of CN and CS; the Young's modulus is slightly smaller. The microstructure and intergranular arrangement are the main factors influencing these parameters. It is also important to specify the scale of the test (macro, micro or nano), the maturity of the shells, the harvesting environment and the climate of the region are very important in the variations often found. Therefore, conducting an effective comparative analysis means integrating all these factors or reducing them by harvesting products from the same area and of the same age. Basically, the analyses carried out here and there just provide a classification range and a criterion to help in the decision making process when selecting materials for specific applications. Figure 7 shows the creep curve of the CS and CN specimens as a function of temperature. With respect to the evolution of the curves in figure 6, it should be noted that the deformation increases with temperature which is clearly justified in table 3.

Rheology and creep analysis
By observing the correlation coefficient (R 2 ) obtained for each rheological model in table 4, the Burger-4 model and the Zener model are showed the best correlation, however, by observing the permanent impressions after discharge and over time, the Burger-4 model is suitable for describing the visco-plasticity of these materials. It shows a correlation trend over all temperature ranges and for both CN and CS. This model adequately describes the phenomenon of indentation creep for these materials. The parameters of the Burger-4 model are given in table 5 and would allow an evaluation of the creep-mechanical parameters describing the visco-plastoelasticity of this materials.
It appears from figure 6 that CN is more influenced by temperature variation than CS, which is consistent with the density values presented by this work and the SEM microstructures observed by Njeugna, et al [52]. Indeed, CN is less dense than CS and CN microstructures show embedded fibers between the grains. Because fibers are more temperature sensitive than the grains of microstructures, also with a lower density, the intergranular distances in CN microstructures are more likely to increase with the temperature gradient. Nevertheless, these results show a high homogeneity of the characteristics of this bio-material. and describe a linear decreasing trend of the calculated parameters: young modulus, hardness, creep coefficient and toughness.
The mechanical results show that the CN and CS materials are very hard and tough comparing to wood product.
Indentation analyses showed two distinct regimes, which are an elastic regime and a plastic regime with strain-hardening. The elastic phase was reduced with increasing temperature ranges. The elastic behaviour is similar to the friction of the microparticles during penetration and when the temperature increases, the intergranular bonding energy will become insufficient to the indentation energies to avoid microcracking, indicating the end of the plastic phase. Plastic behaviour can be understood as a combination of energy absorption mechanisms, including cell crushing, intergranular bond failure, primary wall failure and cell tearing. When the sample densifies by crushing the porosities, the dissipation of frictional energy is greater because the elastic capacity of the materials is almost completely lost.
It is noted that from an isothermal temperature of 70°C, the mechanical properties are strongly influenced, this due to the approach of the glass transition zone. This is confirmed by a reduction in modulus of elasticity, hardness and toughness by half for CS and almost a quarter for CN. Figure 8 shows an Ashby graph for compressive strength (calculated by its relationship to hardness) as a function of density and compressive strength for different materials. CN and CS materials show higher

Conclusion
In this study, the mechanical characteristics and rheological behaviour of certain by-products of cameroonian plants (CN and CS) were experimentally determined at different isotherms by macroindentation. Using a spherical indenter of Φ6mm and for loads up to 500N, several tests were carried out on both materials at isotherms of 30°C, 50°C, 70°C and 90°C. The Oliver and Pharr method exploited in macroindentation made it possible to determine the reduced Young's modulus, hardness, creep coefficient, toughness, mechanical strength and rheological model of these biomaterials. The results show that, apart from the creep coefficient, all other characteristics decrease with temperature in the mentioned range. Temperature has a great influence on parameters such as Young's modulus (its value drops by about 50% between 30°C and 90°C) and toughness (its value drops by about 60% between 30°C and 90°C). Overall, the mechanical characteristics of CN are more sensitive to temperature than those of CS. Conversely, the creep coefficient increases slightly with temperature.
Of the four rheological models tested, the Burger-4 elements model best reflects the behavior of CN and CS. All its results show that CN and CS can be used as reinforcing elements in composite materials. This study also made it possible to classify CN and CS according to an Ashby diagram in the engineer's polymer category.