Jalal Joseph Possik
email: jalal.possik@u-bordeaux.fr

Aicha Amrani
email: aicha.amrani@u-bordeaux.fr

Bruno Vallespir
email: bruno.vallespir@u-bordeaux.fr

Andrea D ' Ambrogio

Gregory Zacharewicz
email: gregory.zacharewicz@mines-ales.fr

A BPMN/HLA-Based Methodology for Collaborative Distributed DES

Keywords: Discrete-Event Simulation (DES), High Level Architecture (HLA), Business Process Model and Notation (BPMN), Distributed Simulation (DS)

In many domains, Discrete-Event Simulations (DES) are usually used to reproduce the behavior of a certain system or process, where events are processed one after another in chronological and sequential order. Classical DES will no longer be a possible solution for Complex and Large-scale systems, System of Systems (SoS), and Performance Evaluation Systems that compare multiple different simulations running simultaneously in parallel. Advances in network and communications made the Distributed Simulation (DS) approach one of the best solutions for the aforementioned Systems Simulations. One of the challenges faced when developing a DS from DES components is the federation behavior including time management and synchronization between these components. In most of the traditional DES platforms, simulations cannot exchange messages, nor change the configuration at run time. This makes the DES connection and integration very hard and at times, impossible to implement. This article presents the method used to integrate different DES components, using High-Level Architecture (HLA) Evolved Standard, Business Process Model and Notation (BPMN), and Jaamsim, a Java open source DES.

I. INTRODUCTION

Across different sectors, Modeling and Simulation (M&S) has become one of the best ways to try, explore, analyze and optimize systems structure, behavior and performance prior to the implementation process. Simulation is necessary to deal with real-world uncertainties, variations, and complexities [START_REF] Ören | Concepts for advanced simulation methodologies[END_REF].

DES is an effective tool for process improvement [START_REF] Barnes | Advanced uses for Micro Saint simulation software[END_REF]. It is a method to simulate real system or process and it is nowadays used in different environments such as manufacturing plants, queuing systems, distribution systems, inventory and delivery systems, health-care, transportation networks, communication networks, and many others [START_REF] Fishman | Discrete-event simulation: modeling, programming, and analysis[END_REF]. In DES, the simulated system changes state or value at discrete points in time, and the simulation moves from one state to another upon an event occurrence [START_REF] Fujimoto | Parallel discrete event simulation[END_REF].

In some cases, DES alone is not an effective solution. The simulation system must be disassembled into subsystems or nodes in order to be parallelized or distributed on a multiprocessing environment for performance enhancements [START_REF] Misra | Distributed discrete-event simulation[END_REF]. In other cases, a collection of interacting simulations is needed to form a more complex system that offers additional functionalities to the existing ones [START_REF] Falcone | Using BPMN and HLA for SoS engineering: lessons learned and future directions[END_REF]. There are also scenarios where users need to compare many different DESs, and this cannot be run sequentially and needs to be also parallelized or distributed on a network of processors [START_REF] Possik | Development of a co-simulation system as a decision-aid in Lean tools implementation[END_REF]. For all the aforementioned scenarios, time management and synchronization protocols are necessary to avoid timing discrepancies and to ensure precise event interconnections and data communication between subsystems or simulations.

In this article, we will study the case where multiple DESs run in parallel on a network of processors. This work is part of a project developed to test the behavior of Lean tools and techniques during context changes. Lean Manufacturing is a systematic method that uses multiple tools and techniques in order to eliminate wastes from the manufacturing processes, improve inventory, quality, and customer satisfaction [START_REF] Amrani | Contribution to a Lean Maturity Evaluation: Leanness Metrics Calculation[END_REF]. The goal of this project is to guide the companies willing to implement Lean Manufacturing in their industries to choose the right Lean tools that suit their production processes and economic contexts.

We use the HLA Evolved Standard to develop a collaborative distributed DES. HLA is an architecture for interoperation and reuse of interacting simulations. The US Department of Defense first developed this Standard in the 90's and now it became an international IEE standard for distributed simulation. HLA was first used in the military domain. Nowadays, it is applicable in many application domains and across wide simulation areas [START_REF] Dahmann | Standards for Simulation: As Simple As Possible But Not Simpler The High Level Architecture For Simulation[END_REF] BPMN is a business process-modeling standard that offers a graphical notation based on a flowcharting technique. BPMN represents the end-to-end flow of a process. The Business Process Management Initiative (BPMI) developed the Business Process Modeling standard. In 2005, this group merged with the OMG (Object Management Group). In 2011, OMG released the BPMN 2.0 version release and changed the name of the method to Business Process Model and Notation. This Business Process Modeling standard became more detailed by using a richer set of symbols and notations for business process diagrams. The main goal of BPMN is to deliver a standard notation easily readable by non-expert users. In the presented work, we used BPMN to clear up the proposed methodology and simplify the understanding of the integration and collaboration between discrete event simulators.

The technical part of the methodology is also discussed in the present work. In this part, we will discuss the Java implementation of this methodology; the methods used to create, join, or destroy an HLA federation, the publish/subscribe mechanism, interactions/parameters communication, objects/attributes communication, time management, DES configuration. The DES used in this paper is JaamSim. We chose Jaamsim as a Discrete Event Simulator because it is a free and open source simulator written in Java language. Using Eclipse or any other integrated development environment, users are able to add/change Jaamsim objects or add their own code in Java, which is familiar to many programmers [START_REF] King | Open-source simulation software "JaamSim[END_REF]. Jaamsim is not developed for distributed simulations and communication to external systems; in this article, we showed that even with such simulators, we could implement the distributed simulation.

The rest of this paper is structured as follows: Section II reviews the background, related work and relevant contributions to distributed simulation. Section III shows the material and methods used to develop the distributed simulation system. The last section is the conclusion and future work.

II. BACKGROUND AND RELATED WORK

A. HLA Standard

Distributed Simulations are very useful in systems engineering. The HLA standard describes a set of services and rules for distributed simulations' implementation. The HLA approach promotes interoperability and reusability. In HLA, the system is considered a federation, a federation is a collection of federates, federates are interconnected through a Run-Time Infrastructure (RTI). The RTI role is to ensure a smooth run of the simulation. Fig. 1 describes the overall architecture of an HLA simulation. In the example we worked on, Jaamsim models are federates that interconnect and connect to other external DESs.

The HLA standard defines:

• Ten architectural rules describing the responsibilities of the entire federation. One of the rules specifies that all data exchanges between federates must go through the RTI. • A federate interface specification delineating the set of services provided by the RTI. These services are required to manage federates during simulation execution. • A Federation Object Model (FOM) that describes the shared objects and interactions used to exchange data.

HLA also supports optional services for time management, allowing the coordination of event exchanges between the existing federates. Time management is responsible for the mechanism of regulating the progression of each federate on the federation time axis. Each federate has a logical time. The RTI guarantees the time synchronization of the federates by consistently advancing the logical times of each federate. The logical time is equivalent to the simulation time in the classical literature of DES.

B. BPMN Standard

BPMN standard is a flowchart method that models the steps of a business process from the ground up. One of the key elements of BPMN is to provide a detailed visual representation of the complete sequence of business activities and information flows. Its purpose is to increase efficiency. It is the enterprise equivalent of the Unified Modeling Language (UML) used in software design. More details about BPMN standard are found in [START_REF] Group | Business Process Model and Notation[END_REF].

Fig. 3 represents an Aeronautic Assembly line model. This model is used as the basic model from which multiple scenarios, with different configurations, are generated. Using HLA, we were able to run these scenarios in parallel and compare the outputs to get the most efficient scenarios. This Aeronautic industry produces four references of an aeronautic fastener. The sales order is sent to the cutting shop, where, based on the product reference, raw material metal is cut into specific dimensions. In the cutting shop, setup time is required to change the settings, for the machine to be able to cut a different line of product; if consecutive products have the same reference, no setup time is required. After the cutting process, the product is sent to the treatment shop, where a thin layer of Zinc is added. The product is then delivered to the Assembly shop. The first machine in the assembly shop will also require a setup time in case of a product reference change. The last process in the production line is the Machining process, where, based on the reference type, a gear is installed to the product. This process also requires a changeover time. The finished good is finally delivered to the warehouse and is ready for delivery process.

C. Related Work

This Section reviews the existing related work and relevant contributions to the distributed simulation domain.

Jayadev Misra proposed a solution that partitioned a simulation to multiple components running on different processors and presented different techniques for deadlock detection and avoidance [START_REF] Misra | Distributed discrete-event simulation[END_REF]. The main objective of his work was to enhance the simulation performance.

In [START_REF] Garro | A Model-Driven Method to Enable the Distributed Simulation of BPMN Models[END_REF], the authors proposed a model-driven method that allowed the generation of an HLA-based code from a BPMN model using a chain of models to text transformations. BPMN and HLA have different techniques and objectives. The authors were able to combine both standards into a modeldriven method that makes the distributed simulation techniques easier to understand for developers and engineers. Others introduced a BPMN extension to address data structures' definition associated with the information exchanged during the execution of the Business Process collaborations [START_REF] Bocciarelli | An HLA-based BPMN extension for the specification of business process collaborations[END_REF]. Their paper defines a model-driven framework for DS based analysis of Business Process in order to fill the gap between HLA and BPMN.

In [START_REF] Youssef | EOS: enterprise operating systems[END_REF], using HLA standard, authors developed an Enterprise Operating System architecture to control and monitor the enterprise's operations. Authors used HLA standard to integrate large distributed environments and synchronize data and actions among existing federates. The authors, in [START_REF] Mclean | Simulation in the international IMS MISSION project: the IMS MISSION architecture for distributed manufacturing simulation[END_REF], presented a reference architecture to interintegrate manufacturing distributed simulations and connect them to other manufacturing software and data repositories.

In a previous study, we developed a Co-Simulation system for industries and enterprises based on MECSYCO (Multi-agent Environment for Complex System COsimulation), in which users specify the simulations input on a web interface then launch the system from the interface [START_REF] Possik | WIP: Co-simulation system serving the configuration of lean tools for a manufacturing assembly line[END_REF]. The system initializes the simulators and runs the simulations simultaneously in parallel. The respective output results appear in a graphical presentation during the simulation runtime process. Each of these simulations represents a different setup or configuration for the same aeronautic assembly line. By varying the inputs, users can easily choose the best configuration/setup that suits the production assembly line.

The purpose of our work is to extend the scope of the previous studies by proposing a methodology to connect different separated DESs using HLA publish/subscribe mechanism and time management. This methodology will be discussed using BPMN for easy access to non-expert users. For the technical savvy, the java coding that has been used during the implementation process will be discussed.

III. MATERIAL AND METHODS

In this part, we will use an example connecting three federates, Master federate, Scenario 1 federate, and Scenario 2 federate. Scenario 1 represents the DES model of Fig. 3; Scenario 2 represents the same model with some modifications in the production design. The aim of this distributed simulation is to determine how these scenarios react to changes in attributes and parameters, and compute the best behavior scenarios. These federates are linked via the RTI constituting a federation. These federation elements use a common Federation Object Model (FOM), an XML file that defines the objects/attributes and the interactions/parameters of the federation. We used the Java library of Pitch pRTI platform [START_REF] Technologies | Pitch pRTI[END_REF] to develop the following part.

A. Federation related Services

First, a federation should be created. As per Fig. 2, when the Master platform starts the simulation, it creates the Federation by calling the RTI Ambassador; this HLA service creates the Federation using a unique Federation name and links it to its corresponding FOM XML file. The method in RTIAmbassador class used to create the federation execution is RTIAmbassador.createFederationExecution("Federation Name", xmlFOMfile). After creating the federation, the Master, as a federate, joins the federation using the RTIAmbassador.joinFederationExecution("Federate Name", "Federate Type", "Federation name to join") method. Next, the Master launches the two DES scenarios that also join the created federation using the same method and parameters. In the example we developed, as per Fig. 4, the object classes created are "Scenario" and "Machine". The Scenario Object Class has the following attributes: Name, SimTime, Run Duration, Material Buffer, and Stock Keeping Unit (SKU). "Name" represents the Scenario Name, "SimTime" is the Simulation Time of the DES during the run time, "RunDuration" determines in years the duration of the simulation scenario, "MaterialBuffer" represents the number of raw materials waiting for the production process, and "SKU" represents the number of units remaining in stock. The Machine Object Class attributes include the number of goods processed, the number of goods in progress, the working time of the machine, the number of workers needed per machine, and the Work In Progress (WIP) that represents the in-process inventory. We subsequently created eight interactions: Scenario Load, Scenario Loaded, Scenario Error, Start/Pause/Stop Simulation, Order Demand Increase, and Order Demand Decrease. For each interaction, we have one or more parameters listed as noted in Fig. 4. The objects/attributes and the interactions/parameters sharing mechanisms (Publish "p", Subscribe "s", Publish/Subscribe "ps") are also listed in Fig. 4.

B. Declaration Management Services

Fig. 6 illustrates the steps used to select the Publish/Subscribe interests of the Object Classes. Each object should first get the handle for the actual object class in order to be published. The method used for this service is RTIAmbassador.getObjectClassHandle("Object Class"). In our example, "Object Class" could be "Scenario" or "Machine". The next step involves creating an Attribute Handle Set using the method create() in the AttributeHandleSetFactory class. Next, one should get the Attribute Handle using RTIAmbassador.getAttributeClassHandle("Object Class Handle", "Attribute") method. One of the attributes could be "Name" that exists in the Object Class "Scenario". Next, the Attribute Handle Set should be added using the method add() in the AttributeHandleSet class. The last step in the declaration part is to Publish/Subscribe the AttributeHandleSet of the Object Class using RTIAmbassador.publishObjectClassAttributes("Object Class Handle", "Attribute Handle Set") and RTIAmbassador.subscribeObjectClassAttributes("Object Class Handle", "Attribute Handle Set") methods.

After the publish Object Class Attribute, a callback from the RTI accesses the startRegistrationForObjectClass("ObjectClass Handle") method.

Registering the Publish/Subscribe for the interaction classes is more straightforward. First, one should get the Interaction Class Handle using the method: RTIAmbassador.getInteractionClassHandle("Interaction Class") then get the Parameter Handle using RTIAmbassador.getParameterHandle("Interaction Class Handle", "Parameter") method.

C. Object Management

Fig. 5 shows the required services to register/discover object instances. RTIAmbassador.registerObjectInstance("Object Class Handle", "the Object Name") is required to register the object instance. After the registration process, a callback is sent to the other existing federates, accessing the method discoverObjectInstance("Object Instance Handle", "Object Class Handle", "the Object Name"). turnUpdatesOnForObectInstance() callback method is accessed in the federate that registered the object instance. The method updateAttributeValues() of the RTIAmbassador class is used to update the attributes related to the registered object instance. After the attribute update, ReflectAttributeValues() callback method is accessed in the other existing federates as per Fig. 7. As for the interactions, the same concept is used with the sendInteraction() method and receiveInteraction() callback method.

D. Time Management

By default, federates have the time regulating service and the time constrained service disabled. To enable the time management services, a federate requests to be a time regulating federate using the method EnableTimeRegulation(), or to be time constrained using the method EnableTimeConstrained(). A federate could be time regulating/constrained at the same time. When these two methods are used, the Federate Ambassador calls back the TimeRegulationEnabled() and TimeConstrainedEnabled() methods. In this work, all DESs have the time regulating/constrained enabled.

The DES Federates in this paper are developed using Jaamsim. Jaamsim is not designed for communications to external systems and not fitted for DS; it is viewed as a black box simulator. As it is an open source software, we were able to run the startSimulation() and pauseSimulation() methods in Jaamsim to Start/Pause the simulations. These methods are linked to the aforementioned interaction's parameters StartSimulation and PauseSimulation. As per Fig. 8, when the DES runs, Jaamsim will add, with each event, a new output line to the log file issued using the Entity Logger option. When an event is processed, the federate will ask for time advancement to send new events using the nextEventRequest() method. The RTI ensures that it will not deliver any message with a Time Stamped Order less than the lookahead time and the federate actual time combined, the lookahead being the time delay that cannot be exceeded between simulations. The larger the lookahead value, the longer it takes for messages to reach the other federates. With a zero lookahead, messages should reach the other federates instantly. These HLA services are used to avoid out of order messages delivery.

If a time advance is granted to the federate, we test the value of X:

• A value that is equal to one means that Jaamsim was already running and there is no need to run it again. • A value that is equal to zero means that Jaamsim was paused and we need to start/resume the simulation again, then assign the value of one to the variable X.

If the "LogicalTimeAlreadyPassed" exception is raised, it implies that Jaamsim simulation should be paused:

• A value of X that is equal to zero means that Jaamsim was already paused and there is no need to pause it again. • A Value of X that is equal to one means that Jaamsim was running and we have to pause it, then assign the value of zero to the variable X.

This way, all Jaamsim DESs will run in parallel sending the output of the simulations almost simultaneously depending on the lookahead value. IV. CONCLUSION AND FUTURE WORK HLA standard does not propose nor precise any particular language to describe the behavioral process of the federation, i.e. group of federates, before to setup and implement. This IEEE standard also does not point out any specific programing language or software use. In this article, we described the methodology followed to define the desired interconnections and data exchange between DESs while running simulations in parallel on a network of processors. The implementation steps are explained using BPMN and the Java library of pRTI. BPMN provides a standard straightforward notation easily readable by non-expert users while Java language describes the technical implementation part.

Many industries are inefficiently implementing Lean tools in their organizations and are facing quality, management, financial, and other failures in their Lean implementations. This simulation system aims to conduct manufacturing industries in choosing the right Lean Manufacturing tools that lead the implementation to success with explaining the planned behavior. Our future work is to develop more models, contexts, and scenarios using this developed distributed simulator in order to obtain relative hypothesis that contributes, helps, and conducts Lean tools implementations in the production domain.

  [START_REF] Yilmaz | Adapting functional mockup units for HLA-compliant distributed simulation[END_REF]. HLA has three versions, HLA 1.3 published by the Defense Modeling and Simulation Office in 1998, HLA IEEE 1516-2000 published by IEEE in 2000, and HLA 1516-2010 published by IEEE in 2010 and known as HLA Evolved[START_REF]IEEE Standard for Modeling and Simulation (M&S) High Level Architecture (HLA)--Framework and Rules[END_REF].

Fig. 1 .

 1 Fig. 1. Global Orchestration

Fig. 2 .

 2 Fig. 2. Create/Join Federation

Fig. 3 .

 3 Fig. 3. Aeronautic assembly line model

Fig. 5 .

 5 Fig. 5. Object Instance Registration

Fig. 6 .

 6 Fig. 6. Object/Attribute Declaration

Fig. 8 .

 8 Fig. 8. Time Advancement, Event-Based


Houda Laaouidi
email: laaouidi.h@gmail.com

| Mostapha Tarfaoui

| Mourad Nachtane

Mourad Trihi

Energy absorption characteristics in hybrid composite materials for marine applications under impact loading: Case of tidal current turbine

The tidal current turbine is the most efficient way to extract energy from the sea. This system can be prone to critical loads such as impact accidental in the installation and maintenance phase. Indeed, several complex modes of damage susceptible to harming the stability of the structure are studied to conceive hybrid composite nozzles with better resistance to damage. For this rea-

son, two scenarios of low-velocity impact of a hybrid composite nozzle (glass/ carbon) were investigated. In both cases, the impact was realized in the region of the trailing edge of the nozzle, and the results obtained were compared between three different laminated. On the other hand, damage modeling was formulated using the finite element method based on the Hashin criteria.

Energy conservation of the nozzle was verified to validate the numerical model. Also, the effects of the impact velocity and the panel's flexibility on the initiation and propagation of damage have been studied. Depending on the results, the stacking sequence significantly influences the formation of damage. However, the results show that the hybrid nozzle with CGG (carbon/glass/glass) stacking has a higher impact resistance compared to other laminates.

K E Y W O R D S

contact/impact, damage mechanics, finite element method (FEM), hybrid fibers composites, marine operation, marine turbine

| INTRODUCTION

In recent years, renewable marine energy (RME) plays an important role in satisfying the increasing energy demand and to reduce the emission of greenhouse gases; it is becoming more and more appreciated, mainly due to its predictability. [START_REF] Nachtane | A review on the technologies, design considerations and numerical models of tidal current turbines[END_REF] Indeed, the application of tidal turbines to exploit tidal currents can only be efficient if the hydrodynamic performance is predicted. Currently, this technology is under development as devices capable of converting the kinetic energy contained in flowing water into electrical power. In a recent study, some researchers [START_REF] Zhang | State of the art in tidal current energy extracting technologies[END_REF][START_REF] Nachtane | Numerical investigation of damage progressive in composite tidal turbine for renewable marine energy[END_REF][START_REF] Uihlein | Wave and tidal current energy-a review of the current state of research beyond technology[END_REF] cited companies that have started to establish tidal current turbine parks, such as Sabella in France, Andritz Hydro Hammerfest (AHH) in Anglesey (Wales, UK), MeyGen in Scotland, GE & Alstom Energy (France), and DCNS, that will start work in the coming years. These projects represent a veritable response adapted to the needs of the industry. For example, the MeyGen project is currently the biggest tidal current development project in the world, and the largest group of multiturbine companies to start the development of this energy system. [START_REF] Mey | SIMEC atlantis energy[END_REF] On the other hand, there is the FloTEC project, which was created in 2016 with funding from the European Union, which seeks to prove the potential of floating tidal systems to produce predictable, low-cost, reliable, and low-risk energy for the European electricity grid. To achieve these objectives, the SR200 turbine, regarded as the most powerful tidal turbine in the world, has been installed. [START_REF]Pioneering turbine sets new benchmark for tidal renewable energy[END_REF] Several types of turbines have been conceived, but the most commonly used are horizontal-axis turbines with two-or three-blade rotors able to extract a great quantity of energy from marine currents. [START_REF] Nachtane | Effects of environmental exposure on the mechanical properties of composite tidal current turbine[END_REF] Even though research on tidal turbines treats many different fields of interest, the most frequently studied subject is certainly power performance. [START_REF] Brunetti | Large eddy simulation of a marine turbine in a stable stratified flow condition[END_REF] The ducted tidal turbine is subject to particular constraints because of the aggressive conditions that reign in the marine environment and maintenance and installation phase. In this context, composite materials occupy a crucial place in developing systems to convert marine renewable energy under severe environmental conditions. Due to their interesting properties, especially high stiffness, their lightness, and excellent corrosion resistance, they represent the perfect solution for structure developers. These conditions require the recourse to laminated composite materials like glass or carbon fiberreinforced polymer. Several studies have been conducted to evaluate the behavior of composites material exposed to impact. For example, Velasco et al indicate [START_REF] Velasco | Interaction between fibres in the transverse damage in composites[END_REF] that damage inflicted on fiber-reinforced composite materials is characterized by progressive degradation of resistance and rigidity due to the formation of micrdamages in fiber and matrix. The damage is generally manifested as matrix cracking, the debonding between the fibers and matrix, and fiber breakage. Several researchers have performed different models of failure criteria to predict damage in composite laminates. [START_REF] Andraju | Continuum and cohesive zone damage models to study intra/inter-laminar failure of curved composite laminates under four-point bending[END_REF] For instance, Xi Li et al [START_REF] Xi | Assessment of failure criteria and damage evolution methods for composite laminates under lowvelocity impact[END_REF] investigated the applicability of failure criteria and damage evolution methods in finite element analysis of composite laminates subjected to low-velocity impact. On the other hand, modeling methods for damage using property degradation and residual strength models have been established by various authors. [START_REF] Mohammad | Damage and residual bending strength in glass-polyester molded grating composite panels after low-velocity impact[END_REF][START_REF] Zhao | A residual strain model for progressive fatigue damage analysis of composite structures[END_REF][START_REF] Jia | Low-velocity impact and post-impact biaxial residual strength tests and simulations of composite laminates[END_REF] Recently, the control of the behavior of composite turbines has progressed enormously. Nachtane et al [START_REF] Nachtane | Effects of environmental exposure on the mechanical properties of composite tidal current turbine[END_REF] studied the effect of environmental impacts on the mechanical properties of a tidal turbine made of glass fiber-reinforced polymer composite. The results showed that damage was observed in different zones of the structure. Ullah et al [START_REF] Fagan | damage mechanics based design methodology for tidal current turbine composite blades[END_REF] analyzed the damage caused by impacts on tidal turbine blades. The composite materials used are composed of glass fiber-reinforced polymers. Furthermore, Tual et al [START_REF] Tual | Characterization of sea water ageing effects on mechanical properties of carbon/epoxy composites for tidal turbine blades[END_REF] analyzed the effects of seawater aging on composite materials for tidal turbine blades. The composite material employed in this study was carbon/epoxy.

According to the literature, several researchers have demonstrated that the fabrication of composites from a single reinforcing fiber is generally not adapted to particularly complex loading situations. [START_REF] Sujon | Experimental investigation of the mechanical and water absorption properties on fiber stacking sequence and orientation of jute/carbon epoxy hybrid composites[END_REF] For example, the carbon fibers have high tensile strength but are brittle to shear forces and thus have a low resistance due to lowspeed impact damage. [START_REF] Wu | Illustrating hybrid effect and damage evolution of carbon/aramid braided composite under low-velocity impact[END_REF] According to Santhanam et al, [START_REF] Santhanam | Experimental investigation on the mechanical properties of woven hybrid fiber reinforced epoxy composite[END_REF] composite materials made from a single reinforcing fiber tend to absorb moisture in a marine environment, which results in a weakening of the composite. To solve these problems, several studies have been conducted on hybrid fiber composites, adding ductile fibers like glass fibers, basalt, and aramid to carbon fiber-reinforced composite materials to increase their resistance to damage. Mahmoud [START_REF] Mahmoud | Experimental and numerical study of the damage mechanisms in hybrid unidirectional/woven composites under impact loading[END_REF] reported that higher impact performance could be observed by applying the same materials with different structures to form a hybrid laminate type. Sun et al [START_REF] Sun | Mechanical properties of hybrid composites reinforced by carbon and basalt fibers[END_REF] have analyzed experimentally and by finite element method the mechanical properties of carbon/basalt composite materials; the results showed that the hybrid effect was positive for tensile and flexural strength. On the other hand, the current studies on hybrid composites are principally based on fiber alignment and ply stacking sequence. [START_REF] Wu | Illustrating hybrid effect and damage evolution of carbon/aramid braided composite under low-velocity impact[END_REF] Only a few researchers have carried out studies on the effect of the stacking sequence on the tensile and flexural strength of hybrid composites. [START_REF] Aranno | Fabrication, experimental investigation of jute fiber reinforced epoxy composites and hybrid composites[END_REF][START_REF] Sujon | Experimental and numerical investigation on the tensile and water absorption behavior of jute/carbon reinforced epoxy[END_REF] In these studies, it was found that placing a relatively stronger fiber on the outside of the composite increases the flexural strength. It was also reported that the tensile strength increased with increasing fiber volume in the hybrid composite. In this context, recourse to hybridization is an excellent method to improve the fracture resistance of composite materials, while keeping adequate mechanical performance for structural application.

The review of the literature indicates that no studies have been conducted in the past on the application of hybrid composites in ducted tidal turbines. In this context, this work aims to investigate the dynamic behavior and the mechanical response of a hybrid composite nozzle under accidental impact during maintenance and installation operations. The prediction of the induced damage on the structure during the impact has been studied by the finite element method by using the Abaqus software. Two different impact scenarios were considered, the impact was realized on the trailing edge zone of the nozzle and the simulated damage was analyzed for different materials.

| STRUCTURAL ANALYSIS AND MATERIALS

| Structure

The hydrodynamic profile of the ducted tidal turbine was determined using Heliciel software, Figure 1A. To analyze the mechanical behavior of the nozzle during a maintenance and installation operation, the numerical model is developed in Abaqus software using the finite element method (FEM). The total diameter of the nozzle is 20 m, and its mass is about 16.99 tons. Figure 1B illustrates the 3D nozzle of the tidal current turbine.

| Materials

Tidal current turbines are generally exposed to accidental impacts during maintenance and installation operations. To respond to industrial needs, usually related to a mass gain problem, hybridization offers an excellent method for improving the fracture resistance of composite materials, while maintaining the adequate mechanical performance for marine renewable energy applications. The composite used in this study is a hybrid laminate submerged in epoxy resin with a thickness of 0.64 mm per layer. [START_REF] Gemi | Investigation of the effect of stacking sequence on low velocity impact response and damage formation in hybrid composite pipes under internal pressure, a comparative study[END_REF] The configurations of the stacking sequence have been established in the following manner: glass/glass/carbon (GGC), carbon/ glass/glass (CGG), and glass/carbon/glass (GCG) extending from the internal surface to the external surface. The total thickness of the laminate is 9.6 mm, and the composite structure layup is (0/45/90/45/0), with n = 15, Figure 2. Tables 1 and2 present the mechanical properties of the composites.

G 12 = G 13= G 23 (MPa) 2833 Xt (MPa) 1006 X c (MPa) 487 Y t (MPa) 46
Y c (MPa) 132 S L (MPa) = S T (MPa) 42
T A B L E 2 Properties of carbon-epoxy [START_REF] Gemi | Investigation of the effect of stacking sequence on low velocity impact response and damage formation in hybrid composite pipes under internal pressure, a comparative study[END_REF] Properties Value ρ (kg/m 3 ) 1238

E 1 (MPa) 1928 E 2 (MPa) 4598
Nu 12 0.32

G 12 = G 13= G 23 (MPa) 1729 Xt (MPa) 1429 X c (MPa) 530 Y t (MPa) 41 Y c (MPa) 145
S L (MPa) = S T (MPa) 83.4

| IMPACT SCENARIOS AND BOUNDARY CONDITIONS

The ducted tidal turbine is exposed to accidental impacts during installation and maintenance operations. Their installation necessitates the use of extremely powerful cranes or lifting systems, which are carried on service ships. The operations are risky in the open sea if the boat itself does not have considerable dimensions to remain stable against the waves during transhipment operations. In this case, two impact scenarios can occur. In the first case, the structure may be subject to impacts related to the components present in the vessel. In the second case, it can be impacted by different surfaces of the ship.

In this context, two different impact scenarios were simulated:

• Case Fixed nozzle and mobile impactor, Figure 3A.

• Case Mobile nozzle and fixed impactor, Figure 3B.

In case 1, a belt wrapped around part of the nozzle was chosen as boundary conditions. Figure 3A shows the encased section and the impactor geometry. In case 2, the boundary condition of the "Encastre" type is applied in the impactor reference point, as represented in Figure 3B.

U1 = U2 = U3 = UR1 = UR2 = UR3 = 0
In the two cases, the length of the impactor is 30 m, its width is 1 m, and its mass is about 1 ton.

For a better turbine conception and better analysis of its behavior under dynamic loads, the structure was exposed on its trailing edge to an accidental impact during maintenance and installation operations. A maintenance description of the system is depicted in Figure 4.

| NUMERICAL MODEL

The finite element modeling was developed in the Abaqus/ Explicit software to accurately predict and analyze the hybrid composite nozzle behavior, which is generally subjected to accidental impacts during maintenance operations. In this regard, the composite hybrid nozzle was modeled as a deformable structure and meshed with the shell quadrilateral S4R type element. On the other hand, the impactor is modeled as a rigid body. As mentioned in the previous section, two impact scenarios were modeled (Case 1 and Case 2). In case 1, the projectile weighs 1 ton, and its velocity was applied as an initial condition in its reference point which is equal to 4 m/s, while in case 2, the

F I G U R E 3 Impact

| Mesh convergence

A modeling strategy was conducted to reduce computation time and optimize the mesh model without affecting the accuracy of the simulation results. This strategy is based on identifying an optimal mesh by studying the convergence of the numerical model, as shown in Figure 5A.

The variation of maximum deflection and maximum stress vs the number of elements is illustrated in Figure 5A. The results of successive calculations seem to converge starting from 129 490 elements with a mesh size of 100 mm length. The value of convergence is calculated from a ratio "mesh size/total size of the structure" of 0.005. It can be seen from Figure 5A that the more the mesh is refined, the maximum stress increases and the maximum displacement decreases. Indeed, it is not suitable to apply quadratic elements in nonlinear structural analyses to such modeling as it takes a lot of calculation time. For this particular reason, the choice in our study consists of using a four-node quadrilateral element with linear interpolation and reduced integration (S4R). This is known for its robustness suitable for large applications and allows better accuracy at a reduced cost by using a fine mesh instead of a coarse mesh. Figure 5B depicts the final mesh size of 100 mm used for the nozzle.

| Damaged material response

The impact at low speed reflects a case of quasistatic loading and represents a crucial industrial case for damage tolerance. These impacts can considerably decrease the residual strength of composite structures without necessarily make visible marks on the outer surface. Studies have shown that damage caused by this type of loading is similar to those resulting from a static indentation test. [START_REF] Guinard | A 3D damage analysis of low velocity impacts on laminated composites[END_REF][START_REF] Chen | Failure Mechananism of laminated composites subjected to static Identation[END_REF][START_REF] Nachtane | Evaluation of durability of composite materials applied to renewable marine energy: case of ducted tidal turbine[END_REF] Thus, indentation tests are currently commonly used for experimental studies of impacts on low-speed impacts.

In this part, the modeling of progressive damage is examined by introducing the formula of different failure modes. In composites materials, damage can be defined in two distinct phases in terms of damage initiation and damage progression. In this model, the constitutive equations for damaged composite materials [START_REF] Matzenmiller | A constitutive model for anisotropic damage in fiber-composites[END_REF] are expressed in the form of:

σ = Mσ ð1Þ
where, σ is the real stress. M is the damage operator, having the diagonal form as shown in Table 3.

The shear damage is a way of identifying in the stack the plies in which the rupture of matrix and fibers occurs. Indeed, the damage variables d f , d m , and d s may have distinct compression and tension values, referenced by

d t f , d c f , d t m , d c
m corresponding to four following modes:

d f = d t f if σ11 ≥0 d c f if σ11 < 0 ( ð7Þ
d m = d t m if σ22 ≥0 d c m if σ22 < 0 ( ð8Þ
The corresponding stiffness matrix is determined from the equation below:

c = 1 D 1 -d f À Á E 1 1 -d f À Á 1-d m ð Þϑ 21 E 1 0 1-d f À Á 1 -d m ð Þϑ 12 E 2 1 1 -d m ð ÞE 2 0 0 0 D 1-d s ð ÞG 12
with

D = 1-1 -d f À Á 1 -d m ð Þϑ 12 ϑ 21 ð10Þ
where, D, E

| Damage initiation criteria

The approach to detect the failure by damage mechanics is complex and requires knowledge of specific failure parameters. An alternative to facilitate the analysis of the rupture consists of adopting rupture criteria. Fiber deterioration in compression and tension and matrix failure in compression and tension were defined by Hashin's as four failure criteria for composite materials. This criterion is implemented in the Abaqus Code. Thus, in our study, this criterion is adopted to treat the problem related to the reduction of the elastic properties of laminates and to evaluate their degradation.

T A B L E 3 The constitutive equations of damaged composite laminates

Designation of formulas Formulas

Equations no.

The damage operator (2)

M = 1 1-d f 0 0 0 1 1-d m 0 0 0 1 1-d s
The fiber damage

d f = 1-1-d t f 1-d c f (3)
The matrix damage

d m = 1-1 -d t m À Á 1-d c m À Á (4)
The shear damage

d s = 1-1-d t f 1-d c f 1 -d t m À Á 1-d c m À Á (5)
The damaged compliance matrix

H = 1 1-d f À Á E 1 -ϑ 12 E 2 0 -ϑ 12 E 1 1 1-d m ð ÞE 2 0 0 0 1 1 -d s ð ÞG 12
The initiation criteria are described as follows [START_REF] Nachtane | Damage prediction of horizontal axis marine current turbines under hydrodynamic, hydrostatic and impacts loads[END_REF] :

• Fiber tensile failure σ11 ≥0 ð Þ F t f = σ11 X T 2 + α τ12 S L 2 ð11Þ
• Fiber compressive failure σ11 < 0 ð Þ F c f = σ11 X C 2 + α τ12 S L 2 ð12Þ
• Matrix tensile failure σ22 ≥0 ð Þ F t m = σ22 Y T 2 + τ12 S L 2 ð13Þ
• Matrix compressive failure σ22 < 0 ð Þ F c m = σ22 2S T 2 + Y C 2S T 2 -1 " # σ22 Y C + τ12 S L 2 ð14Þ
F t f , F c f , F t m
, and F c m are the four modes of failure identified in Hashin criteria, the coefficient αrepresents the contribution of shear stress on fiber tensile, and σ11 , σ22 , τ12 , the stress tensor.

Where, X T , X C : denote the tensile and the compressive strengths in the direction of the fibers. Y T , Y C : denote the tensile and the compressive strengths in the transverse direction. S L , S T : denote the longitudinal and the transverse shear strengths of the composite.

| Damage evolution

The material stiffness progressively deteriorates according to a variable d, when the damage initiation criterion has been achieved. The values of this variable vary from zero when the damage begins to one (d = 1) when complete failure has happened in the fiber or matrix element. [START_REF] Tarfaoui | Design and optimization of composite offshore wind turbine blades[END_REF] The failure criterion is defined in terms of the energy release rates associated with the damage variables corresponding to the four failure modes. In the case of a linear softening process, the variable reflecting the evolution of damage for each mode (i) is defined as follows [START_REF] Mohammed | Study of composites ducts for optimal design of an horizontal axis tidal turbine[END_REF] :

d = δ f i,eq δ i,eq -δ 0 i,eq δ i,eq δ f i,eq -δ 0 i,eq ð15Þ
In the softening part, the equivalent displacement of each mode (i) satisfies:

δ 0 i,eq ≤ δ i,eq ≤ δ f i,eq ð16Þ
The zone area controlling softening is given by:

δ f i,eq -δ 0 i,eq = 2G i δ 0 i,eq ð17Þ
where G i represents the energy dissipated during the propagation of the damage, δ 0 i,eq denotes the equivalent displacement, σ 0 i,eq indicates the equivalent initial stress, and δ f i,eq refers to the equivalent displacement inducing the deletion of the element.

| RESULTS AND DISCUSSION

The damage resulting from an accidental impact is capable of affecting the ability to perform the intended function, even when the area of apparent damage is very small. [START_REF] Gning | Damage development in thick composite tubes under impact loading and influence on implosion pressure: experimental observations[END_REF][START_REF] Tarfaoui | Dynamic response and damage modeling of glass/epoxy tubular structures: numerical investigation[END_REF][START_REF] Tarfaoui | Scale and size effects on dynamic response and damage of glass/epoxy tubular structures[END_REF][START_REF] Gning | Prediction of damage in composite cylinders after impact[END_REF][START_REF] Tarfaoui | Residual strength of damaged glass/epoxy tubular structures[END_REF] Indeed, taking into consideration the low manoeuvring speed during maintenance and installation operations, the impact behavior during a low-energy impact must be studied. Hybrid composite structures possess greater rigidity than metallic materials. Nevertheless, due to the stratification of their layers and the weakness of the interfaces, this makes them extremely sensitive to shocks. This damage to laminate is not easy to identify. The absence of comprehension of impact tolerance of tidal current turbine systems is a major issue that prevents further use. It is essential to assess and predict the damage resulting from an accidental low-velocity impact to enhance the integrity and safety of hybrid composite structures in the maritime environment.

As mentioned in the preceding sections, two impact scenarios were investigated in the trailing edge zone of the nozzle during the maintenance operation, Figure 3. In this part, the results of the finite element simulation of both cases are presented by examining the mechanical behavior of the structure under low-velocity impact loadings. Indeed, the impact energy of the two scenarios studied is given in Table 4.

| Case 1

The damage that appeared during the impact study in the first scenario is analyzed in this section. The impact was realized with low velocity (V = 4 m/s) on the trailing edge area of the nozzle. The Hashin criterion for fiber and matrix damage was adopted. [START_REF] Gning | Damage development in thick composite tubes under impact loading and influence on implosion pressure: experimental observations[END_REF] The progression and formation of damage seen in materials are presented.

| Energy conservation

This section describes the energy variation of the CGG, GCG, and GGC configurations, Figure 6. The same trends are observed in all curves. The energy variation confirms the energy conservation theory of the system under investigation. Indeed, it appears that global energy remains constant during the whole duration of the calculation and is the expected energy impact. To validate the theory of energy conservation, the internal energy of the structure is equal to the energy of damage plus to the energy of deformation.

It is noted that: ALLAE, artificial energy; ALLDMD, damaging energy; ALLSE, strain energy; ALLKE, kinetic energy; ALLIE, internal energy; and ETOTAL, total energy.

Depending on the energy level, most studies on the impact of drop weight indicate three different modes of interaction between the impactor and the material. In the case of a very small quantity of energy absorbed by the composite, the projectile rebounds. Furthermore, if the majority of the energy is absorbed by different modes of damage, no rebound will be achieved. In the case of a high energy level, a perforation can be identified. Figure 7 shows energy curves for a drop-weight impact study for three materials where impactor rebound occurred. Throughout the impact study carried out, the rebound occurred for each hybrid composite examined. As shown in Table 5, the hybrid composite GGC absorbs 1.67 kJ of energy, which is significantly higher than other types of configurations. The following section showed that a large quantity of damage has accumulated in this material. So, it is clear that this laminate will absorb more energy. On the other hand, CGG composite absorbs less energy due to its high rigidity. As illustrated in this figure, the force-time curves of the three configurations are quite similar. Indeed, the impactor force grows with the structure contact and attains its peak value, and then the contact force diminishes. During the impact, the trailing edge area sustained a vibration, which appeared as a fluctuation at the level of the force-time curve. The first peak occurs when the damage starts to form. The fluctuations that follow also reveal the formation of damage in the structure, which can be cracks in the matrix or fiber breakage. The curves in Figure 8 also represent the variation of velocity during impact for the three configurations studied. This figure shows a progressive decrease in impactor speed until reaching zero, which corresponds to the initial phase of the elastic return. In this case, the impactor is probably hindered by the hybrid nozzle and thus loses a large part of its kinetic energy into deformation energy. As illustrated in Figure 8, the total duration of the impact is approximately 0.6 seconds. At this time, the contact force becomes nil, and the velocity begins to stabilize. So, there was a loss of contact between the impactor and the nozzle at that moment. On the other hand, the configuration GGC stabilizes rapidly compared to others. The principal cause behind this behavior is that the response to the impact of the nozzle changes as a function of the stacking sequence. Thus, it is evident that the force evolution after the first peak varies differently for the three materials under investigation.

| Damaged structures

As presented in Table 6, the greatest maximum contact force is 27.88 kN and corresponds to the GCG configuration, while the CGG configuration receives the lowest maximum contact force, which is 21.95 kN. Figure 9A compares the impact study responses in terms of impactor displacement for the three configurations. From an overall point of view, the simulation results show similar trends. In addition, the results presented in Table 6 indicate that the highest maximum displacement values are observed in the GGC configuration, while the lowest is found in the GCG and CGG configurations. In terms of damage energy, we can see from Figure 9B that the GGC configuration is the most damaged and CGG laminate is the last to be damaged. As Table 6 also shows, the CGG configuration obtains the lowest maximum damage energy. From the results, it is clear that this configuration has a higher stiffness response and therefore provides less impactor displacement. These results demonstrate that the material acts elastically when the carbon layer is situated on the internal surface, and two fibers layers of glass are situated on the external surface. So, the glass fibers protect the carbon layers.

The results of the different types of energy of the three materials studied indicate that the majority of the impact energy dissipates in the form of rigid and flexible movements of impact region (trailing edge), while a small part of the impact energy is absorbed in the nozzle as damage.

The low-impact energies lead to a sharp drop in resistance to implosion pressure. This decrease corresponds to the appearance of intralaminar cracks rather than delaminations. Impact damage favors a local implosion failure mechanism. Figure 10 shows the damaged areas of the tension matrix on the plies of CGG, GCG, and GGC laminates. The absence of the damaged zones was observed in the tension fibers, which is the reason that only illustrative cartography of the damaged areas of the tension matrix has been presented. Indeed, on the CGG laminate, the damage is little, while on the GGC laminate, a slight increase was observed because the external surface of the GGC stratified is covered with the carbon fiber layer that is exposed to high contact load and very easily damaged on contact. Indeed, the constraints occurring in these regions could generate the creation of a zone where adjacent plies are delaminated. The mechanical performance of the nozzle is susceptible to be affected by the appearance of this mode of damage and its development.

5.2 | Case 2

| Effect of the staking sequence

In this impact scenario, the nozzle with its trailing edge impacts a plane surface during the maintenance operation, so the impact energy is expected to be high given that the mass of the nozzle is of the order of several tons. In the previous case, the damage that appeared at the nozzle was not very large. In this second case, the results of the damage assessment are presented for V = 4 m/s and m = 16.99 tons, which results in the impact energy of more than 135 kJ. Figure 11 shows a comparative curve of the contact forces with the damage energy generated in the nozzle for the three laminates studied. It can be observed in the three laminates that the damage energy tracks the contact force history curve, with maximum damage energy accumulated where there is the highest contact force. Indeed, at the point where ALLDMD appears, the contact force curve (at the first peak) displays an oscillating nature with a varying slope. This demonstrates a change in material rigidity and damage growth in the nozzle. However, at this energy level of 135 kJ, the smallest values of maximum contact force are found in the GGC configuration, while the highest value is observed in the GCG configuration, as shown in Table 7.

Regarding damage energy, the most damaged material is the one with a GCG configuration, while the CGG material is the most resistant, Table 7. As already seen in the first case, the material becomes more resistant to damage formation, especially when the carbon layer is situated on the internal surface and two fiber layers of glass are situated on the external surface. These changes in the curve of contact force and damage energy correspond to a physical phenomenon. In fact, when the incident energy is greater than 8 kJ, the damage mechanism changes, and there is a growth of intralayer cracks and delamination. However, this rise in the density of the intralaminar cracks occurs after all the interfaces have separated.

A considerable difference in nozzle movement after impact for the three materials can also be observed from Figure 12. For the GCG and GGC configuration, velocity is dominant at the midpoints of the nozzle (Figures 12B,C), and thus a large deformation of the structure after impact is detected. However, for the impact of the nozzle in the CGG laminate, the velocity and motion of the nozzle are not sufficiently dominant as compared to the other laminates.

| Damage in tension

Figure 13 presents significantly the effect of the impact on the behavior of the layers stratified. The damage is very large and concentrated at the trailing edge of the nozzle for all three configurations. It can be deduced from this figure that a perforation of the structure has taken place in the impact zone given that the impact energy is very high since the mass of the nozzle is of the order of several tons. Indeed, from a comparative point of view, deformations and damage to the tension matrix of the GCG and GGC configurations are more important. On the other hand, no damaged regions on the tension fibers were observed for all three configurations.

| Damage in compression

The results obtained in the previous sections confirmed that the CGG configuration was resistant to shock, while the GCG and GGC configurations were the most damaged. To better visualize these results, Figures 14 and 15 GCG and GGC laminates is greater than 1, which signifies the existence of damage in these failure modes. Indeed, the size of the areas that concentrate damage on GCG and GGC laminates is larger than the size of the CGG, Figures 14 and15. This finding completes the energy results discussed previously. This study analyzed comprehensively the response of a hybrid composite nozzle under impact during a maintenance operation. It was indicated that operations are risky in the open sea if the vessel itself is not large enough to remain stable against waves during transhipment operations. This can lead to complex damage modes in the nozzle, capable of harming their structural integrity. In this context, a numerical simulation of progressive damage based on the Hashin criterion was conducted to predict failure modes. Two impact scenarios were studied and three types of hybrid laminates were adopted in order to identify the best stacking sequence, allowing the formation of damage on the composite hybrid nozzle subjected to a low-velocity impact at the trailing edge area. The energy conservation of the nozzle was verified to validate the numerical model. In addition, the results of the forcetime curves of the three configurations were quite close to each other. Indeed, during the impact, the trailing edge area was damaged, which appeared as fluctuations at the level of the force-time curve. The results of the two impact scenarios demonstrated that the stacking sequence significantly influences the formation of damage. However, the results showed that the identified damage modes were large in GGC laminate. In contrast, the damage concentrated in the CGG configuration was low compared to the other laminates. Based on these results, we concluded that the carbon layer is perfectly protected by glass layers and gives the most resistance for damage formation. In the first impact scenario, most of the impact energy was dissipated as rebound energy and only about 3.1% was dissipated as damage energy. Concerning the second case, 9.25% was dissipated as damage energy, which resulted in a perforation of the nozzle with the plane surface at the contact region. For the designer, research on the behavior of a tidal current turbine under shock is of great interest.

Even small damage may have a significant influence on structure sustainability.

F I G U R E 1

 1 Nozzle of the marine current turbine [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 2 The stacking sequence configurations [Colour figure can be viewed at wileyonlinelibrary.com]T A B L E 1 Properties of glass-epoxy[START_REF] Gemi | Investigation of the effect of stacking sequence on low velocity impact response and damage formation in hybrid composite pipes under internal pressure, a comparative study[END_REF]

  scenarios [Colour figure can be viewed at wileyonlinelibrary.com] nozzle displaces at a speed of 4 m/s, and the impactor is fixed.

F

  I G U R E 4 Context description [Colour figure can be viewed at wileyonlinelibrary.com] F I G U R E 5 The final mesh of the numerical simulation [Colour figure can be viewed at wileyonlinelibrary.com]

F I G U R E 6

 6 Impact energy evolution during the study (m = 1 ton,V = 4 m/s) [Colour figure can be viewed at wileyonlinelibrary.com]

Figure 8

 8 Figure8shows the force and velocity-time graphs for different configurations of the stacking sequence of material.

F I G U R E 1 0

 1 Representation of laminate damage zones (DAMAGEMT) [Colour figure can be viewed at wileyonlinelibrary.com]

F I G U R E 1 1

 1 Contact force with damage energy (ALLDMD) of the three laminates [Colour figure can be viewed at wileyonlinelibrary.com]

F I G U R E 1 2

 2 Velocity profile after the impact of the three structures [Colour figure can be viewed at wileyonlinelibrary.com]

  show a comparative damage status of the fibers and matrix in compression of these three configurations. The damage status DAMAGEFC is less than 1 for the CGG laminate, which indicates the absence of damage in this failure mode, Figure14A. On the other hand, the level of damage DAMAGEFC and DAMAGEMC observed on the F I G U R E 1 3 Representation of the damage zones of the laminates under study (DAMAGEMT) [Colour figure can be viewed at wileyonlinelibrary.com]

F I G U R E 1 4

 4 Failure criterion of the fiber in compression (DAMAGEFC) [Colour figure can be viewed at wileyonlinelibrary.com]

  1, E 2 , and G 12 are undamaged material moduli. ϑ 12 , ϑ 21 are undamaged material Poisson's ratios.

  [START_REF] Sevkat | Drop-weight impact of plain-woven hybrid glass-graphite/toughened epoxy composites[END_REF]

  The impact energy of the two scenarios studied

			Case 1		Case 2
				Impact		Impact
		Mass	Velocity	energy	Velocity	energy
	Configurations	(tons)	(m/s)	(kJ)	(m/s)	(kJ)
	CGG	16.99	4	8	4	135.99
	GCG	16.99	4	8	4	135.99
	GGC	16.99	4	8	4	135.99

T A B L E 4

  Maximum values of displacement, contact force,

	and damage energy
			Max
			damage
		F max	energy
	Materials	(kN)	(kJ)
	CGG	315.129	7.58462
	GCG	315.909	12.4301
	GGC	309.609	11.1076

T A B L E 7

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CONFLICT OF 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.


Angélique Teyssier
email: angelique.teyssier@outlook.com

Jean-Michel Schmitt

Rodica Chiriac

Christelle Goutaudier

2 O at 25 °C

Keywords: solid-liquid equilibria, solubility, ore mining, aluminium hydroxysulfate characterisation, Al8(SO4)5(OH)14.34H2O

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Natural ores mined to extract various metallic cations are often composed of a variety of aluminosilicates. These include feldspars (calcium, potassium or sodium aluminosilicates) and iron-magnesium aluminosilicates. During the acid processing of these ores, the temporary precipitation of solid phases may be observed. This frequently leads to over-consumption of reactants or even stops operation due to clogged industrial equipment. As a consequence, precipitates have to be removed and the cost of such a process is very high. Understanding the nature of these solid phases and how they appear would help to overcome the major challenge of avoiding precipitation and improve processing conditions.

A white precipitate is very often observed. Analyses have shown that aluminium, calcium and sulfates are the major constituents of the precipitates, as calcium sulfate and aluminium hydroxide and/or sulfate. Besides these, a large number of aluminium hydroxysulfates, which may be formed in acid mine drainage or in acid water rich in sulfate, have been reported in the literature [1][2][3][4][5][6][7][8]. These aluminium hydroxysulfates may be the potential precipitates causing clogging. However, the solid phases are often amorphous or poorly crystallized, hence complex to characterise. They are also generally absent from current thermodynamic databases so they need to be better defined. For this purpose, it is necessary to study the liquid-solid equilibria in a complex system: the isothermal and isobaric H2O-Ca 2+ , Al 3+ // O 2-, SO4 2-quaternary diagram defined on the basis of the observed precipitates as represented in Fig. 1 by the basic components Al2O3, Al2(SO4)3, CaO, CaSO4 and H2O. To determine this system, binaries, located on the edges of the pyramid, and ternaries, corresponding to its faces, need to be studied at 25°C and 1 atm, which are the average temperature and pressure of the operations.

Binaries and several ternaries especially those involving calcium oxide or hydroxide have already been described in the cement chemistry [START_REF] Cameron | The system lime, gypsum water at 25°[END_REF][START_REF] Cameron | Solubility of Calcium Sulphate in Aqueous Solutions of Sulphuric Acid[END_REF][START_REF] Hulett | The solubility of gypsum[END_REF][START_REF] Jones | The quaternary system CaO-Al2O3-CaSO4-H2O at 25[END_REF][START_REF] Jones | The Quaternary System CaO-Al2O3-CaSO4-H2O at 25°C. Equilibria with Crystalline Al2O3-3H2O, Alumina Gel, and Solid Solution[END_REF][START_REF] Taylor | Cement chemistry[END_REF][START_REF] Wang | Phase equilibrium of CaSO4-Ca(OH)2-H2O system[END_REF][START_REF] Wells | Study of the system CaO-Al2O3-H2O at temperatures of 21° and 90°[END_REF]. These solids are found in alkaline environments thus are generally absent in the acid processing of ores. Since the solid phases observed are calcium sulfate and aluminium hydroxysulfate, Al2(SO4)3-CaSO4-H2O and Al2O3-SO3-H2O are the two systems considered.

Aqueous binary systems

Since temperature and pressure are fixed, determining an aqueous binary system at 25°C is similar to determining the solubility of a compound in pure water at 25°C. Al2O3 is not soluble in pure water at this temperature, so only the solubilities of aluminium sulfate and calcium sulfate, which are already known (Al2(SO4)3: 27.8 w% ± 0.4 w% [1,[START_REF] Henry | The System Aluminum Sulfate--Sulfuric Acid--Water at 60°[END_REF][START_REF] Pascal | Nouveau traité de chimie minérale Tome VI Bore, aluminium, gallium, indium, thallium[END_REF][START_REF] Taylor | The system Al2(SO4)3-H2SO4-H2O[END_REF] and CaSO4: 0.208 w% ± 0.005 w% [START_REF] Cameron | Solubility of Calcium Sulphate in Aqueous Solutions of Sulphuric Acid[END_REF][START_REF] Hulett | The solubility of gypsum[END_REF][START_REF] Wang | Phase equilibrium of CaSO4-Ca(OH)2-H2O system[END_REF][START_REF] Posnjak | The system CaSO4-H2O[END_REF]), are studied. At this temperature, in saturated solutions, solid phases exist as hydrated solids. However if it is certain that the stable solid phase for calcium sulfate at 25°C is gypsum (CaSO4.2H2O), there is an uncertainty about the number of water molecules in the stable aluminium sulfate hydrate Al2(SO4)3.nH2O at this temperature: n=16 [START_REF] Henry | The System Aluminum Sulfate--Sulfuric Acid--Water at 60°[END_REF][START_REF] Taylor | The system Al2(SO4)3-H2SO4-H2O[END_REF][START_REF] Bassett | The basic aluminium sulphates[END_REF][START_REF] Bassett | Pickeringite and the system MgSO4-Al2(SO4)3-H2O[END_REF], n=17 [1,[START_REF] Ho Fang | Alunogen, Al2(H2O)(SO4)3.5H2O : Its atomic arrangement and water content[END_REF] and n=18 [START_REF] Kuznetsov | X-ray diffraction investigation of solid phases in ternary aqueous systems consisting of nickel, sodium, and aluminum sulfates at 25-65°C[END_REF] molecules of water were found in literature.

Aqueous ternary system Al2(SO4)3-CaSO4-H2O

Few reliable data were found in literature about this system at 25°C. Jones [START_REF] Jones | The quaternary system CaO-Al2O3-CaSO4-H2O at 25[END_REF] found two points of the solubility curve for very low aluminium sulfate concentrations, which are 0.192 w% CaSO4, 0.146 w% Al2(SO4)3 and 0.203 w% CaSO4, 0.040 w% Al2(SO4)3. These liquids are in equilibrium with gypsum. There are no data for concentrated aluminium sulfate solutions.

Aqueous ternary system Al2O3-SO3-H2O

The solid-liquid equilibria have already been represented for this system at 25°C [1,[START_REF] Bassett | The basic aluminium sulphates[END_REF][START_REF] Dobrev | Glass formation and condensation in the alumina-sulfur trioxide-water system[END_REF], 60°C [START_REF] Henry | Phase Rule Investigation of the System Al2O3-SO3-H2O at 60°, Basic Region[END_REF] and above 100°C [START_REF] Dyson | New Phases in the System Al2O3-SO3-H2O at Temperatures above 100[END_REF]. Nevertheless little data are available about solid phases, especially in the more basic area for low sulfur trioxide concentrations. Bassett and Goodwin [START_REF] Bassett | The basic aluminium sulphates[END_REF] and Bigham and Nordstrom [1,[START_REF] Bigham | Iron and aluminum hydroxysulfates from acid sulfate waters[END_REF] reported a large number of stable or metastable aluminium hydroxysulfates, listed in Table 1 1 , which are, in most cases, poorly crystallised. Glassy solids or gels were also observed, sometimes mixed with very small crystals. Reaching the thermodynamic equilibrium could take weeks or months, so the determination of the solid phases was not trivial. The authors also noticed the possibility of solid phases evolving after solution removal or during filtration. It was particularly difficult to determine the number of water molecules in some aluminium hydroxysulfate hydrates and the composition of the solids was often not really known. Moreover, the ICCD (International Centre for Diffraction Data) database's reference records are old, low-quality and most of them have been deleted from the database. Consequently, there are little data about the crystal structures of these solid phases.

The aims of this work were to determine the solid-liquid equilibria at 25°C in the Al2(SO4)3-CaSO4-H2O and Al2O3-SO3-H2O ternary systems, in order to define aqueous phase compositions and to identify and characterise the solid phases. A statistical study on single-crystal X-ray diffraction led to identifying the stable aluminium sulfate hydrate at 25°C.

Material and methods

2.1. Mixture preparation 2.1.1. Binary systems and Al2(SO4)3-CaSO4-H2O Aluminium sulfate octadecahydrate (Sigma-Aldrich®, ≥ 98 % purity) and calcium sulfate dihydrate (Sigma-Aldrich®, ≥ 99 %) were used to prepare mixtures. Aluminium sulfate and/or calcium sulfate were weighed in a centrifuge tube, and the exact amount of deionised water was added. A stirrer bar was added to each solution and tubes were put in a thermostated reactor where mixtures were stirred for about one week, which was long enough to reach the equilibrium state, based upon titrations conducted at one week, one month and longer, without change.

Ternary system Al2O3-SO3-H2O

Based on the method already described in literature [START_REF] Bassett | The basic aluminium sulphates[END_REF]- [START_REF] Johansson | The Crystal Structures of [Al2(OH)2(H2O)8](SO4)2.2H2O and [Al2(OH)2(H2O)8](SeO4)2.2H2O[END_REF], solutions were prepared with aluminium metal and sulfuric acid (Sigma-Aldrich®, p.a., 95.0-97.0 % purity), however no mercury or another catalyst was used. Solutions of 40 g were prepared to have enough liquid samples for chemical analyses after phase separation. The desired quantities of deionised water and sulfuric acid were weighed in a centrifuge tube. As the action of sulfuric acid on aluminium leads to dihydrogen formation, aluminium was weighed separately and added portionwise, and centrifuge tubes were opened often to avoid pressure increases and exploding tubes. When all aluminium was in solution, tubes were put in a thermostated reactor, where mixtures were stirred for at least 1 week for the acid region and up to 3 months for the more basic region, until the equilibrium state was reached. In some mixtures in the more basic region, precipitation did not occur after several months. A platinum wire was then added to induce the formation of solid phases. Stirring was then stopped and solutions were centrifuged to separate solid and liquid phases.

Liquid phase titration

To define the solubility curve, the liquid phase was determined by complexometric titration for cations and thermotitration for sulfates, and not by gravimetric methods.

Cation determination

Calcium and aluminium ions in solution were determined by a complexometric method. To avoid interference, aluminium was titrated first and calcium was titrated second, after aluminium complexation. Titration was done automatically using an automatic burette [Titrando® 905, Metrohm] and a photometric sensor [Optrode, Metrohm]. As the photometric sensor had eight available wavelengths (from 470 to 660 nm), it allowed selective titration of ions in solution. Detection of colour change was also more sensitive with the sensor than the human eye. Tiamo™ was the software used to handle data and determine end-point.

Indirect titration was used to determine aluminium ion concentration. A sample was taken and an excess of 1,2diaminocyclohexanetetraacetic acid disodium salt solution (DCTA, Fluka, 0.1 mol.L -1 ) was added to the sample and warmed for a few minutes to complex aluminium. After cooling, the mixture was buffered with hexamethylenetetramine (Sigma-Aldrich®, ≥ 99.5 % purity) around pH = 5 and a coloured indicator, xylenol orange (Sigma-Aldrich®, ACS Reagent) in KCl, was added. The solution was yellow, which is the colour of the free indicator in solution. Next, excess DCTA was titrated with zinc sulfate solution (Fluka, 0.05 mol.L -1 ) at 574 nm until the solution turned red, the colour of indicator-Zn 2+ complexes.

To determine calcium ion concentration, an excess of triethanolamine (Sigma-Aldrich®, ≥ 99 % purity) was added and the sample was warmed for a few minutes to complex aluminium ions and avoid interference or aluminium hydroxide precipitation with the pH increase. After cooling, sodium hydroxide solution was added to the mixture to reach a pH near 12 -12.5. Murexide (Sigma-Aldrich®, ACS Reagent) in KCl was added as coloured indicator and the solution became pink due to the formation of indicator-Ca 2+ complexes. Finally, calcium ions were titrated with ethylenediaminetetraacetic acid disodium salt solution (EDTA, Fluka, 0.01 mol.L -1 ) at 610 nm until the solution turned purple, which is the colour of the free indicator in solution.

Each titration was performed at least three times with good reproducibility.

Sulfate determination

Sulfate ions were determined by thermometric titration. Barium chloride solution was added to the mixture, leading to the precipitation of barium sulfate. Titration was done automatically using an automatic burette [859 Titrotherm, Metrohm] and a temperature sensor [Thermoprobe, Metrohm]. Tiamo™ was the software used to handle data and to determine end-point.

In the sample, deionised water and ethanol were added in a ratio 3:1, as experiments showed that better results were obtained with ethanol [START_REF] Williams | Thermometric titration of sulphate[END_REF] since barium sulfate is nearly insoluble in water and insoluble in ethanol. In some samples, hydrochloric acid was added to prevent aluminium hydroxide precipitating due to too high a pH. Sulfate ions were then titrated with barium chloride solution at 1.0 mol.L -1 (Sigma-Aldrich®, ≥ 99 % purity). When the reaction took place, the temperature of the solution increased until the end-point and this change was monitored according to the volume of titrant added. After the end point the temperature was stable or decreased.

Each titration was performed at least three times with good reproducibility.

Solid phase characterisation

Structural characterisation by X-ray diffraction

The solid phases were determined using powder X-ray diffraction (XRD) or single-crystal X-ray diffraction, according to the nature of the solid. If solid phases were determined by powder X-ray diffraction, experimental diffractograms were compared with the ICDD database.

XRD powder analyses were recorded on a BRUKER D8 Advance diffractometer or on a Panalytical X'PertPro MRD diffractometer with a copper anticathode tube (λ (Cu Kα1) = 1.54060 Å, λ (Cu Kα2) = 1.54443 Å), in air at room temperature. Both of them have a Bragg-Brentano configuration in θ/θ (fixed sample). To prepare the sample, some solid phase was taken from the biphasic mixture and rapidly dried with a filter paper to avoid the possible decomposition or dehydration of the solid. The solid phase was then deposited on a specific holder. Time of experiment depended on the solid phase, its crystallinity and its stability after the mother solution was removed. The diffractograms which were obtained were compared to the ICDD database using the X'Pert HighScore software.

Single-crystal X-ray diffraction data were collected at room temperature on an Oxford Gemini diffractometer with a molybdenum anticathode tube (λ (Mo Kα) = 0.71073 Å) and equipped with a CCD camera. An analytical absorption correction based on the crystal shapes was applied. The structures were solved by direct methods using the SIR97 program combined with Fourier difference analyses, and refined against F (I/σ(I) > 3) by using the CRYSTALS program. All non-hydrogen atoms were anisotropically refined.

Determination of solid phase compositions

If the solid was amorphous or could not be identified in the database, titration of the solid was required. The dry or moist solid phase was dissolved in water with small amount of hydrochloric acid, and each element of the solid was determined as described for the liquid phase. Some samples were also determined using energy-dispersive X-ray spectroscopy (EDS) and scanning electron microscopy (SEM) [FEI Quanta FEG 250], either to confirm XRD determination or to obtain an elementary analysis when comparison with the ICDD database led to more than one possibility.

For the more basic solid phase, titration of the solid phase was not accurate and the EDS results only gave the Al/S ratio. As a consequence thermogravimetric analyses were done using a thermogravimetric analyser [TGA/DSC 2 HT, Mettler Toledo]. The measurements were carried out in a flowing nitrogen atmosphere and a temperature range from 30 to 1200°C in a 150 µL alumina crucible with a pierced lid. The heating rate was 10°C.min -1 and the mass of the samples was about 10-11 mg. A blank analysis with empty crucibles was run before sample analyses and then the blank curve was subtracted from the sample curve. The first derivative curve (DTG) was used to evaluate the mass loss steps.

Results and discussion

Aqueous binary systems at 25°C under atmospheric pressure

The solubility limits and the stable solid calcium sulfate and aluminium sulfate phase were determined at 25°C and compared to data available in literature as shown in Table 2. No significant differences in the solubility limits were observed. Gypsum (CaSO4.2H2O) is the stable solid phase identified, which is in accordance with the literature at this temperature. In X-ray powder diffraction, the diffractogram obtained for aluminium sulfate solid phase was compared to the diffractograms in the ICDD database. The diffractograms of aluminium sulfate hexadecahydrate, heptadecahydrate and octadecahydrate are almost the same, so it is difficult to be certain about the hydration degree of aluminium sulfate. However, after several days, small single-crystals were observed in the saturated solution of aluminium sulfate, so a statistical study was conducted on single-crystal X-ray diffraction to determine the number of water molecules present in the stable aluminium sulfate hydrate at 25°C. To have reliable data, another saturated solution was prepared and the study was conducted on five crystals from the two solutions.

The crystals look like small plates. The formula which is found by single-crystal X-ray diffraction is [Al(H2O)6]2(SO4)3.3.8H2O. As Fig. 2 presents, 15.8 molecules of water are in the stable aluminium sulfate hydrate at 25°C, with 12 of them being linked with aluminium. All refinement details are available in Table 3; those of the statistical study run on the three crystals from the first solution are given in the first column. The results from the two other crystals from the second mixture are presented in the second column. As the two refinements of the statistical occupancy recovered and the two crystal structures are identical, the molecules of aluminium sulfate hydrate have the same number of uncoordinated water molecules, taking into account the uncertainty of the refinement.

Subsequently, the stable aluminium sulfate hydrate at 25°C will be noted as Al2(SO4)3.15.8H2O.

Al2(SO4)3-CaSO4-H2O

Twelve mixtures were prepared to precisely describe the solid-liquid equilibria of the Al2(SO4)3-CaSO4-H2O system in the isotherm at 25°C. Table 4 presents the initial mixtures for the liquid phase composition and the corresponding solid phase in equilibrium. Fig. 3 illustrates the experimental results for this ternary diagram. As calcium sulfate is much less soluble than aluminium sulfate, the X axis is cut in order to see the liquid region, but the conodes cannot be drawn in the diagram. This isotherm shows two biphasic regions (liquid + solid): liquid + Al2(SO4)3.15.8H2O and liquid + CaSO4.2H2O and one three-phase region (liquid + two solids) with a variance of zero: liquid L1 + Al2(SO4)3.15.8H2O + CaSO4.2H2O. The composition of the invariant liquid, which was determined precisely with very low uncertainty, is 0.051 w% CaSO4; 27.75 w% Al2(SO4)3. Fig. 4 illustrates the XRD patterns confirming the triphasic region. The identification of the solid phases is simple and unambiguous. Solid-solid equilibrium regions have not been studied in this work as only the solubility curve was needed to be determined. Moreover this ternary diagram is simple as equilibrium state was reached rapidly and there is no double aluminium-calcium compound in equilibrium with a liquid phase.

Al2O3-SO3-H2O

Table 5 presents the mixtures initially prepared, the liquid phase composition and the corresponding solid phase in equilibrium. Fig. 5 depicts the experimental results for the ternary diagram Al2O3-SO3-H2O at 25°C (solid lines). Bassett and Goodwin's [START_REF] Bassett | The basic aluminium sulphates[END_REF] work is plotted in dashed lines and only the main differences are drawn in this diagram.

The experimental solubility curve and the two first biphasic regions: liquid + Al2(SO4)3.15.8H2O (solid A), liquid + Al(SO4)(OH).5H2O (solid J), are almost the same as those given in the literature. Two other biphasic areas are observed: liquid + solid T and liquid + solid V. This latter region is larger than the one described by Bassett and Goodwin [START_REF] Bassett | The basic aluminium sulphates[END_REF]. Contrary to identifying solid phases A and J, which was simple and unambiguous, identifying solid phases T and V was more complex as the comparison with diffractograms of the ICDD database leads to more than one record for solid T and to no record for solid V.

To be in accordance with phase-rule equilibria, two biphasic domains must be separated by a triphasic area with an invariant liquid and two solid phases; three are expected: L1 + solid A + solid J, L2 + solid J + solid T and L3 + solid T + solid V.

Identification of solid phase T

First powder X-ray diffraction analyses, done on this solid, did not enable the solid phase to be determined. Indeed, the study highlighted the rapid decomposition of the solid phase into another after liquid removal. Consequently, peaks of two or more phases are observed in the diffractograms. Fig. 6 presents the diffractograms' evolution and so the time dependence of the solid phase decomposition. The main solid phase which seems to appear during decomposition corresponds to the phase described by Sabelli and Santucci [START_REF] Sabelli | Rare sulfate minerals from the Cetine mine, Tuscany, Italy[END_REF]: Al3(SO4)2(OH)5.9H2O. However, the authors analysed this solid in the presence of gypsum (CaSO4.2H2O), so some peaks in the record do not match the experimental diffractograms. A few very small peaks in the experimental pattern do not fit with the record and could be due to the formation of aluminium hydroxide.

In the second analyses, a Mylar® film was used to stop or at least to slow down the decomposition process, so as to observe only peaks of the initial aluminium hydroxysulfate which is in equilibrium with the liquid phase. The Mylar® film presents a wide peak around 26° (2θ) in powder X-ray diffraction, as showed in Figs. 1011. Peaks obtained for the hydrated aluminium hydroxysulfate do not match the solid phase described by Bassett and Goodwin [START_REF] Bassett | The basic aluminium sulphates[END_REF]: Al10(SO4)6(OH)18.37H2O. However, most of them seem to fit with the Al10(SO4)6(OH)18.31H2O solid phase, but the record of this solid has been deleted from the current ICDD database. Comparison with another diffractogram in the database shows that peaks in the solid phase Al8(SO4)5(OH)14.34H2O correspond to those of the experimental diffractogram. This solid phase was described by Casey et al. [START_REF] Casey | A New Aluminum Hydroxide Octamer, [Al8(OH)14(H2O)18](SO4)5•16H2O[END_REF]; 7 years were required for crystals to be obtained, which could be analysed by single-crystal X-ray diffraction. Based on these data, the powder diffractogram was calculated and all peaks do match the experimental ones.

To confirm its stability in the mother solution, the solid phase of the same mixture was analysed by powder Xray diffraction at a different time (1 to 18 months) without any change in the diffraction peaks.

Aluminium and sulfate in the solid were also titrated to verify the stoichiometry. To avoid decomposition, the solid phase was not completely dried. Instead it was dried very quickly on a filter paper to remove liquid. Results of this moist solid phase titration are available in Table 6 and are represented by triangles in Fig. 7. The line linking the dots which correspond to the liquid phase, the initial mixture and the moist solid phase, converge on solid phase Al8(SO4)5(OH)14.34H2O and not on Al10(SO4)6(OH)18.37H2O. Al8(SO4)5(OH)14.34H2O is the phase in equilibrium with the liquid phase and its decomposition leads to the formation of Al3(SO4)2(OH)5.9H2O and aluminium hydroxide, as described in the equation below, which agrees with X-ray diffraction analyses.

𝐴𝑙 (𝑆𝑂 ) (𝑂𝐻) . 34𝐻 𝑂 ⎯⎯ 5 𝐴𝑙 (𝑆𝑂 ) (𝑂𝐻) . 9𝐻 𝑂 + 𝐴𝑙(𝑂𝐻) + 23 𝐻 𝑂

Identification of solid phase V

The characterisation of this phase was even more complex, as no record corresponds to this solid. In addition, depending on the initial mixture, the solid phase was crystallised to varying degrees and X-ray diffraction peaks were not all correctly defined. At this time, structural refinements by the Rietveld method have not been possible. However, there is no difference between the wet and the dry solid phase in powder XRD, so this solid does not decompose after solution is removed.

Nevertheless, the straight line linking the liquid phase and the initial mixture converge to the solid phase Al10(SO4)3(OH)24.xH2O, so different techniques were used to confirm the chemical composition of solid V.

In the first step, solid phase titration was attempt, but not all the solid dissolved even with the use of concentrated hydrochloric acid. The stoichiometry of the solid phase could not be determined.

In the second step, energy-dispersive X-ray spectroscopy and scanning electron microscopy analyses were conducted on eleven samples to determine the Al/S ration and to prove that the solid is homogenous. SEM of the compound highlights the disordered formation of nanocrystalline grains (<1µm). The EDS analyses indicate that submicron size grains have an Al/S ratio between 3.01 and 3.62 which supports the formation of a solid phase like Al10(SO4)3(OH)24.xH2O. However this technique does not give any reliable data about the amount of oxygen or hydration. Consequently, thermogravimetric analyses were planned and carried out on several solid phases from the higher pH area. Experimental conditions were chosen based on previous experiments conducted on aluminium sulfate hydrate [START_REF] Pelovski | The thermal decomposition of aluminum sulfate in different gas phase environments[END_REF][START_REF] Çılgı | Thermal decomposition kinetics of aluminum sulfate hydrate[END_REF] and especially on basic aluminium sulfates [START_REF] Kloprogge | Thermal stability of basic aluminum sulfate[END_REF][START_REF] Földvári | Aluminium sulfates and hydroxysulfates reported in the literature. Mineral name Formula Stoichiometry in the Al2O3-SO3-H2O system ICDD record Aluminite Al2(SO4)(OH)4.7H2O Al2O3.SO3.9H2O 00-043-0669 (I) Alunogen Al2(SO4)3[END_REF]. The thermogravimetric curve shown in Fig. 8 looks the same as those found in literature [START_REF] Kloprogge | Thermal stability of basic aluminum sulfate[END_REF][START_REF] Földvári | Aluminium sulfates and hydroxysulfates reported in the literature. Mineral name Formula Stoichiometry in the Al2O3-SO3-H2O system ICDD record Aluminite Al2(SO4)(OH)4.7H2O Al2O3.SO3.9H2O 00-043-0669 (I) Alunogen Al2(SO4)3[END_REF] and presents different mass loss steps. Between 30 to 700°C, water and hydroxyl groups are lost and above 800°C, SO3 groups evolve. As reported before, the water and hydroxyl group losses occur in several steps and correspond to 32.6% and 10.9% mass losses respectively. Physically adsorbed water is lost first, then the molecules of water coordinated to the aluminium atoms and finally dehydroxylation. The last mass loss of 18.3% is split into two steps (16.7% + 1.6%), as it was described by Földvári [START_REF] Földvári | Aluminium sulfates and hydroxysulfates reported in the literature. Mineral name Formula Stoichiometry in the Al2O3-SO3-H2O system ICDD record Aluminite Al2(SO4)(OH)4.7H2O Al2O3.SO3.9H2O 00-043-0669 (I) Alunogen Al2(SO4)3[END_REF], and matches the loss of SO3 groups. Powder XRD analysis shows that the final product is alumina, so if the hypothesis of ten atoms of aluminium in the initial molecule is right, the mass loss of 18.3% corresponds to the loss of three SO3 groups and thus the mass losses of 32.6% and 10.9% are equivalent to 32 water molecules. Therefore the initial stoichiometry of solid V can be written as 5Al2O3.3SO3.32H2O or Al10(SO4)3(OH)24.20H2O.

Identifying solid phases V and T completes the description of the ternary system Al2O3-SO3-H2O at 25°C and highlights the presence of four two-phase regions: liquid + Al2(SO4)3.15.8H2O; liquid + Al(SO4)(OH).5H2O; liquid + Al8(SO4)5(OH)14.34H2O and liquid + Al10(SO4)6(OH)24.20H2O. Three triphasic areas were also observed: L1 + Al2(SO4)3.15.8H2O + Al(SO4)(OH).5H2O; L2 + Al(SO4)(OH).5H2O + Al8(SO4)5(OH)14.34H2O and L3 + Al8(SO4)5(OH)14.34H2O + Al10(SO4)6(OH)24.20H2O. The XRD patterns shown in Figs.9-11 respectively confirm the delineation of these three regions.

The compositions of the liquid invariants are: L1 (0.198 w SO3; 0.086 Al2O3); L2 (0.150 w SO3; 0.072 Al2O3) and L3 (0.047 w SO3; 0.030 Al2O3).

Conclusion

In this work, the 25°C isotherm for the Al2(SO4)3-CaSO4-H2O and Al2O3-SO3-H2O ternary systems have been defined experimentally under atmospheric pressure. The goals of this study were to determine the nature of the solid phases, their stability and solubility, since understanding solid phase precipitation can help prevent it and the clogging which occurs during acid ore mining.

The determination of the Al2(SO4)3-CaSO4-H2O system highlights only the formation of gypsum and aluminium sulfate hydrates, so there is no Al-Ca double compound in equilibrium with a liquid phase. Defining solubility curves for the aluminium hydroxysulfates in the Al2O3-SO3-H2O ternary was more complex, as there are a large number of aluminium hydroxysulfates reported in the geological, geochemical and chemical literature. Most of these solids are not well defined, as they are amorphous or poorly crystallised, dehydrate rapidly, and are often metastable. However, the use of X-ray diffraction and other techniques led to the characterisation of the stable solid phases in the ternary systems. Some inconsistencies about these phases have been resolved, in particular the degree of hydration in some hydroxysulfates. The rapid change of some aluminium hydroxysulfates was also underlined with the decomposition of solid T when the mother solution is removed. Once again, this proves that characterising and determining the chemical composition of these phases is not simple.

In future work, to predict the appearance of these aluminium hydroxysulfates during ore processing the solubility constants will be determined by modelling the experimental results. The standard uncertainties u are u(wCa) = 0.002%, u(wAl) = 0.05%

Fig. 5 Fig. 6 Fig. 7

 567 Fig.5Ternary system Al2O3-SO3-H2O at 25°C and 1 atm.

3 Fig. 8

 38 Fig. 8 Thermogravimetric curve (in solid line) and 1 e derivative of the thermogravimetric curve (in dashed line) of the solid phase Al10(SO4)3(OH)24.20H2O.

Table 2 .

 2 Solubility limit in the binary systems Al2(SO4)3-H2O and CaSO4-H2O at 25°C (expressed in percent by weight).

	Literature		This work
	Solubility limit	Solid phase	Solubility limit	Solid phase

Table 3 .

 3 Single-crystal X-ray diffraction refinement details for complexes 1-5 and ligand L 2 .

	1LS-Al	2LS-Al

Table 4 .

 4 Solid-liquid equilibrium data in the ternary system Al2(SO4)3-CaSO4-H2O at 25°C.

		Initial mixture composition (%w)	Liquid phase composition (%w)	Solid phase in equilibrium
		CaSO4	Al2(SO4)3	CaSO4	Al2(SO4)3
		0.000	29.71	0.000	27.80	Al2(SO4)3.15.8H2O
		0.019	29.02	0.023	27.78	Al2(SO4)3.15.8H2O
		0.034	28.40	0.040	27.71	Al2(SO4)3.15.8H2O
	L1	0.180	28.00	0.051	27.75	Al2(SO4)3.15.8H2O + CaSO4.2H2O
		0.201	25.02	0.074	24.97	CaSO4.2H2O
		0.206	23.02	0.088	22.98	CaSO4.2H2O
		0.250	20.03	0.112	19.94	CaSO4.2H2O
		0.635	16.00	0.144	16.14	CaSO4.2H2O
			10.02	0.173	10.13	CaSO4.2H2O
		0.252	10.02	0.171	10.09	CaSO4.2H2O
		0.998	5.02	0.185	5.10	CaSO4.2H2O
		0.490	0.00	0.208	0.00	CaSO4.2H2O

Table 5 .

 5 Solid-liquid equilibrium data in the ternary system Al2O3-SO3-H2O at 25°C.

		Initial mixture composition (w)	Liquid phase composition (w)	Solid phase in equilibrium
		SO3	Al2O3		Al2O3
		0.343	0.039	0.339	0.015	Al2(SO4)3.15.8H2O
		0.275	0.060	0.257	0.041	Al2(SO4)3.15.8H2O
	L1	0.247	0.114	0.198	0.086	Al2(SO4)3.15.8H2O + Al(SO4)(OH).5H2O
		0.205	0.100	0.181	0.080	Al(SO4)(OH).5H2O
		0.200	0.100	0.166	0.075	Al(SO4)(OH).5H2O
		0.189	0.100	0.157	0.072	Al(SO4)(OH).5H2O
	L2	0.190	0.110	0.150	0.072	Al(SO4)(OH).5H2O + Al8(SO4)5(OH)14.34H2O
		0.148	0.090	0.134	0.065	Al8(SO4)5(OH)14.34H2O
		0.143	0.095	0.113	0.057	Al8(SO4)5(OH)14.34H2O
		0.107	0.068	0.089	0.046	Al8(SO4)5(OH)14.34H2O
		0.090	0.060	0.073	0.037	Al8(SO4)5(OH)14.34H2O
		0.070	0.050	0.051	0.030	Al8(SO4)5(OH)14.34H2O
		0.101	0.091	0.049	0.029	Al8(SO4)5(OH)14.34H2O
	L3	0.060	0.055	0.047	0.030	Al8(SO4)5(OH)14.34H2O + Al10(SO4)3(OH)24.20H2O
		0.048	0.045	0.039	0.023	Al10(SO4)3(OH)24.20H2O
		0.040	0.040	0.029	0.016	Al10(SO4)3(OH)24.20H2O
		0.030	0.030	0.021	0.011	Al10(SO4)3(OH)24.20H2O
		0.015	0.025	0.004	0.002	Al10(SO4)3(OH)24.20H2O
	The standard uncertainties u are u(w)=0.001

Table 6 .

 6 Mixtures in the two-phase region: liquid-Al8(SO4)5(OH)14.34H2O. Square-based pyramid representing the quaternary system H2O-Al 3+ , Ca 2+ // O 2-, SO4 2-at isothermal and isobaric conditions. Fig.4XRD pattern of powder solid phase, triphasic region L1 + Al2(SO4)3.15.8H2O + CaSO4.2H2O, at 25°C.

	Initial mixture composition (w)	Liquid phase composition (w)	Moist solid phase (w)	Solid phase in equilibrium
	SO3	Al2O3	SO3	Al2O3	SO3	Al2O3
	0.143	0.095	0.113	0.057	0.201	0.181	Al8(SO4)5(OH)14.34H2O
	0.107	0.068	0.089	0.046	0.206	0.199	Al8(SO4)5(OH)14.34H2O
	0.070	0.050	0.051	0.030	0.187	0.181	Al8(SO4)5(OH)14.34H2O
	The standard uncertainties u are u(w)=0.001

Fig. 2 XRD structure of the stable aluminium sulfate hydrate at 25°C.

  Fig. 9 XRD patterns of powder solid phase, triphasic region L1 + Al2(SO4)3.15.8H2O + Al(SO4)(OH).5H2O, at 25°C. Fig. 10 XRD patterns of powder solid phase, triphasic region L2 + Al(SO4)(OH).5H2O + Al8(SO4)5(OH)14.34H2O, at 25°C. (SO ) 5 (OH) 14 .34H 2 O Mylar® Fig. 11 XRD patterns of powder solid phase, triphasic region L3 + Al8(SO4)5(OH)14.34H2O + Al10(SO4)3(OH)24.20H2O, at 25°C. Al 10 (SO 4 ) 3 (OH) 24 .20H 2 O

									Al 8 (SO 4 ) 5 (OH) 14 .34H 2 O
									Total mass loss
									61.8%
	Relative Intensity (a. u.) Relative Intensity (a. u.) Relative Intensity (a. u.)		Mass loss 32.6%			Mass loss 10.9%		Solid mixture of the triphasic region Al(SO 4 )(OH).5H 2 triphasic region Solid mixture of the Al(SO 4 )(OH).5H 2 O Solid mixture of the triphasic region
									Mass loss
		TG							16.7% Al 2 (SO 4 ) 3 .15.8H 2 O
		DTG							Mass loss
	6	8	10		12	14	16	18	20	1.6% 22	24
	5	10	15	20	25 2 Theta (°)	30	35	40	45	50
		10		20		30 2 Theta (°) 2 Theta	40		50

8

Several solid phases, with high sulfur trioxide content, were also reported in literature[START_REF] Taylor | The system Al2(SO4)3-H2SO4-H2O[END_REF], but are not given in Table1.

Acknowledgements

This work has been supported by CIFRE/ANRT doctoral grant no. 2012/0596.