Jorge Martinez Leal

Carole Charbuillet
email: carole.charbuillet@ensam.eu

Stephane Pompidou
email: s.pompidou@i2m.u-bordeaux1.fr

Nicolas Perry
email: n.perry@i2m.u-bordeaux1.fr

Jorge Martínez Leal

Stéphane Pompidou

Recycling chains : a proposal for an exhaustive definition

come

INTRODUCTION

Before the 1970's, the recycling industry was faintly developed. Since then, this industry has experienced an important growth and has even reached industrial and economic maturity in some sectors (ADEME 2012). Indeed for some years now, the use of recycled materials has increased as they have become more and more attractive because of their always-better preserved mechanical properties, for still a profitable price. Integrating recycled materials thus becomes a strategic action for companies, while improving their image with consumers who seek more and more ecofriendly products.

Furthermore, regulations become stricter about the environmental impacts of products (e.g. Directives 2008/98/EC, 2012/19/EU, 2011/65/EU, 2000/53/EC, etc.). End-of-life goods must now preferentially be recycled than energy recovered or landfilled. In this context, availability of recycled materials increases and they are now real alternative to first extraction ones for manufacturing processes (ADEME 2015).

Nowadays, many approaches and many studies focus on improving waste management (e.g. reversed logistics, closed loop supply chain management, green supply chain management and sustainable supply chain management) [START_REF] Seuring | From a literature review to a conceptual framework for sustainable supply chain management[END_REF][START_REF] Sarkis | An organizational theoretic review of green supply chain management literature[END_REF][START_REF] Govindan | Reversed logistics and closed-loop supply chain: A comprehensive review to explore the future[END_REF]. Nevertheless, recycling chains do not seem fully developed, neither well taken into account in industrial supply chains. The main problem actually lies in both quality and quantity variations of material flows. In order to better integrate recycled materials in industry (e.g. parts manufactured with 100% recycled materials, or at least partially integrated in high-performance products), stability and reproducibility of recycling processes, and more globally of all steps of the recycling chain, have to be ensured.

While recycling chains have been operating for quite a long time, there is still a lack of knowledge regarding the fundamentals of such systems. A complete definition and an exhaustive description of these treatment chains are needed as a common reference for future studies.

Firstly, the main steps of a component's lifecycle and its best end-of-life options will be detailed. Then focusing on the recycling option, a standard recycling chain will be defined and described as exhaustively as possible in all its dimensions. Lastly, perspectives of this work on (i) optimization of treatment chains, (ii) identifications of synergies between chains, and (iii) integration of ground realities in the product design phase, will be proposed.

COMPONENT'S LIFE AND END-OF-LIFE 1. Notion of component

Before broaching the lifecycle concept, the notion of component (that we chose to use rather than product) has to be clarified. Actually in this paper, this word will refer indifferently to:

-a whole product; -a module or a unit (i.e. a product subset); -an elementary part (i.e. a module subset), possibly 3/21 -a multi-material part (e.g. a composite, an architectured mix of polymers, etc.); -or a homogeneous one (e.g. a mono-material or an alloy); -or a part offcut in the manufacturing process; as its properties can be assessed globally. However, the other terms can also be used if the scale of analysis is accurately defined.

In this way, depending on the chosen degree of precision, assessing the impacts of a component throughout its life and after is all the more difficult due to the fact that its structure is complex. The more a product contains modules and sub-parts, the more the factors to take into account to analyse its end-of-life.

The component's added value

The added value consists of any improvement provided to a component (i.e. elementary part, module or product) that makes it worth more.

Value is added at every step of the component's manufacturing process. However, it clearly depends on the component's own nature and function. In this way, the material added value must clearly be differentiated from the functional added value.

1. The material added value is mainly related to less complex components (as elementary parts). In this way, a component's added value results first from the material's ownvalue (e.g. strategic materials, rare earth metals, etc.). Nevertheless, value can also result from every process necessary to get the required material (e.g. plastics from crude oil, metals from ore, alloys, etc.) or from the manufacturing process itself (e.g. additive manufacturing).

2. The functional added value is mostly related to modules or to whole products. Here, it is the function of the component which must be preserved. Indeed, much more than its constitutive materials, the component's value results for example from its design (which ensures its efficiency) or from the complexity of assembly. However here again, a specific manufacturing process can even add functional value to a mono-material key part or a subset (e.g. complex gear train obtained by additive manufacturing).

The component's lifecycle

The term lifecycle only refers here to the major activities in the course of the product's lifespan. A component lifecycle is usually divided into five main consecutive steps, as sketched in figure 1.

The dotted arrow depicts schematically the main principle of circular economy (etymologically by closing the loop): materials that stem from end-of-life components can be reinjected as raw materials in a next lifecycle. Usually called secondary raw materials, they will be used to manufacture a similar component or a new one.

The main steps of the lifecycle are briefly described in the next paragraphs (Le [START_REF] Diagon | Integration of end-of-life options as a design criterion in methods and tools for ecodesign Proceedings of Joint Conference on Mechanical[END_REF]. This stage also includes the production of recycled materials (i.e. secondary raw materials; cf. below, § 4.3).

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b. Manufacturing

The second step includes all manufacturing operations, such as raw materials transformation, production operations in the industrial process, thermal and mechanical treatments, assembly and packaging. These operations are specific for each component.

c. Transportation and logistics

This step includes all transport and logistics issues (acquisition, delivery, etc.) in relation to the component throughout its lifecycle. Consequently, these operations do not only concern the distribution phase as suggested by figure 1 (i.e. between the end of manufacturing and the purchasing sites), but can actually be found between or in all of the other stages.

d. Use and maintenance

This phase of the lifecycle focuses on the period in which the product is used, i.e. between its purchase and its end-of-life. It also includes all the maintenance operations needed for increasing its lifespan: curative and preventive maintenances, upgrading and reuse (resale, donation, sharing and pooling).

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e. End-of-life When the product becomes unused (e.g. because of a malfunction), it is taken for waste. However, several ways do exist to extend the life of either the whole product (and thus, to preserve part of its value) or of only some subsets. That's why it is generally more suitable to talk about the end-of-life phase. Details of this key step of our study are given in the next paragraph.

The component's end-of-life

The five main options to treat an end-of-life component are listed below, from the most valuable to the least profitable solution (Le [START_REF] Diagon | Integration of end-of-life options as a design criterion in methods and tools for ecodesign Proceedings of Joint Conference on Mechanical[END_REF]).

1. First of all, the reuse option mainly consists of the recovery of the whole product before it becomes waste. This option involves resale, donation, pooling, etc. The component will be reused for the same function for which it was designed.

This end-of-life option is clearly the best in terms of maximising of the preservation of both functional and material added values. Nevertheless, it is more effective if the manufacturer himself implements and manages an economic model of services.

2. The second way is the remanufacturing process.

When the end-of-life is managed by the manufacturer, it may consist of the product refurbishment. Here again, if an economic model of services is implemented, performances of this end-of-life option can be maximised.

Nevertheless, this option more often consists in recovering modules (or in some cases parts) which will be reassembled as a same product or an upgraded one, during a later manufacturing process. However, it is only possible if previous design choices ensure an easy disassembly. Only then, modules may be cleaned, modified, adapted or simply reassembled; their functional value is preserved.

3. The recycling is the third possible way of treatment.

Here, material valorisation is sought. It mainly consists in extracting materials (e.g. ferrous or non-ferrous metals, strategic materials, etc.) from the waste flow, and regenerating them in so called secondary raw materials. Then, they may be used for manufacturing the same product they came from or a different one. Secondary raw materials are usually more eco-friendly than primary ones, and theoretically have the potential for other recycling loops.

It should be underlined that the recycling process consists of several steps such as collection, depollution, cleaning, dismantling, part and/or material identification, grinding, sorting (before or after grinding; recycling with disassembly then has to be differentiated from recycling without disassembly), etc. The reprocessing of materials is strictly speaking the last step of the recycling process.

The process efficiency will be improved as a function of the dismantling and sorting quality (e.g. avoiding downcycling mainly due to a bad separability). Then, early design 6/21 choices could obviously ease disassembly, improve accessibility to (sub-)parts and target materials, etc. In time, it will be guaranteed to supply better secondary raw materials for following manufacturing processes.

4. The fourth end-of-life option consists of energy recovery. Here, combustible waste is incinerated, with or without other waste, in order to recover heat.

5. Lastly, the worst end-of-life option consists of landfilling and burying (e.g. in old quarries) the inert waste that couldn't be treated by any of the previous ways. This treatment also requires pre-sorting in order to separate toxic from non-toxic waste, and inert materials.

These end-of-life options and their connections with the main steps of the component's lifecycle are sketched in figure 2.

Figure 2: Major end-of-life options and their connections with the main stages of the component's lifecycle (left). Comparison of their relative interest in terms of added value (right).

Lastly, these options heavily depend on the nature of the component (e.g. from the material offcut to the whole product). We attempt to summarize the suitability of such and such option (cf. table 1). However, this simplified approach should be refined depending on the knowledge of both component functional and material values.

Towards a better recycling rate a. Environmental impacts of the end-of-life

A component inevitably impacts the environment almost continuously, from the extraction of the raw materials, during the manufacturing process and all through its use phase (energy used for its working, associated substances rejected in water or in the air, etc.). But even in the end-of-life phase, the environment remains impacted by the landfilled parts (e.g. land occupation or constitu-7/21

+ + + + + + + + + Energy recovery -- -- -- --- --- Landfill ---- --- - ---- ----
Table 1: Suitability of the five main end-of-life options depending on the nature of the component, from the most suitable (+ + + +) to the least suitable (----).

ent toxicity), or by the reprocessing or recycling treatments (e.g. energy consumption, supplies needed for the process, etc.). However, as previously mentioned, design choices may assure an easier disassembly of the product, a better materials separability, or a greater reintegration of secondary raw materials in a following manufacturing process.

In order to improve design choices, a better knowledge of recycling chains could first help to reduce the impacts of end-of-life components by better taking into account the reality on the ground. Thus, more than just the processes involved in recycling, the whole chain itself has to be described listing:

-the recycling process (i.e. type of chain, main steps, processes, stakeholders, flows and specifications); -the chain structure and organization; -and all internal and external factors. This is the aim of the following part.

THE RECYCLING CHAIN 1. Existing definitions

Firstly, one must notice that depending on authors, expressions like recycling network, recycling system, recycling industry or recycling process may all refer to a recycling chain. However, we still prefer to use the latter locution which echoes the supply chain (i.e. the management of the flows of goods and services).

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Without proposing a definition of the recycling chain, most authors prefer to focus on defining recycling as a series of processes ( [START_REF] Schaik | The optimization of end-of-life vehicle recycling in the European Union[END_REF][START_REF] Chancerel Perrine | Observatoire de la filière Véhicules hors d'usage Année 2013: Rapport annuel de la mise en oeuvre des dispositions réglementaires aux véhicules hors d'usage[END_REF]). In the same logic but in the particular context of WEEE (waste electrical and electronic equipment), Hagelüken (Hagelüken 2006 a, b) states that "The [recycling] chain consists of different subsequent steps which are collection, dismantling, shredding/pre-processing, and end-processing of the various materials and metals. These steps are interlinked and interdependences are crucial". This definition emphasises the importance of synergies between stakeholders.

According to Maudet-Charbuillet (Maudet-Charbuillet 2009), all elements that have an influence on the chain in some way must be identified. In this way, she specifies that valorisation chains are complex systems which depend on both internal characteristics (i.e. technical, structural and organizational) and external factors (e.g. comparison with raw materials, geographical and temporal variabilities, etc.). Thus, all these elements have to be taken into account when defining a valorisation chain.

Lastly, Rosu and Tilloy [START_REF] Rosu | Analyse technico-économique et environnementale de filières de recyclage de matériaux pour une aide à la conception de produit orientée fin de vie[END_REF] proposed a more complete definition: "[A recycling chain involves] the whole set of internal and external stakeholders implied in the conversion of waste into recycled raw material as well as the exchanges of material, money and knowledge in accordance with legislations, in order to limit the impact of raw materials extraction on the environment". However, what this definition comes down to say is that reducing raw materials extraction is the main drive for recycling (which is usually not the case). It also implies that involved stakeholders exchange more knowledge about their own know-how, skill, etc., rather than information about the components they treat (i.e. products specifications and properties, performance indicators, etc.).

Our definition of recycling chain

Mainly based on the definition of Rosu and Tilloy [START_REF] Rosu | Analyse technico-économique et environnementale de filières de recyclage de matériaux pour une aide à la conception de produit orientée fin de vie[END_REF], we propose the following definition:

"A recycling chain is an industrial system that involves the whole set of processes and internal and external stakeholders implied in the conversion of waste into recycled material (i.e. secondary raw materials) as well as the exchanges of material, money and information, in accordance with legislation, in order to:

-reduce the impact of raw materials extraction; -reduce the quantity of waste that is incinerated or landfilled; -and primarily, keep the material added value of the product's components."

Independently of the other differences mentioned above, this definition emphasises the fact that a recycling chain is an industrial system, and should be considered as such in order to become competitive and to reach an economic stability.

Schematic depiction of a recycling chain

A component lifecycle (previously sketched in figure 1) is detailed in figure 3, with a focus on its end-of-life and specifically on the recycling chain. It aims to identify the main stakeholders, pro-9/21

DESCRIPTION OF A RECYCLING CHAIN

As previously expressed, recycling chains are complex systems. In order to better analyse them, it is necessary to describe chains with both internal and external parameters. This description will allow us to fully understand these systems as they are reflecting the current situation.

Internal characteristics

Internal characteristics can be divided into (a) technical, and (b) structural and organizational. a. Technical These characteristics refer to all aspects related to methods, techniques, know-how and requirements, within the recycling chain.

1. Chain type. First of all, three types of recycling chains can be differentiated [START_REF] Carole | Proposition d'outils et démarches pour l'intégration de filières de recyclage de matières plastiques dans la "supply chain" automobile[END_REF], depending on the nature of the component to recycle. In this way, if the component is -a product, the recycling chain only focuses on the treatment of a specific one (e.g. ELV (end-of life vehicles), WEEE (waste electrical and electronic equipment), etc.); -a part, the chain aims to preserve functional and/or material values (e.g. PCBs (printed circuit board) must be treated separately in a specific recycling chain); -a material, each chain only integrates a specific material (e.g. cardboard, glass, etc.), independently of the product it comes from.

2. Valorisation circuit. Each step (and sub-step) characterises the chain. Recycling process can usually be divided in:

-Collection. Waste is collected from houses, dumpsters, collecting points, industries, etc. and conveyed to treatment centres; -Depollution. Hazardous materials are removed from the waste in order to be safely treated and to avoid contamination of materials later in the recycling process; -Disassembly. Each component that can be reused or need to be treated separately (in order to preserve its value or because of a too complex recycling process) is removed; -Shredding. The objective is to grind the component into small particles, before separation (e.g. ferrous and non-ferrous metals, plastics, etc.); -Recycling. Lastly, this process transforms recovered materials into secondary raw materials.

Stakeholders of the valorisation.

They can be collectors, depollution operators, dismantlers, shredders, recyclers, etc. But one may be charged with multiple operations.

11/21 4. Input characteristics. These are the characteristics of the waste entering the recycling process. This is key information because the effectiveness of the recycling process is tightly linked to waste properties. Some of these characteristics are listed below: -Origin of components (i.e. nature of the last user, e.g. individual or industry); -Complexity (e.g. product/module assembly, mono or multi-material, etc.); -Localisation (e.g. waste coming from surroundings, from a remote area within the same country or from another country, etc.); -Valorisability (e.g. disassemblability, separability, recyclability, etc.); -Deposit characteristics (e.g. weight, volume, toxicity, economic value, etc.). These characteristics can induce important choices in the valorisation circuit (e.g. choosing if some parts need to be dismantled or not), and then in the efficiency of the recycling process.

5. Output product characteristics. This refers to the final product characteristics (e.g. mechanical properties, physical form, etc.). These characteristics are usually required by the purchaser (i.e. the market).

b. Structural and organizational

Structure and organization of the recycling chain are as important as the technical characteristics previously listed. Indeed, these features will directly impact flows of material, information and money.

1. Financial organization mode. It specifies who administrates and finances the recycling chain. Three main financial organizational modes can be found [START_REF] Carole | Proposition d'outils et démarches pour l'intégration de filières de recyclage de matières plastiques dans la "supply chain" automobile[END_REF].

-The manufacturer's administration. In this organization mode (cf. figure 4.a), the producer organises and finances the recycling of his own products, at least until the last step of waste conditioning. In other words, the manufacturer treats waste until it is no longer considered as such (thanks to one valorisation chain), or ensures its disposal.

-Administration by an external organism. In this organization mode, an external organism (private or public) organises and finances the recycling chain. Several organisms may interact in the chain and each one can treat many products (cf. figure 4.b). While material flows do not change (compared to manufacturer's administration), the external organism is now responsible for managing the waste.

-The free market. This is more a scenario than an organization mode. It consists of a set of independent stakeholders who all seek to valorise waste, with a maximum profit. In contrast with both previous financial modes, there is no responsible for the end-of-life. As a consequence, each actor is supposed to find his own balance without the influence of either the state or the manufacturers (cf. figure 4.c).

2.

Structure. This feature relates to the principle of a circular economy; more specifically it refers to the final destination of products to be recycled. In this way, structure can be:

-opened-loop: the recycled materials do not return to their original application; -closed-loop: the recycled materials do return to their original application. -Legislation. The recycling chain was created with an environmental motivation, specifically to respect legislation; -Business. The recycling chain was created with an economic motivation, i.e. to generate profits.

External factors

The external factors refer to all elements that impact the efficiency of the chain or affect it in any way.

a. Raw materials price

Price of primary raw materials directly impacts the recycling chain. Indeed, recycled materials are in constant comparison with first generation ones (ADEME 2015), not only from a physical or mechanical point of view, but also economically. Consequently, it is usually expected that secondary raw materials must be cheaper than new ones, even when both have the same quality.

b. Geographic variability

Recycling chains' stakeholders are usually spread over large territories as chains are usually -decentralized (a same process is carried out at different locations); -and multilevel (recycling processes may be subsequently carried out at different locations); systems. As a consequence, the chain is highly impacted by geographic variability [START_REF] Diagon | Integration of end-of-life options as a design criterion in methods and tools for ecodesign Proceedings of Joint Conference on Mechanical[END_REF]. Depending on their location, differences between stakeholders of the same chain can be found in (1) legislation, (2) economic and material resources and (3) in the community' attitude to recycling practices. These differences are shortly detailed below: 1. Legislation. Laws differ between states, and even from one area to another in the same country, but they all constrain recycling chains ; 2. Resources. Economic resources vary from one country to another and even between cities. Taking this into account, one must note that available logistic resources (e.g. number of collecting points) and their distribution (i.e. variability in density) may benefit or limit the operating mode of the recycling chain;

3. Community attitude to recycling practices. Some communities are more eco-friendly than others. Thus, it is important to see how to encourage less environmentally conscious ones to participate to the recycling process.

c. Temporal variability

Product life expectancy (1) and product evolution (2) are the most important factors of temporal variability; they both impact the recycling chain (Mathieux 2002). 14/21 1. Product life expectancy. The efficiency on recycling of the (re-)design of a component can only be assessed when it reaches its end-of-life and not before. This can be problematic for long-life products. Indeed, the longer a component is used, the harder it is to improve the chain and to implement effective eco-design strategies. It results from the difficulty to link design to end-of-life. Life expectancy can be split in three categories: -Short life. A product with a short life expectancy will stop being useful rapidly and will be binned quickly (e.g. packaging and disposable products); -Average life. The meaning of average could obviously change from product to product; however, we propose to set the limit at two years (e.g. electronic devices, kitchenware, etc.); -Long life. This category addresses all products used for more than two years (e.g. cars).

2. Product evolution. Products are in constant evolution. Sometimes, it only consists of minor changes (e.g. changes in food packaging). Nevertheless, it can also significantly affect the products design (e.g. composition of electric cars). Thus, recycling procedures must anticipate these changes in order to prevent the impact of these evolutions.

d. Interaction with other existing chains This characteristic refers to the degree of integration of a chain with other existing chains [START_REF] Fleischmann | [END_REF]. It aims at checking if other chains already treat the same materials or have similar processes that could eventually be applied to the chain so we can take advantage of existing knowledge in order to better meet market expectations and demands. The only two possible options are:

1. New system. There is no other similar system; 2. Extension of an existing system. There is a similar system which must be studied.

e. Interaction with other end-of-life options

Other end-of-life options which interact with the assessed recycling chain can be identified. For example, there may be interactions with remanufacturing, energy recovery, and/or disposal (cf. figure 3). These interactions must be identified in order to be improved.

Synthesis. Multidimensional representation

Figure 5 is a multidimensional representation of a recycling chain which seeks to include all the axes needed to take into account when characterizing these systems. Its main objective is to show that a recycling chain is not only defined by internal characteristics but also by external elements that affect it in a positive or negative way.

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An indicator must convey a causal relationship with a measured (i.e. indicated) quantity. It then expresses a synthesis of information, potentially from different types. Hence, the indicator enables knowledge exchanges between several stakeholders from different worlds. The more it reflects reality and it is understandable, the more it is usable.

Assuming that n internal or external factors have been clearly identified and defined (cf. above), let P i be the i th evaluated quantity   1   i n . Then, n indicators must be built to characterize the n P i ; they are called r i and constitute the n-tuple

  1   i i n r r .
We propose that they are all built as dimensionless ratios (e.g. value of the property reduced to a reference datum) in order to be easily combined. As an example, r i could be built as:

*  i i i P r P
where P i * is a reference quantity of the same physical nature as P i .

b. Notion of index

An indicator which results from the aggregation of n others is called an index.

Like so, the efficiency index of the recycling chain will result from the aggregation of the n indicators r i . Let R be this index.

In that case, we aim at defining the map f such as:

  1 2
, ,..., ,...,  i n R f r r r r which reflects as best as possible the reality of the chain.

f is an aggregation function of the n-tuple

  1   i i n r r
. The choice of this map is a priori complex.

For example, f must be -independent of the order of the r i ; -invariant by permutation of the r i ; -monotonic; -etc. All these assumptions will have to be argued by examining the consequences of each decision on the R index.

Improving recycling chains and developing synergies between them

Armed with the R-index, it will be easier to compare the efficiency of all or part of a recycling chain, to another one. As a consequence, we aim to:

-identify the least effective part of a recycling chain in order to improve it; -optimize the recycling of a component by referring it to the best recycling chain (or the most effective stakeholder); -propose new end-of-life options for a component by better preserving its added value. 17/21 2. Taking into account the best end-of-life option from the design phase Lastly, a better knowledge of the real effectiveness of each end-of-life option expressed by a numerical index could easily be taken into account from the design phase.

a. Formalization of the design phase

The impact of the design of a component on the preservation of its added value (namely on the choice of the best end-of-life option) has previously been underlined.

In order to introduce a better vision of the end-of-life reality from the design phase (i.e. in design tools), the component design cycle has to be detailed.

As defined by [START_REF] Pahl | Engineering Design: A Systematic Approach[END_REF], it can be divided into the following main steps.

1. Early design. The early design phase is mainly based on the customers' needs. In this way, the products' main function is translated by designers in a technical requirements list that also takes into account the constraints related to the market, a business strategy, technology, legislation, etc.

2. Preliminary design. The preliminary design usually involves the following two steps:

 the conceptual design aims to define the functional structure. Many concepts are developed to answer the needs previously listed, then compared to assess issues that could stem from every choice. A solution principle is thus selected;

 the architectural design consists in assessing the previous proposal. The most suitable structure from technical and economic points of view is chosen, including components (shapes and materials), pre-sized or nonstandard constituents, etc.

3. Detail design. In the detail design step, the selected architecture is mocked up by CAD, optimised and finally approved. A definition file containing all sized parts and assembly drawings is provided (the definitive layout).

4. Industrialisation. Lastly, the industrialisation phase aims to choose the best manufacturing process, optimising the supply chain, drafting a quality plan, and eventually implementing a prototype to be tested.

b. Areas of improvement of the design step

The R-index being a mathematical tool, it could be quite easily taken into account either in classical design or in eco-design tools, depending on the available data at each step. But the best phase to integrate this knowledge will have to be discussed as an outlook of our preliminary work (cf. figure 6).

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CONCLUSIONS

Recycling chains have been operating for quite a long time. Nevertheless they are still not fully developed. It is mainly due to the complexity of such systems (as schematically shown in figure 3), but also to the lack of theoretical principles on this area.

Our proposed definition and description of a recycling chain are the first step on the way to a complete analysis and full comprehension of these systems. Indeed, it gives a preliminary perspective of the subject at hand. Firstly, the definition fully describes a recycling chain; it regroups the most basic information such as stakeholders, processes and flows (material, information and money) and also takes into account important elements such as legislation and motivation. In that regard, one must pay special attention to the motivation. On one hand, our definition emphasises the environmental motivation when it specifies that recycling chains reduce the impact of raw material extraction and the quantity of waste which is going to be incinerated or landfilled. On the other hand, it also considers the economic motivation when it is specified that these chains seek to preserve material 19/21 added value, and primarily when it emphasises that a recycling chain is an industrial system. This duality of motivations is important because both need to be considered and satisfied so that a balance can be found.

The description of recycling chains has been split into internal characteristics and external factors. The first aims to subdivide the recycling chain into simple identifiable and sometimes quantifiable elements and to specify the way in which they are related to each other. The second aims to list the extra-chain elements which are in constant interaction with the chain. These descriptions can be used as a preliminary support for any chain analysis.

The next step of this work is to fully characterise the recycling chain (using an index or indicators) in order to improve both the chain itself and the component design, always taking into account current situation and legislation and end-of-life evolutions to come.

Figure 1 :

 1 Figure 1: Simplified representation of a component's lifecycle

Figure 3 :

 3 Figure 3: Schematic depiction of a recycling chain within the component's lifecycle.

Figure 4 :

 4 Figure 4: Financial organization mode. (a) Manufacturer's organization. (b) Administration by an external organism. (c) Free market.

Figure 6 :

 6 Figure 6: Component development process (blue boxes) and its connection to its later lifecycle (green boxes). The end-of-life options are listed from the most to the least preferred. We now aim to connect knowledge of recycling chains (and more generally of end-of-life), from the design phase (dotted arrows)

ACKNOWLEDGEMENTS

The authors would like to express their thanks to the ADEME (French Environment and Energy Management Agency) for their financial support and the EcoSD Network (French association which encourages collaboration between academic and industrial researchers in the ecodesign fields) for its aid and support.

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PERSPECTIVES 1. Evaluating the efficiency of a recycling chain

The main perspective of the present work is to provide one index (or if not, as few as possible) characterizing the efficiency of all or part of a recycling chain, taking into account the internal and external factors previously listed. But above all else, it should be mentioned that an index results from the aggregation of several indicators.

a. Concept of an indicator

An indicator is a state or an evolution assessment tool which may be used as support for a decision.


Mehdi

Keywords: Decision making, Novel concept, Set-based design, Maturity, Conceptual

published or not. The documents may come

A risk-based approach to drive conceptual design taking into account low-maturity products

Introduction

In a broad sense, the ability of decision makers to choose the best concept in engineering design is strongly conditioned by two factors : (i) having a clear definition of design objectives, and (ii) being able to evaluate or predict the performance of initial design concepts. In practice, it is very difficult to Medhi El Amine 1, Nicolas Perry 2 , Jérôme Pailhès 2 predict accurately the performance of novel and immature concepts and design objectives are usually vague and imprecise in the early phases of a development project. Paradoxically, life-cycle cost can be impacted up to 70% by decisions taken during conceptual design phase [START_REF] Zimmer | Global aircraft predesign based on constraint propagation and interval analysis[END_REF]. The challenge is how to support the decisions that are made in light of uncertainty and ambiguity.

In order to minimize risk and reduce the cost of regret in later development stages, many design departments adopt the approach called parallel set narrowing process [START_REF] Morgan | The Toyota Product Development System : Integrating People, Process and Technology[END_REF][START_REF] Sobek | Toyotas Principles of Set-based Concurrent Engineering[END_REF] which consists of developing several concepts in parallel until enough knowledge is acquired to facilitate the selection of the most appropriate one in regard of design requirements (Fig. 1). Although developing many concepts is effective in minimizing risk, the usefulness of such a practice is limited by the substantial cost and time required for the development activities. Eliminating operations are thus required to reduce the initial set of proposed concepts such that it can be supported by company resources and allocated budgets.

Many authors recognize the importance of assessing and integrating maturity in decision making [START_REF] Pahl | Engineering design A systematic approach[END_REF][START_REF] Ullman | The Mechanical Design Process[END_REF][START_REF] O'brien | Design maturity assessment for concurrent engineering coordination[END_REF]. Within our context, concept maturity is defined according to Dunn [START_REF] Dunn | Simultaneous engineering side-by-side to success[END_REF] : "Maturity makes possible a "linear" design process, each stage flows sequentially -no backtracking. Non-maturity results in an "orbital process", a circular sequence of repetition, the total time taken being several times that for the linear process". According to this definition, a concept becomes more mature when it requires fewer modifications. Indeed, once a concept is chosen to be developed by the company, designers start embodiment design stage which consists in rough arrangements and selections of structural dimensions, materials, components and technologies [START_REF] Pahl | Engineering design A systematic approach[END_REF]. For an immature concept, these choices are made with insufficient knowledge and, as a result, the required performance is usually not met. The impact of concept maturity is thus closely related to initial requirements. Some authors even define maturity as the association of knowledge and performance [START_REF] Beth | CMMI for Development : Guidelines for Process Integration and Product Improvement[END_REF]. As shown in Fig. 1, the progress of concept development is accompanied by a narrowing in the set of possible embodiment choices combinations (finite elements analysis, mechanical tests) until the most suitable combination of these choices is found. The clarification of design objectives also accelerates the narrowing process as shown in Fig. 1. Concept maturity is thus increasing. Apart from the risk of non-completion of design requirements, cost overruns and schedule delays are very frequent when developing immature concepts [START_REF] Katz | The Relationship of Technology and Design Maturity to DoD Weapon System Cost Change and Schedule Change During Engineering and Manufacturing Development[END_REF]. This aspect should be taken into account when selecting concepts. It is highly recommended that companies have a concept with a high degree of maturity [START_REF] O'brien | Design maturity assessment for concurrent engineering coordination[END_REF][START_REF] Katz | The Relationship of Technology and Design Maturity to DoD Weapon System Cost Change and Schedule Change During Engineering and Manufacturing Development[END_REF]. On the other hand, the desire to be distinguished from the competition and to keep pace with a rapidly changing market, means that decision-makers are encouraged to adopt an innovation strategy by developing novel concepts. Market competitiveness through innovation is the common strategy of developed companies. In addition, the companys long-term sustainability may depend on its innovation strategy [START_REF] Sharif | Innovation strategy, firm survival and relocation : The case of Hong Kong-owned manufacturing in Guangdong Province[END_REF]. In summary, the choice of the set of concepts to develop in the context of SBCD is driven by both the need for performance improvement and failure risk limitation.

Decision making process in engineering design

Generally speaking, the procedure of decision making in engineering design is composed of four steps cited below [START_REF] Guitouni | Tentative guidelines to help choosing an appropriate MCDA method[END_REF][START_REF] Collignan | Arc-elasticity and hierarchical exploration of the neighborhood of solutions in mechanical design[END_REF]. The error in final decision making is due to the association of imprecisions occurring in each of the four steps (Fig. 2). Understanding these decision making process and imprecisions occurring in each step is a first step for an effective integration of concept maturity degree.

The definition of a solution. When a concept is proposed, it is usually necessary to define a concrete solution by fixing embodiment design choices (rough arrangements and selections of structural dimensions, materials, components and technologies). For a concept with low maturity, designers do not have sufficient knowledge to define the wright combination of these choices. Many approximations and hypothesizes are thus usually adopted. These can be a source of errors in the evaluation of the concept.

The observation step. Data are generated about each concept (mass, maximum stress, carbon footprint, etc.) and are required to assess the satisfaction of each criterion. In this work, they are noted OV (observation variables). These variables are evaluated using behavior models (finite element models, expert judgments, mechanical tests, historic data, etc.) that can be inaccurate and thus induce imprecision in estimated values.

The interpretation step. Designers express their preferences for each design criterion on the basis on data collected in previous step (observation variables). Designers preferences and requirements can also contain imprecision. The procedure of interpretation is normalized in our study. For each criterion, an interpretation variable (noted IV) between 0 and 1 is affected to express design satisfaction degree.

The aggregation step. Designers combine IV for each design criterion in order to determine the best alternative(s). In this step, imprecision can affect criteria relative priority and compensation degree between criteria.

In literature many multi-criteria decision aid (MCDA) method are proposed. In this work, we consider only those specific to engineering design problems. In this framework, a recognized method is that of Method of Imprecision (MoI) proposed by Wood and Antonsson [START_REF] Wood | Computations with imprecise parameters in engineering design : background and theory[END_REF]. It allows designers to formalize impression in concept evaluation using fuzzy logic [START_REF] Zadeh | Fuzzy Sets[END_REF]. Each concept is then evaluated using several preference values which are finally aggregated into a generalized preference. The MoI proposes axioms to provide a framework for application to the field of engineering design, and the ability to use different strategies to express the will of designers. However, when evaluating concepts with different maturity degree, two main limits can be detected : (i) the axiom of annihilation leads to a total discrimination to concepts that does not satisfy one of criteria, whereas for an immature concept. (ii) The evaluation of concepts is based on a unique indicator which leads to no distinction between concepts of different maturity degree, whereas an immature concept presents a real risk for the company.

Concept selection methods in literature

Various concept selection methods exist in the literature. Choosing the most appropriate method is itself a critical decision as different methods can yield different outcomes for the same problem [START_REF] Guitouni | Tentative guidelines to help choosing an appropriate MCDA method[END_REF][START_REF] Okudan | Concept selection methods a literature review from 1980 to 2008[END_REF][START_REF] El Amine | Selection and use of a multi-criteria decision aiding method in the context of conceptual design with imprecise information : Application to a solar collector development[END_REF]. The choice of the most appropriate method is very dependent on the decision making situation [START_REF] Roy | Questions guiding the choice of a multicriteria decision aiding method[END_REF]. The decision-maker must be aware of the underlying principle of the chosen method and verify that it is in accordance with his own decision-making situation. The state of the art proposed in this section aims to verify that the concept selection methods proposed in the literature are appropriate for our decision-making process.

Multi-Attribute Utility Theory (MAUT) is one of the most recognized and accepted methods in decision making. It was initially proposed by Neumann and Morgenstern [START_REF] Neumann | Theory of games and economic behavior[END_REF] for economic decision-making. Pahl and Beitz [START_REF] Pahl | Engineering Design[END_REF] were the first to incorporate MAUT into a systematic engineering design process. They suggest six steps for applying MAUT in engineering design : (i) design criteria are first established (such as cost, resistance, durability, etc.), (ii) these criteria are rated on a scale of 0-100 such that the sum of the weights for all criteria is equal to 100, (iii) evaluation parameters are then defined to enable quantification of concept comparisons with one another (This corresponds to step 1 in Fig. 2), (iv) scores are assigned as a utility to each of the evaluation parameters (This corresponds to step 2 in Fig. 2), (v) utility theory is used to calculate the concept value, which is the product of the criterion parameter score and the criterion weighting (This corresponds to step 3 in Fig. 2), (vi) concepts are ranked based on overall utility and the concept with the highest utility score is selected. According to Scott and Antonsson [START_REF] Scott | Aggregation functions for engineering design trade-offs[END_REF], the use of a weighted sum in engineering design is not appropriate since the aspect of decision-making cannot be compensated, contrary to decision in the field of economics, where all aspects of decision can always be translated into associated cost. He proposed a set of mathematical axioms that must be respected by an aggregation operator when dealing with an engineering design decision.

Pahl and Beitzs [START_REF] Pahl | Engineering Design[END_REF] utility theory does not directly accommodate the analysis of imprecisely characterized alternatives. By extending uncertainty representations to model imprecision explicitly, it is possible to apply the principles of utility theory to such problems. This can be done by using discrete/continuous intervals or fuzzy logic. The expected utility for a given concept is thus not known precisely and becomes an interval or fuzzy representation. However, this can lead to situations of indeterminacy [START_REF] Malak | Multi-attribute utility analysis in set-based conceptual design[END_REF], meaning that the decision-makers have no rational basis for choosing one concept over another.

Based on a fuzzy representation of expected concept utilities (as shown in Fig. 3), Roubens [22] proposed the metric of weak dominance than can be interpreted, when applied to a given concept A, as the truth value of the statement "Concept A is better than X, for every concept X in the set of proposed concepts". By producing a single value of concept evaluation, it eliminates the problem of indeterminacy and thus facilitates the selection of a concept. However, it does not assess risk and expected utility separately since each design concept is assessed using single numerical attribute.

Technology Readiness Level (TRL), a 9-level ordinal scale, related to a 9-level semantic scale [23], is a widely used metric in the aeronautics, aeros-pace and weapons industry to assess maturity of developed concepts. It allows decision-makers to ensure that a concept has enough maturity to be introduced into the system. Conrow [24] argues that mathematical operations performed on TRL metrics can lead to systematic errors because of their ordinal nature. He proposes a calibration of the TRL scale based on an analytic hierarchical process (AHP) that results in estimated cardinal values being assigned to each TRL scale level, allowing for mathematical analysis using TRL as an independent variable. It has therefore become possible to aggregate it with other metrics. The state of progress of an innovative technology (that is defined by TRL) can be linked to eliminating imprecision in design definition and a concept with a higher TRL score has a better chance of being feasible. However, TRL remains a coarse metric for the maturity of the concept. It does not allow for a fine assessment on the state of imprecision in design definition.

Proposed approach

As explained in introduction, when decision makers are establishing the set of concepts to develop for downstream phases of development process, their choices are driven by two different and complementary tendencies. On the one hand, they want to obtain rapidly a feasible concept with high maturity degree in order to reduce risk. On the other hand, they wish to develop novel concepts that elicit a higher performance than existing products. The essence of the proposed approach is to propose two numerical metrics that represent these two tendencies. They can constitute an understandable and useful support for decision makers when choosing concepts to develop. The procedure of their calculation is described in this section. A parametric aggregation function is also proposed at the end of this section to allow decision makers to establish the set of concepts to develop with the desired trade-off between the two metrics. The entire approach is illustrated in Fig 3.

Required data

In order to use the proposed metric (the ability to satisfy requirement and concept performance), a set of preliminary data is required. Design criteria are first established with the acceptance threshold for each one depending on decision makers needs. The annihilation axiom is specific to engineering design [START_REF] Wood | Computations with imprecise parameters in engineering design : background and theory[END_REF]25,26] and is considered in our approach. It states that if the satisfaction for any one criterion of the proposed design is null (acceptance thresholds not reached) then the design is not valid regardless the satisfaction degree of the other criteria.

Weights are then assigned to criteria to express their relative importance degrees. They are denoted wj (for a criterion j). Given the heterogeneous nature of the criteria, it is difficult and risky to directly assign weights to criteria. In our work, the analytical hierarchy process (AHP) was used to define Figure 3 Steps of the proposed approach these weights. The use of pairwise comparison is more appropriate to deal with criteria of heterogeneous natures [START_REF] Guitouni | Tentative guidelines to help choosing an appropriate MCDA method[END_REF]. Another advantage of the AHP is the consideration of the hierarchical decomposition of criteria. However, this method is subject to a consistency constraint. In order to limit the inconsistencies that occur when performing pairwise comparisons, the Consistency Ratio (CR) proposed by Saaty [27] was used as a guidance to check for consistency. As recommended by Saaty [27], a value of 0.1 was used as threshold for CR.

The set of possible concepts is then generated. This can be achieved by patent analysis, creativity procedures, analysis of existent concepts from previous projects/competitors, etc.

Finally the pre-dimensioning of the proposed concepts is performed by the design team. Indeed, the evaluation of a concept usually requires the definition of a concrete solution. It means that embodiment design choices such as rough arrangements and selections of structural dimensions, materials, components and technologies must be fixed. Since the product design is strongly driven by manufacturing requirements (Fig 7), the pre-dimensioning of manufacturing process is also performed in order to evaluate manufacturability criteria. OV (observation variables) are then generated as a result of this step. This data are then converted to IV (interpretation values) in accordance with decision makers preferences and requirements.

3.2 First metric : the Ability to Satisfy Requirements (ASR)

In the previous step, a first architecture of product is established by fixing the different choices in embodiment design. This allows designers to evaluate the proposed concept against each criterion, including manufacturability criteria. For an immature concept, designers do not have sound basis when fixing these choices and, as a result, one or more criteria are often not satisfied. In our formulation of the problem it means that one or more OVs do not reach the corresponding acceptance threshold. It results in a zero IV. In practice, designers do not systematically reject the concept. They consider the fact that modifications could eventually be introduced in embodiment design choices to insure the satisfaction of these criteria. It usually takes many iterations of trial-error to find the right combination of embodiment design choices. This procedure can be very time consuming when many concepts are proposed. In a broad sense, the proposed maturity metric, denoted ASR (Ability to Satisfy Requirements), evaluates the opportunity of reaching design requirements by exploring the set of possible solutions in embodiment design. The steps of its calculation are described in this paragraph. An illustrative example is shown in Fig 4 . It represents the case of non-achievement of requirement on maximum angular deformation of the truss concept.

Only unsatisfied criteria are considered in the evaluation the ASR. For each of these criteria (denoted j), a maturity index related to this criterion is evaluated and denoted ASR j . A four-step procedure is used to evaluate this index :

Step (i) Identify embodiment design choices (structural dimensions, materials, components and technologies) that have a significant impact on the OV considered. This task can be done by the association of experience/intuition of designers and the behaviors models used in the pre-dimensioning step.

Step (ii) Describe the level of imprecision in these embodiment design choices. As mentioned before, the low maturity of a concept is manifested by the imprecision when making a choice for an embodiment design element. This step consists of describing this imprecision by identifying the remaining possible choices that designers are unable to settle. Step (iii) Evaluate the impact of the established imprecisions on the OV using fuzzy numbers. This consists of evaluating of changing the embodiment design element (in the set of possible choices) on the on the OV estimated at pre-dimensioning step. This can be performed using behavior models used at the pre dimensioning step. Since the used model can very rough at this design stage, fuzzy numbers are used to capture designers imprecision when evaluating the impacts. It concerns immaturity of manufacturing process, imprecision in behavior models and, imprecision in embodiment design choices.

Step (iv) Sum the fuzzy impacts of all the imprecisions and add to the nominal OV. The different imprecision impacts are summed together to obtain a total impact on OV. This quantity is then added to the nominal value of the OV that was evaluated in pre-dimensioning step. After that, ASR j of the criterion j is calculated as the ratio between the overlap surface (intersection between possible values of OV and admissible values) and the possible values. This overlap region is graphically represented in Fig 5 . The -cut method is used to calculate this value and explained below.

ASR j = 1 N N i=1 C i (1) x =            0 if S i < F i g S i -F i g F i d -F i g if F i g < S i ≤ F i d 1 if S i ≥ F i g (2)          F i g = a + i N × (b -a) F i d = c + i N × (d -c) S i = S g + i N × (S d -S g ) (3)
The final maturity index is obtained by the multiplication of all ASR i as shown in Equation 5. The product was used since the annihilation axiom is adopted in our case. Achieving acceptance threshold for each criterion is a required condition for the acceptance of the concept.

ASR = i ASR i (4)
As the development progress, concept maturity increases and many infeasible combinations are progressively eliminated. The proposed procedure offers a simple but also a rough way to evaluate the opportunity of improving an OV related to unsatisfied or pseudo-satisfied criteria. The fuzzy numbers and related arithmetic are a powerful tool to capture and propagate imprecision related to product definition and also designer estimations. Two main considerations are not included within this approach : the possible synergies between two or more embodiment design features when they are changed together and, the impact of an embodiment design feature on the other criteria when its changed. However, we argue that these data are difficult to obtain at very upstream step of product development process. More advanced development tasks (later development steps) are required for this. In many industries, design department need to fix a maturity threshold for product with critical role in the global system [START_REF] Katz | The Relationship of Technology and Design Maturity to DoD Weapon System Cost Change and Schedule Change During Engineering and Manufacturing Development[END_REF]28,29]. It allows the different stakeholders to know whether the concepts of the program have acceptable levels of risk. The department of defense for example fixes a threshold of T RL = 6 [28]. In our approach, this threshold is defined by two conditions : (i) the ASR of this concept must be higher than 0.9 (ii) a prototype of the concept must be tested in a relevant environment (equivalent to T RL = 6) as a proof of the validity of behaviors models. In this paper, a concept verifying these conditions is called Reference concept.

Second metric : Overall Performance (OP)

The ASR metric proposed in the previous paragraph is representative of the confidence given to a concept since it measures the opportunity of reaching acceptance thresholds of unsatisfied criteria. However, this is insufficient when screening concept. Decision making should have a more global view about concept performance by taking into account also the strengths of concept.

Otherwise, the question that decision makers need to consider is : if the decision is made to invest resources and time in development activities to settle unsatisfied criteria, how much the global performance of the concept could be. The question is especially pertinent when a pre-existing concept exist which has already been developed and tested.

The OV are transformed into IV which are dimensionless variable between 0 and 1. It represents the desirability degree for a given OV. The OP metric is obtained by the aggregation of IV using generalized ordered weighted averaging (GOWA) operator (equation 6) proposed by Yager [30]. This function was chosen since a multitude of compensation degree between criteria can be used by varying the parameter s between -10 and 10.

OP = s n j (IV j ) 2
(5) j is the criterion index. w j is the weight of criterion j. n is the number of criteria.

In many case of development projects, company has a mature concept that result from previous development project.

In this case, the interest of developing a novel concept is to realize a better performance. It is thus appropriate that the aggregation function considers the reference concept in determining the performance of the new concepts. The equation ( 6) is thus modified to use the distance from the reference concept.

The expression becomes :

OP r = S n j w j p i IV j -IV r j S (6)
IV r j is the IV of criterion j for the reference concept. pi is a parameter introduced to take into account the sense of the improvement. p i = 1 when the improvement is positive and p i = -1 when the improvement is negative.

Aggregation of the two metrics

Once the two metrics are estimated (ASR and OP ), the decision makers can choose the appropriate concepts by applying the desired trade-off between the confidence aspect (represented by ASR metric) and the performance aspect (represented by OP metric). Here, since only two metrics are treated, the decision maker can do without the use of an aggregative function ; the decision maker is able to aggregate intuitively both metrics. However, an aggregation function is provided to constitute a further support to the decision makers. This aggregation function is given in the Equation 8. The weighed product was used since it yields a zero score when ASR or OP is null.

f agg = OP α × ASR 1-α (7)
is a parameter introduced to adjust the trade-off level desired by decision makers. When establishing the set of concepts to develop. We argue that the most suitable case when constructing the set of concepts to develop is take values from different regions along the interval [0, 1]. In this way, the constructed set of concepts will contain mature concepts (high ASR) that minimize risk and innovative concept that highlight a better performance (high OP ). The choice of the set of concepts to develop must also take into account the planned budget for the development project.

In the next section, the proposed methodology is applied to an example from a real product development project. The objective is to measure the usefulness of the methodology in our industrial case.

Application on industrial case

Compared to photovoltaic panel, the major advantage of Concentrating Solar Power (CSP) is the possibility of storing thermal energy which allows the production electricity without interruption. The component studied in our case is the solar collector. Its main function is to concentrate and redirect sunlight onto absorber tubes to heat up the working fluid. The recovered heat is then used to generate high pressure steam which drives a turbine in order to produce electricity. The solar collector is composed of a reflecting surface and a metal structure, whose function is to give and maintain reflecting glass shape (Fig. 6). A mounting device is performed between the reflecting surface and the metal structure to ensure the connection between the two. Solar collector is driven by a rotation movement in order to track the movement of the sun. In our study, only the design of supporting structure (see Fig. 6) is treated. The manufacturing of reflectors represents the main investment cost of a plant [31]. It is thus important to reduce the structure mass and also manufacturing cost. In addition, in order to maintain a good thermal efficiency of the plant, a high reflection performance is required from the collector. This implies that the elastic deformation of the structure must remain as low as possible. A high level of precision must also be considered when manufacturing the collector and fixing the reflecting surface. The entire criteria and there weights (obtained by AHP) are shown in Fig 7 . However, acceptance thresholds cannot be shown because of confidentiality restrictions. A prior work has been performed within a design department developing a solar collector for CSP plant. It allows having enough knowledge of the product to use as a case study (observation variable, decision makers preferences, criteria relative priority). However, the data given in study case analysis will be limited due to confidentiality restrictions. As a result of the pre-dimensioning step, each concept is evaluated. It should be noted that the pre-dimensioning of manufacturing process is also performed during this phase to allow assessing of criteria related to manufacturability. Table 1 and 2 shows respectively the results of observation (dimensionless values) and interpretation steps. Concerning the aggregation function used to calculate OP metric. Equation 6was used since none of proposed concepts respects the two conditions to be considered as a reference concept. The parameter s was fixed to 2. The aggregation function becomes thus the quadratic mean (Equation 6). OP metric was first calculated using nominal values of IV (IV in Table 2). Imprecisions was then taken into account. Results of ASR and OP metrics (with estimated variations) are shown in Fig 8 . Estimating the variations in OP values is important since it allows taking into account the impact of possible variations in the embodiment design choices made in the pre-dimensioned version (for example variations shown in Fig. 4).

OP

= n j w j IV 2 j (8)
As mentioned before, it is suitable in a product development project to have both mature/reliable concepts and innovative concepts with potentially better performance. However, in order to reduce risk, obtaining mature and reliable concept is a more pressing issue for decision makers. For this reason, RSS concept was chosen first to be developed. Its development began before the other concepts in the context of a previous project with many validation tests (T RL ≥ 6). The criterion of wind resistance is not satisfied due to the evolution of acceptance threshold in comparison with the previous requirements. However, the step of calculating the ASR metric elicits a high flexibility in possible modifications of embodiment design features (addition of stiffeners, miner increase of structure height) to raise the wind resistance to the acceptance threshold. The ASR was thus approximated to 0.87. The priority of design development is to continue the development of this concept until the desired maturity is reached. The equation ( 7) is then used in this case. The ASR and OP metrics are shown in Fig 8 . TrS1 is a novel concept for the company and its low mass make it a very attractive concept because of the high weight of material cost criterion. Its OP metric is equal to 0.64 (the highest value). However, for this first pre dimensioned version, some of the criteria are not satisfied and thus many modifications should be done to satisfy all criteria. That explains the low ability to meet requirements obtained for this concept ASR = 0.25. The third and later concept that was retained retain is TS1. It represents a good trade-off between OP and ASR metrics. The remaining concepts (rectangular tube, welted truss, hybrid truss) were abandoned because they present a low tradeoff between OP and ASR metrics. The budget allocated to product development is also a point to consider because it limits the number of concepts that can be developed in parallel. The obtained results for the two metric agree well with the expectations for this upstream phase in collector development process. As illustrated in Fig. 9, the choice of the three concepts by design department at the beginning of development project was well approved by the used metrics. It was remarked that the procedure of calculating ASR metric allows designers to easily elicit concepts with low opportunity of feasibility. As the product design is much driven by manufacturing process and this later has a low maturity. The main limit of the proposed methodology is the non-inclusion of manufacturing process maturity.

Conclusion and future developments

Decision making in conceptual engineering design have an important impact on overall life cycle cost. The need of supporting decision making by adequate theories and methodologies is thus greatest at this stage. This paper present a general framework to carry out concepts screening based on the two main decision makers considerations which are the reduction of risk related to immature concepts and improvement of global performance. A first metric assess concepts ability to meet requirements and a second metric is proposed to assess concepts global performance. A parametric aggregation function was also proposed to support decision making using the two metrics. The main interest of these two metrics is to give a support for decision makers by allowing them to choose the set of concepts to develop with the desired trade-off between the confidence aspect (assessed by ASR metric) and the performance aspect (assessed by OP metric).

The obtained results for the two metric agree with the expectations for the early phase in collector development process. The choice of the three concepts by the design department at the beginning of development process was well approved by the used metrics. It was also remarked that the procedure of calculating ASR metric allows designers to easily elicit concepts with low opportunity of satisfying requirements and thus to prevent there development. However, the main limit of the proposed approach is the non-inclusion of manufacturing process maturity, especially for a context in which product design is highly driven by manufacturing process considerations. For further development, the integrating of manufacturing process maturity will be investigated. It is also planned to apply the proposed approach to another case studies to enhance its validity and eventually some other tools to allow its use in a more general context. Finally, more advanced stages in product development process will be investigated.

Figure 1

 1 Figure 1 Schematization of global development process in the context of set-based design

Figure 2

 2 Figure 2 Decision-making process in engineering design

Figure 4

 4 Figure 4 Illustrative example of ASR calculation procedure

Figure 5

 5 Figure5Using the Vertex method to map design space to performance space (case of one design parameter and one environment parameter)

Figure 6 Figure 7

 67 Figure 6 Schematization of solar collector

Figure 8 Figure 9

 89 Figure 8 Results of OP and ASR metrics calculation for each concept

Table 1

 1 Observation variables

	Design Concepts	TrS1	TrS2	TrS3	RSS	TS1	TS2
	C1	4.31	4.21	4.21	19.7	12	11
	C2	0.031 0.028	0.033 0.015	0.011	0.011
	C3	687	654	751	1230	850	940
	C4	20	20	25	25	25	15
	C5	11.5	7.37	7.37	22	19.8	25
	C6	3	5	3	2.4	3.5	3.5
	C7	99	89	53	81	86	78
	C8	0.0	0.2	0.0	0.8	0.0	0.0
	C9	13	13	10	19	13	18
	C10	0.6	0.7	0.5	0.7	0.0	0.0
	C11	3	7	2	2.5	3.5	4

Table 2

 2 Interpretation variables

	Design Concepts	TrS1	TrS2 TrS3	RSS	TS1	TS2
	C1	0.8	0.8	0.8	0.0	0.5	0.5
	C2	0.0	0.3	0.0	0.7	0.7	0.6
	C3	0.0	0.0	0.0	0.3	0.7	0.6
	C4	0.5	0.5	0.7	0.7	0.7	0.0
	C5	0.7	0.9	0.9	0.4	0.3	0.2
	C6	0.3	0.1	0.8	0.7	0.6	0.6
	C7	0.0	0.0	0.7	0.4	0.3	0.4
	C8	0.0	0.2	0.0	0.8	0.0	0.0
	C9	0.7	0.7	0.7	0.9	0.7	0.9
	C10	0.6	0.7	0.5	0.7	0.0	0.0
	C11	0.7	0.0	0.8	0.7	0.5	0.6

1.Laboratoire d'Innovation Durable et de Recherche Appliquée (LIDRA)UniversiapolisAgadirMorocco 2.Arts et Métiers ParisTechTalenceFrance


Hortense Laeuffer
email: h.laeuffer@i2m.u-bordeaux1.fr

Brice Guiot
email: brice.guiot@u-bordeaux.fr

Jean-Christophe Wahl
email: jean-christophe.wahl@u-bordeaux.fr

Nicolas Perry
email: nicolas.perry@ensam.eu

Florian Lavelle
email: florian.lavelle@cnes.fr

Christophe Bois
email: christophe.bois@u-bordeaux.fr

A MODEL FOR THE PREDICTION OF TRANSVERSE CRACK AND DELAMINATION DENSITY BASED ON A STRENGTH AND FRACTURE MECHANICS PROBABILISTIC APPROACH

Keywords: transverse crack, delamination, fracture mechanics, in-situ microscopy

The aim of this study is to provide a relevant description of damage growth and the resultant network for leakage prediction in liner-less composite vessels. A damage meso-model built on strength and energy criteria as proposed in FFM (Finite Fracture Mechanics) is introduced. Both criteria have to be fulfilled for the creation of the first transverse crack of the RVE (Representative Volume Element). The increase of crack density and the propagation of micro-delamination at crack tips are managed by Fracture Mechanics using the energy release rate. In this way the effect of ply thickness is explicitly accounted. The energy release rate at the meso-scale (RVE scale) is calculated from a multiscale approach. Numerical results show that, in [0 2 /90 1 /0 2 ] and [0 2 /90 3 /0 2 ] lay-ups under tensile stress, no delamination should occur for values of the energy release rates from the literature. This conclusion is reinforced by crosssection examinations through the width of specimens submitted to tensile loading. Delamination almost disappears after removing a few microns of the surface. Experimental results also highlight a preliminary step in the damage scenario with small cracking rate, likely driven by weak areas (defects locations). The modelling of this step being fundamental for the prediction of first leak paths, it was introduced through a probabilistic approach.

Introduction

Designing liner-less composite vessels for launch vehicles enables cost and weight savings at the same time, and is therefore a core issue for aerospace industry. One challenge of this application is to reach the permeability requirements with the composite wall itself. Pristine composite laminate meets the permeability requirement, but damage growth may occur for low thermo-mechanical loading cases, with very little effect on the stiffness. Transverse cracks and micro-delamination in adjacent plies may connect together (Fig. 1), resulting in a leakage network through the composite wall. The aim of this study is to provide a relevant description of damage growth and the resultant network at the meso-scale for leakage prediction. To do so a damage model based on Finite Fracture Mechanics is introduced. The model Finally variability is introduced thanks to probabilistic distributions of material properties.

Damaged model description

Damage variables

The meso-damage state of each ply of a laminate can be described by two damage densities, as illustrated in Fig. 2: the crack density ρ, which is the average number of transverse cracks over the observed length L, and the delamination length µ, which is the average length of delamination at each crack tip. The corresponding dimensionless variables are defined by: the crack rate :

ρ " ρh " n L h (1)
the delamination rate :

μ " µρ " µ n L (2)
where h denotes the ply thickness and n the number of cracks observed on the length L.

Damage effect on the elastic properties

Damage effect on the elastic properties is modelled as a compliance increase ∆S , and numerically identified by the multi-scale approach developed by Huchette et al. [START_REF] Huchette | Sur la complémentarité des approches expérimentales et numériques pour la modélisation des mécanismes d'endommagement des composites stratifiés[END_REF]. In practice, ∆S has been computed using homogenization technique on a batch of RVEs (Fig. 3) defined by a large range of damage states p ρ, μq, and the response of ∆S was shown to be in the form of Eq. 4 and 5.

ε ´εth " S : σ " ´S 0 `∆S ¯: σ

∆S " S ´S 0 " ρHp ρ, μq

where Hp ρ, μq is the tensor of damage effects and is written as:

H p ρ, μq " H ρ 1 `ρH ρ 2 `μH μ (5)
The components of the tensors of damage effect

H ρ 1 , H ρ 2
, and H μ have been identified in [START_REF] Huchette | Sur la complémentarité des approches expérimentales et numériques pour la modélisation des mécanismes d'endommagement des composites stratifiés[END_REF] for the material used in this study (namely, M21/T700), and are thus used herein as input parameters of the damage model.

Each tensor of damage effect

H ρ 1 , H ρ 2
and H μ was shown to be in the following form:

1 E 1 ´ν12 E 1 0 ´ν12 E 1 1 E 2 0 0 0 1 2G 12 fi ffi fl (

Damage evolution laws

We propose to build the evolution laws of the damage meso-model on strength and energy criteria as proposed in FFM (Finite Fracture Mechanics) [START_REF] Ponces Camanho | Prediction of size effects in notched laminates using continuum damage mechanics[END_REF][START_REF] Tual | Multiscale model based on a finite fracture approach for the prediction of damage in laminate composites[END_REF]. Both criteria have to be fulfilled for the creation of the first transverse crack of the RVE. The increase of crack density and the propagation of microdelamination at crack tips are managed by Fracture Mechanics using the energy release rate. In this way the effect of ply thickness is explicitly accounted. The effect of damage on Helmholtz free energy at the meso-scale (RVE scale) is calculated from the multiscale approach introduced in the previous section [START_REF] Bois | A multiscale damage and crack opening model for the prediction of flow path in laminated composite[END_REF][START_REF] Huchette | Sur la complémentarité des approches expérimentales et numériques pour la modélisation des mécanismes d'endommagement des composites stratifiés[END_REF]. The energy criteria is built on the evolution of this free energy according to damage by defining related thermodynamic forces.

Thermodynamic forces

The thermodynamic forces y ρ and y μ are conjugate to the damage variables ρ and μ and can be derived from the Helmholtz free energy Ψ " 1 2 σ : S : σ. By using the damaged compliance tensor defined in Eq.3 and 4, we obtain y ρ and y μ:

y ρ " BΨ B ρ " 1 2 " σ : B B ρ ´S 0 `∆S ¯: σ  " 1 2 "´h ρ1 22 `2 ρ h ρ2 22 `μ h μ 22 ¯S 0 22 σ 2 22 `´h ρ1 66 `2h ρ2 66
`hμ 66 ¯2 S 0 66 σ 2 66 ı (7)

y μ " BΨ B μ " 1 2 " σ : B B μ ´S 0 `∆S ¯: σ  " 1 2 ρ " h μ 22 S 0 22 σ 2 22 `hμ 66 S 0 66 2 σ 2 12 ı (8)

Initiation and growth criteria

Damage initiation and growth requires that both energetic and strength criteria are verified. We propose to base the energetic criterion that drives crack propagation on Finite Fracture Mechanics. The Griffith criterion, illustrated in Fig. 4(a), is based on the variation of elastic energy Ψ induced by the creation of new area of crack surface. This variation of energy have to be greater than the energy G required to propagate the crack:

∆Ψ " G∆a (9)
where G denotes the energy release rate from the fracture mechanics and ∆a the new surface of crack. As proposed in [START_REF] Tual | Multiscale model based on a finite fracture approach for the prediction of damage in laminate composites[END_REF] for transverse crack propagation, this criterion can be extended to the creation of transverse crack by the equivalence between an increment of crack density d ρ and the corresponding increment of crack area. The increment of crack area da for a unit volume is therefore defined by:

da V " wh L dρ whL " d ρ h ( 10
)
This equivalence is illustrated in Fig. 4.

Then, criterion functions can be built by associating the thermodynamic forces to the energy required for creating the new surface of crack da in the volume element V. A critical energy release rate and the increment of crack surface area can then be defined for both damage variables.

When a criterion function is negative, there is no evolution of its associated damage variable. When the function becomes positive, damage growth occurs so that the equilibrium remains satisfied. In addition to the energetic-criterion functions, the strength criterion for initiation is based on transverse and shear strain :

ˆε22 ε r 22 ˙2 `ˆε 12 ε r 12 ˙2 ´1 ě 0 (11)
Where ε r 22 and ε r 12 denotes the strength threshold for failure in mode I and II.

The three criteria have to be fulfilled, i.e. be positive or null to allow damage to initiate and propagate.

If the criterion for propagation of delamination is not fulfilled while the two others are, transverse crack propagate alone.

Simulation results

Simulations were carried out on [0 2 /90 1 /0 2 ] and [0 2 /90 3 /0 2 ] lay-ups under tensile loading. Except for G ρ and G μ material constants come from [START_REF] Bois | A multiscale damage and crack opening model for the prediction of flow path in laminated composite[END_REF]. Fig. 5

Experimental validation

The identification of this model relies on experimental observations of damage growth for cracking mode I and II. Tensile test were carried out on specimens polished on one edge so that transverse crack and delamination at crack tips could be identified with an optical microscope (Fig. 6). A length of 100 mm was observed for several loading cases, and tested layups were [0/90 n /0], [+45/-45] s and [0/+67.5/-67.5 2 /+67.5/0]. Only [0/90 n /0] results are presented in this paper. A specific protocol was applied for the identification in order to bypass the issue of edge effects. The evolution of damage densities according to applied strain for two ply-thickness are presented in Fig. 7. Results highlight a preliminary step in the damage scenario with small cracking rate, likely driven by weak areas (defects locations). The modelling of this step being fundamental for the prediction of first leak paths, it was introduced in the evolution law through a probabilistic approach.

Introduction of the effect of variability

We propose to introduce variability in the model by running simulations on a set of values of the damage thresholds G ρ and ε r 22 . The average response of the model is computed from the results for every possible combination of the threshold values. A weight is assigned to each value, so that it is possible to take into account the density of probability of a threshold to take each value of the set. Results are presented on Fig. 9. Preliminary step in the damage scenario with small cracking rate is described even though that the density of probability was not accurately identified.

Conclusion

A damage meso-model with strength and energy criteria was introduced. Evolution of damage densities is managed by Fracture Mechanics using the energy release rates. Numerical results show that no delamination should occur for values of the energy release rates from the literature. This conclusion is reinforced by cross-section examinations through the width of specimens submitted to tensile loading: delamination almost disappears after removing a few microns of the surface. This confirms that standard identification techniques overestimate micro-delamination length. Experimental results also highlight a Hortense Laeuffer, Brice Guiot, Jean-Christophe Wahl, Nicolas Perry, Florian Lavelle, Christophe Bois ECCM17 -17 th European Conference on Composite Materials Munich, Germany, 26-30 th June 2016 8 preliminary step in the damage scenario with small cracking rate, likely driven by weak areas (defects locations). The modelling of this step was introduced applying variability on the damage thresholds. Confrontation of experimental and simulation results show a good ability of the model to describe the evolution of damage densities, although a more accurate identification of the damage parameters have to be performed.

Figure 1 .

 1 Figure 1. Transverse crack and delamination : crack network in two damaged plies and micrograph of one transverse crack with delamination at crack tip

Figure 3 .

 3 Figure 3. Representative Volume Element for the identification of damage effects [1, 2]

Figure 4 .

 4 Figure 4. Creation of a new area of crack surface in two types of specimens.

  (a) show that no delamination occur for ratio of G ρ and G μ consistent with literature[START_REF] Gohorianu | Interaction entre les défauts d'usinage et la tenue en matage d'assemblages boulonnés en carbone/époxy[END_REF]. To allow delamination to occur (Fig5(b)), the energy release rate for delamination G μ has to be set to the half of G ρ. This point is discussed further in next section.

Figure 5 .

 5 Figure 5. Prediction of damage densities in the transverse ply of [0 2 /90 1 /0 2 ] and [0 2 /90 3 /0 2 ] lay-ups for two sets of energy release rates G ρ and G μ (ply thickness h " 0.26 mm and h " 0.78 mm, G ρ " 0.13 MPa.mm).

Figure 6 .

 6 Figure 6. Damage observation under tensile loading test

Figure 7 .Figure 8 .

 78 Figure 7. Damage densities vs longitudinal strain for [0 2 /90/0 2 ] and [0 2 /90 3 /0 2 ] lay-ups (h " 0.26 mm and h " 0.78 mm) obtained at the surface of the edge of the specimen

Figure 9 .

 9 Figure 9. Crack rate for two ply-thickness with variability of the damage thresholds

Hortense Laeuffer, Brice Guiot, Jean-Christophe Wahl, Nicolas Perry, Florian Lavelle, Christophe Bois

Acknowledgments

The authors would like to thank the council of Region Aquitaine for their support.