Y Ayed

C Robert

G Germain

A Ammar

Orthogonal micro-cutting modeling of the Ti17 titanium alloy using the crystal plasticity theory

Keywords:

The development of computation means has allowed the simulation of complex mechanical problems. The first simulations of manufacturing processes at the microstructure scale, namely in the field of machining, have recently emerged. In this study, and on the basis of previous research, a novel approach to machining simulation is proposed. A crystal plasticity behavior law has thus been implemented and its parameters have been identified, for each of the two phases constituting the material. This is achieved through experimental tests conducted under extreme conditions of temperature and strain rates. Numerical models are composed of grains in the form of Voronoï cells. Random crystal orientations have also been assigned to each grain. This has subsequently allowed the simulation of the machining process. Access to local physical parameters such as crystal orientations, their evolution and phase transition thus presents a major breakthrough in this field.

Introduction

Titanium alloys are widely used in the aeronautical, aerospace and biomedical fields thanks to their excellent strength-to-weight ratio, their good mechanical properties, even at high temperatures, and their corrosion resistance. Despite these characteristics, titanium alloys are difficult-to-cut materials, and their poor machinability presents a challenging problem [START_REF] Ezugwu | Titanium alloys and their machinability-a review[END_REF][START_REF] Jawaid | Tool wear characteristics in turning of titanium alloy ti-6246[END_REF]. In order to deal with this issue, it is indispensable to investigate the different phenomena interacting during machining. Nowadays, using the best experimental means (infrared thermography, high speed camera, Digital Image Correlation, etc.), it is still impossible to access the cutting zone. Thus, numerical simulation of the cutting process provides additional information [START_REF] Yaich | Numerical analysis of constitutive coefficients effects on fe simulation of the 2d orthogonal cutting process: application to the ti6al4v[END_REF][START_REF] Ayed | Development of a numerical model for the understanding of the chip formation in high-pressure water-jet assisted machining[END_REF][START_REF] Caruso | Numerical simulation of surface modification during machining of nickel-based superalloy[END_REF][START_REF] Lindgren | Towards predictive simulations of machining[END_REF]. However, this modeling is hampered by the complexity of the process and the strong interaction of different complex physical phenomena in too short a time lapse and in a very small area. Indeed, as reported by Garcia-Gonzalez et al. [START_REF] Garcia-Gonzalez | Tool rake face temperature distribution when machining ti6al4v and inconel 718[END_REF], the cutting temperature measured by different experimental means such as infrared thermography varies from 700 • C to up to 1000 • C (depending on cutting conditions). Temperature levels estimated by numerical simulations are in the same range of the experimental ones [START_REF] Wang | Metallurgical-based prediction of stress-temperature induced rapid heating and cooling phase transformations for high speed machining ti-6al-4v alloy[END_REF][START_REF] Arrazola | Metal cutting experiments and modelling for improved determination of chip/tool contact temperature by infrared thermography[END_REF]. The machined surface undergoes large deformations and complex thermal cycles. As reported by Outeiro et al. [START_REF] Outeiro | Experimental and numerical assessment of subsurface plastic deformation induced by ofhc copper machining[END_REF], plastic deformation levels are very high and vary from 1.8 to 3.4 (OFHC copper). If we add to all these issues the integration of the dynamic constitutive equations and friction, the task becomes even more complex. For all these reasons, the modeling of machining is particularly dependent on the scientific evolutions of experimental, numerical and computational means.

Over the last two decades, the numerical simulation of machining has witnessed significant advances. Most previous cutting models use the phenomenological behavior law of Johnson-Cook (JC) [START_REF] Johnson | A constitutive model and data for metals subjected to large strains, high strain rates and temperature[END_REF] which has allowed researchers to closely study some physical phenomena during the chip formation process. Nevertheless, it is important to point out that this type of modeling does not provide enough information at the local level; at this scale, as a matter of fact, microstructure characteristics (especially grain size and phase transformation) impacts material behavior.

With increasingly complex and quickly evolving computing means, recent years have seen further progress in this area as more complex models have been proposed. The studies conducted by Simoneau et al. [START_REF] Simoneau | Chip formation during microscale cutting of a medium carbon steel[END_REF][START_REF] Simoneau | Grain size and orientation effects when microcutting aisi 1045 steel[END_REF][START_REF] Simoneau | Modeling the effects of microstructure in metal cutting[END_REF] led to the development of a cutting model which takes account of material phases. It should be noted that the behavior of each phase is modelled by the JC constitutive law. This has allowed for more accurate simulations at the levels of chip formation, temperature fields and cutting forces. The same procedure was used by Obikawa et al. [START_REF] Obikawa | Microscopic phase-dependent residual stresses in the machined surface layer of two-phase alloy[END_REF] Cutting speed parameters. Mohammed et al. [START_REF] Mohammed | Modeling the effect of the microstructure of compacted graphite iron on chip formation[END_REF][START_REF] Mohammed | Modeling the effect of compacted graphite iron microstructure on cutting forces and tool wear[END_REF] developed a cutting model that takes into account the effect of the microstructure of compacted graphite iron on chip formation. Based on physical behavior laws, and in particular the mobile dislocation density theory, other recent research studies aimed to predict the grain refinement resulting from the phenomenon of dynamic recrystallization [START_REF] Ding | Modeling of grain refinement in aluminum and copper subjected to cutting[END_REF][START_REF] Liu | A unified material model including dislocation drag and its application to simulation of orthogonal cutting of ofhc copper[END_REF][START_REF] Fernandez-Zelaia | A microstructure sensitive grain boundary sliding and slip based constitutive model for machining of ti-6al-4v[END_REF]. These researches have shown the need to use constitutive material behavior laws based on the theory of crystal plasticity in order to develop more realistic models. Indeed, the models based on crystal plasticity present many advantages, especially the ability to simulate and predict the evolution of the texture of a material under strong thermomechanical solicitation. The researches conducted by Peirce et al. [START_REF] Peirce | Material rate dependence and localized deformation in crystalline solids[END_REF] and Asaro et al. [22,[START_REF] Asaro | Texture development and strain hardening in rate dependent polycrystals[END_REF], and which were based on Schmidt's study [START_REF] Schmidt | Uber die schubverfestigung von einkristallen bei plastischer deformation[END_REF], have paved the ground for the development of this research axis.

Other research work has focused on the simulation, at the microstructure scale, of processes such as deep drawing [START_REF] Boudifa | A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming[END_REF][START_REF] Geng | Effect of crystalline anisotropy and forming conditions on thinning and rupturing in deep drawing of copper single crystal[END_REF][START_REF] Zhang | Physically based crystal plasticity fem including geometrically necessary dislocations: numerical implementation and applications in micro-forming[END_REF], ultrasonic consolidation [START_REF] Siddiq | A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation[END_REF], bending [START_REF] Zhang | Micro-bending of metallic crystalline foils by non-local dislocation density based crystal plasticity finite element model[END_REF] and stamping [START_REF] Kraska | Virtual material testing for stamping simulations based on polycrystal plasticity[END_REF]. The use of the crystal plasticity (CP) theory has permitted to have a physical insight into grain size effect, damage, texture effect and to have an accurate prediction of the forming limit diagrams (FLDs) at different temperature levels [START_REF] Cyr | Modeling the formability of aluminum alloys at elevated temperatures using a new thermo-elasto-viscoplastic crystal plasticity framework[END_REF]. The modeling of multiphase materials has allowed for a better understanding of certain deformation and damage mechanisms. In the case of dual-phase steels, this type of modeling has given a better insight into failure mechanisms, shear localisation and the contribution of each phase [START_REF] Kadkhodapour | A micro mechanical study on failure initiation of dual phase steels under tension using single crystal plasticity model[END_REF][START_REF] Woo | Stress-strain relationship between ferrite and martensite in a dual-phase steel studied by in situ neutron diffraction and crystal plasticity theories[END_REF][START_REF] Jeong | Effect of kinematic stability of initial orientation on deformation heterogeneity and ductile failure in duplex stainless steel during uniaxial tension[END_REF]. In the case of titanium alloys, more realistic simulations have been carried out by taking into account the material behavior of the 𝛼 and 𝛽 phases [START_REF] Gerday | Mechanical Behavior of Ti-5553 Alloy. Modeling of Representative Cells[END_REF][START_REF] Bin | Crystal plasticity finite element study of incompatible deformation behavior in two phase microstructure in near Κ titanium alloy[END_REF].

The modeling of the machining process using a polycrystalline model has recently emerged with the study conducted by Zhang et al. [START_REF] Zhang | An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes[END_REF]. This model has the advantage of using the assumption of a 2D plane strain and then significantly reducing computation time. Kinematic and isotropic hardening have been implemented, assuming no rotation of crystal orientations. To take account of the damage at the intragranular scale, the authors have proposed a model based on the Lemaitre and Chaboche damage model. Intergranular fracture has been modeled by using cohesive elements at grain boundaries. The comparison between the numerical model and the experimental results for many cutting conditions seems to give good results. Meanwhile a combination of the finite element method and Smoothed Particle Hydrodynamics (SPH) was employed by Abolfaz et al. [START_REF] Zahedi | Fesph modelling of orthogonal micro-machining of f.c.c. single crystal[END_REF] in order to determine the influence of crystallographic orientations on the evolution of the cutting forces. A similar test was performed for the simulation of copper machining [START_REF] Demiral | Numerical modelling of micro-machining of f.c.c. single crystal: influence of strain gradients[END_REF][START_REF] Tajalli | Simulation of orthogonal micro-cutting of fcc materials based on rate-dependent crystal plasticity finite element model[END_REF]. The study carried out by Tajalli et al. [START_REF] Tajalli | Simulation of orthogonal micro-cutting of fcc materials based on rate-dependent crystal plasticity finite element model[END_REF] showed that the initial grain orientation affects the morphology of the chip and the cutting forces. The recent study carried out by Li et al. [START_REF] Li | Fem-simulation of machining induced surface plastic deformation and microstructural texture evolution of ti-6al-4v alloy[END_REF] proves the capability of this kind of modeling for an accurate prediction of the deformed material texture.

These different studies have evidenced the pertinence of this approach and the need to reinforce current research in the field. The work proposed in this study is thus inscribed within this perspective of continuity. The material used in the present study, Ti17, has a millimetric grain size (Fig. 1). The Ti17 (Ti-5Al-2Sn-4Mo-2Zr-4Cr) is a beta-rich titanium alloy. As reported by R.R. Boyer [START_REF] Boyer | An overview on the use of titanium in the aerospace industry[END_REF], Ti17 has been developed by General Electric Aircraft Engines. Known for its deep hardenability and high fracture toughness, it can be used below 400 • C. As a case in point, it is actually used in some Compressor stages of the GE90 engine. The tensile strength of the material (𝜎 UTS ) is around 1110 MPa and its elongation at break varies from 5% to 8%.

It therefore seems interesting to explicitly model the microstructure to take into account crystal modifications which may occur during chip formation. The main objective of this study is to develop a model which allows for the machining simulation of the Ti17 using the crystal plasticity theory. This research has been carried out as follows:

-Model the gains with Voronoï cells; -Model the 𝛽 phase with 12 slip systems (BCC structure) and the 𝛼 phase with 24 slip systems (HCP structure) [START_REF] Mayeur | A three-dimensional crystal plasticity model for duplex ti-6al-4v[END_REF][START_REF] Zhang | An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes[END_REF][START_REF] Li | Crystal plasticity modeling of the dynamic recrystallization of two-phase titanium alloys during isothermal processing[END_REF]; -Implement a crystal plasticity constitutive equation considering isotropic hardening and damage evolution; -Take into account the rotation of the crystal lattice (finite transformations); -Take into account phase transformation.

The list of the 36 slip systems is shown in Table 1. The disorientation between the HCP and the BCC systems has also been taken into account.

Crystal plasticity modeling

Implementation of a crystal plasticity constitutive equation

The numerical integration of crystal plasticity equations is often challenging. Indeed, the major two obstacles are the strong nonlinearity of these equations and the considerable computation time needed. Several algorithms with implicit [START_REF] Beaudoin | Three-dimensional deformation process simulation with explicit use of polycrystal plasticity models[END_REF][START_REF] Anand | A computational procedure for rate-independent crystal plasticity[END_REF][START_REF] Zecevic | A new implementation of the spectral crystal plasticity framework in implicit finite elements[END_REF] and explicit [START_REF] Dumoulin | Investigation of integration algorithms for rate-dependent crystal plasticity using explicit finite element codes[END_REF][START_REF] Li | An efficient parallel-operational explicit algorithm for taylortype model of rate dependent crystal plasticity[END_REF] integration schemes have been set up. As reported by Rashid et al. [START_REF] Rashid | A constitutive algorithm for rate-dependent crystal plasticity[END_REF] and Dumoulin et al. [START_REF] Dumoulin | Investigation of integration algorithms for rate-dependent crystal plasticity using explicit finite element codes[END_REF] the explicit integration scheme seems to be more suitable for highly non-linear problems. An interesting comparative study of the integration of crystal plasticity equations has been carried out by Harewood and McHugh [51]. The authors tested explicit and implicit (theta method) integration schemes using ABAQUS FEM solver. They demonstrated that the explicit integration scheme is more efficient in the case of large deformations, especially when there is contact between two or more solids.

In order to incorporate strain rate sensitivity, large deformations and damage evolution, the Boudifa constitutive behavior equation [START_REF] Boudifa | A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming[END_REF] has been used for this study. However, it has been modified to take thermal softening into account. Due to the extreme conditions of high strain rates, high temperatures, and tool/chip contact during chip formation, explicit integration has also been adopted.

Kinematics

In order to take into account the large deformations in the cutting process simulation, a finite deformation framework has been adopted. In this formulation, it is assumed that the crystalline lattice undergoes elastic deformations and rigid body rotations; the material flows through the crystal lattice and it is deformed plastically by the crystalline slip. Hence, to describe material motion, it is necessary to use two coordinate systems. The first is attached to the crystal lattice (rotates with the crystal lattice) and the second is attached to the material (rotates with the material). Hence, the deformation gradient tensor F can be decomposed into two components: an elastic part F e which includes the elastic deformations and the rigid-body rotations, and an plastic part F p , that describes the crystalline slip. Fig. 2 illustrates the decomposition of the deformation gradient tensor.

This decomposition of the deformation gradient tensor can be written as follows:

F = F e F p , F = RU (1)
R is the rigid rotation tensor and U is the right stretch tensor. The velocity gradient L also consists of an elastic part (L e ) and a plastic part (L p ):

L = ḞF -1 = L e + L p (2)
L p = F e Ḟp F p-1 F e-1 = D + W (3) L = D e + D p + W e + W p (4)
D e and D p represent respectively the elastic and plastic strain rates. The rotation of the crystal lattice is represented by the elastic part of the spin tensor W e = Ω = ṘR T . Plastic deformation is assumed to be due to the slip within the crystalline lattice. Thus, the plastic part of the velocity gradient can be written as follows:

L p = N s ∑ s=1 ̇𝛾s n s 0 m s 0 ( 5
)
N s is the number of slip systems while n s 0 and m s 0 represent, respectively, the normal to the slip plane (s) and the slip direction; ̇𝛾s is the shear rate.

The elastic part of the velocity gradient, then, becomes:

L e = L -L p = ḞF -1 - N s ∑ s=1 ̇𝛾s n s 0 m s 0 ( 6
)
It is now possible to calculate the crystal orientations variation as:

n s = F e n s 0 ( 7
)
m s = m s 0 F e-1 (8)

Constitutive relations

In the case of large deformations, FEM codes provide the Green-Nagdhi and/or the Jauman rate to calculate stress change during deformation. The stress rate ▿ * 𝜎 , which designates the corotational stress rate seen by a rotating observer with the crystal lattice, is given by equation [START_REF] Arrazola | Metal cutting experiments and modelling for improved determination of chip/tool contact temperature by infrared thermography[END_REF].

▿ * 𝜎 = σ -W e 𝜎 + 𝜎W e (9)
Indeed, the change rate of the Cauchy tensor 𝜎 in the material corotational frame, according to W, can be expressed as:

▿ 𝜎 = σ -W𝜎 + 𝜎W ( 10
)
Based on equations ( 9) and ( 10), the corotational stress on axes rotating with the material can be expressed as following:

▿ 𝜎 = ▿ * 𝜎 - ( W -W e ) 𝜎 + 𝜎 ( W -W e ) (11)
The Kirchhoff stress 𝜏 can be obtained from the Cauchy stress 𝜎 using equation [START_REF] Simoneau | Chip formation during microscale cutting of a medium carbon steel[END_REF].

𝜏 = det (F) 𝜎 (12)
Thus, the resolved shear stress 𝜏 s on the slip system s is expressed as:

𝜏 s = n s 𝜏m s (13)

The case of a multiphase material

In the proposed model, it is assumed that total deformation is the same in different phases 𝜑 i :

𝜀 = 𝜀 𝜑 i ( 14
)
In this case, the stress tensor is the volume average of the stresses in each phase. The evolution of stresses can be calculated as follows:

𝜎 = N 𝜑 ∑ i=1 f 𝜑 i 𝜎 𝜑 i (15) σ = N 𝜑 ∑ i=1 ( f 𝜑 i σ𝜑 i + ̇f𝜑 i 𝜎 𝜑 i ) ( 16
)
The fraction of each phase is represented by f 𝜑 i . Regarding the damage, a scalar variable D G , which represents the overall damage in the grain, can be defined as follows:

1 -D G = N 𝜑 ∑ i=1 f 𝜑 i ( 1 -D T 𝜑 i ) (17)

Energy relations

As reported by Boudifa [START_REF] Boudifa | A micromechanical model for inelastic ductile damage prediction in polycrystalline metals for metal forming[END_REF], the free energy is written according to an additive decomposition of an elastic part and inelastic part:

𝜌𝜓 ( 𝜀 e , q s , d s ) = 𝜌𝜓 e ( 𝜀 e , D T (d s ) ) + 𝜌𝜓 p ( q s , d s ) ( 18
)
where 𝜌 is the material density, D T is a macroscopic variable for measuring of the damage, 𝜀 e is the elastic deformation, q is the internal variable of isotropic hardening and d s is the damage variable at the slip system level. In order to take into account the impact of damage evolution on the mechanical behavior of the material, effective state variables are used (ε e ; τ).

εe = √ 1 -D T 𝜀 e and τ = 𝜏 √ 1 -D T (19)
At the level of the slip systems, the effective internal isotropic hardening variables (q s ; Rs ) are written as follows:

qs = √ 1 -d s q s and Rs = R s √ 1 -d s (20)
The elastic and the plastic parts of the free energy are presented, respectively, by equations ( 21) and [START_REF] Zhang | Physically based crystal plasticity fem including geometrically necessary dislocations: numerical implementation and applications in micro-forming[END_REF]. Where  is the elasticity tensor, Q is a parameter and H is a matrix which represents the interactions between the different slip systems.

𝜌𝜓 e ( 𝜀 e , D T (d s ) ) = ( 1 -D T ) 1 2 𝜀 e ∶ 𝜀 e ( 21
)
𝜌𝜓 p ( q s , d s ) = Q 2 N s ∑ s=1 N s ∑ r=1 H rs q s q r ( 22
)
Fig. 5. The polycrystalline model. From these equations, the evolution of associated forces variables can be determined (Y s represents the damage force):

𝜏 = 𝜌 𝜕𝜓 e 𝜕𝜀 e = ( 1 -D T ) 𝜀 e ( 23
)
R s = 𝜌 𝜕𝜓 p 𝜕q s = Q √ 1 -d s N s ∑ r=1 H rs q r ( 24
)
Y s = 𝜌 𝜕𝜓 p 𝜕d s = 1 2
Rs qs

1 -d s = 1 2 R s q s 1 -d s (25)

Dissipation

The yield function and the plastic potential are defined by equations ( 26) and [START_REF] Zhang | Physically based crystal plasticity fem including geometrically necessary dislocations: numerical implementation and applications in micro-forming[END_REF].

f s = |τ s | + 𝛼 ⟨σ s n ⟩ + N s ∑ r=1 d r -Rs -𝜏 0 (26)
The plastic potential Φ s is calculated as follows:

Φ s = f s + bq s Rs + Φ s d (d s , Y s ) ( 27
)
σn represents effective normal stress; 𝛼, b and 𝜏 0 are model parameters. The damage part of the plastic potential Φ s d is proposed by equation [START_REF] Siddiq | A thermomechanical crystal plasticity constitutive model for ultrasonic consolidation[END_REF]. 𝛽 d , Y 0 , m and S are the damage parameters.

Φ s d = 1 𝛽 d + 1 ⟨ Y s -Y 0 S ⟩ 𝛽 d +1 + 1 ( 1 -d s ) m ( 28
)
In addition to state variables, effective resolved shear stress and effective normal stress are expressed as:

τ s = 𝜏 s √ 1 -d s and σs n = 𝜎 s n √ 1 -d s (29)
On the basis of plastic potential, the evolution of isotropic hardening and damage is expressed as:

qs = -λs 𝜕Φ s 𝜕R s = λs √ 1 -d s ( 1 -λs q s ) ( 30
)
ḋ s = -λs 𝜕Φ s 𝜕Y s = λs ⟨ Y s -Y 0 S ⟩ 𝛽 + 1 ( 1 -d s ) m ( 31
)
λs represents the viscoplastic multiplier. K and n are two parameters. λs =

⟨ f s K ⟩ n + (32)
The slip rate ̇𝛾s is determined using equation [START_REF] Woo | Stress-strain relationship between ferrite and martensite in a dual-phase steel studied by in situ neutron diffraction and crystal plasticity theories[END_REF].

̇𝛾s = λs 𝜕Φ s 𝜕𝜏 s = λs √ 1 -d s sign(𝜏 s ) (33)
The plastic deformation rate at the grain level is calculated on the bases of the Schmid factor 𝜇 s and it is expressed as:

εp = N g ∑ s=1 λs √ 1 -d s ( sign(𝜏 s )𝜇 s + 𝛼(m s ⊗ m s ) N s ∑ r=1 d r
)

and εp = N g ∑ s=1
̇𝛾s 𝜇 s for 𝛼 = 0 (34)

Phase transition

The modeling of phase transition for multiphase titanium alloys is a difficult task due to the complexity of the microstructure and the high dependence of the phase transformation on heating and cooling kinetics. In the case of this study, a simple model (equation ( 35)) was chosen; its parameters have been identified at equilibrium by J. Teixeira [START_REF] Teixeira | Etude expérimentale et modélisation des évolutions microstructurales au cours des traitements thermiques post forgeage dans l'alliage de titane Ti17[END_REF]. It should be noted that this choice is justified by the simplicity of the model and the lack of data in the literature concerning this issue, notably at high heating and cooling rates. However, this contribution presents a step towards upgrading an already very complex cutting model.

Initially, the Ti17 Titanium alloy contains two phases (𝛼 and 𝛽). Depending on temperature evolution, a phase transformation may occur. From a certain level of temperature, "Transus 𝛽", the material will be composed of only the 𝛽 phase. Equation ( 35) permits to calculate the 𝛼 phase rate (Z(T) 𝛼 ) in function of the temperature; with Z eq (20 ∘ C) 𝛼 = 0.67, A = 0.1015 and T 𝛽 = 880 ∘ C ( [START_REF] Teixeira | Etude expérimentale et modélisation des évolutions microstructurales au cours des traitements thermiques post forgeage dans l'alliage de titane Ti17[END_REF]).

Z(T)

𝛼 = Z eq (20 ∘ C) 𝛼 ( 1 -exp ( -A(T 𝛽 -T) )) (35)
The main calculation steps are presented in Fig. 3.

Constitutive equation parameters identification

Given that the Ti17 is a two-phase material, the mechanical behavior of each phase has been identified independently. Compression tests at various strain rates (0.1s -1 ,1s -1 , 10s -1 , 100s -1 ) and at different temperature levels (between 25 • C and 800 • C) have been performed on the GLEEBLE 3500 machine. In addition, a heat treatment has been performed to carry out compression tests on specimens containing only 𝛽 phase.

The determination of the constitutive equation parameters is performed by the reverse optimization method. In this respect, the Lavenberg-Marquardt optimization algorithm has been used. This identification is performed in two stages. Initially, five hardening parameters are determined and this is followed by the identification of four damage parameters, some of which are determined for each temperature level. For each step, the identification procedure is as follows:

- Fig. 4 shows the difference between the mechanical behavior of the 𝛽-treated Ti17 and the as-delivered Ti17.

The geometrical model used for the identification of the constitutive equation is presented in Fig. 5. The 100 grains constituting the model are generated and meshed using NEPER software [START_REF] Quey | Large-scale 3d random polycrystals for the finite element method: generation, meshing and remeshing[END_REF]. A mesh convergence procedure has been carried out by varying the type and the number of elements per grain from 14 elements/grain to 795 elements/grain. The simulations have been carried out using multi-core parallel computing (Intel(R) Xeon(R) X5690 3.47 GHz). The obtained results are shown by Table 2 and Fig. 6.

A better mesh convergence has been obtained with C3D8RT elements. An important integration points number per grain is required of C3D4T elements.

Crystalline orientations have been randomly assigned to each grain; the disorientation between 𝛼 and 𝛽 phases has been taken into account ( [START_REF] Zhang | An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes[END_REF][START_REF] Martin | Numerical Multiscale Simulation of the Mechanical Behavior of Beta-metastable Titanium Alloys Ti5553 and Ti17[END_REF]). Since the constitutive equation does not take into account the evolution of temperature, hardening and damage parameters have been identified at each temperature level. Elasticity constants (C ii ) also vary depending on temperature ( [START_REF] Ogi | Titanium's high-temperature elastic constants through the hcp-bcc phase transformation[END_REF]).

Figs. 7 and8 show the results of the identification of the constitutive equation parameters for the 𝛽 and 𝛼 + 𝛽 phases at different strain rates. Thus, it can be seen that the material is sensitive to the strain rate, notably from 1s -1 . Similar tendencies have been obtained for both phases. It is also noted that failure strain decreases when strain rate increases. In addition, experimental trials show that fracture occurs more rapidly for the 𝛽 phase. The oscillations observed at 100s -1 are mainly due to dynamic phenomena (impact tests have been carried out to reach this strain rate level). Table 3 presents the values of the different parameters for each phase at 25 • C. Parameters k and n influence sensitivity to strain rate; parameters Q and b allow to adjust the slopes of the curves. At this stage, a proper identification of parameters K and n permits a good reproduction of material behavior according to strain rate. To adjust the initiation and the evolution of damage, it suffices to adjust the S, m and 𝛽 d parameters.

Fig. 9 shows the results of the identification of these parameters for different temperature levels. Experimental tests show that the Ti17 conserves very good mechanical properties up to 600 • C, when the thermal softening occurs. In order to identify the parameters of the constitutive equation for each temperature level, the procedure is as follows: update the 𝜏 0 parameter that reflects the decrease in yield for each temperature level, then calibrate the slopes of the curves, which change under the action of thermal softening, by acting on parameters Q and b.

Tables 4 and5, respectively, illustrate the evolution of parameters 𝜏 0 , Q and S for the two phases.

Overall, the identified parameters make it possible to reproduce material behavior for a margin of error that does not exceed 6% as illustrated by Table 6.

Orthogonal cutting model

Orthogonal cutting is a special machining configuration where the cutting edge must be perpendicular to the direction of the cutting speed V c and to the direction of the feed rate V f . In this particular case of machining, workpiece width (W w = 0.25 mm) becomes equivalent to the depth of cut. The cutting force is assumed to be proportional to W w . This simplifies the understanding of physical phenomena and the examination of data. Based on the work of Ayed et al. [START_REF] Ayed | Development of a numerical model for the understanding of the chip formation in high-pressure water-jet assisted machining[END_REF], a 3D orthog- 7 presents the thermal as well as the mechanical properties of the tool.

In order to study the impact of grain number and crystallographic orientations on chip formation and cutting forces evolution, three microstructures have been generated including, respectively, 1 grain, 10 grains and 60 grains. The workpiece has been meshed with 68000 C3D8RT elements as shown in Fig. 11. Concerning the friction coefficient between the tool and the workpiece, a model taking into account the variation of the friction coefficient in function of the sliding velocity has been adopted ( [START_REF] Rech | Identification of a friction model-application to the context of dry cutting of an aisi 1045 annealed steel with a tin-coated carbide tool[END_REF]). Previous work, carried out by Ayed et al. [START_REF] Ayed | Development of a numerical model for the understanding of the chip formation in high-pressure water-jet assisted machining[END_REF] has permitted to experimentally identify this variation (between 0.57 and 0.42 for Ti17). During chip formation, internal heating caused by plastic deformation has also been considered (The Taylor-Quinney coefficient has been set at 0.9). In order to simulate temperature distribution, thermal exchanges between the tool, the workpiece and the chip have taken into account. The simulations have been carried-out using ABAQUS/Explicit.

Chip formation

The main objective of this study is to develop a cutting model that allows to carry out more pertinent simulations and to access the cut- ting area, which is otherwise experimentally inaccessible. Such a model must take into account the behavior of the material over a wide range of temperatures and strain rates, as well as the crystallographic orientations of the gains and their evolution. This is a very challenging issue due to the complexity of the cutting process. Indeed, during chip formation, the workpiece is subjected to extreme loads, and heat is generated by plastic deformation and friction at the tool/chip interface. It should be noted that damage parameters must be properly identified to ensure the separation of the chip from the workpiece. Fig. 12 shows an example of simulation at a cutting speed of 125 m/min. As this graphic representation suggests, the grains have been highly deformed in comparison with their initial configuration (Fig. 11), notably in the chip. In addition, the figure shows the localisation of the deformation on the formed shear bands. Variable SDV4 represents the accumulated shear on all slip systems ∑ 𝛾 cum . The temperature reached in these areas of high deformations varies between 800 • C and 900 • C.

Impact of cutting speed and grain number

To evidence the effects of these parameters, three cutting speeds and three grain sizes have been tested. First of all, a model including 60 grains has been set up. Then, four simulations have been carried out at different cutting speeds. The sensitivity of the cutting forces to the cutting speed is shown by Fig. 13. At the cutting speeds of 100 m/min and 125 m/min, effort levels are close. A slight difference is observed in comparison with the effort obtained at a cutting speed of 75 m/min. Although the model takes into account the effect of heating and the degradation of mechanical properties related to temperature, the viscosity effect in the constitutive equation appears more important.

In order to verify the relevance of these simulations, orthogonal cutting tests have been carried out on a Leadwell LTC25iL CNC lathe. Cutting forces have been measured using a Kistler 9257B piezoelectric dynamometer; Fig. 14 shows the experimental setup. The average values of experimental and numerical cutting forces remain close.

The implemented constitutive equation allows, inter alia, to ensure the phase change which may occur. Fig. 15 shows the influence of the cutting speed on the evolution of the 𝛽 phase rate in the workpiece and the chip (SDV2). Increasing the cutting speed, as a matter of fact, results in an increase in the 𝛽 phase rate, especially at the tool/chip interface and the shear band. In fact, when cutting speed increases, internal heat generation due to plastic deformation also increases. The progressive temperature rise thus allows phase transition to take place. For the tested configurations, the machined surface does not undergo phase change.

In order to study the effect of grain number, two other microstructures have been generated (10 grains and 1 grain). In this step, cutting speed is set at 125 m/min. Fig. 16 shows the results of these simulations. It can be remarked that the trends and the magnitudes of the curves are close. The number of grains does not seem to have a major effect on the cutting effort; however, a slight difference is noticed with the model including a single grain.

Different simulations have been performed with different sets of orientations randomly assigned to each grain. Two grain sizes have been tested (V c = 125 m/min). Initially, three sets of orientations have been tested for a model consisting of 60 grains. Fig. 17(a) shows the results obtained. On the basis of these results, the cutting force does not seem to have been significantly influenced by grain orientations. Using a single grain model, the effects of grain orientations have then been tested. As with the previous test, Fig. 17(b) does not show significant differences in cutting force evolution. It can therefore be concluded that changing the initial random grain orientations does not considerably influence the cutting force.

Overall, these results are in agreement with experimental machining tests. Indeed, the average experimental cutting force does not undergo major changes even after repeating the same test several times. For each test, different grains with random orientations are solicited during the cutting process, but this has no significant effect on the average cutting force.

After this phase, which is relative to the analysis of cutting forces, the geometry of the chip has been investigated. The analysis of chip formation demonstrates that the shear angle changes depending on grain orientations. Fig. 18 shows the morphology and shear angles of the chip for three sets of orientations (V c = 125 m∕min). In addition, the shear angle on both sides of the workpiece is not identical and is characterized by a variation up to 17 • (Fig. 18(b)).

Such a change of the shear angle impacts chip morphology. Figs. 18 and 19 illustrate this variation. The localization of the deformation and its intensity likewise vary. Indeed, the accumulated shear on all slip systems SDV4

(∑ 𝛾 cum ) , shows a heterogeneous distribution of the deformation along the chip, which changes from one orientation to another.

Another advantage of the present model is the possibility to simulate the evolution of crystalline orientations under the action of various loads. Monitoring the evolution of textures has been done for the workpiece as well as for the chip. Figs. 20 and21 show the evolution of texture during the machining of a workpiece containing 10 grains. Subjected to high deformation levels, the chip undergoes the most intense orientations evolution; by contrast, the change of orientations in the workpiece is less significant.

Because it is still impossible to follow the evolution of the material texture in real time during machining, the proposed model is a reliable tool capable of predicting the orientations evolution during machining or material forming.

Machinability of the 𝛽 phase

The Ti17 is known for its low machinability (high chemical reactivity, high mechanical properties and great cutting forces), which raises productivity problems (notably, the sharp increase in machining time). A heat treatment followed by the machining of the 𝛽 phase may present a potential solution to improve its machinability.

The identification of the behavior of the two phases makes it possible to simulate the machining of the 𝛽-treated Ti17 and then compare the resulting cutting forces with the as-delivered material (before heat treatment). In order to carry out this simulation, two models, respectively containing 10 and 60 grains, have been established. The identified set of parameters relative to the 𝛽 phase has been used and the initial 𝛽 phase rate has been set to 100%. Fig. 22 shows the results of these simulations. A decrease in cutting force ranging from 13% to 17% can thus be observed.

To confirm these numerical results, experimental tests of machining (milling) have been carried out. First, a series of machining operations has been performed on the as-delivered material. The experiment has been repeated three times. The average cutting force F c (𝛼 + 𝛽) ranges from 790N to 824N. Then, a heat treatment has been done (phase 𝛽) followed by a second series of tests. The average cutting force F c (𝛽) varies from 650N to 690N. A decrease between 12% and 21% is noted, which confirms the predictions of the numerical model. It can therefore be concluded that the machinability of the material is slightly improved after the heat treatment.

Discussion and model evaluation

Most existing cutting models are based on the JC behavior law and damage model. This constitutive equation has the advantage of being implemented by default in most finite elements software. Indeed, it is relatively easy to identify and it permits to take into account the main material phenomena (hardening, dependence on strain rate and temperature). Although it gives good results at the macro-scale level, it has shown some limits, especially in treating metallurgical mechanisms and some physical phenomena.

The cutting model proposed in this paper is based on a micro-scale approach using a crystal plasticity constitutive equation with an explicit representation of grains (voronï cells). This approach opens up new perspectives, especially to optimize the microstructure and so enable the development of new alloys in order to improve the machinability of materials. This approach is more demanding than previous ones because it requires a more complex identification procedure for the different phases of the material. However, it allows for a more thorough study of chip formation and the stresses undergone by the surface of the workpiece which impact surface integrity (residual stress). This approach at the microstructural scale can eventually be compared to local observations in the tool tip [START_REF] Pottier | Sub-millimeter measurement of finite strains at cutting tool tip vicinity[END_REF] using the virtual fields method.

The first scientific challenge that was faced by this study was to implement the crystal plasticity constitutive equation while taking into account the large deformations, gain orientations evolution and phase transformation. However, it seems appropriate to continue developing the model, especially with the consideration of more accurate relations for the interaction between the different slip systems. In addition, it would certainly be rewarding to add a more accurate modeling of the behavior of grain boundaries. The first results of the machining simulations are very promising. Indeed, they demonstrate that grain size and orientations have no significant influence on the cutting force. At the level of the most solicited areas, material texture undergoes significant evolutions.

The second scientific challenge met was to identify the behavior of the different phases of the material and to investigate their impact on the machining of the Ti17. It has been evidenced in this respect that the machining of the 𝛽 phase results in a lower cutting force. Indeed, the rate and the inhomogeneity of the distribution of the phases in the microstructure of the material may be taken into account with the proposed model. It should be noted that the phase transition model could be significantly improved. The constitutive equation should also be modified to take into account more physical phenomena.

The proposed approach thus opens numerous perspectives for identifying thermo-mechanical loads in the tool tip and for material optimization. Indeed, this model presents venues to investigate the impact of grain size and orientations as well as phase transformation on the machinability of materials, which presents an important tool for the development of new materials.

Conclusion and perspectives

The present study has allowed the implementation of a crystal plasticity behavior law which takes into account large deformations and crystal orientations evolution. In addition, the behavior of the two phases present in the material has been identified on the basis of the reverse method. Certain parameters of this constitutive equation have also been identified at different temperature levels. An innovative 3D orthogonal cutting model has been established. This has allowed the simulation of chip formation, phase transformation (𝛼 → 𝛽), texture evolution and cutting forces.

The impacts of grain number and orientations on the cutting force have further been studied. The results did not show a significant influence of grain size or crystal orientations on the global response of the material, especially the cutting force. Nevertheless, due to grain orientations evolution, the texture of the material undergoes significant changes. Combined with the use of a crystal plasticity constitutive equation, the explicit modeling of grains by voronï cells has enabled us to reach promising results. In addition, the developed model presents an approach which compliments Zhang's work [START_REF] Zhang | An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes[END_REF].

However, there are still issues that require development. Indeed, the interaction between slip systems could improve model predictions; it would therefore be interesting to identify the interactions between the 36 slip systems. Of course, the current model can be further improved by the integration of the behavior of grain boundaries and by taking into account the effects of thermal softening.

Fig. 1 .

 1 Fig. 1. As-delivered material microstructure.

Fig. 2 .

 2 Fig. 2. Decomposition of the deformation gradient tensor ([48]).

Fig. 3 .

 3 Fig. 3. Main calculation steps.

Fig. 4 .

 4 Fig. 4. Mechanical behavior of the 𝛽-treated Ti17 and the 𝛽+𝛼 Ti17 at different strain rates (0.1s -1 and 10s -1 at 25 • C).

Fig. 6 .

 6 Fig. 6. Mesh convergence test ( ε = 10s -1 ).

Fig. 7 .

 7 Fig. 7. 𝛽-treated Ti17 behavior at different strain rates.

Fig. 8 .

 8 Fig. 8. Ti17 (𝛼 + 𝛽) behavior at different strain rates.

Table 3 Fig. 9 .

 39 Fig. 9. Experimental and identified curves at different temperature levels.

  Identification of 𝛽 phase parameters: these are identified on the basis of tests carried out on 𝛽 treated specimens (one phase, T = 25 • C and different strain rates levels); -Identification of 𝛼 phase parameters: knowing the 𝛽 phase data, 𝛼 phase parameters are then identified (two phases, T = 25 • C and different strain rates levels); -Identification of 𝛼 + 𝛽 material parameters at different temperature levels (200 • C, 400 • C, 500 • C, 600 • C, 700 • C and 800 • C).

Fig. 10 .

 10 Fig. 10. Geometric model including the cutting tool and the workpiece.

Fig. 11 .

 11 Fig. 11. Different voronoï cells mesh generation: (a) 10 grains, (b) 60 grains.

Fig. 12 .Fig. 13 .

 1213 Fig. 12. Example of cutting simulation at 125 m/min: (a) localisation of the deformation (∑ 𝛾 cum ) , (b) grains deformation.

Fig. 14 .

 14 Fig. 14. Orthogonal cutting tests: (a) Experimental setup, (b) cutting forces measurement.

Fig. 15 .

 15 Fig. 15. 𝛽 phase rate: (a) V c = 75 m/min, (b) V c = 100 m/min.

Fig.

  Fig. Grain number influence (V c = 125 m∕min).

Fig. 17 .

 17 Fig. 17. Impact of crystal orientations on the cutting force: (a) 60 grains, (b) 1 grain.

Fig. 18 .

 18 Fig. 18. Shear angle variation as a function of grain orientations: (a) orientation 1, (b) orientation 2, (c) orientation 3.

Fig. 19 .

 19 Fig. 19. Impact of grain orientations on chip morphology.

Fig. 20 .

 20 Fig. 20. Evolution of gain orientations in the chip, {110} (10 grains).

Fig. 21 .

 21 Fig. 21. Evolution of gain orientations in the workpiece, {110} (10 grains).

Fig. 22 .

 22 Fig. 22. Cutting force evolution during orthogonal cutting simulation of the 𝛽-treated Ti17 and the 𝛼 + 𝛽 Ti17.

  by modeling the ferrite and pearlite with two different material

	Nomenclature 𝛼 Alpha phase	f 𝜑 i 𝜀 𝜑 i 𝛽	Phase fraction Phase deformation Beta phase
	F	Deformation gradient tensor	f s	Yield function
	R	Rigid rotation tensor	𝜌	Material density
	U	Right stretch tensor	D T	Macroscopic damage variable
	L	Velocity gradient tensor	q	Internal state hardening variable
	D	Strain rate tensor d s	d s	Damage variable at the slip system level
	N s	Slip systems number	X	Effective variable
	n s 0 m s 0 ̇𝛾s	Slip plane normal Slip direction Shear rate	R s  H	Internal state hardening variable Elasticity tensor Interaction matrix
	W e ▿ 𝜎 𝜏 𝜏 s	Spin tensor Cauchy tensor rate Kirchhoff stress Resolved shear stress	Y s Φ s Φ s d λs	Damage force Plastic potential Damage part of the plastic potential Viscoplastic multiplier
	D G	Overall damage in the grain	Z(T) 𝛼	𝛼 phase rate
			V c

Table 1

 1 Crystallographic slip systems.

	Slip systems for the 𝛼 phase
				[	]
	Basal <a>	{0001}	1120	3
		{	} [	]
	Prismatic <a>	1010		1120	3
		{	} [	]
	Pyramidal <a>	1101		1120	6
		{	} [	]
	Pyramidal <c + a>	1011		1123	6
	Slip systems for the 𝛽 phase
		{110} [111]	12

Table 2

 2 Comparative study of the computing time depending on integration points number per grain and elements type.

		C3D4T			C3D8RT
	Elements/grain	50	103	678	14	107	795
	Computational time (min)	30	41	350	6	87	1380

Table 4

 4 Evolution of parameters depending on temperature (𝛽 phase).

	𝛽 phase	200 • C	400 • C	500 • C	600 • C	700 • C	800 • C
	𝜏 0 (MPa)	323.4	323.4	323.4	323.4	226.8	96.6
	Q (MPa)	67.5	44	10	-16.5	-23	-20

Table 5

 5 Evolution of parameters depending on temperature (𝛼 phase).

	𝛼 phase	200 • C	400 • C	500 • C	600 • C	700 • C	800 • C
	𝜏 0 (MPa)	346.5	346.5	346.5	346.5	243	103.5
	Q (MPa)	74	48.4	11	-18.5	-26	-22

Table 6

 6 Identification error estimation. Energy ∫ 𝜎𝜀d𝜀 (Jm -3 10 6 )

		Experimental results	Numerical simulations results	Error (%)
	𝛽 phase, 𝜀 = 0.1s -1	197.82	198.53	0.35
	𝛽 phase, 𝜀 = 10s 1	117.76	118.62	0.73
	𝛼 + 𝛽, 𝜀 = 0.1s 1	264.5	275.5	4.16
	𝛼 + 𝛽, 𝜀 = 10s 1	277.8	295.1	6.22
	𝛼 + 𝛽, 600 • C	438.67	456.13	3.98
	𝛼 + 𝛽, 200 • C	189.28	187.27	1.06

Table 7

 7 Thermal and mechanical properties of the tool[START_REF] Rech | Identification of a friction model-application to the context of dry cutting of an aisi 1045 annealed steel with a tin-coated carbide tool[END_REF].

	Density, 𝜌 (Kg/m 3 )	12800
	Elastic modulus, E (GPa)	630
	Poisson's ratio, 𝜈	0.22
	Specific heat, C p (J∕Kg ∘ C)	226
	Thermal conductivity, 𝜆 (W∕m ∘ C)	44


Hayfa Ayadi
email: ayadihayfa.ing@gmail.com

Ahmed Zouinkhi

Thierry Val

Boumedyen Boussaid

Naceur Abdelkrim

A multimode and multithreshold approach for energy efficiency in Internet of things systems

Keywords: Wireless sensor network, Internet of things, IEEE 802.15.4, energy, cluster tree

The IEEE 802.15.4 is designed for wireless personal area networks. Indeed, wireless personal area network turns out to help greatly in maintaining a flexible mode of communication within limited area networks. It is in this context that our present study can be set, in which the beacon-enabled mode is enabled with cluster tree topology to reach the scope of a rather extended network, whereby the network turns out to be clustered into several subgroups. Every single subgroup is characterized by its specific duty cycle which is configured by its correspondent personal area network coordinator. Therefore, many modes are enabled in the same network. Based on a very special mathematical model developed by us for energy consumption, the personal area network coordinator detects the actual level of energy in the battery of node. Then, an interesting comparison is made with the multiple thresholds which are already set. After that, both beacon order and superframe order (the standard IEEE 802.15.4 parameters) are recomputed with reference to the remaining energy.

Introduction

The Internet of things (IoT) has recently been established as a common terminology, frequently applied in the field of technology. Also dubbed Internet of Everything as well as Industrial Internet, IoT stands for a recently devised technology involving the entirety of devices capable of maintaining a particular mode of communication without the intervention of any human interference. Actually, the term Things in the Internet refers to all kinds of machines and devices destined for establishing a social life-based communication. [START_REF] Farooq | A review on internet of things (IoT)[END_REF] The IoT is a newly coined term which has made its appearance in the very recently elaborated research works. Indeed, it could be considered as an extension of the revolution taking place in the area of machine-tomachine-based communication (M2M), helping in the establishment of communicative interactions between everyone and everything. It is actually these features which accord the IoT its global worldly character. In effect, these things are capable of detecting data and sending them wirelessly, which turns them out to be smart. These smart things have the capacity of evaluating data collected from sensing materials, establishing communication with them, and taking appropriate timely decisions along with applying them. It allows different objects the opportunity to interact with their relating environment via the multiple senses available: hearing, sensing, and thinking. It is, therefore, due to this wide range of advantages that the IoT is presently implemented in a large array of domains such as the smart home, 2 transportation, [START_REF] Puiu | A public transportation journey planner enabled by IoT data analytics[END_REF] agriculture, [START_REF] Minbo | Information service system of agriculture IoT[END_REF] healthcare, [START_REF] Fernandez | Opportunities and challenges of the internet of things for healthcare: systems engineering perspective[END_REF] industry, [START_REF] Zolotova´i | Industry IoT gateway for cloud connectivity[END_REF] and entertainment, [START_REF] Kim | Sports analytics & risk monitoring based on hana platform: sports related big data & IoT trends by using HANA in-memory platform[END_REF] as illustrated in Figure 1. Still, despite the various advantages it displays, the IoT is faced with diverse challenges, particularly, that associated with an immense number of connected devices, each entailing a specific identification. Such a state is likely to culminate in an immense range of nomenclatures that require the introduction of an effective identity management system. As a matter of fact, such a system needs to be dynamic enough for the identity's distinctiveness to be well safeguarded and preserved. Indeed, the system has to be capable of managing and assigning a uniquely specific identity for such a wide range of objects. As the IoT contributes remarkably in connecting several devices to the various corresponding technologies and services with which they are intermingled and associated, numerous problems are most likely certain to emanate, owing to this noticeable diversity. Consequently, interoperability and standardization turn out to be serious issues associated with IoT systems. As it is the case within all information transmissions, an encryption system proves to stand as a critical necessity for data to be effectively transmitted from the physical environment. Similarly, the problem of fault detection [START_REF] Saihi | A real time centralized fault detection application in wireless sensor networks[END_REF][START_REF] Saihi | Hidden Gaussian Markov model for distributed fault detection in wireless sensor networks[END_REF] and energy provision also represents a very serious issue which contributes to developing many approaches in order to well control the energy consumed in the wireless sensor network (WSN) as well as the IoT systems. [START_REF] Ayadi | Multi operating mode for energy adaptability in wireless sensor network[END_REF][START_REF] Ayadi | Energy efficiency in WSN[END_REF][START_REF] Mekki | USEE: a uniform data dissemination and energy efficient protocol for communicating materials[END_REF] In fact, as the IoT system associated data rate continues to grow, the consumed energy also increases remarkably, and in this respect, green energy would stand as an interesting alternative. Many applications consist of deploying billions, or trillions, of different objects and connecting them via the Internet network. The main problem always with the wireless communication is the energy consumption of the devices because of the wireless battery devices' capacity which is so limited. In addition to that in most of the cases, the wireless networks are deployed in a very special environment which is characterized by its inaccessibility. All the circumstances cited prove the importance of the energy in this field. [START_REF] Jara | The internet of everything through ipv6: an analysis of challenges, solutions and opportunities[END_REF] In this regard, several models have been proposed with the aim of devising a clear IoT system-relevant architecture but were met with several challenges, mainly those relating to the QoS, scalability, reliability, and interoperability. Still, certain basic layers appear to stand as too crucially critical to be incorporated in such an architecture, namely: the perception layer, network layer, middleware layer, along with the application layer, as illustrated in Figure 2. [START_REF] Khan | Future internet: the internet of things architecture, possible applications and key challenges[END_REF] Dubbed perception layer or device layer is responsible for maintaining the physical data, 15 and as such, the system's sensors are in their entirety connected to this layer. Their major task consists in identifying the data sources, and, naturally, sensing all the relevant environmental factors, such as temperature, humidity level, and vibration. In a second place, the collected data are transformed into digital data, prior to being diffused across the network. [START_REF] Khan | Future internet: the internet of things architecture, possible applications and key challenges[END_REF] Concerning the second layer, called network layer, it is assigned the role of receiving digital signals from the perception sensors and transmitting it to the following layer, that is, the middleware layer via other technology means, such as 3G, wireless or wired media, for instance, ZigBee, WiMAX, Bluetooth, or WiFi, using specific protocols such as ipv6. Regarding the third layer, the middleware layer, it is allotted the task of managing the received information, prior to storing it in the database. The stored data are then processed and automated decisions are taken based on the results reached. As for the fourth layer, it consists in the application layer, which designates the appropriate application mode fit for the IoT system, for example, a healthcare application, smart farming, and industry. Finally, there comes the business layer, responsible for devising models, flowcharts, and graphs, based on the application layer emanating data. It is actually considered as the most important layer, owing mainly to the best business model selection it could provide, whereby the relevant analysis results may be displayed.

IoT systems pertaining technologies

The IoT network consists in a joint interaction among a wide range of various technologies, involving a large array of sensors, culminating in the emergence of the WSN. In effect, the WSN is considered as the major contributor of the IoT, whereby a great number of sensors are intricately interconnected and inter-nodal data turn out to be transmitted in such a way as to give birth to networks of smaller range. It is actually this interconnection between the small-range networks which lies at the origin of the creation of IoT networks. In its real sense, the IoT network is a collection of several diverse technologies, such as the IEEE 802.165.4 and ZigBee. Noteworthy, also, is that a wide array of protocols turn out to be established on the basis of the IoT, worth citing among which are the 6LoWPAN and Z-Wave. 15 ZigBee and IEEE 802. 15.4 As a matter of fact, even though the IoT network appeals to a wide range of technologies, the ZigBee remains still the most commonly appropriate one. ZigBee technology. ZigBee is defined as a wireless communication technology destined to fit for application with low-rate sensors. It also englobes a physical layer, a medium access control (MAC) layer, a network layer, and an application layer. Just like the 6LoWPAN, the ZigBee is based on the IEEE 802.15.4 standards regarding both of its physical and MAC layers, while the upper layer is defined by its proper technology. It is also defined to comply well with three particular devices, specifically, the full function device (FFD) and the reduced function device (RFD), exclusively allowing for three topologies to be maintained: the mesh, the tree, and the peer-to-peer topologies. Similarly, it undertakes a typical classification of nodes into three kinds enclosing the coordinator, end devices, and the router. The coordinator is responsible for paving the convenient route fit for maintaining data transmission. Besides, it serves to select the most appropriate topology useful for the network, in addition to initializing all the other parameters, including the operational parameters and the network's identifier, along with maintaining the channel's frequency. 15 As for the end device, it is characterized with a low-rate and low-power capacity, involving a number of environmental parameters detecting devices. Concerning the third component, that is, the routers, they constitute the major instruments responsible for ensuring the coordination of activities between the end devices and the coordinator. It can maintain easy connections with other routers in the network.

IEEE 802.15.4 standard. It is worth recalling that the IEEE 802.15.4 constitutes the major technology fit for equitable manipulation via the IoT networks. [START_REF][END_REF] Indeed, such technology displays the most appropriate choice fit for interaction with the IoT system's relating physical and MAC layers. Actually, this standard was initially invented for the purpose of solving similar challenges facing the WSN, particularly, the low-rate, versus the great area, coverage associated with the wireless local area network (WLAN) and wireless metropolitan area network (WMAN).

Still, energy constitutes the most serious trouble encountered by most of the wireless-based modes of communication, including the wireless personal area network (WPAN) family, simply formed of both physical and MAC layers. As it is the case with the ZigBee technology, its associated nodes could be of either an FFD or an RFD in type. The major related imposition is that the coordinator node must necessarily be of an FFD in type, while the end devices have to incorporate (RFD) pertaining nodes. To note, the FFD-related nodes are characterized by their remarkable energy storage capacity, with respect to the other RFD-associated nodes. As for the topological models enabled to fit well for an interactive co-integration with this particular technology, they are the peer-to-peer, tree, and mesh architectures. With respect to the tree topology, communication need be established between one personal area network (PAN) coordinator and at least a single end device. Regarding the peer-to-peer topology, however, communication could be established between a pair of nodes of the same type. [START_REF][END_REF] As for the mesh technology, every node is apt to communicate with any other node in the network, even if it does not pertain to the same range.

The IEEE 802.15.4 technology encompasses two main layers, namely, the physical layer and the MAC layer. The physical layer has two major roles to play, mainly, maintaining all data services required along with managing the physical layer. It is able to provide the possibility of applying up to 27 channels for the three bands available, specifically: a single channel within the 868 MHz range, 10 channels within the 915 MHz range, along with 17 channels within the 2.4 GHz range band. Noteworthy, also, is that a set of just three data rates could be provided via this standard mode, namely, 20, 40, and 250 kbps. [START_REF][END_REF] The same applies to the MAC layer, dedicated to perform such crucial functions as maintaining the MAC management service as well as the MAC data service, along with managing the beacon-relevant data, selecting the appropriate transmission channel, ensuring the link quality indication (LQI), energy detection (ED) in addition to monitoring and dealing with the radio transceiver's activity. Similarly, the MAC layer is mainly responsible for maintaining the beacon transmission process, in addition to managing the guaranteed time slot (GTS) and fulfilling the crucial role of ensuring the data transmission security. [START_REF][END_REF] In this respect, the IEEE 802.15.4 technology helps provide two modes of activities: the beacon-enabled mode and the non-beacon-enabled mode. Regarding the first mode, the PAN coordinator periodically sends a beacon frame to the entirety of the network's nodes to maintain a full range synchronization of their activities in addition to controlling the nodes' duty cycle through determining their relevant activity periods and sleeping spans, as defined via both of the superframe duration (SD) and the beacon interval (BI). [START_REF][END_REF] Both of the SD and BI are described in the formulas appearing below, that is, relation (1) and relation (2), respectively [START_REF][END_REF] BI = a Base Superframe Duration 3 2 BO 1 BO 14

SD = A Base Superframe Duration 3 2 SO 0 SO BO 14 ð1Þ
The SD period indicates the node's activity duration throughout which it is able to send or receive data from other nodes in the network. Hence, intervening with the SD period would certainly contribute remarkably in monitoring the energy amount as consumed by the node. As for the second duration interval, it concerns the situation in which the node remains still in a sleeping state. [START_REF][END_REF] To note, the SD duration is characterized by its superframe order (SO). It also comprises 16 equal-size slots as presented by Figure 3. [START_REF][END_REF] It starts with the beacon frame, which plays a critical role within the IEEE 802.15.4, as it is assigned the task of synchronizing the entirety of the network involved members. In this context, a pair of successive beacons will help define the actual BI. Regarding the active period, it consists of two different components, namely: the contention access period (CAP) and the contention free period (CFP). Throughout the CAP period, the node undertakes to send data via the carrier sense multiple access with collision avoidance (CSMA/CA) protocol. With respect to the CFP interval, however, appeal is made to the time division multiple access (TDMA) protocol, as exclusively deployed in this particular context. The two possible uses, relevant to the implementation of the CSMA/CA protocol, relate to the deployment of either of its associated versions: the slotted mode or the unslotted one. As far as this work is concerned, the focus of interest is exclusively laid on the slotted version of the CSMA/CA protocol, as illustrated in Figure 4. 15 In the first stage, we proceed with a small test which is done in order to discover the state of the battery life of the node. Then, the backoff exponent (BE) value is set to macMinBE. After that a small delay is chosen in which the node tries to proceed to the canal of transmission after exploring its state (idle or free). The next step is about defining the relevant parameters, which stand as follows: BE represents the backoff exponent, while NB denotes the number of times the slotted algorithm proves to request the congestion window backoff, and CW designates the congestion window. In the next stage, two clear channels are waiting to discover the transmission canal-associated potential. Then, based on the canal status, a relevant appropriate decision is taken. [START_REF] Koubaa | A comprehensive simulation study of slotted CSMA/CA for IEEE 802.15.4 wireless sensor networks[END_REF] Thus, either relevant data will be transmitted or an extra short-span duration is awaited, for a potentially possible appropriate canal availability to be checked.

Related work

It is worth highlighting that in association with the IEEE 802.15.4 technology, three possible approaches appear to be accessible for the node consumed energy to be effectively monitored, as applied within this particular standard. They involve intervening with SD, intervening with BI, or else modifying both of the SD and the BI-associated intervals. Actually, restricting the active period could well stand as the most convenient and simplest alternative, whereby the communication span between the network members can be noticeably controlled. Many authors have demonstrated a remarkable interest in such a solution. Thus, on establishing a small-scale comparison with the initialized threshold, should the superframe occupation ratio (OR) turns out to be inferior to the initial threshold, a second test needs to be accessed, whereby the OR would be compared to a second threshold. A second proceeding lies in intervening with the beacon order (BO) in such a way as the SO value turns out to be fixed and the BO liable to manipulation, based on parameters such as the network traffic load adaptive algorithm (BOAA). [START_REF] Neugebauer | A new beacon order adaptation algorithm for IEEE 802.15.4 networks[END_REF] Indeed, they have devised a new approach, dubbed dynamic superframe adjustment algorithm (DSAA), whereby the SO value can be selected on the basis of a small comparison, to be established in terms of a certain network-associated parameters, such as the collision rate. [START_REF] Lee | Study on a dynamic superframe adjustment algorithm for IEEE 802.15.4 LR-WPANs[END_REF] In turn, they have set up another approach which they called the duty cycle algorithm (DCA), whereby they considered adjusting the SO parameter with reference to the queuing delay, queue size, data rate, and energy consumption. To this end, they used a fixed value of the BO, wherein a mere change in SO would lead to a conservation of the BI, which is likely to affect the sleeping period. [START_REF] Jeon | DCA: Duty-cycle adaptation algorithm for IEEE 802.15.4 beacon-enabled networks[END_REF] In addition, the adaptive algorithm to optimize the dynamics (AAOD) also stands as another model useful for dealing with the SO value management, [START_REF] Hurtado-Lo´pez | An algorithm to optimize the dynamics of IEEE 802.15.4 networks[END_REF] that rests on the same principle. Adaptation of the SO parameter proves to exclusively rely on the number of packets received. Should their number exceeds a predefined threshold, the SO value would then be decreased, and inversely, however (i.e. in the opposite case), the SO would increase. Another protocol, highly dependent on the superframe occupied period, is also considered to fit well with this very technique; it consists of the adaptive MAC protocol (AMPE). [START_REF] Farhad | A traffic aware dynamic super-frame adaptation algorithm for the IEEE 802.15.4 based networks[END_REF] Actually, this procedure is dedicated to just comply with small networks characterized by start topology and is predestined to help lengthen the beacon period. Similarly, relying on the same node sleepingperiod maximization principle, the individual beacon order adaption algorithm (IBOAA) stands as a simple technique, whereby the node-associated lifetime could be managed. [START_REF] Gao | An individual beacon order adaptation algorithm for IEEE 802.15.4 networks[END_REF] Hence, it follows, in this respect, that the most effective method turns out to be that which helps in effectively and simultaneously managing both of the BO and SO relating values. Indeed, several approaches have been devised to address such a challenge. In the study by Oliveira et al., [START_REF] Oliveira | A duty cycle self-adaptation algorithm for the 802.15. 4 wireless sensor networks[END_REF] for instance, the authors try to control the duty cycle through intervening simultaneously with the BI and SD. Thus, the duty cycle self-adaptation algorithm (DBSAA) appears to stand as the most striking manifestation of this particular technique. Actually, the duty cycle proves to rely heavily on four network-related parameters, namely, the number of packets received by the coordinator, the number of source nodes, the superframe OR, along with the collision ratio (CR). Moreover, Salayma et al. [START_REF] Salayma | Battery aware beacon enabled IEEE 802.15.4: an adaptive and cross-layer approach[END_REF] used cross-layer method named the battery aware and reliable beacon enabled IEEE 802.15.4 (BARBEI). This method proves its efficiency by the different simulation results published. Salayma et al. [START_REF] Salayma | Optimal beacon and superframe orders in WSNs[END_REF] change both the values of the BI and the SD and then study theirs impacts in the performance of the WSN. In addition to that, another approach was developed based on the traffic load of the network. The best results are presented by both (BO = 7, SO = 5) values. [START_REF] Kavian | Adaptive IEEE 802.15.4 Mac protocol for wireless sensor networks[END_REF] All the approaches are summarized in Table 1. Most of the cited works do not give importance to the actual energy level in the battery, but in our approach, this level intervenes mainly in the manner of computation of the BO and SO.

The proposed approach

This work's subject of interest lies in an attempt proposed to manage the last energy amount remaining in Moreover, the beacon data has many other advantages such as the synchronization between all nodes of the network. The framework envisages that every node should send its relevant data to the correspondent coordinator, which would proceed with computing the battery held E R , prior to comparing it with the initial energy threshold Et1 as presented in Figure 5. Should it prove to record a decrease, the (BO1, SO1) are then computed. The same procedure is also reiterated with respect to the entirety of the remaining nodes N and thresholds M which are threshold 2, threshold 3, and threshold 4, as clearly illustrated in Figures 5678. The figures describe the different levels (P1, P2, P3, and P4) manipulated by our approach which is named: a multimode and multithreshold approach for IoT systems (M2-ABEM). The levels (P1, P2, P3, and P4) are equal consecutively (1.5%, 1%, 0.8%, 0.6%) of the initial energy.

Energy formula

Our proposed model for energy consumption takes into consideration the different state of nodes: emission, reception, idle, sleep, and overhearing and overmitting. [START_REF] Salayma | Battery aware beacon enabled IEEE 802.15.4: an adaptive and cross-layer approach[END_REF] It is actually during the transmission phase that the node appears to consume the most important quantity of energy. Throughout the emission span, when the node undertakes to send its relevant data, the node proves to consume a certain quantity of power, dubbed emission energy E em Á E em , as described by expression below

E em = (nbt sd 3 Ttt 3 Eb) + 2 3 U 3 I 3 CCA 3 Tp back ð3Þ
where nbt sd denotes the number of data frames existing in the SD, Eb stands for the binary energy, Ttt represents the frame size, I stands for the current value, U represents the voltage value, CCA is the clear channel assessment, and Tp back is described by expression below

Tp back = (2 cst back À 1) 3 20symbol ð4Þ
The cst back stands for the backoff period. Similarly, the node also appears to lose a certain energy quantity during the reception phase, dubbed E rc , as depicted by expression (5), below

E rc = nbr SD 3 Eb ð5Þ
where nbr SD representing the number of bits acquired throughout the SD period. Moreover, and during both of the overhearing and overmitting phases, the energy consumed, as represented by E o , turns out to be expressed by formula ( 6)

E o = nbr tr 3 dtra 3 Eb 3 PER ð6Þ
where nbr tr expressing the number of bits transmitted by node; dtra representing the frames size (bit); Eb is the binary energy, while PER depicts the error rate attained in the form of packet average transmitted without being well received. As for the collision associated energy E col , it is calculated in accordance with formula ( 7)

E col = Tatt 3 U 3 I 3 Nbpk ð7Þ
where Tatt represents the little temporal period necessary to access to the transmission canal; Nbpk denotes the number of attempts the node has made to send data without receiving any acknowledgment from the other side. Hence, the sleep technique remains the best option useful for managing and intervening with the energy amount available in the node's battery, and, thereof, the network's lifespan as a whole. Actually, the IEEE 802.15.4 standard is well known for its disposition to make such a process achievable. Thus, the energy consumed throughout the sleep period E SLP could be depicted in the expression below

E SLP = Eb 3 (BI À SD) ð8Þ
While the energy consumed during the idle state can be rendered through equation ( 9)

E i dle = T S IFS 3 U 3 I ð9Þ
where T S IFS represents the SIFS duration which is defined as the short interframe spacing (SIFS) periods, U denotes the voltage value, and I depicts the current value. Worth reminding is that our interest is focused on monitoring the nodes' associated life spans within a star topology, as manipulated via the IEEE 802.15.4 beacon-enhanced mode. The network is composed of several subgroups, each being made up of a PAN coordinator and a number of nodes. The network nodes are, in their entirety, interconnected through the node sink. It is at this level that our innovative approach can be set, as constructed around the idea that every node bears a number of specific IEEE 802.15.4 parameters (BO, SO) associated values within the cluster tree topology. At every interaction period or interval, the node issues a decision to send its specific parameters to the corresponding coordinator, which, in turn, undertakes to execute a computation procedure of the energy amount remaining in the node's battery E R . Once the relevant value is discovered to be inferior or equal to the already preset threshold, the coordinator will then execute a computation procedure in relevance with the IEEE 802.15.4 initial parameters. The same algorithmic process is rehearsed for four times still getting all the thresholds machined, which is likely to culminate in the prevalence of a large array of modes within the network. Actually, for an effective management of the very last amount of power to take place, an auto-adaptive procedure of this energy quantity proves to be crucially imposed. In effect, such an approach turns out to be considered as a multi-threshold and multi-mode processing of activities within the IEEE 802.15.4 technology. Accordingly, the quantity of energy remaining in the battery appears to be computed via the expression ( 10)

E R = Eini À Ec ð10Þ
Eini is the initial energy and the entirety of energy quantity consumed Ec could be calculated as the sum of all kinds of energy modes, as depicted by equation ( 11)

Ec = E em + E col + E o + E SLP + E rc + E idle ð11Þ
The IEEE 802.15.4 parameter's intervention

Within the context of a highly extended network, the first step consists in collecting the necessary parameters from the nodes so as to draw the nodes' consumed energy EC, thus getting the amount of battery remaining power. In the second stage, the reached amount is compared to a specified threshold, prior to computing the corresponding BO and SO values. Hence, with respect to the Beacon-enabled duration, the node consumed power turns out to be provided by formula ( 12)

E BI = BI T tt 3 E T ð12Þ
where BI being the beacon interval period; T t t designating the length of the frame; and E T representing the energy wasted in order to send a frame data. Still assuming that E BI which presents the energy lost during the beacon interval is inferior to the remaining energy, as described by expression ( 13)

E BI E R ð13Þ
the relation ( 14) turns out to be attainable by means of both relations ( 12) and ( 13), such as

BI T tt 3 E T E R ð14Þ
where the BI interval, as specified by the IEEE 802.15.4 standard, proves to be expressed through equation ( 15)

BI = 15, 36 3 10 (À3) 3 2 BO ð15Þ
thereby, transforming expression (15) into expression ( 16)

(15, 36 3 10 (À3) ) 3 2 BO T tt 3 E T E R ð16Þ
On the basis of equation ( 14), 2 BO appears to be defined by relation ( 17)

2 BO E R 3 T tt 15, 36 3 10 (À3) 3 E T ð17Þ
and the BO value is given by equation ( 18)

BO 3 log(2) log E R 3 T tt 15, 36 3 10 (À3) 3 E T ð18Þ
In case of extra charge status, the BO turns out to be equation ( 19)

BO = log E R 3 T tt 15, 36 3 10 (À3) 3 E T log(2) ð19Þ
For a rather effective management of the remaining quantity to last even longer, a proportion of just 10% of the remaining energy is manipulated, dubbed E R1 , as depicted by expression ( 20)

E R1 = E R 3 0:1 ð20Þ
and, consequently, BO turns out to shift to equation ( 21)

BO = log 0:1 3 E R 3 T tt 15, 36 3 10 (À3) 3 E T log(2) ð21Þ
Regarding the SD case, just 70% of the BI period appears to be exploited. Therefore, SO proves to be expressed through the relation ( 22)

SO = 0:7 3 log 0:1 3 E R 3 T tt 15, 36 3 10 (À3) 3 E T log(2) ð22Þ
When the level of energy reaches the level P1, the M2-ABEM starts and the node continues to send its information to its PAN coordinator periodically until the P2 is reached and the duty cycle is changed another time according to the M2-ABEM. The same step is repeated with all the levels.

The different steps of the M2-ABEM are presented clearly by the algorithm presentation below.

The Et k presents the kme threshold energy.

Implementation and simulation results

In order to achieve our goals, an appeal is made to the INETMANET/OMNET++ simulator. It is worth noting that the OMNET++ simulator constitutes the Objective Modular Network Testbed in C++ and is considered as the most realistic wireless networkassociated simulator. It stands as an object-oriented modular and a discrete event network-simulation framework. As a multidisciplinary tool, OMNET++ displays a wide range of advantages associated with modeling both modes of the communication networks:

Algorithm 1. Proposed algorithm approach: M2-ABEM algorithm.

Input: N NODES NUMBERS for x 0 to N do if Coordinator Receive Energy Consumption = true then for k 0 to M do Storage Energy Remaining(E R) if (E R\= Et k ) then
Node fault energy = True;

BO k = log 0:13E R 3Ttt 15, 36310 (À3) 3E T log (2)
SO k = 0:73

log 0:13E R 3Ttt 15, 36310 (À3) 3E T log(2) else BO k = BO kÀ1 ; SO k = SO kÀ1 ; end send (BO k , SO k ) end end end
wired and wireless. [START_REF] Kavian | Adaptive IEEE 802.15.4 Mac protocol for wireless sensor networks[END_REF] In addition to providing a smallscale prototype model to the relevant protocols, OMNET++ is also applicable for validation ends of the hardware architecture. Besides, it helps well in remarkably simplifying the software system-related complexities. The simulator-associated parameters are depicted in Table 2. With respect to our proposed network, it appears to enclose 25 nodes, along with 8 PAN coordinators and a node sink. It involves eight subgroups, each of them being made up of a single coordinator and three nodes. The simulation is triggered with the sink node sending of all the beacon frames to the PAN coordinator, for the entire network activities to be well synchronized. Then, as part of its assigned roles, the PAN coordinator undertakes to dispatch the beacon frames to the network children. Every single subgroup is characterized by detaining specific IEEE 802.15.4 (BO, SO)-associated parameters. At this level, it is mandatory for the PAN coordinator and sinks to be FFD nodes in type, even though the remaining nodes could be RFD in type, as illustrated in Figure 9.

Thus, PAN node P1 stands as the major responsibility for the nodes (0, 1, 2) and, jointly, they form subgroup 1. As for PAN P2, it represents is the main parent for the nodes (13, 14, 15) making up, together, the subgroup 2. While subgroup 3 involves PAN P3 along with its three pertaining children (5, 6, 7). Concerning subgroup P4, it is modeled by PAN 4, along with the nodes (17, 18, 19), and PAN P5 stands as the major responsibility in charge of the nodes (26, 27, 28), forming subgroup 5. As for PAN P6, it serves as the parent of the nodes (30, 31, 32), forming together the subgroup 6 and the subgroup 7 is controlled by the P7 and composed by the nodes (23, 24, 25). However, PAN coordinator 8 is the response of the nodes (9, 10, 11) constituting the subgroup 8.

Accordingly, the PAN proceeds with sending beacon frames to its children, periodically, in a bid to synchronize the relevant activities. Each subgroup has its proper specific BI and SD-associated parameters. Thus, three modes pertaining to the same network could be depicted. The peculiarity of this work lies in enabling every subgroup to self-manage the real energy range available to its nodes. Actually, the presence of eight subgroups within the network helps yield a variety of applicable modes, at a rate of about three modes per network. It is the PAN which sets the energy threshold values. In our particular context, four thresholds can be distinguished, helping to periodically change the IEEE 802.15.4-relevant parameters for four times. The duty cycle value is changed four times, DC1, DC2, DC3, and DC4, with the increase in the traffic loads as presented through Figure 10. In this way, the network's multimode and multi-threshold turns out to be simultaneously manipulated. In the first step, every node undertakes to send its pertinent data to the corresponding coordinator, and relying on the above-cited formula, the coordinator proceeds with computing the entirety of energy levels as consumed by the relevant nodes. It then continues with computing the remaining power amounts, while comparing them with the initial threshold.

Simulation results comparison

Once a node's consumed energy proves to be inferior to the set threshold, it will be marked as the risked node (fault energy). Its pertaining coordinator will, then, proceed with executing the second step, which deals with changing the node's both (BO, SO) values, for the sake of an effective exploitation of the remaining energy quantity. This procedure is repeated on a regular basis, and the quantity of battery residing power is regularly checked by the coordinator. In our case, the node number 30 suffers from energy fault. So the algorithm starts in order to postpone its death by decreasing its activity by intervening in its duty cycle. It is included in the subgroup number 6. Its IEEE 82.15.4 parameters are set by its PAN coordinator number 6. When it detects that the energy lasted in the battery of its child (node number 30) is less than the first threshold (Th1), it launches our algorithm as presented by Figure 11. With 300 packets/ s the energy consumed in this node also decrease under the second threshold (Th2) which set of the second intervention with the second duty cycle (DC2). Also, at 500 packets/s the EC becomes equal to Th3 which leads to our third intervention and finally our last try was at 700 packets/s used the DC4. The M2-ABEM is set on with node 30 and all the results performance of this node was even compared to four other approaches, already proposed to control the nodes' energy consumption process within the framework of IEEE 802.15.4 technology. The four methods, the subject of comparison, are: battery aware beacon enabled IEEE 802.15.4: the adaptive and cross-layer approach (BARBEI); [START_REF] Salayma | Battery aware beacon enabled IEEE 802.15.4: an adaptive and cross-layer approach[END_REF] the AAOD of IEEE 802.15.4 Network (AAOD); [START_REF] Hurtado-Lo´pez | An algorithm to optimize the dynamics of IEEE 802.15.4 networks[END_REF] the optimal beacon and superframe orders (OBSO) in WSNs; [START_REF] Varga | Modeling and tools for network simulation[END_REF] and IEEE 802.15.4 with (BO, SO) = (7, 5). [START_REF] Salayma | Optimal beacon and superframe orders in WSNs[END_REF] In this regard, a number of parameters were tested, namely, the queuing delay, end-to-end duration, in addition to all modes of energy consumption events, that is, those relating to the states of the collision, sleep, emission, and reception along with the overhearing and overmitting periods. The traffic load ranges from 100 packets/s to 900 packets/s. Figure 12, illustrates the queue delay evolution as scored with respect to the entirety of observed approaches, concerning traffic load evolution within the node. The OBSO presents the best results for this performance compared to all other approaches which encourage to adopt this method in the applications which have problems concerning the queue delay. The end-to-end parameter, as shown in Figure 13, highlights the increase in the endto-end characteristic delays with the increase in the network registered traffic load. The M2-ABEM appears to score the most effective results, as compared to the OBSO, IEEE 802.15.4, and the AAOD approaches.

The stable state-related energy consumption

It is worth reminding that for an effective data transmission, the node has to go through two different states: a transient state and a stable one. Throughout the first state, the node may well prove to be too busy transmitting or receiving information. Similarly, it might well suffer from a noticeable overhearingovermitting associated problem. Besides, sleeping could be enabled in this case. In such a case, our proposed design turns out to be marked by the presence of four phases, as emanating from the four set up thresholds. Figure 14 depicts the simulation experiment results, as recorded concerning the collision state-relevant data.

Regarding that state, the consumed energy appears to mark an increase that coincides with the growth in the number of data packets. Except for the OBSO approach, all the other approaches (AAOD, BARBEI, and the IEEE 802.15.4) appear to score an increase in the energy lost throughout the collision incidence. Actually, the most striking results turn out to be displayed through our proposed M2-ABEM approach.

The same applies to the evolution of energy as consumed during the node's emission state (Figure 15). All the cited approaches proved to display a consumption decrease with the increase in the number of message packets, except for the BARBEI approach, which proved to decrease throughout the entire simulation experiment. In addition, and within a very high traffic load, the M2-ABEM appears to yield nearly the best results, displaying the minimal energy consumption value. In effect, once the number of packets proves to rise, the M2-ABEM scored values appear to reach the same rates as those recorded by the AAOD method.

Regarding the overmitting and overhearing cases, however, power loss, as scored via the different methods, turns out to increase with the evolution in the number of packets, except for the BARBEI approach (Figure 16). In this respect, the M2-ABEM appears, also, to exhibit the most effective results once the traffic load proves to be lower than 500 packets/s. In addition, the M2-ABEM-associated values are discovered to increase at a remarkably quicker pace than those recorded through the AAOD and OBSO architectures. Even in the reception state, the M2-ABEM seems to display the least values with respect to the other approaches in the high traffic load (Figure 17). Worth noting, also, is that owing to traffic load intensity and duty cycle increase, the node turns out to endure and suffers from a remarkable energy shortage, resulting in a noticeable increase in energy loss during the sleep period (Figure 18). Once again, the M2-ABEM is discovered to record effective increase scores with respect to energy consumption.

The transient state-related energy consumption

To note, the idle state represents the unique case, a component of the transient state. Actually, all the cited approaches appear to demonstrate a decrease in energy consumed at this state level as presented by Figure 19. The M2-ABEM-associated values prove to indicate a decrease ranging from 5.2 to 4.9 J. As for the IEEE 802.15.4, it sounds to score the most effective results with respect to all the other models. Our proposed approach succeeds in reaching the best results compared to all other methods in many parameters studied such as the collision energy in addition to the reception energy. So the M2-ABEM presents the lowest results in the reception energy and collision energy. Moreover, it presents always the best results compared to the IEEE 802.15.4 (7,5) for the end-to-end parameter and to the overhearing and the overmitting. For the AAOD approach, our method describes the best results in the end-to-end parameter in addition of course to the reception and the collision states. The M2-ABEM presents also the best results compared to the OBSO in all kinds of parameters except the idle state and the overhearing and overmitting states. Finally, comparing to the BARBEI, our approach describes also the best results for emission state. Figure 20 describes the sum of all kinds of energy consumed by node 30: emission energy, reception energy, idle energy, sleep energy, as well as overhearing and overmitting energy. It is clear that our approach M2-ABEM presents the best results for energy consumed which is decreasing with the increase in the traffic loads.

Conclusion

The major contribution of this work lies, mainly, in the establishment of diverse modes interacting within the same network enabling the technology of IEEE 802.15.4. Therefore, the network was composed of many subgroups. Every subgroup turns out to be characterized with special IEEE 802.15.4-associated parameters (BO, SO). In addition to that, a wide range of thresholds are enabled by every PAN coordinator when it detects an energy fault in its subgroup in order to procure highly adaptive intervention. So periodical messages are sent by the nodes to their PAN coordinator in which they inform about their different pieces of information. At this level, every coordinator undertakes to compute the energy remaining in each node's respective battery and then detects the node displaying energy shortage fault when its remaining energy appears to be lower than the initially set threshold.

After that, our proposed approach M2-ABEM is launched. So, the coordinator will intervene by changing the node's duty cycle through modifying both of the (BO, SO) values. In order to prove the efficiency of our algorithm, a comparison was established with four other approaches: battery aware beacon enabled IEEE 802.15.4, the AAOD of IEEE 802.15.4 network, the OBSO in WSNs, and the IEEE 802.15.4 with (BO, SO) = (7, 5). In future work, our proposed approach (M2-ABEM) will be validated with real testbed.

Figure 1 .

 1 Figure 1. Internet of thing application.

Figure 2 .

 2 Figure 2. IoT system relating architecture.

Figure 3 .

 3 Figure 3. Frame composition.

Figure 4 .

 4 Figure 4. CSMA/CA slotted algorithm.

  Dynamic superframe adjustment algorithm (DSAA) 19 * Duty cycle algorithm (DCA) 20 * The network traffic load adaptive algorithm (BOAA) 18 * The adaptive algorithm to optimize the dynamics (AAOD) 21 * The adaptive MAC protocol (AMPE) 22 * The individual beacon order adaption algorithm (IBOAA) 23 * The duty cycle self-adaptation algorithm (DBSAA) 24 * Reliable beacon-enabled IEEE 802.15.4 (BARBEI) 25 * BO: beacon order; SO: superframe order. *The approach is included in the correspondent field (BO values, SO values or both).

Figure 5 .

 5 Figure 5. Threshold number 1.

Figure 6 .

 6 Figure 6. Threshold number 2.

Figure 7 .

 7 Figure 7. Threshold number 3.

Figure 8 .

 8 Figure 8. Threshold number 4.

Figure 9 .

 9 Figure 9. Multi-mode network.

Figure 10 .

 10 Figure 10. Duty cycle change.

Figure 11 .

 11 Figure 11. Energy consumed of node 30.

Figure 12 .

 12 Figure 12. Queue delay of the node with fault energy (node number 30).

Figure 13 .

 13 Figure 13. End-to-end delay of the node with fault energy (node number 30).

Figure 14 .

 14 Figure 14. Energy consumed in collision state of the node with fault energy (node number 30).

Figure 15 .

 15 Figure 15. Energy consumed in emission state of the node with fault energy (node number 30).

Figure 16 .

 16 Figure 16. Energy consumed in overhearing and overmitting state of the node with fault energy (node number 30).

Figure 17 .

 17 Figure 17. Energy consumed in reception state of the node with fault energy (node number 30).

Figure 18 .

 18 Figure 18. Energy consumed during the sleep state of the node with fault energy (node number 30).

Figure 19 .

 19 Figure 19. Energy consumed in idle state of the node with fault energy (node number 30).

Figure 20 .

 20 Figure 20. Energy adjustment of the node with fault energy (node number 30).

Table 1 .

 1 Related work.

	BO values	SO values	SO and BO values

Table 2 .

 2 Simulation parameters.

	Parameters	Values
	Simulation time	100 s
	Network size	(800, 400)
	E initial (J)	18,720
	Nodes number	29
	PAN number	1
	Channel frequency	2.4 GHz
	Radio type	IEEE 802.15.4 radio

Acknowledgements

We thank Professor Thierry VAL of IRIT Toulouse for the participation in this research work.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Ministry of the Higher Education and Scientific Research in Tunisia.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.