Ioana Filipas Deniaud

François Marmier
email: marmier@mines-albi.fr

Didier Gourc
email: gourc@mines-albi.fr

Xavier Labaume
email: xavier.labaume@bee-eng.fr

How risks and innovativeness influence the selection of partner in NPD alliances

Keywords: alliances, design project, innovation, risk management

Most often, if a new product is complex, a unique company doesn't have all the competences or means to achieve alone its development. In this case alliances must be formed to carry on the development project. However, alliances often meet difficulties in achieving their objectives. That is mainly due to difficulties of communication between partners, or to missing skills or means required to go further in the innovative development. To successfully overcome risks of collaboration dysfunction, an alliance must be created between partners able to communicate, presenting a complementarity in the project and being presenting a maximum of characteristics useful for the new project. This paper aims to increase our understanding of how to make alliance with the purpose of exploring the opportunities emerging from a partner innovativeness and risks management. We present an original model of alliance assessment composed by two partners intending to develop a particular innovative project. Based on this model, we propose a decision support system helping choosing firms for an alliance. A case study from the aeronautical industry is presented and results are analysed.

I. INTRODUCTION

Future success of a company often requires firms to regularly launch new products. In New Product Development (NPD) projects [START_REF] Gupta | Accelerating the development of technology-based new products[END_REF][START_REF] Tushman | Winning through Innovation[END_REF][START_REF] Richtnér | Squeezing R&D: A Study of organizational slack and knowledge creation in NPD, using the SECI model[END_REF] technological innovations and organizational changes such as alliances are needed to create fundamentally better products with new features and lower costs [START_REF] Wohlfeil | Critical Success Factors for the Strategic Management of Radical Technological Innovation[END_REF]. As the range of firm's technology expands, firms must learn. It needs more knowledge that can be difficult to acquire in the market. So firms seek collaboration with other firm to expend their knowledge and developed new products [START_REF] Cowan | Network structure and the diffusion of knowledge[END_REF].

The NPD is the result of a collaborative process in projectbased teams. These teams include members with different skills in a company or between companies working networked [START_REF] Malone | Inventing the Organizations of the 21st Century[END_REF]. Companies almost never innovate alone [START_REF] Edquist | Systems of Innovation Approaches -Their Emergence and Characteristics[END_REF][START_REF] Baum | Don't go it alone: Alliance network composition and startups' performance in Canadian biotechnology[END_REF][START_REF] Hagedoorn | Inter-firm R&D partnerships: An overview of major trends and patterns since 1960[END_REF][START_REF] Corsaro | Actors' heterogeneity and the context of interaction in affecting innovation networks[END_REF]. Therefore companies develop them by promoting effective collaborations with other firms having complementary assets [START_REF] Cowan | Bilateral collaboration and the emergence of innovation networks[END_REF] that add significant benefits for the NPD [START_REF] Schiele | How to distinguish innovative suppliers Identifying innovative suppliers as a new task for purchasing[END_REF]. Companies can collaborate with research laboratories (public or private), start-ups or even competitors. In NPD project companies are looking to make alliances, each company offering specific expertise. NPD alliances are made for different purposes: gain access to knowledge, innovate, reduce costs, be more flexible [START_REF] Baldwin | Managing in an age of modularity[END_REF][START_REF] Oh | Influences of supplier capabilities and collaboration in new car development on competitive advantage of carmakers[END_REF] and share technology [START_REF] Petersen | A model of supplier integration into new product development[END_REF].

Depending on project time the company that initiates the NPD project may seeks partners with a strong creative potential (especially in early phases -design: more exploratory) towards simple subcontractors (especially at the end of the project: production and commercialization -more exploitation). In the early phases of NPD a broad range of decisions need to be made even when little information is available [START_REF] Ulrich | Product design and development[END_REF]. In this paper we are especially interested in the exploration phases of NPD project, which imply creativity and generate innovation. Concerning this context Schiele [START_REF] Schiele | How to distinguish innovative suppliers Identifying innovative suppliers as a new task for purchasing[END_REF] underlines that a typical problem is how to chose partners "who is more likely to fully understand the challenge, pose limited problems in collaboration and finally, who is the most likely to contribute with an innovative solution."

Despite the evident importance that partner's innovativeness plays during NPD partners/supplier selection [START_REF] Cowan | Bilateral collaboration and the emergence of innovation networks[END_REF][START_REF] Schiele | How to distinguish innovative suppliers Identifying innovative suppliers as a new task for purchasing[END_REF][START_REF] Johnsen | Supplier involvement in new product development and innovation: Taking stock and looking to the future[END_REF][START_REF] Brettel | Innovation Culture, Collaboration with external partners and NPD performance: Innovation culture and NPD performance[END_REF][START_REF] Pulles | Identifying innovative suppliers in business networks: An empirical study[END_REF], there is limited research in the NPD area that focuses specifically on the concept of partner innovativeness, or which has defined the type of innovativeness that it considers, as part of the selection criteria. In this paper, partner innovativeness is investigated as a key feature of collaboration.

The manager objective is to enhance the performance of the NPD project. Generally, in a project, manager firstly specifies competences he needs to perform the project and then identifies partners having those competences. But when it comes to a new product development partners must also be able innovate and to develop new skills. Cuervo-Cazurra and Un [START_REF] Cuervo-Cazurra | Why some firms never invest in formal R&D[END_REF] discussed different type of R&D collaboration and their impact on innovation and NPD. In this context the project manager should be able to choose partners considering both partners' innovativeness and risks.

The selection of partners in inter-firm collaboration received little attention thus far in the voluminous literature on strategic alliances, innovation and risk management. In this paper we outline an approach of decision making in partners selection for NPD projects. Our approach considers partner innovativeness as the main features of collaboration. This article is organized as follows. Firstly, theoretical background concerning innovation in alliances for NPD is done. Then factors influencing the selection of partners in inter-firm alliances for NPD are presented. We emphasis research limitations concerning partners' innovativeness influences in NPD alliances. Even a lot of research exists (case studies and empirical studies) almost all these studies have eschewed analytical analysis. In a second time we propose a model based on analytical approach. The model takes into account Alliance's innovativeness resulting from the partner selection itself. Finally, a case study from the aeronautical context illustrates our proposals.

II. THEORETICAL BACKGROUND: INNOVATION IN ALLIANCES

A. NPD Alliances

Since 1960, in the R&D alliances, firm increasingly prefer contractual partnership (nonequity alliance) to joint venture (equity alliance) [START_REF] Hagedoorn | Inter-firm R&D partnerships: An overview of major trends and patterns since 1960[END_REF]. To encourage innovation in NPD, companies have the choice between two types of non-equity alliances: unilateral alliance (R&D contract…), bilateral alliance (joint R&D,…).

In unilateral alliance one partner provides founds to another partner for specified R&D development. In this case there are no knowledge sharing between partners and innovation level tends to be low.

In bilateral alliance, partners combine their knowledge and competences [START_REF] Dosi | The nature of the innovative process[END_REF]. This re-combination can create new knowledge and innovations that will become the drivers of the alliance [START_REF] Cowan | Bilateral collaboration and the emergence of innovation networks[END_REF][START_REF] Baum | Network-independent partner selection and the evolution of innovation networks[END_REF]. As underlined in introduction of this paper NPD project is related to innovation potential of the partners. For those reasons we are focusing on this kind of NPD alliance also called "co-development alliance" in Emden et al., [START_REF] Emden | Collaborating for new product development: selecting the partner with maximum potential to create value[END_REF] and defined as a "nonequity-based collaborative relationships enjoined by two or more firms to create value by integrating and transforming disparate pools of know-how related to new product or service development". It can be done in particular bilateral relations with the purpose of improvement in technology and know-how. For example agreements for joint R&D, simultaneous engineering, joint design and/or technology. In this context partner selection became crucial.

B. Innovation in NPD

NPD projects can be range from incremental improvements to radical innovation. Firms pursuing innovation must maintain a balance between learning from external (exploration) and internal sources (exploitation). Too much exploitation is unlikely to lead to higher-order learning, whereas too much exploration is expensive and may produce many underdeveloped concepts and ideas [START_REF] March | Exploration and exploitation in organisational learning[END_REF].

In NPD, few firm's specific resources may lead to firm's competitive advantage [START_REF] Prahalad | The Core Competence of the Corporation[END_REF][START_REF] Barney | Firm resources and sustained competitive advantage[END_REF]. In this way, an alliance is created by pooling the various resources of the partners.

Linnarsson et al. [START_REF] Linnarsson | Overcoming the innovation-alliance paradox: a case study of an explorative alliance[END_REF] highlight the tension between dynamics of innovation (demanding freedom and flexibility) and logic of alliance (demanding well defined situation). Indeed, in NPD alliance each partner has a dual function. On one hand, it ensures resource allocation function for the acquisition, the implementation and control of innovation (exploitation). In addition, the company provides resources creation function. In the same line Link & Bauer [START_REF] Link | Cooperative Research in U.S. Manufacturing: Assessing Policy Initiatives and Corporate Strategies[END_REF] explains that NPD alliance is related to joint development of new product offering an opportunity for exploration [START_REF] Bessant | Managing innovation beyond the steady state[END_REF]. This involves the sustained joint creation of property and knowledge for the partners, requiring them to bring in resources and work together on a constant basis [START_REF] Das | A risk perception model of alliance structuring[END_REF]. Then NPD alliances should manage in the "dual logic of both partnering and innovation" [START_REF] Prange | Collaborative New Product Alliances: A Review of the Literature and Research Perspectives[END_REF].

III. SELECTION OF PARTNERS

More than 50% of innovative projects involve collaboration with external partners [START_REF] Barczak | Perspective: Trends and Drivers of Success in Practices: Results of the 2003 PDMA Best Practices Study[END_REF]. To realize those collaborative works a form of cooperative arrangement, named "strategic alliance", must to be done between partners [START_REF] Das | Resource and risk management in the strategic alliance making process[END_REF].

Traditional selection criteria (cost, quality and delivery) do not characterize innovative and challenging NPD characteristics for an effective partner's selection [START_REF] Araz | Supplier Evaluation and Management System for Strategic Sourcing Based on a New Multicriteria Sorting Procedure[END_REF]. Nevertheless, NPD projects involve technological uncertainty because firms don't know which technology to implement in their new product. Firms should select and collaborate with competent suppliers. Therefore, as it is observed in a wide literature review on selection suppliers/partners for NPD, the impact of technological uncertainty makes unclear how firms should select suppliers [START_REF] Melander | Impact of Technological Uncertainty in Supplier Selection for NPD Collaborations: Literature Review and a Case Study[END_REF].

A. Partner innovativeness

In NPD alliance the choice of partners is determined in order to reach a potential for innovation [START_REF] Cowan | Bilateral collaboration and the emergence of innovation networks[END_REF][START_REF] Schiele | How to distinguish innovative suppliers Identifying innovative suppliers as a new task for purchasing[END_REF][START_REF] Johnsen | Supplier involvement in new product development and innovation: Taking stock and looking to the future[END_REF][START_REF] Pulles | Identifying innovative suppliers in business networks: An empirical study[END_REF]. Firm innovativeness is the potential capability and willingness of the partner to generate greater innovation value in a NPD alliance [START_REF] Pulles | Identifying innovative suppliers in business networks: An empirical study[END_REF][START_REF] Oke | Strengthening the innovation chain: The role of internal innovation climate and strategic relationships with supply chain partners[END_REF][START_REF] Kalaignanam | Asymmetric new product development alliances: Win-win or win-lose partnerships?[END_REF]. A wide literature concerns partners/suppliers selection and buyer-supplier relation in NPD alliances. Since partner's innovativeness is one of the key aspects of NPD collaboration, this section presents factors that contribute to partner's innovativeness.

In NPD alliances outcomes are difficult to define upfront and the resource transaction and capability development change the mutual innovation potential [START_REF] Prange | Collaborative New Product Alliances: A Review of the Literature and Research Perspectives[END_REF]. Nevertheless, in most cases, the innovations performance of the alliance is associated to the output of NPD project (new product or new technology). Some authors emphasize the importance to select partner with high innovation potential. In this line authors speak about innovativeness [START_REF] Araz | Supplier Evaluation and Management System for Strategic Sourcing Based on a New Multicriteria Sorting Procedure[END_REF], innovative capability [START_REF] Johnsen | Supplier involvement in new product development and innovation: Taking stock and looking to the future[END_REF][START_REF] Samson | Innovation capability in Australian manufacturing organisations: An exploratory study[END_REF], research capability [START_REF] Howells | The Growth and Management of R&D Outsourcing: Evidence from UK Pharmaceuticals[END_REF] creativity [START_REF] Emden | Collaborating for new product development: selecting the partner with maximum potential to create value[END_REF] or overlapping knowledge's [START_REF] Feng | A method for partner selection of codevelopment alliances using individual and collaborative utilities[END_REF]. But there is relatively little academic research on how measures partner innovativeness.

In the Resource-Based view literature, partner innovativeness is always correlated with product innovativeness and measured with an output variable: In Stuart et al. [START_REF] Stuart | Interorganizational alliances and the performance of firms: A study of growth and innovation rates in a high-technology industry[END_REF], partner's innovativeness was measured as the log of the total number of published patents of a local partnership in the previous year. Kalaignanam et al. [START_REF] Kalaignanam | Asymmetric new product development alliances: Win-win or win-lose partnerships?[END_REF] capture the innovativeness of the partner firms by counting the number of the patent citations received by the partner firms in the five years prior to the focal alliance date. Song et al [START_REF] Song | Supplier's involvement and success of radical new product development in new ventures[END_REF], discuss suppliers implication in NPD and quantify the success of radical innovation by measuring the margin and sales. Nieto and Santamaria [START_REF] Nieto | The importance of diverse collaborative networks for the novelty of product innovation[END_REF] use a control factor for the intensity of internal R&D (ratio of internal R&D expenditure to total sales) to explain the production of innovations. This measure is criticized by Adams et al [START_REF] Adams | Innovation management measurement: A review[END_REF] arguing that the high levels of R&D intensity may simply masks innovation process inefficiencies.

This ex-ante evaluation is inefficient in partner selection. The partner selection should be made in the early stages of the project. A more interesting view is presented in Knowledge-Based Management literature: the potential for innovation derives from the cognitive distance between potential stakeholders. Nooteboom et al. [START_REF] Nooteboom | Optimal cognitive distance and absorptive capacity[END_REF] describes an inverse-Ushaped benefit-distance relationship that arises from the tradeoff between absorptive capacity [START_REF] Cohen | Absorptive capacity: a new perspective on learning and innovation[END_REF] and novelty gain. These authors take into account the costs of alliance formation when these alliances are profitable. Nooteboom et al. [START_REF] Nooteboom | Optimal cognitive distance and absorptive capacity[END_REF] points out that "Novelty gain" increases with cognitive distance between partners. Innovation level is directly proportional with novelty gain. Alcantara et al. [START_REF] Alcantara | Legitimacy in international joint ventures: It is still needed[END_REF] pointed that firms with greater innovation capabilities possess cutting-edge knowledge about product technologies and have greater absorptive capacities to assess and assimilate externally generated technical knowledge. Higher absorptive capacity implies that partners have higher similarity to each other [START_REF] Cowan | 16 Fits and Misfits Technological Matching and R&D Networks[END_REF].

Cowan et al. develop a knowledge-based model of R&D

alliance in which firms seek to innovate [START_REF] Cowan | 16 Fits and Misfits Technological Matching and R&D Networks[END_REF]. The key assumption is that the strategic decision to forge an alliance is based both on similarities and complementarities of two participating firms. Complementarity between partners is also mentioned by several researches [START_REF] Feng | A method for partner selection of codevelopment alliances using individual and collaborative utilities[END_REF][START_REF] Littler | Factors Affecting the Process of Collaborative Product Development: A Study of UK Manufacturers of Information and Communications Technology Products[END_REF][START_REF] Sivadas | An examination of organizational factors influencing new product success in internal and alliance-based processes[END_REF][START_REF] Zolghadri | Innovative Product and Network of Partners Co-Design: Context, Problems, and Some Exploratory Results[END_REF]. With a "risk management" point of view an alliance presents relational risks that are those regarding cooperation and performance risks that are those regarding future states of the alliance objectives. A well-designed alliance therefore permits by it self to minimise both relational risk end performance risk that tend to be high [START_REF] Osborn | Forms of inter-organizational governance for multinational alliances[END_REF].

However, despite a literature presenting notions of similarity between partners leading to aptitudes to communicate and complementarity conferring to each partner a usefulness and a strong involvement in the project, there is a lack relative to the fact to combine these points with a vision of the requirement of the project (skills, means,…). The following section presents therefore presents our proposal to fill this lack.

IV. MODEL

This work is focused on alliances between two partners. Several collaborations can be studied for a given innovative project. The choice of an alliance means an adaptation and appropriation of the project. Little account is taken of the potential to innovate when choosing a collaborator for a NPD project. By taking into account the fact that a well-selected partner lead to decrease the risk level and to a better NPD performance, the originality of this approach is to give to the decision-maker a visibly on criteria to assess possible collaborations.

A. Data on the project, the possible alliances

In this section, concepts are defined and modelled in the case of an alliance to innovate. P: a provisional project that consists in achieving a deliverable. P requires an alliance of two firms.

SC(P):

Set of Characteristics (knowledge, technologies, location, size,… ), identified as necessary to answer to the specific need of a P. a: an alliance between two firms v and w (a=1…A), A being the number of alliance studied with different potential partners for the project.

V v : The vector containing the firm v's characteristic portfolio. V v z =1 if v has the characteristic z ∈ SC(P). Else V v z =0.
V vw : the number of commonalities in SC of two firms v and w for joint innovation, i.e. the number of characteristics known to v (V v z =1) and to w (V w z =1).

S vw : the number of complementarities in SC(P) of two firms v and w for joint innovation, i.e. the number of characteristics known by v but not by w.

B. Objective function: The innovation potential of the alliance

The criterion used in this study is the potential to innovate of the alliance for a given NPD project. For successful innovation, firms v and w must both be similar to and complement each other [START_REF] Cowan | 16 Fits and Misfits Technological Matching and R&D Networks[END_REF]. In the case of challenging projects, the alliance should have a good coverage of the required characteristics. With γ + ϕ + λ =1.

V. RESOLUTION APPROACH

A. Positioning of the proposed work

The resolution approach developed in this section (Fig. 1) aims helping the Project manager (decision maker) in selecting the best alliance for a given innovative project. The development proposed here are only devoted to collaborative alliances between two partners. The proposed approach uses project data and potential collaborator information. Based on these data, for each studied alliance, an evaluation of IP is done. Regarding these Couples{Alliance; evaluation}, the project manager will make the decision of collaboration.

B. Innovation potential assessment

A new project can be perceived as being technically rather simple or rather difficult if there are really challenging activities. Moreover, two firms may also have already successfully achieved collaboration but that could be the first collaboration between two partners or having a past common project presenting difficulties.

Therefore, the expert in charge of building the collaboration can have different a perceptions of the respecting importance of each sub criteria composing IPa. Its subjective perception of the technical difficulty of the project and a factual overview of the alliance lead the expert to establish different the weight. A first analysis on how this four kind of context can be perceived and how it influences the weighting of the sub criteria provided in Table 1. Cases SK and SN consider projects rather simple. CK and CN consider projects in which there is an important technical challenge.

In case SK it is a matter of carrying out a simple project with a collaborator with whom the company has already worked in the past. This one is well known by the company. The level of confidence in this collaboration is high. The IP index will therefore be based mainly on a complementarity sought between the partners. This is important because it justifies that each partner finds its place in the project. The similarity loses its importance because companies know each other and know how to communicate. The project being simple, if it becomes necessary to develop additional characteristics (skills through trainings,…), the alliance will succeed to do so. Coverage is not a predominant criterion. The IPa index will therefore be calculated by giving a lot of weight to the complementarity between the members of the alliance. In case SN the project is judge simple. Experts are confident in the estimates. However, either it is the first time that companies collaborate either they already try to manage projects without succeeding. In this situation it is important that the companies of the alliance can communicate and understand each other. Therefore, the similarity becomes important. The complementarity remains also important to justify the place of each partner in the alliance. The IPa index will therefore be calculated by giving more weight to the similarity and complementarity.

In cases CK and CN, there is a real technical challenge to be overcome in the project. In these two cases, the experts will try to maximize the margins to take precautions in case of risk occurrences.

In case CK, the potential collaborator is known. Therefore, similarity is not an important focus (as previously evoked for case SK). On the other hand, it is important that partners be complementary and contributes to the project success. Due to the potential technical difficulties, the coverage should be as high as possible to ensure that the project can be successfully completed.

In case CN, the challenge is important and we rely on collaborators with whom we never work. It is therefore necessary to ensure that the companies are sufficiently similar to be able to understand each other; sufficiently complementary to be able to bring to the project is that the coverage of the project is important to ensure that it is achievable.

In fact it is a continuum that best describes the importance given to the each sub criteria of in the calculation of IPa.

VI. ILLUSTRATION ON A DESIGN PROJECT

The following illustrative case has been developed jointly with our industrial partner, specialized in the aeronautical context. This project is based on a real and current project with respect to the ARP 4754A regulation [START_REF]Aerospace Recommended Practice) Guidelines for Development of Civil Aircraft and Systems[END_REF]. In this study, our partner has the role of a Main Company (MC) intended to plan a specific design project. This project presents significant technical challenges and innovations. MC doesn't have all the characteristics to carry out the project by its own.

Presentation of the potential collaborators

Two potential collaborators are identified (noted A and B). Past projects already have succeeded with A. With this project, that would be the first time that MC collaborates with B. And the objective of MC is to select either A or B to create an alliance.

Table 2 presents the 16 characteristics required to ideally perform the project (specific means, skills…). The ones provided by Main Company and by each one of the potential partners are also presented. Some characteristics can be provided by one or more potential collaborators, meaning that some similarity can be identified. Some characteristics can be provided only by some potential collaborators meaning that a complementarity is possible. Some characteristics are not provided at all meaning that the coverage will not be full and that these characteristics will have to be developed during the project.

A. Results

In accordance with the importance of each subcriterion of IPa in the context of the project, the project manager has to evaluate the coefficients γ, ϕ and λ.

Table 3 presents the calculation of the (a) Similarity, the (b) Complementarity and the (c) Coverage based on table 2, as described in equation 1.

Following the analysis presented in table 1 and with respect with γ + ϕ + λ =1 coefficients are proposed by MC, in table 4, to weight the sub criterion. For this illustrative case, the approach permits to compute IP a for each industrial context SK to CN. Depending on the project context A or B can be preferred. That is mainly due to the fact that B presents a highest similarity to MC. But A presents a better complementarity to MC and the coverage of MC+A of the required characteristics for the project is higher. This leads naturally to explain why in the case SN and CN where project are complex and partners must exchange to overcome the difficulties together, the collaboration MC+B presents slightly better results. At the opposite, when projects seem quite simple, a high complementarity influences the assessment. In such case the alliance MC+A therefore presents better results.

The fact that the project presents significant technical challenges and innovations leads to use the contextual case CK or CN to modulate the coefficients (γ ; ϕ ; λ) (i.e. table 1). The fact that MC has already collaborated with A precise the contextual case to CK. The potential to Innovate for this project is therefore assessed to 0,71. This project could be the first opportunity for MC and B to collaborate. The contextual case is then CN and the Potential to Innovate for this project is therefore assessed to 0,55.

The comparison is therefore favourable to the alliance between MC and A.

B. Discussion

MC already ran projects in the four industrial contexts evoked in section 4.2. The analysis was done in both way. Which sub criterion is important? What is the influence of the project context to assess the weights? And then, knowing that the weighting is done base on the expert experiences, which past projects can help to assess the weights in each case?

Once results where computed: are the results consistent? Is this consistency due to the correct choice of the sub criterion and of the weights?

In the case SK, projects are mainly oriented to codevelopment with integration at the end. Both partners don't need to precisely know them. Jobs are well done by each partner and there is no need to develop (and spend time or energy) the skills that are well carried on by the partner.

The complementarity is not naturally what company search in a first intention to succeed a complex project. Therefore, this sub criterion can be the most difficult one to be assimilated in the analysis. However by going down deeply in examples of past projects, lot of examples show that complementarity was really important to the success of a project.

In case CK and CN, the first feeling of the partner was to be afraid to miss a particular characteristic that could be impossible to develop during the project. The first statement was that "if the project is complex, that means that characteristics are really hard to acquire". By going down again to concrete past examples, it appears that this assertion was in part true: when the project is launch, it is difficult to complete the characteristics portfolio. However the success of the project was clearly due to the capacity of partners to communicate to overcome difficulties. This approach takes up the technical perspective that a project manager or a business manager can have. The results and the recommendations that it brings thus correspond to what could expect of people having this type profile.

In large companies such as our industrial partner, when "technical services" have proposed a company to collaborate, the purchasing department will look for other companies, in a larger perimeter, with the same profile of characteristics. The costs of collaborations will be studied and it is possible that an entirely different company could be retained for collaboration.

VII. CONCLUSIONS

The choice of partner influences the project, the deliverables, the planning, and therefore it has an effect on the success of innovative project. Partners' experience of the alliance helps in designing and achieving the project. However many estimation are made to build the project.

Each stakeholder can have a factual vision of the characteristics they carry on to the alliance (skills, technical means,…). But it remains difficult to assess the innovation potential of the alliance for a project. Indeed there is a need of assistance to establish this innovative potential of an alliance. This assistance should utilize available data and expertise to give a first view on answer to the following questions: Is the project likely to succeed if we choose to work with a specific partner? Is it more risky to work with this company than with another? Does the fact that a company is partially similar reduces the risk of a project failure? What type of project should be worried if all the characteristics are not covered from the outset by the alliance?

In this paper we propose a model to characterize the contribution of each partner in an alliance to the success of a particular project. We focus on alliances composed by two partners. We consider the similarity of companies, their complementarity and their coverage of the characteristics required for the project. Depending on the fact that the project is judged rather simple or rather difficult and if a collaboration has already been achieved with the studied partner or not, we identify how to weight these specificities to assess an innovation potential of an alliance for a given project. Therefore, the proposed approach that allows assessing the potential to innovate and succeed of a given project.

With this help, the decision maker can choose the most appropriate partner using both its factual knowledge of the partners and its subjective perception of the need of the alliance.

A software program can confirm human reasoning but it can't replace the expert and its perception and conviction in decision making to confirm whether a decision is the best one or not. In that way, we illustrate our proposal on a case study, we discuss results in order to improve the understanding of the effect of the similarity, complementarity and coverage on decision in the potential to innovate in different project context.

Next, it becomes necessary to analysis the sensitivity of the approach to the judgmental assessment of the weight of the sub criteria when calculating the potential to innovate. To confirm the feasibility of the project by integrating a more analytic vision of the risk should be done as well. Scenario should be studied and recommendation to manage risk should be made. In that way future works will be focused on how assisting the expert to determine strategies to manage risks.

  IP a : the Innovation Potential of a for the given project. It depends on three sub criteria (a) the proportion of commonalty, (b) the equivalency in the complementarity and (c) the coverage of SC by a. Then: γ, ϕ and λ are three coefficients that are subjectively chosen by the project manager in accordance with the importance of each sub criteria in the context of the project.

Fig. 1 .

 1 Fig. 1. Overview of the global process of Alliance selection and positioning of our proposed approach

Fig. 2 .

 2 Fig. 2. Weighting of the sub criterion of IPa

TABLE I .

 I CRITERIA FOCALISATION DEPENDING ON THE CONTEXT

			Alliance
			Partner known or past project succeeded	First collaboration or past project with difficulties
	Technical complexity of the project	Project technically simple High technical challenges	(SK) Confident with the optimist estimation for the project Calculate IP knowing that complementarity is important (CK) Maximize the margin (budget and time) in case of difficulties Calculate IP knowing that complementarity and coverage important	(SN) Confident with the optimist estimation for the project Calculate IP knowing that similarity and complementarity important (CN) Maximize the margin (budget and time) in case of difficulties Calculate IP knowing that similarity, complementarity and coverage are important

TABLE II

 II

			.	USEFUL CHARACTERISTICS FOR THE PROJECT
	SC(P) V MC V A V B	1 2 3 4 5 6 7 8 9 10 11 12 x x x x x x x x x x x x x x x x x	13 x x	14	15 16 x x x x
			TABLE III.	CALCULATION OF EACH SUB CRITERION
		Alliance	(a) Similarity	(b) Complementarity	(c) Coverage
		MC+A MC+B	0,30 0,41	0,8 0,75	0,65 0,6

TABLE IV .

 IV WEIGHTING OF SUB CRITERION AND IP A RESULTS

			IP a
	Alliance	Case SK (0;1;0)	Coefficients (γ ; ϕ ; ) Case SN (0,45;0,45;0,1) Case CK (0;0,4;0,6)	Case CN (0,4;0,2;0,4)
	MC+A MC+B	0,8 0,75	0,56 0,58	0,71 0,66	0,54 0,55


Maxime Bordival

Yannick Le Maoult

Fabrice Schmidt

Optimisation of preform

come

INTRODUCTION

Among the techniques devoted to the manufacture of PolyEthylene Terephtalate (PET) bottles, the twostage Stretch-Blow-Moulding (SBM) process is probably the most popular. This process involves the manufacture of structurally amorphous semiproducts, called preforms, made by injection moulding of PET resin. A reheating step is necessary to heat the preforms to the appropriate temperature distribution above the glass transition, which is typically around 80°C for PET. This stage is generally performed using infrared (IR) heaters, taking advantage of the semitransparent behaviour of PET submitted to IR radiation. In a second stage, the preforms are stretched using a cylindrical rod, and blown using two levels of air pressure. Then, the bottles are cooled down by a mould whose temperature is regulated using cooling channels.

The heating conditions, that control the preform temperature distribution, strongly affect the blowing kinematics (stretching and inflation), and consequently the thickness distribution of the bottle. Temperature also affects the orientation induced by biaxial stretching, which in turn, affects mechanical, optical and barrier properties of bottles [1].

Regarding to BM, Lee and Soh [2] presented a FE optimization method to determine the optimal thickness profile of a preform, given the required wall thickness distribution for the blow-moulded part. More recently, Thibault et al. [3] proposed an automatic optimization of the preform geometry (initial shape and thickness) and operating conditions, using the nonlinear constrained algorithm Sequential Quadratic Programming (SQP). The robustness of the method was discussed through a comparison with experiments performed within industrial conditions. SQP was also used in order to optimize heating system parameters [START_REF]Proc. of the Int. Conf. ESAFORM[END_REF]. The ABSTRACT: This study presents an optimization strategy developed for the stretch-blow moulding process. The method is based on a coupling between the Nelder-Mead optimization algorithm, and Finite Element (FE) simulations of the forming process developed using ABAQUS®. FE simulations were validated using in situ tests and measurements performed on 18.5g -50cl PET bottles. To achieve that, the boundary conditions were carefully measured for both the infrared heating and the blowing stages. The temperature distribution of the perform was predicted using a 3D finite-volume software, and then applied as an initial condition into FE simulations. Additionally, a thermodynamic model was used to predict the air pressure applied inside the preform, taking into account the relationship between the internal air pressure and the enclosed volume of the preform, i.e. the fluid-structure interaction. It was shown that the model adequately predicts both the blowing kinematics and the thickness distributions of the bottle. In a second step, this model was combined to an optimization loop to automatically compute the best perform temperature distribution, providing a uniform thickness for the bottle. Only the last part will be fully detailed in this paper. In this work, we propose a numerical optimization strategy for SBM. For that, we developed an iterative procedure allowing to automatically compute the best temperature distribution along the preform length, providing a uniform thickness for the bottle. We solve the optimization problem by coupling FE simulations to the Nelder-Mead optimization algorithm (nonlinear simplex). Results were validated by careful in situ tests and measurements performed on 18.5g -50cl PET bottles. To achieve that, special attention was given to the measurement of boundary conditions required for both the infrared heating stage, and the blowing stage.

OPTIMIZATION OF PREFORM TEMPERATURE

The performance of a bottle manufactured by SBM is drastically affected by its thickness distribution. In order to achieve bottles with appropriated thickness distributions, it is more desirable to adjust the process conditions, and to use the same design of preform for making different shapes of bottles. This approach aims to minimize the cost associated with the design of a new perform (especially the manufacture of a new injection mould). Determining adequate operating conditions remains nevertheless costly and time consuming. Different approaches are possible, such as trial-and error methods, or design of experiments. Both of them require a large number of experiments (or simulations), especially when the parameters are strongly interdependent. As a consequence, they become inadequate and impracticable for complex problems. In contrast, the optimization algorithms make the optimization process fully automatic, and from this point of view, yield a significant assist in the development cycle.

In this section, we propose to couple an optimization algorithm to FE simulations in order to optimize the temperature distribution along the preform length. The goal will be to provide an homogeneous thickness for the bottle. Infrared heating and blow moulding numerical models have been fully detailed in a previous paper [START_REF]Proc. of the Int. Conf NUMIFORM[END_REF]. A typical blow moulding simulation is presented in figure 1 where we compare the thickness distribution computed, and the thickness profile measured. Measurements were averaged on a set of three trials. We observe a good agreement along most part of the bottle (less than 15 % error on the mean thickness).

Parameterisation and constraints

In order to describe the temperature distribution along the preform length, we consider three optimization variables. They correspond to three temperatures located at different heights of the preform, as illustrated by figure 2. The whole temperature distribution is then deduced using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) method [START_REF] Fritsch | [END_REF]. To provide an accurate interpolation, an additional temperature is added on the preform neck. This fourth temperature is not optimized, but fixed to 80°C, which corresponds approximately to the glass transition of PET. Indeed, throughout the reheating stage, the preform neck is generally protected from IR radiation in order to prevent its temperature from exceeding the PET glass transition. This approach aims to prevent any deformation of the bottle neck during the forming process. Finally, to simplify the problem, the temperature is assumed to be uniform through the preform thickness. The optimization variables are constrained using lower and upper bounds, corresponding respectively to the PET glass transition temperature, and to the PET crystallization temperature. These two physical limits have been naturally chosen to prevent serious strengthening of the structure from appearing, in which case, any deformation would be proscribed during the forming stage. Let us note that neither linear nor nonlinear constraint is required.

Objective function

In this application, we attempt to provide a uniform thickness for the bottle. This objective must be mathematically formulated by an appropriate costfunction. A simple way to proceed is to define the objective function F as the standard deviation of the computed thicknesses, as following:

( )

∑ = - - = n 1 i 2 i th th 1 n 1 ) x ( F r (1)
where x r represents the set of optimization variables, n is the number of nodes along the bottle height, i th is the thickness at the node " i ", and th is the mean thickness. The nodal thicknesses are computed using a Python script that we have developed into ABAQUS® FEM software. Such a function is null for a bottle with perfectly uniform thickness.

Choice of an Algorithm

The choice of the optimization algorithm is closely related to the type of cost function. In our application, we attempt to minimize a nonlinear realvalued function, subject to bound constraints. In addition, strong mechanical and geometric nonlinearities could induce significant numerical instabilities, making the objective-function noisy, and therefore non-differentiable. As a consequence, the gradient-based algorithms might not be adapted to this type of problem. In contrast, the direct search methods (which do not require the computation of the cost-function gradient) remain particularly adapted to the non-derivative optimization. Among this family of methods, the Nelder-Mead simplex algorithm is probably one of the most popular. However, this local method provides relatively slow convergence rates [7]. Nevertheless, when the derivatives can not be explicitly written, this method can save a significant amount of computation time compared to gradient-based methods. Indeed, the computation of the cost-function gradients can become strongly time consuming when they are approximated using the finite-difference method. This is particularly true when the number of optimization variable is large. On the other hand, the Nelder-Mead simplex algorithm is restricted to unconstrained problems. In this work, we used the method proposed by Luersen et al. [START_REF] Luersen | Proc. of the Int. Conf. on Eng. Comp. Tech[END_REF] in order to add bound-constraints into the Nelder-Mead simplex algorithm available in Matlab® .

Results and discussion

All numerical results reported in the sequel were obtained on a 2.8 GHz-512 Mo Pentium 4. Figure 3 displays the decrease of the objective-function value in terms of the number of optimization iterations. We observe that the objective function is reduced by 60% of its initial value after the first iteration, and by more than 80% at the end of the optimization process. Consequently, the thickness distribution of the formed bottle is 80% more uniformed after optimization. The algorithm converges after 5 iterations, which involves only 10 objective-function evaluations (that is to say, 10 FE simulations).

On average, one cost-function evaluation requires 26 min CPU. Thus, the total CPU time required for the optimization is approximately 3h20min. Figure 4 illustrates the temperature distribution along the preform length before and after optimization. Initial conditions were chosen in order to apply a uniform temperature (100°C) on the preform. Such temperature distribution leads to a strongly nonuniform thickness distribution for the bottle, as illustrated by Fig. 5. After optimization, there is a temperature gradient along the perform length, which provides a more uniform thickness and a full blowing of the bottle. Fig. 4 also illustrates the optimal temperature distribution determined by Logoplast Company using an experimental trial-and-error method. This result has been obtained using the same preform, but with a different shape of mould. However, we can notice that there is a good agreement in the trends between the temperature profile experimentally determined within industrial conditions, and the temperature distribution computed using our optimization method.

CONCLUSION

For SBM optimization, we have proposed a practical methodology to numerically optimize the temperature distribution of a PET preform, in order to provide a uniform thickness for the bottle.

Encouraging preliminary results have shown the viability of our approach. However, it would probably be more desirable to directly optimize the process parameters of the heating systems. But to do so, both the infrared-heating simulation and the blowing simulation would need to be included into the optimization loop, resulting in further complications essentially due to long computation times.

Nevertheless, this approach would implicitly account for the influence of the temperature distribution through the preform thickness, which is of prime interest.

  Key words: Stretch-blow moulding, PET bottles, heat transfer, finite element method, optimization. Optimisation of Preform Temperature Distribution For the Stretch-Blow Moulding of PET Bottles M. Bordival, Y. Le Maoult, F.M. Schmidt CROMeP, Ecole des Mines Albi, Campus Jarlard, 81000 Albi, France objective was to homogenize the temperature along the preform length, by modifying the process parameters related to the IR oven. It is interesting to point out that authors questioned the relevance of the objective chosen for the optimization.

Fig. 1 .

 1 Fig. 1. Wall thickness distribution of the bottle. The error bars show ± 1 standard deviation for a set of 3 trials.

Fig. 2 .

 2 Fig. 2. Temperature distribution along the preform length -Optimization variables.

Fig. 3 .

 3 Fig. 3. Objective-function value versus iterations.

Fig. 4 .

 4 Fig. 4. Initial and optimized temperature distributions along the preform length.

Fig. 5 .

 5 Fig. 5. Thickness distribution of the bottle before and after optimization.

ACKNOWLEDGEMENTS

This study was conducted within the frame of 6th EEC framework. STREP project APT_pack; NMP -PRIORITY 3. www.apt-pack.com. Special thanks to Logoplast Technology for manufacturing the preforms, and QUB for their collaboration.


N Lebaal
email: lebaal@enstimac.fr

S Puissant

F M Schmidt

Rheological parameters identification using in situ experimental data of a flat die extrusion

Keywords: Polymer, Extrusion, Numerical simulation, Identification

Viscosity is an important characteristic of flow property's and process ability for polymeric materials. A flat die was developed by Mailleferextrusion, to make rheological characterisations. In this paper, the rheological parameters of the melt are identified through optimisation by a response surface method. The objective is to minimize the differences between the measured pressure obtained in flat die and the pressures computed by one-dimensional finite difference code programme. An objective function is defined as the global relative error obtained through the differences between measured and computed pressures. This objective function is minimised by varying the rheological parameters. For this minimisation, two methods are used, i.e. the local response surface and the global response surface. The rheological parameters permit to calculate the viscosity. Then, we compare this calculated viscosity with an experimental viscosity measured on a capillary rheometer to validate our method.

Introduction

The defects of extrusion (like the weld-lines, the fairly uniform exit velocity distribution throughout the extrusion and problems of stagnation zones) are influenced by the geometry of the die of extrusion as well as by the operating conditions such as temperature of regulation, flow rate and the rheological parameters of melt. In fact, if the rheology of most generic polymers is well known, the plastics used on production extrusion lines are seldom known because the polymer is obtained by blending or adding different additives. So, in the first step and in order to validate the method of optimisation, we will identify the rheological (behaviour) parameters of the plastic melts starting from the experimental data obtained in a flat die. Our objective is to identify the rheology of a plastic melt directly from on-line production, without using conventional measurements on dies capillary standard.

A certain number of viscosity models have been published [START_REF] Agassant | Polymer Processing. Principles and Modelling[END_REF][START_REF] Rauwendahl | Polymer Extrusion[END_REF], such as the well-known Power-law model, the Ostwald-Waele model, the Cross model, the Carreau model, and so on. Liang [START_REF] Liang | Characteristics of melt shear viscosity during extrusion of polymers[END_REF] investigated the melt viscosity in steady shear flow of several polymers by employing a capillary rheometer and the characteristics of shear viscosity. Geiger and Kuhnle [START_REF] Geiger | Analytische Berechnung einfacher scherstromungen aufgrund eines fliebgesetzes vom carreauschen typ[END_REF] used a empirical correlation between density, pressure and temperature to obtain a rheological model. Choosing one of these rheological laws, we will identify its parameters. We will use classical design of experiments [START_REF] Goupy | Plans d'Expériences Pour Surfaces de Réponse, Industries Techniques[END_REF] and algorithm of optimisation called the response surface method, with a moving least squares approximation [START_REF] Liew | Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method[END_REF][START_REF] Krongauz | Enforcement of essential boundary conditioned in mesh less approximations using finite elements[END_REF]. The experimental points are obtained with a standard extruder feeding at various flow rates of the flat die. Two series of tests were carried out, with different thickness of die to cover a sufficient range of shear rate to make rheological characterisations.

The optimisation benchmark

A flat die produced by Maillefer-extrusion [START_REF] Schläfli | Filière Rhéométriques Théorie/Filière Plate, Internal Report of Nokia Maillefer[END_REF] (Fig. 1) is equipped with four pressure transducers, spaced 100 mm apart; however, only the pressure difference between the first

Numerical simulation parameters

The measurement of viscosity cannot be obtained directly because the shear rate is unknown as well as the three parameters for the Power-law. On the other hand, three physical parameters related to viscosity such as pressure, temperature and the flow rate are directly measurable. We will use onedimensional finite difference calculation software by sections [START_REF] Agassant | Polymer Processing. Principles and Modelling[END_REF][START_REF] Rauwendahl | Polymer Extrusion[END_REF], to calculate the variation of pressure with the Powerlaw for each point of measurement. The choice of this geometry was made in order to respect correction factor [START_REF] Huneault | Evaluation of the FAN Technique for Profile Die Design[END_REF][START_REF] Kim | A simple approach to determining threedimensional screw characteristics in the metering zone of extrusion processes using a total shape factor[END_REF]. The shape factor, which is the thickness to width ratio, h/W equals 0.1 and 0.05.

Design variables and objective functions

The Power-law is defined as: There are three variables (K, m and β) for a Power-law with a thermal dependence of the Arrhenius type.

η = K 0 e β 1 T γm-1 (1)
The objective of this simulation to identify the rheological parameters K, m and β. This is done by minimizing the objective function representing the value of the sum of the quadratic difference between the calculated pressures and the experimental pressures for all point of measurement.

J = npm (p exp -p cal ) p exp 2 (2)

Optimisation procedure

Choice of algorithm

The algorithm of optimisation must be carefully chosen when one single analysis requires several hours of CPU time. Non-deterministic or stochastic methods such as Monte-Carlo method and genetic algorithm [START_REF] Renders | Algorithmes Génétiques et Réseaux de Neurones[END_REF] can obtain global minimum, but they need a lot of evaluations for the functions to converge. Gradient methods [START_REF] Sun | Global convergence of no monotone descent methods for unconstrained optimisation problems[END_REF] require the computations of the gradients of the functions, such as BFGS [START_REF] Morales | A numerical study of limited memory BFGS methods[END_REF] and SQP [START_REF] Horowitz | Quadratic programming solver for structural optimisation using SQP algorithm[END_REF]. The computation of gradients by finite difference is time consuming and depends on the perturbed parameters. For the above reasons, we decided to choice a response surface method.

Response surface method

The method of response surface consists of the construction of an approximate expression of objective function starting from a limited number of evaluations of the real function.

The main idea is to approximate the objective function through a response surface. In order to obtain a good approximation, we used a moving least square method. In this method, the approximation is computed by using the evaluation points by design of experiments around the locus, where the value of the function is needed.

Moving least-squares approximation

We will use moving least-square interpolations in order to approximate the response surface of objective function. Let the dependent variable be f(x) in the domain S and the approximation f (x).

f (x) = p(x)a T (x) (3)
The nodes are defined by x 1 , . . ., x n , where x 1 = (x 1 , y 1 ) in two-dimensional (2D), x 1 = (x 1 , y 1 , z 1 ) in three-dimensional (3D); p(x) is a polynomial basis and a T (x) is the vector of coefficients. The polynomial basis of order two in two di- mensions is given by:

P i = 1(x)(y) 1 2 (x) 2 (x)(y) 1 2 (y) 2 (4)
In the moving least-square interpolation, at each point x, a is chosen to minimize the weighted residual:

J(a) = w i (f i -P(x) T a(x)) 2 ⇒ J(a) = 1 2 (F -Pa) T (F -Pa) (5)
where w i is a weight function, such that w is non-zero over a domain of influence.

In order to find the coefficients, we obtain the minimum of J(a) by J ′ (a) = 0 So we have:

a(x) = Q -1 BZ (6)
where

Q = P T WP (7)
and

B = P T WQ (8)
The iterative procedure stops when the successive points are superposed with a certain tolerance ε = 10 -3 .

Local response surface

This method is based on traditional minimisation by the algorithm of Fig. 2, with the use of a local response surface of variable in each point. We fixed a step of grid at 0.01 × X 0 , where X 0 is the initial value of the variable of optimisation.

The initial values are: K 0 = 12,000 Pa s, m 0 = 0.64 and β 0 = 1078 K. We used a uniform local grid.

The constraints for the variables of optimisation K, m and β are, respectively, 400 Pa s< K < 20,000 Pa s, 0.01 < m <1 and 500 K < β < 3000 K for the first constraint, and n × P for the second constraint, where P is the step of the grid and n is the number of points of grid.

Global response surface

The objective of this technique is to reach the global minimum on the field domain: the constraints are similar to the previous constraints in the local response surface method. Initially, at first iteration we constructed a grid of 5 × 5 × 5 points (125 points) for a global approximation. Then, for each iteration, we constructed a grid of 3 × 3 × 3 (27 points) for the local approximation. In Fig. 4, the evolution of the parameter K is shown in function of the iteration. We can see that it is varying quite fast at the beginning of the optimisation, until the ninth step. Its total variation is about 16%.

Results

Local response surface

In Fig. 5, the evolution of the parameter m in function of the iteration, we notice that the variation is fast at the beginning of the optimisation, until the 11th step. Its total variation (36%) is more important than for K.

As in Fig. 7, the variation of beta in function of iteration step, we can observe that this parameter is quite stable at the beginning and starts to change after iteration 11, when K and m have almost their final value.

Result of global response surface

The solution is obtained after six iterations with a precision of 8.4 × 10 -4 and a CPU time is 1 h and 13 min. We can observe that the convergence process is much faster in terms of iteration steps needed. But the computation time is longer. Also, in this method, the three parameters are evolving together in the first iteration steps before reaching values close to the final one.

Comparison of the two methods

In Table 3, in function of the operating parameters (slit height, output and temperature), we have reported the pressures measured and recalculated using the identified rheological parameters, so as the relative error (relative difference between the two). We notice that the solution obtained by the method (1) local response surfaces is more accurate, but with an increased computing time. The difference in time between both methods is 30 min. On the other hand, the global response surface method (2) avoids local minimum. This can be improved by varying the design of experiments and the method of approximation to optimise the computing time CPU.

Pressures

In Fig. 11, the measured pressures and computed pressures obtained with the identified rheological parameters are plotted. There is only a small discrepancy, which means that our method is very robust and gives very good results for both global and local methods. This is also confirmed through the relative error for methods (1) and ( 2), which are, respectively, 9.14 × 10 -3 and 2.9 × 10 -2 . Fig. 13. Computed and measured viscosity method (2).

Viscosity

In the graph of viscosity obtained by the coefficients found through the response surface method (Figs. 12 and 13), we can observe that there is no discrepancy between the points of measurements obtained in capillary rheometer and the viscosity obtained by the method of optimisation except in the zone, where high shear rates appear.

Conclusion and prospects

We conclude that we obtain good results using the response surface methods (global and local). It means that this method allows us to determine the rheological parameters of polymers directly on a production line. By on will not forced to make measurements on standard capillary rheometers. And also this method will allow us to measure the parameters in industrial conditions, starting from the real geometry even if complex, using pressure measurements, flow rates and temperatures.

Future works

Also to test the Kriging method [START_REF] Trochu | Non-linear modelling of hysteretic material laws by dual Kriging and application[END_REF], we will have to improve precision (CPU time) of the global response surface approximation.

We will use the same approximation method to apply on a real 3D geometry to identify the rheological parameters and then to optimise the geometry of die extrusion tolls. The extrusion simulations will be processed by using the REM3D ® [START_REF]REM3D, User's Manuals[END_REF] FEM software.

Fig. 1 .

 1 Fig. 1. Geometry of the flat die.

Fig. 2 .

 2 Fig. 2. Optimisation algorithm.

Fig. 3 Fig. 3 .

 33 Fig. 3 represents the evolution of the objective function and Figs. 4-6 represent, respectively, the variation of the coefficients of the constitutive law K, m and β during the process of optimisation. In iteration 20, the value of the function objective obtained is 8 × 10 -5 , with K = 9826 Pa s, m = 0.4179

Fig. 4 .

 4 Fig. 4. Evolution of K during the process of optimisation (the local method).

Fig. 5 .

 5 Fig. 5. Evolution of m during the process of optimisation (the local method).

Fig. 7 rep-Fig. 6 .

 6 Fig. 6. Evolution of β during the process of optimisation (the local method).

Fig. 7 .

 7 Fig. 7. Convergence of the objective function (the global method).

Fig. 8 .

 8 Fig. 8. Evolution of K during the process of optimisation (the global method).

Fig. 9 .

 9 Fig. 9. Evolution of m during the process of optimisation (the global method).

Fig. 10 .

 10 Fig. 10. Evolution of β during the process of optimisation (the global method).

27 4 . 9 ×

 49 10 -3 40 8.1 × 10 -3 resents the evolution of the function objective and Figs. 8-10 represent, respectively, the variables of optimisation K, m and β. The optimum parameters are: K = 10,500 Pa s, m = 0.4027 and β = 1194 K.

Fig. 11 .

 11 Fig. 11. Experimental and calculated pressure with parameters determinate by method (2).

Fig. 12 .

 12 Fig. 12. Computed and measured viscosity method (1).

Table 1

 1 Experimental data slit 5 and 10 mm

	Q (kg/h)	T (K)	P (bar)	ρ (kg/m 3 )	h (mm)
	11.2	439	53	779	5
	60	448	99	779	5
	143	465	125	773	5
	239	483	138	767	5
	10.9	458	12.7	779	10
	69.2	468	26	772	10
	189.5	483	34.3	761	10
	339.5	502	36.7	755	10
	and the last transducer was considered for the analysis. A first
	series of tests has been realized with the flat die. Measure-
	ments were made with two different slit heights at different
	extrusion speeds for one type of material (LDPE). The ex-
	perimental values are listed in Table 1. The properties of the
	polymer (a LDPE grade) are referenced in Table 2.

Table 2 Properties

 2

	0.115

of the polymer under study and geometry Specific heat, C p (J/(kg K)) 1900 Conductivity, k (W/( • C m))

Table 3

 3

	Results of optimisation
	h (mm)	P measured (bar)	P (bar) local (1) recalculated	Relative error (1)	P (bar) global (2) recalculated	Relative error (2)
	5 5 5 5 10 10 10 10	5 3 9 9 125 138 12.7 26 34 36.7	5 2.11 9 6.69 121.6 132.9 1 2.49 25.15 34.69 3 9.	2.8 × 10 -4 5.4 × 10 -4 7 .3 × 10 -4 1 .3 × 10 -3 2.7 × 10 -4 1.0 × 10 -3 1.2 × 10 -4	49.32 91.03 116.8 130.4 12.48 24.89 34.66	4.8 × 10 -3 6.4 × 10 -3 4 .3 × 10 -3 3 .0 × 10 -3 3.0 × 10 -4 1.8 × 10 -3 3.7 × 10 -4

Acknowledgment

The support of Maillefer-extrusion is gratefully acknowledged.


G Saint-Martin

Fabrice Schmidt
email: schmidt@enstimac.fr

Pierre Devos

Christophe Levaillant

Voids in

Keywords: Injection moulding, Voids, Quality, Mass, Density

published or not. The documents may come

Introduction

A policy of weight reduction of aeroplanes had been followed for the last 10 years. Equipment designers have been trying to substitute conventional metallic alloys (steel, titanium, aluminium, etc.) for non-structural aeroplane parts. As a consequence, there is currently considerable interest in short fibre-reinforced thermoplastic composites. These materials are easily processed and they also offer advantages of low cost and mass or special characteristics (chemical and fire resistance), very useful in the civil aeronautical field. The injectionmoulding process allows the creation of very complex shapes without post machining, and can even be justified with relatively short runs (high added-value parts). How-ever, the substitution of die cast metallic parts by injection-moulded reinforced polymer parts often leads to very important thickness changes which can result in the generation of void defects [START_REF] Bevis | Thick section reinforced thermoplastics injection moulding, in: 2nd Inter-national Conference: Fiber Reinforced Composites[END_REF].

The aeronautical industry produces very complex parts (fan wheels, butterfly valves, etc.) which have to support important stresses for a long time (usually 60 000 h for a civil plane). As voids can lead to stress concentrations and premature breaking [START_REF] Beall | Thick walls encourage sink marks and voids[END_REF][START_REF] Beall | Uncontrollable dimensions sink marks and internal voids[END_REF], their detection in injectionmoulded parts is crucial. The most common method used to detect voids consists of the observation of cut sections in critical thick regions. However, this method is destructive and it cannot be used when the quality control has to be done on 100% of the parts. In that case, parts are often controlled by their mass. This global parameter can be a good indicator for voids detection, but it is very sensitive to volume variations [START_REF] Saint-Martin | Advanced controls and measurements for the injection moulding of a short fiber reinforced polymer[END_REF]. Moreover, mass control does not take into account density variations inside the part.

In this paper, we present a non-destructive quality con-trol method which can be used as an alternative to traditional mass measurements: density control. This method is evaluated using short fibre-reinforced injection-moulded thick parts. We first briefly studied the effect of holding pressure, mould and melt temperature, and injection speed on the density of the injectionmoulded parts. Then, several holding pressure levels are used to produce the parts. We also proceed to complementary destructive controls in order to have a better understanding of density variations throughout the thickness, and to detect voids inside the injection-moulded parts. This leads to the definition of an optimum interval for the holding stage of the injection-moulding process, set using density measurements.

Experimental

Material

The polymer we used for the study is a natural Ultem 2300-1000 supplied by General Electric Plastics. It is a 30% short glass-fibre reinforced polyetherimide. This grade is widely used in the aeronautical field because of its good mechanical properties. Moreover, in case of fire, its smoke rate and toxicity are very low. The given mass density for this polymer is 1.51 g/cm 3 .

Injection-moulding equipment

The parts were manufactured on a 175-ton DK-Codim injection-moulding machine. The maximum injectable volume is 319 mm 3 . If necessary, the polymer melt temperature can be set up to 420 °C, and the mould temperature can be set up to 230 °C. For Ultem grades, a drying operation is necessary before processing, which is realised at 140 °C for 5 h with an air-circulating oven.

The mould cavity geometry is a set of two 7-mm thick plates, constituting two modular inserts (see Fig. 1). The gates are optimised in order to have a linear flow front along the plate width. A complete real-time data acquisition system is added together with the injection-moulding machine. Data acquisition is based on self-developed Labview software, using up to 16 data channels. Pressure transducers and temperature sensors can help to understand the polymer thermodynamic evolution inside the mould cavity during the injection moulding cycle.

Injection moulding experiments

A first experiment series was realised using the Taguchi method [START_REF] Pillet | Introduction aux plans d'expe ´riences par la me ´thode Taguchi[END_REF]. The studied processing parameters are listed below:

ț Mould temperature (level 1, 140 °C ; level 2, 180 °C) ț Melt temperature (level 1, 380 °C ; level 2, 420 °C) ț Hydraulic holding pressure (level 1, 0 MPa; level 2, 10 MPa) ț Injection speed (level 1, 20 mm/s; level 2, 50 mm/s).

All other process parameters were kept constant. The output data of the experiment series is the apparent density of the injection-moulded parts. Each plate of the set was cut at the end of the gate (see Fig. 1). The density measurements were realised using the ISO1183 standard. The immersion liquid was distilled water at 23 °C. The part apparent density was calculated as below:

d app ϭ M 1 M 1 ϪM 2 (1)
where M 1 is the mass of the part, and M 2 is the mass of the immersed part.

The hydraulic holding pressure level explains 80% of the effects on the apparent density. Both mould and melt temperatures explain 5% of the effects. The injection speed effect is not significant. Some moderated interactions appear between the holding pressure and temperatures. Considering these results, we decided to study the effect of the holding pressure level in further experiments.

The second series of injection moulding experiments involved variation of the hydraulic holding pressure with the levels set at 0, 1, 2.5, 5, 7.5, 10 and 12 MPa. The holding stage duration was set to 20 s, and was kept constant like all the other process parameters. Melt and mould temperatures were respectively set to 406 and 180 °C. The injection speed was set to 30 mm/s for the filling of the plates. The feed channels were fed at an injection speed of 20 mm/s, and the gates at 10 mm/s in order to avoid a slight jetting phenomenon.

A superposition of the different polymer pressure cycles inside the cavity is presented on Fig. 2 (where HPL means hydraulic pressure level). The packing level is similar for all cycles. The slight variations are due to the packing-holding shift, which is realised using an imposed hydraulic pressure. When the hydraulic pressure level increases, the polymer pressure decreases more slowly, and the shrinkage compensation becomes more efficient. All injection-moulded parts did not present any visible faults which leads to very strong solidified skins during holding and cooling stages. As a consequence, the thermal shrinkage phenomenon leads to void creation instead of surface shrinkage.

Global mass and density measurements

Fig. 3 shows mass and apparent density vs. the hydraulic holding pressure level (HPL). We notice an almost linear variation for the mass and an important saturation effect for the apparent density when HPL

ͩ ∂M ∂d app ͪ HPLՅ5 MPa ϭ V ( 2
)
where M is the mass, d app the apparent density, and V the volume of the controlled part (50 cm 3 in this case).

For HPL values over 5 MPa, Eq. ( 2) is not valid. This second region does not respect the basic physical relationship between mass and apparent density, but is a saturation effect corresponding to the creation of wire edges, mould opening and residual stresses [START_REF] Vincent | Evaluation of residual stresses in injection moulded thermoplastics and fiber reinforced thermoplastics[END_REF].

Density measurements throughout thickness

Previous apparent density measurements only give us global information. It is well known that the thermodynamic history of the polymer has an effect on the density [START_REF] Agassant | Polymer Processing[END_REF][START_REF] ´gnier | Anisotropie des proprie ´te ´s dimensionnelles et me ´caniques des polyme `res injecte ´s[END_REF]. As this thermodynamic history can change through the thickness, we made destructive apparent density measurements as presented in Fig. 5.

Three 20 × 20 × 7 mm 3 square samples are cut in the middle of the parts. They correspond to HPL values of 0, 5 and 10 MPa. Successive polishing operations and apparent density measurements were made, as shown in Fig. 5. Each layer's density can then be measured, using a reverse recurrence method:

∀ k[1 ; nϪ1] , d k ϭ 1 H k ϪH kϪ1 • ͩ H k D k (3) Ϫ nϪ1 i ϭ k h i d iͪ and h n ϭ H n ; d n ϭ D n
Fig. 6 shows the evolution of the polymer density through the thickness for the three HPL levels tested. First, HPL has a slight effect on the thickness of the part. Then, the density of both skin and core layers of the thickness are not much affected by HPL. The most important differences are located in intermediate layers. Many voids are observed inside intermediate layers for HPL = 0 MPa. Some small voids are still observed at the same place for HPL = 5 MPa. For HPL = 10 MPa, no voids are observed but the density changes through the thickness. Hence, the global apparent density of a part corresponds to the average value of a complex variation.

Global voids rate measurements

Ten parallelepiped samples were cut from each injection-moulded plate, as shown in Fig. 7. Their sections were polished and observed with an optical microscope coupled to a CCD camera. An image analysis was then performed using Aphelion software. Voids were detected with a threshold operation and we calculate a global void rate t V as:

t V ϭ 1 V • k V kͫ i ͩ Sv i S i ͪͬ ( 4
)
where i is the image number, S i the image surface, Sv i the void surface in the image, k the number of the parallelepiped sample, V k the volume of the parallelepiped sample, and V the volume of the plate. In Fig. 8, the evolution of void rate is plotted vs. the hydraulic holding pressure level. For HPL over 5 MPa, the injection-moulded parts are void free. Below this value, voids rate increases when HPL decreases.

Discussion

The hydraulic holding pressure level has a significant effect on void rate (see Fig. 8). In our experiments, the minimum HPL value leading to void free parts is between 5 and 7.5 MPa. Complementary injectionmoulding experiments and void observations show that this minimum value is 6.5 MPa [START_REF] Saint-Martin | Advanced controls and measurements for the injection moulding of a short fiber reinforced polymer[END_REF].

While increasing HPL, the mass increases with an almost linear profile (see Fig. 3). On the contrary, the apparent density increases with a significant change of slope, corresponding to the minimum HPL value leading to void free parts. Then, from this point of view, apparent density measurements are more accurate than mass measurements for void detection.

The loss of the mass-density proportionality over HPL = 5 MPa is also an important factor (see Fig. 4). This means that a high HPL leads to a volume increase, but not to a density increase (mould opening, wire edges creation, etc.). This is a very common error in the industry when injection moulders are setting a process. They usually measure the mass and define processing parameters, only using these measurements. This application shows that this method is relatively imprecise. It can lead to void-free parts, but also, for example, to important residual stresses. Therefore, if dissection is not possible (because of cost or time problem for example), apparent density measurements can be a good alternative.

The apparent density control method needs a double mass measurement (one in the air, and one immersed). The investment required for its application is not acceptable for most of the industrial cases (high productivity fields). Nevertheless, it is mainly intended for high added-value products, where cycle time does not really matter. The aeronautical field is a good example.

The particular case of this 7-mm thick plate still has to be checked on another geometry. Other injection moulding experiments were then realised on a butterflyvalve body. While increasing HPL values, we measured mass and apparent density of the produced parts. The results are reported in Fig. 9. The material is a black Ultem 2300-1000 from General Electric Plastic. The results are similar to the ones we described for the thick plate. While HPL increases, the mass increases with an almost linear profile. On the contrary, the apparent density presents a slope change corresponding to the beginning of the optimum HPL interval (approximately from 5.1 to 6.5 MPa). Over this interval, the butterfly-valve bodies include significant residual stresses and become fragile. Below this interval, destructive dissections show Fig. 9. Mass and apparent density vs. HPL for an industrial part. some voids. Thus, this phenomenon of slope change with the apparent density vs. HPL is applicable to other cases.

Density measurements through the thickness show some significant variations, even for high HPL values (see Fig. 6). This is due to the thermodynamic history of the polymer. Cooling is, for example, slower in the core layer than in the skin layer [START_REF] Vincent | Evaluation of residual stresses in injection moulded thermoplastics and fiber reinforced thermoplastics[END_REF][START_REF] Agassant | Polymer Processing[END_REF][START_REF] ´gnier | Anisotropie des proprie ´te ´s dimensionnelles et me ´caniques des polyme `res injecte ´s[END_REF]. Therefore, an apparent density must be considered as an average value. The local density depends on the position through the thickness and on the position in the part. This explains why average density values reported on Fig. 6 are slightly different from the ones reported in Fig. 3. Predicting a local density of an injection-moulded part is a complicated scientific challenge [START_REF] Saint-Martin | Advanced controls and measurements for the injection moulding of a short fiber reinforced polymer[END_REF][START_REF] Vincent | Evaluation of residual stresses in injection moulded thermoplastics and fiber reinforced thermoplastics[END_REF][START_REF] Agassant | Polymer Processing[END_REF], but this study shows that it is possible to use global apparent density measurement as a quality control tool for void detection and process setting.

Conclusions

This study suggests that apparent density control can be a good non-destructive method for void detection. Mass control is not able to indicate void presence to injection moulders, or even on residual stresses creation. Therefore, for high added-value products that cannot be tested by a destructive method (100% control), mass measurements are not sufficient for setting the process.

This study also shows an interesting phenomenon concerning voids location. In Fig. 6, we notice that voids are located in intermediate layers of the thickness. This is a surprising result, because we first expected voids to be in the core layer (where the polymer temperature is the highest). As a consequence, we are currently study-ing the effect of HPL and reinforcement rate on void location and morphology (shape, size, quantity, etc.) [START_REF] Saint-Martin | Advanced controls and measurements for the injection moulding of a short fiber reinforced polymer[END_REF].

We are also currently evaluating other non-destructive methods in order to detect voids in thick injectionmoulded parts. Ultrasonic and X-rays controls appear to be interesting and very sensible approaches for detecting this defect [START_REF] Saint-Martin | Advanced controls and measurements for the injection moulding of a short fiber reinforced polymer[END_REF]. However, for a complicated geometry (butterfly-valve body, for example) theses methods are hardly applicable due to thickness variations. Then, the apparent density control is again the easiest and cheapest method to use for non-destructive void detection.

Fig. 1 .

 1 Fig. 1. The injection mould and the manufactured bunch.

Fig. 2 .

 2 Fig. 2. Injection-moulding pressure cycles.

Fig. 3 .

 3 Fig. 3. Mass and apparent density vs. hydraulic holding pressure level.

Fig. 4 .

 4 Fig. 4. Mass vs. apparent density.

Fig. 5 .

 5 Fig. 5. Density measurement method throughout thickness.

Fig. 6 .

 6 Fig. 6. Polymer density variation throughout thickness.

Fig. 7 .

 7 Fig. 7. Voids rate measurement method.

Fig. 8 .

 8 Fig. 8. Voids rate vs. hydraulic holding pressure level.

Acknowledgements

The authors wish to thank S. Leroux for assistance with image analysis, and E. Jourdain for helpful work on this project. Special thanks go to C. Rossignol (Liebherr Aerospace) for the injection-moulding experiments on butterfly-valves bodies.