Mizuki Shinozaki

Faïda Mhenni
email: faida.mhenni@supmeca.fr

Jean-Yves Choley
email: jean-yves.choley@supmeca.fr

Aiguo Ming
email: ming@mce.uec.ac.jp

Reuse of SysML Model to Support Innovation in Mechatronic Systems Design

Mechatronic systems are inherently complex as they are multidisciplinary, integrating both hardware (electronical, mechanical) and software components. A huge effort is needed in the early design stages to take into account the requirements and constraints of the different stakeholders. A system model is needed to facilitate the communication between the collaborators from different domains. These efforts may be considered as a time loss by several companies. However, when a system model is available (i.e. electrical actuator for aircraft industry), it seems obvious that designing a new variant of the system with a modification of a set of requirements requires much less human effort, as it profits from the reuse and change of the already existing models of the previous system. In this paper, we propose to show the usefulness of the capitalization and reuse of system models by showing how a SysML model of an E-Taxiing (Electric Taxiing) aircraft system can be reused in order to design a new innovative HEPS (Hybrid Electric Propulsion System).

I. INTRODUCTION

Designing new systems is getting more challenging due to their increasing complexity, the evolving customer and market needs, the rapid pace of new technologies and the sharp competitiveness. The integration of new functionality and new technologies requires collaborators from different domains such as mechanical, electrical and computer science designers, as well as multiphysics and safety experts to work together on the same system using different models with different tools at different levels of abstraction.

In order to ensure the consistency of all these models, system architects are key designers as their role is to share data, parameters, information and models with all the members of the design team. Model-Based Systems Engineering (MBSE) provides system architects with means to ensure the consistency of the whole model of a complex system where requirements, structure and functions of the system can be expressed with models instead of documents.

Usually, new products are obtained from progressive updates and changes of already existing ones. Indeed, companies usually integrate parts of their existing products to deliver new ones in order to save time and benefit from their previous design and testing efforts. This has the benefits of reducing risks and cost in the design of engineered products [START_REF] Cross | Engineering Design Methods: Strategies for Product Design[END_REF]. However, as the complexity of engineered systems is increasing, managing the changes needed for new variants or similar products is also increasingly challenging. Fricke et al. in [START_REF] Fricke | Design for changeability (dfc): Principles to enable changes in systems throughout their entire lifecycle[END_REF] stated that the current system development shall face three key factors that are: a dynamic market, technological evolution and a variety of environments that imply design changes even at late stages of the design process. To cope with these factors, system design shall support design changes at any time of the design process or even during the operational phase of the system. Indeed, systems that have relatively long lifecycles, such as aeronautic systems, shall be designed with the ability to be changed during their operational phase to comply with evolving regulations and also include some new technologies either to stay ahead of competition or to enhance the efficiency and the operational cost of their products. For instance, several studies are conducted in order to replace conventional hydraulic actuators of the flight control surfaces such as ailerons, spoilers etc. with EMAs (Electromechanical Actuators) [START_REF] Derrien | Electromechanical actuator (EMA) advanced technologies for flight controls[END_REF]. Recent electric technology development also gives innovative ideas of adding new functionality to the landing gear such as E-Taxiing (Electric Taxiing) and HEPS (Hybrid Electric Propulsion System) to reduce fuel consumption. E-Taxiing allows the aircraft to use only electric motors while switching off conventional main engines during taxiing [START_REF] Nicolas | etaxi: Taxiing aircraft with engines stopped[END_REF], [5], [6], while HEPS upgrades E-Taxiing and allows hybrid Take-off and landing in addition to electric taxiing [START_REF] Schwarze | Operation and Performance Evaluation of Novel Electric-Wheel-Driven Hybrid-Electric Propulsion Systems on Standard Short Range Passenger Airplanes[END_REF].

In this paper, we propose to demonstrate how a system model of the E-Taxiing system can be reused to save design effort and time while designing a new innovative HEPS. The design of both systems is performed using the SysML language based on the methodology proposed by Mhenni et al. [START_REF] Mhenni | A SysML-based methodology for mechatronic systems architectural design[END_REF]. We assume that the E-Taxiing system design model already exists and we will demonstrate how to reuse it to design the new HEPS system.

The paper is organized as follows. First an overview of related work is given in section II. Next, the proposed approach for model reuse is presented in section III. Section IV presents the case study applying the proposed approach to design the HEPS reusing the E-Taxiing model . Finally, the paper is concluded in section V.

II. RELATED WORK

A. Integrated design of complex system and MBSE

Gotoh et al. proposed a model-driven development method for complex multidisciplinary systems design based on the requirements modeling [START_REF] Gotoh | Model-driven development for electrical/mechanical/soft integrated products with sysml[END_REF]. In this method, the requirements model has four layers: target product and context (L0), high level functions (domain) and cross-domain functions (application) (L1), system elements independently of the realization method (L2) and system composition elements taking into account the realization method (L3). Each layer has behavior, structure, constraint / technical specification and requirement qualification elements that are decomposed from the initial stakeholder requirements. Authors have examined the possibilities of the method by modeling an example of intelligent crane system using SysML. This study highlights how the understanding of the design intentions, the improvement of communication among different domains designers and the reuse of the model are facilitated. However, the link between the requirement model and the logical model is not discussed.

Eguchi et al. have also used a model-driven development method under the assumption of initial appropriate components structures, and decomposed and refined models by analyzing relationships between components and activities in relevant activity diagrams [START_REF] Eguchi | Impact analysis of design change based on requirement model of mechatronics product[END_REF]. Starting with an appropriate structure may shave the number of design iterations, even if it may be quite difficult for designers to work with a predefined topological structure of the system.

A SysML based methodology for mechatronic systems design is proposed by Mhenni et al. [START_REF] Mhenni | A SysML-based methodology for mechatronic systems architectural design[END_REF]. This methodology is made up of two phases : a Black Box Analysis and a White Box Analysis. The Black Box Analysis phase is an external point of view dedicated to the requirements definition and analysis independently from the solution (i.e. the system is considered as a black box). The resulting set of requirements will be the baseline for the next design phase, the White Box Analysis. This phase is dedicated to modeling functional and components-based structure and behavior of the system, with respect to the previously defined requirements.

B. Methodology for engineering change

In the software development field, Hoda et al. in [START_REF] Hoda | Efficient improvement of software testing by visualizing the impact of software modifications[END_REF] proposed a method that facilitates to developers understanding and handling the impact of software modifications due to modified customer requirements and derived products development, in order to reuse an existing software. The proposed method visualizes the impact of modifications using Requirement-to-Component and Component-to-Component relationships on a duality chart to facilitate the understanding even to nonspecialists. Therefore, developers can easily handle not only components that need modification but also test range and test policy that depend on the variety of "Add", "Modify" and "Delete" modification in the test process.

The impact analysis of mechatronic system design change based on requirement model (respects the methodology of [START_REF] Gotoh | Model-driven development for electrical/mechanical/soft integrated products with sysml[END_REF]) using SysML with TBD (Topdown-oriented Behavior Design system) framework and DSM (Design Structure Matrix) is studied by Eguchi et al. [START_REF] Eguchi | Impact analysis of design change based on requirement model of mechatronics product[END_REF]. They tackle the extraction of affected model elements due to added or/and changed requirements from existing requirement models in order to clarify their impact and reuse. The impact analysis is performed to trace changed elements on DSM that is constructed from components, object flows, states, actions and values of requirement model element. However, relationships of DSM are limited to input / output and composition of components. Therefore more detailed relationship definition such as "refine", "derive" and "satisfy" may give a better understanding.

Jeong et al. proposed a design method to support design change on long-life products such as vessels and plants [START_REF] Jeong | Design of changeable product structure with the consideration of change propagation[END_REF]. Lifetime-scenario is described by technological and environmental changes that are expected during the design in order to build a model easily changeable in the future, on the product information model that is composed by Componentnetwork and Constraint-network. The design change proposal is evaluated by risk of grown resource and ease of design adjustment. As their contribution, derivation and evaluation of design change proposal may be valid, however design support using suggestion of impact propagation is not valid enough.

III. DESCRIPTION OF THE MODEL-REUSE APPROACH

This section describes the reuse approach allowing to benefit from existing models in the design of new products sharing a set of requirements with the existing ones. By reusing existing models, the brainstorming, design efforts and rationale for previous choices are capitalized, thus, avoiding to designers to redo previous work. This approach only applies if the new system has several common points with the existing one, i.e. the new system is an enhanced version of the previous one with the purpose of adding new technologies or new functions. This approach is based on the top-down design methodology presented in [START_REF] Mhenni | A SysML-based methodology for mechatronic systems architectural design[END_REF]. The input point of this approach is an existing model built following the previously mentioned approach and a set of requirements of the new product to be designed. The requirements of the new product shall include some requirements in common with the initial system. In general, the new set of requirements RN can be divided into three subsets with respect to the requirements of the initial system:

• RN1: a subset of requirements that are identical to a subset of the initial system requirements.

• RN2: a subset of requirements that are a modified version of a subset of the initial system requirements.

• RN3: a subset of new requirements.

In the same way, the set of the initial requirements are divided into three subsets with respect to the new system requirements:

• RI1: a subset of requirements that are identical to a subset of the new system requirements RI1=RN1.

• RI2: a subset of requirements that are a modified version of a subset of the new system requirements.

• RI3: a subset of requirements suppressed in the new system. The design of the new system follows the same topdown SysML-based approach as in the design of the initial system. However, the different processes of the design (i.e. Requirement definition, Functional specification etc.) will be fed with the corresponding models built during the design of the initial system and these models will be updated according to the changes as shown in Figure 1. The first step is then the update of the existing requirements model by adding the new requirements RN3, modifying RI2 into RN2 and discarding RI3. Thanks to the traceability links established in the initial model, it is easy to manage the impact of the requirements changes on the system model. Indeed, the system model elements (functions, components etc.) that are no longer linked to requirements shall be removed from the model and new model elements shall be added to satisfy the new requirements. Model elements linked to modified requirements shall be modified in turn to comply with the new requirements. At the functions level for instance, there will also be three subsets of functions in the initial and new system models. A subset of functions FN1 in the new system that are identical to a subset FI1 of the functions of the initial system, a subset FN2 of functions of the new system that are a modified version of a subset FI2 and a subset FN3 of the new functions in the new system that replace the subset FI3 of the initial system functions. The components shall be allocated to the new set of functions. Components allocated only to functions of the subset FI3 shall be deleted from the design of the new system. Then, the designers have the choice to either add new components to achieve the new functions or to modify the existing components to make them achieve more functions. The choice depends of different criteria such as the feasibility, cost, available volume etc.

IV. REUSE OF SYSTEM MODEL FOR NEW SYSTEM WITH MODIFIED REQUIREMENTS

A. Description of the E-Taxiing system

Most of the on-ground operations (except the push-back) are performed using the main engines of the aircraft. While most aircraft are equipped with turbofan main engines optimized to minimize fuel consumption during airborne operations, the efficiency of the main engines is very low for on-ground operations. Therefore, the German Aerospace Center (DLR) has developed an E-Taxiing system in order to enable electric taxiing and push-back using in-wheel electric motors integrated in the Nose Landing Gear (NLG) of an Airbus A320 [START_REF] Michael | High integrated electric machine for aircraft autonomous taxiing[END_REF]. The E-Taxiing system allows the aircraft to move autonomously on the ground (during the taxiing phase) wile the main engines are stopped, electrical energy being provided by the on-board Auxiliary Power Unit (APU).

B. Procedure of reuse of SysML model of existing system

Hybrid Electric Propulsion System (HEPS) is used as a case study in this paper. The HEPS is intended to achieve new functions in addition to the electric Taxiing. The new SysML model of the HEPS is obtained by modifying the E-Taxiing SysML model according to the procedure described in the previous section.

The corresponding new stakeholder requirements are "Hybrid propulsion take-off" and "Hybrid brake landing with energy harvesting". In the following, we will show how the HEPS system is designed starting from an already existing E-Taxiing system model by modifying it to comply with the new set of requirements. The different steps of the modification process are detailed here after with the new diagrams. On these diagrams, lime and green color elements show modified elements and aqua and blue color elements show the added elements.

• Global Mission and initial requirements of the E-Taxiing are reused to build the new requirements model for the HEPS, and modifications are considered with added and/or changed requirement. Figure 2 shows the new requirements diagram. To be adapted to the HEPS, some requirements need to be modified such as the on-board energy source that shall have additional electric storage for take-off and landing (for energy harvesting and storing), and the integrated HMI, etc. Other requirements are modified, such as the electric energy harvesting during landing.

• In the Context model, a new actor, "Thrust lever" is added and the association with the "Brake system" is modified to satisfy the new requirements. The actors of the HEPS are represented in Figure 3.

• External Interfaces are also updated and new external interfaces are added to the model to allow the system to interact with the added actors (in this case the "Thrust lever"). Some interfaces are also modified in consequence. Indeed, "Skid condition" and "Thrust level" are added and "Commands" and "Feedback ports are modified on the new diagram given in Figure 3.

• In addition to the services provided by the E-Taxiing system, the HEPS provides new services shown in the use case diagrams in Figure 4.

• Engineering requirements are given in a new requirement diagram and take into account all the requirements identified in the previous steps. New requirements are added such as "Capability of disengagement during rotating wheels". The new diagram is shown in Figure 5.

• The functional breakdown has also been updated. New external pins are added in consistency with the external interfaces such as "Thrust-level, "Skid-condition, "Usercmd" and "User-Feedback" pins are modified. Some functions are also modified and other ones are added as shown in the activity diagram is given in Figure 6.

. External Interfaces

• As the HEPS is required to perform new functions compared to the E-Taxiing system, new components are added and are allocated to the new functions added to the functional breakdown. The IBD in Figure 7 gives the different components of the system and their interactions. In order to explain how an existing SysML-based system model may be reused for a new innovative design, we have shown how to turn an electric taxiing system (EGTS) model into a hybrid-electric propulsion system (HEPS) model. Indeed, the reuse of an existing model for a new design project seems less time-consuming, provided the initial SysML model has been systematically built using an univocal and exhaustive system engineering methodology, e.g. with a black box and a white box analysis, encompassing a set of consistent viewpoint diagrams (requirements, structure, behavior, etc.) enriched with relevant essential traceability links. This paper highlights that both with a set of initial traceability links and a traceability matrix, it is much systematic and convenient to unveil the affected SysML objects that have to be modified, removed or added, depending on the requirements changes and the propagation of the change impact, when switching from an initial well-proven system to a new innovative one. Performing such an improvement process on initial SysML modeling allows capitalization of previous systems engineering studies, thus making SysML modeling more effective and acceptable to designers and experts. Since our study mainly focuses on the left side of the Vee-cycle with requirements, functional and components structures definition, future work will have to focus on verification that a similar reuse process can be applied to the right side of the Vee-cycle with integration, verification, validation, qualification and certification. Furthermore, safety considerations and geometrical aspects should be taken into account in these reuse processes to shave development time and cost of new innovative systems among an industrial domain.

Fig. 1 .

 1 Fig. 1. Change Management Based on the V-Cycle Representation

Fig. 2 .Fig. 3

 23 Fig. 2. Requirement Diagram: Global Mission and Initial Requirements

Fig. 4 .

 4 Fig. 4. New Provided Services for the HEPS

Fig. 5 .

 5 Fig. 5. Requirements Specification

Fig. 7 .

 7 Fig. 7. Logical Architecture


Sofiene Helaili
email: sofiene.helaili@ept.rnu.tn

Moez Chafra

Yvon Chevalier

Natural fiber alfa/epoxy randomly reinforced composite mechanical properties identification

In recent years, there has been a growing interest in the international scientific community to study natural fiber composites. Natural fibers have interesting mechanical features, such as strength, lightness, and elongation at break. Natural fibers are also bio-sourced, biodegradable and recyclable. When used with plastic or recyclable matrices, natural fiber composites, such as alfa fiber, can also be reused and recycled. The growing global environmental and new environmental regulations have encouraged research on new recyclable composites environment friendly. The recyclable composite must satisfy minimal mechanical properties to be widely used in furniture, automotive or construction industries. To produce a natural fiber composite that can be fabricated widely, in this paper, composite materials were fabricated using the Epoxy resin as matrix and the natural Alfa fiber (tipa tenacissima L.) as reinforcement. The Alfa fibers are short and randomly distributed. Molding tech-nique is used to produce the composite. To judge the usage of the composite in structural applications, the mechanical properties of the biobased composite are identified by numerical homogenization and by experi-ments. The finite elements numerical homogenization technique is based on a representative cell reinforced with short fibers. Tensile tests were performed. The experimental results validate the numerical model. The results show that reinforcing with Alfa fibers with a 10% volume fraction increase the elastic modulus by about 24.16% compared to Epoxy. Composite failure stresses reached 28.01 MPa which is higher than 14.64 MPa the value of the unreinforced Epoxy failure stress experimentally determined. With better arrangement and higher concen-trations, such composites can at least be used for secondary structural uses.

Introduction

There has been considerable interest in designing new materials for several specific applications within the past decades, such as building more resistant and lighter structures, for example cement mortars [START_REF] Ajouguim | Impact of Alfa fibers morphology on hydration kinetics and mechanical properties of cement mortars[END_REF], thermal insulation, for example when used in compacted earth bricks [START_REF] Ajouguim | Effect of Alfa fibers on the mechanical and thermal properties of compacted earth bricks[END_REF], or acoustic-insulation, as an example composite material based on alfa and wood fibers [START_REF] Cherradi | Acoustic properties for composite materials based on alfa and wood fibers[END_REF][START_REF] Sair | Alfa fiber-polyurethane composite as a thermal and acoustic insulation material for building applications[END_REF]. Moreover, there has been a rising interest in using natural fibers, especially biodegradable ones, Palm fibers [START_REF] Masoud | Experimental analysis of heat-affected zone (HAZ) in laser cutting of sugar palm fiber reinforced unsaturated polyester composites[END_REF], Jute [START_REF] Prasad | Mechanical performance of jute and basalt fiber geogrid-reinforced epoxy hybrid composite material[END_REF], Alfa [START_REF] Mechakra | Mechanical characterizations of composite material with short Alfa fibers reinforcement[END_REF][START_REF] El-Abbassi | Elaboration, analyse et modélisation mécanique numérique d'agro-composites à base de fibres courtes d'alfa[END_REF], and other natural fibers [START_REF] Zini | Green composites: an overview[END_REF][START_REF] Bogoeva-Gaceva | Natural fiber eco-composites[END_REF]. Applications have spread to automotive and are becoming widely used in civil engineering, aerospace, and biomechanics [START_REF] Helaili | Pressure Calculation and Fatigue of a Trans-tibial Prosthetic Socket Made from Natural Fiber Composite[END_REF] as well.

Examples of such materials include the Alfa plant, which is abundant in North Africa (see Fig. 1) and South Europe in the West Mediterranean region. Tunisia possesses substantial resources of Alfa plants with promising physical and mechanical characteristics. These resources can be positively exploited while preserving availability. For example, there is growing interest in using Alfa-based composites in the medical field in Tunisia, specifically in orthopedic applications. Volumes fractions, orientations of Alfa fiber [START_REF] Brahim | Influence of fibre orientation and volume fraction on the tensile properties of unidirectional Alfa-polyester composite[END_REF][START_REF] El-Abbassi | A review on alfa fibre (Stipa tenacissima L.): From the plant architecture to the reinforcement of polymer composites[END_REF] and replacing glass fibers in composite materials was studied [START_REF] Abdallah | Could alfa fibers substitute glass fibers in composite materials[END_REF]. Effects of chemical treatments on mechanical and permeability properties was studied [START_REF] Bledzki | Composites reinforced with cellulose based fibres[END_REF][START_REF] Chafra | Directional damage and failure of composite materials under cyclic loading[END_REF], mechanical behavior of a polypropylene reinforced with alfa fiber shows good characteristics [START_REF] Zrida | Numerical study of mechanical behaviour of a polypropylene reinforced with Alfa fibres[END_REF][START_REF] Arrakhiz | Mechanical and thermal properties of polypropylene reinforced with Alfa fiber under different chemical treatment[END_REF]. Alfa fibers can be used with a matrix combined to supplementary materials as a hybrid composite [START_REF] Rajesh | Experimental Characterization for Natural Fiber and Hybrid Composites[END_REF][START_REF] Benyamina | Study and modeling of thermomechanical properties of jute and Alfa fiber-reinforced polymer matrix hybrid biocomposite materials[END_REF].

It has been shown that these plants are chemically [START_REF] Labidi | Alfa fiber/ polypropylene composites: Influence of fiber extraction method and chemical treatments[END_REF] inert, and a priori, no dermatological or respiratory reactions are reported due to harvesting or fabrication. To manipulate the Alfa plant, no special protective equipment is necessary.

In Tunisia, most raw materials used in the fabrication of orthopedic devices are imported. That raises the cost of manufacturing and puts a burden on the Tunisian economy. Therefore, this work's main goal is to incorporate local materials in the fabrication of orthopedic devices. It is planned to achieve this aim by elaborating a new composite material where the reinforcement consists of natural fibers extracted from Alfa plants [START_REF] Berrekheroukh | Experimental and numerical models to study the creep behavior of the unidirectional Alfa fiber composite strength by the photoelasticity method[END_REF] or Agave [START_REF] Prasad | Physical and mechanical properties of rambans (Agave) fiber reinforced with polyester composite materials[END_REF].

Materials and methods

The natural fibers are extracted from Alfa leaves. Alfa (Esparto) is a plant that grows in dry areas of the West Mediterranean region and can be found abundantly in the Tunisian Midwest. It is used mainly in the production of high-quality paper and cellulose paste. It is a common plant that grows in semi-arid areas in the Mediterranean region. Its height is between 50 and 80 cm, the diameter of the fiber rope varies between 1 and 2 mm; its harvest is organized once per year over six months (September to February).

To be suitable for reinforcement, the Alfa plant must go through an extraction process that transforms it from the leaf form to the essential microfiber. Transformation from the leaf form to the microfiber form was performed to remove lignin, which connects the fibers as ropes. The chemical process consists of boiling the ropes or sheets in sodium hydroxide and bleach. It is noted that boiling in sodium hydroxide and bleach process leads to significant degradation of the fibers under the action of this oxidizing agent that attacks all substances accompanying the cellulose, leaving only the micro-cellulosic fiber or fibril.

Based on reference [START_REF] Bessadok | Alfa fibres for unsaturated polyester composites reinforcement: Effects of chemical treatments on mechanical and permeation properties[END_REF] the fibers were modified by chemical treatments, maleic anhydride, styrene, acrylic acid, and acetic anhydride. The acetic anhydride and the styrene treatments allowed an increase in the moisture resistance and the mechanical properties of the fibers and allowed a decrease of the water permeability of the composite. Boiling in sodium hydroxide and bleach has another advantage of reducing the fibers' moisture uptake. Reviews the latest trends in chemical modifications and characterizations of natural fibers are detailed in reference [START_REF] John | Recent developments in chemical modification and characterization of natural fiber-reinforced composites[END_REF]. In its natural state, the Alfa fiber absorbs water and swells (up to 1% in its long axis and 15% in its radial axis), which detrimentally affects the fiber's mechanical characteristics and could lead to premature failure of the resulting composite. Chemically treated and combined with Epoxy, the alfa fiber-reinforced composite can have better mechanical properties [START_REF] Mittal | Natural fiber-mediated epoxy compositesa review[END_REF][START_REF] Arrakhiz | Tensile, flexural and torsional properties of chemically treated alfa, coir and bagasse reinforced polypropylene[END_REF]. Alfa fiber reinforced composites can be used as structures for crash safety applications [START_REF] Helaili | Hybrid Aluminum and Natural Fiber Composite Structure for Crash Safety Improvement[END_REF] and for prothesis in the biomechanics field.

The natural fiber's mechanical properties are determined by direct measurement using a tensile machine in accordance with the ISO 13934-1 [29] standard. Properties are listed in the table below Table 1 from Ref. [START_REF] Helaili | Anisotropic visco-elastic properties identification of a natural biodegradable ALFA fiber composite[END_REF].

Finite element model description and hypothesis

Two finite element models are developed. The first is Alfa/Epoxy 10%, which is identical to physical test specimens. The second model varies fiber concentration from 11% to 17%.

Finite elements models are developed using ANSYS APDL solver. Tetrahedral first order finite elements were used to have a better meshing effect between the matric and the fibers. The mesh size was decreased until the results converged in constant values not depending on the mesh size. The fibers are randomly distributed. The interface between the fiber and the matrix is considered as glued, no sliding in considered.

The elementary representative volume is shown in Fig. 2. To determine the homogenized equivalent properties of the composite, the cell is subject to different elementary displacements. The mean stress and the mean strain are then calculated to determine the composite moduli.

Numerical homogenization approach

For an orthotropic material, the stiffness matrix C has the following form:

[C] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ C 11 C 12 C 13 0 0 0 C 12 C 22 C 23 0 0 0 C 13 C 23 C 33 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 55 0 0 0 0 0 0 C 66 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
To determine the homogenized stiffness matrix C, three tensile tests and three shear tests should be applied. As an example, test 1 is a tensile test in Y1 direction (see Table 2). The imposed displacement is E = <1,0,0,0,0,0>.

The following table summarizes all these tests. After applying these six tests, all components of the stiffness matrix can be determined and then the elastic moduli of the material given by the following matrix form:

[ C -1 Hom ] = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1 E x -υ yx E y -υ zx E z 0 0 0 -υ xy E x 1 E y -υ zy E z 0 0 0 -υ xz E x -υ yz E y 1 E z 0 0 0 0 0 0 1 2G yz 0 0 0 0 0 0 1 2G zx 0 0 0 0 0 0 1 2G zy ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
Components are then identified, and results are given in the results section in Table 3.

Preparation process

Resin 862 and Epikure W were mixed, respecting the ratio 100: 26.4, for half an hour through magnetic stirring. After homogenizing, the solution was degassed under a vacuum to remove trapped gasses. To make the composite, alfa fibers were randomly placed in manually made silicone molds (to get appropriate samples for electrical and mechanical tests). Then, the Epoxy solution was cast onto the molds (see Fig. 3), and the remaining air bubbles were gently removed.

The samples were heated, cured for 2 h at 90 • C, and progressively cooled to room temperature. Finally, they were left in the desiccator until they were dried entirely to remove humidity.

The length of the specimens (see Fig. 4) is 150 mm, the width is 25 mm, and the measured thickness is 5.54 mm.

Methods

The experimental work was conducted according to ISO 527-4 [START_REF]Plastics -Determination of tensile properties -Part 4: Test conditions for isotropic and orthotropic fibre-reinforced plastic composites[END_REF]. ISO 527-4 is an international testing standard for determining the tensile properties of fiber-reinforced plastic composites. Type 2 specimens are rectangular with a constant cross-section and are suitable for testing fiber materials with thermoset and thermoplastic matrices. Type 2 is used (see Fig. 4).

The composite testing machine (see Fig. 5) is the Instron 5866 from Texas A&M University. For the composite specimens, the applied loads vary from zero to 3880,11 N for Test A, 1209,78 N for Test B and 539,23 N for Test C (see Fig. 6).

Specimens made from the Epoxy matrix non reinforced with Alfa fibers are made to determine stress at failure and elastic modulus of the non-reinforced matrix.

Results

Results of the finite element analysis

After simulation and identification of the elastic moduli of the composite for several alfa fiber volume fractions, the results are indicated in Table 3. Transversal elastic moduli Ey and Ez are vary close, this leads that the composite is a transverse isotropic material rather than an orthotropic material. Longitudinal module Ex is different and higher than transvers moduli.

Results of experimental work

Based on the specimen's dimensions and the measured tensile strain and tensile stress, the calculated modulus of elasticity is 4.62 GPa for Test A, 4.29 GPa for Test B and 3.92 GPa for Test C (see Fig. 7).

Compared to the modulus of elasticity of Epoxy, which is 3.78 GPa, the Alfa fiber added more stiffness to the composite and have shown better values of elongation before failure. Composite failure stresses reached 28.01 MPa (see Fig. 7) which is higher than 14.64 MPa the value of the unreinforced Epoxy failure stress (see Fig. 8).

The tests values are reported in Table 4:

Discussion

The composite materials studied in this paper present many advantages, such as good mechanical strength. Due to the abundance of Alfa plants in Tunisia and the molding technique used, this solution is a lowcost solution. The homogenized numerical results show a good correlation with the physical test results. The estimated error reached 7.31% for Test A. During the manufacturing process, the conventional treatment is minimal, reducing the overall cost and energy consumption. The natural fibers of these plants offer excellent thermo-mechanical properties in addition to the low weight. It has been shown that these plants are "Inert" and a priori no dermatological (during harvesting) or respiratory reactions (during fabrication). Hence, no special protective equipment is necessary, as is the case with mineral fibers. In terms of the environment, these materials are biodegradable and recyclable. The reinforcement with alfa fiber, shows an improvement in the elongation

Table 2

Tensile and Shear stresses in the identification method. at failure from 0.39% for a non-reinforced matrix to 0.60% for reinforcement in the case of Test A. The specimen used in Test A have seems to have a good interface adhesion between the matrix and the fibers because this is the same hypothesis used in numerical model that give close results. If the process of fabrication guarantees the adhesion between the fibers and the matrix, the composite can give good mechanical properties such as the stress at failure, the elastic modulus and elongation at failure.

Conclusion

The numerical analysis in this paper showed a linear increase of the composite flexural modulus with increased fiber content (see Table 3), with a substantial increase in stress and elongation at failure compared to a non-reinforced Epoxy (see Table 4). Reinforcing with Alfa fibers with a 10% volume fraction increase the elastic modulus by about 24.16% compared to Epoxy. The improvement of mechanical properties is proved in reference [START_REF] Arrakhiz | Tensile, flexural and torsional properties of chemically treated alfa, coir and bagasse reinforced polypropylene[END_REF] and can reach 56-75% in tensile modulus. The incorporation of fibers in the resin with a good arrangement has brought an improvement in the composite strength and extension observed in test A. The fibers are also expected to prevent crack propagation, which improves the structure's expected life. Other mechanical properties like compression, bearing, and shear properties can be studied before a wide usage in industrial applications.

Fig. 1 .

 1 Fig. 1. Alfa plant.

Fig. 2 .

 2 Fig. 2. Elementary finite element cell with randomly distributed fibers.

Fig. 3 .

 3 Fig. 3. Alfa/Epoxy composite mold.

Fig. 4 .

 4 Fig. 4. Alfa/Epoxy test specimen's.

Fig. 5 .

 5 Fig. 5. Instron 5866 tensile test machine.

Fig. 6 .

 6 Fig. 6. Tensile force vs. Tensile Strain curves for tests A, B & C.

Fig. 7 .

 7 Fig. 7. Tensile force vs. Tensile Strain curves for tests A, B & C.

Fig. 8 .

 8 Fig. 8. Tensile force vs. Tensile Strain curves for Unreinforced Epoxy.

Table 1

 1 Characteristics of the ALFA fiber.

		Mean Value	Variation rate (%)	Tolerance interval at 95%
	Modulus of elasticity (GPa) Failure stress (MPa) Elongation at failure (%)	18.42 229.3 1.43	30.5 31.7 27.9	8.7;25.3 145;368.3 0.83;4.8

Table 3

 3 Mechanical properties of Alfa/Epoxy randomly reinforced composite.

	Fiber %	10%	11%	12%	13%	14%	16%	17%
	Ex (MPA) Ey (MPA) Ez (MPA) Gxy (MPA) Gyz (MPA) Gzx (MPA) Nu xy Nu xz Nu yz Density (kg/L)	4984.3 4316.5 4308.9 1615.3 1572.7 1637.3 0.3547 0.3607 0.3654 1.1838	5387.5 4391.1 4392.6 1619.7 1590.9 1620.7 0.3566 0.3570 0.3759 1.1864	5532.5 4473.4 4443.7 1650.0 1605.9 1634.1 0.3577 0.3571 0.3768 1.188	5680.4 4503.1 4485.1 1667.5 1631.2 1654.4 0.3580 0.3578 0.3799 1.1912	5825.4 4584.5 4565.6 1692.8 1646.9 1685.9 0.3589 0.3584 0.3792 1.1936	6116.8 4769.0 4703.9 1753.8 1668.7 1712.7 0.3605 0.3590 0.3781 1.1984	6256.0 4741.1 4730.4 1756.8 1720.7 1753.2 0.3602 0.3604 0.3841 1.200

Table 4

 4 Ex elastic modulus in the x-direction.

	Material	Epoxy	Alfa/Epoxy Test A	Alfa/Epoxy Test B	Alfa/Epoxy Test C
	Extension (mm) Elongation % Load (N) Tensile strain (mm/mm) Tensile stress (MPa) Ex (10% -Table 3) (GPa) %error to FEM model	0,58 0,39 464,92 3,87 E-03 14,62 3,78 24,16%	0,91 0,60 3880,11 6,06 E-03 28,01 4,62 7,31%	0,136 0,09 1209,78 2,036 E-03 8,73 4,29 14,33%	0,15 0,10 539,23 0,993 E-03 3,89 3,92 21,35%

Acknowledgments

Special thanks to Professor Ridha BEN CHEIKH and many thanks to our colleagues from the ENIT Laboratory: Materials, Optimization, and Energy for Sustainability (LR-MOED-ENIT / LR-11-ES16) for their help in the treatment of Alfa fiber.

Special thanks to Professor Zoubeida Ounaies and Texas A&M University.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.