Véronique Hofman

Marius Ilie

Elodie Long

Kevin Washetine

Christian Chabannon

Dominique Figarella-Branger

Bruno Clément

Laurence Mabile

Anne Cambon-Thomsen

Pascal Boucher

Georges Dagher

Robert Hewitt

Barbara Parodi

Paul Hofman
email: hofman.p@chu-nice.fr

Measuring the contribution of tumor biobanks to research in oncology: Surrogate indicators and bibliographic output

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

Summary:

The number of biobanks, in particular hospital-integrated tumor biobanks (HITB), is increasing all around the world. This is the consequence of an increase in the need for human biological resources for scientific projects and more specifically for translational and clinical research.

The robustness and the reproducibility of the results obtained depends greatly on the quality of the biological samples and the associated clinical data. They also depend on the number of patients studied and on the expertise of the biobank that supplied the samples. The quality of a research biobank is undoubtedly reflected in the number and overall quality of the research projects conducted with samples provided by the biobank. Since the quality of a research project can be measured from the impact factor of resulting publications, this also provides some indication of the quality of a research biobank. However, this method of assessment faces a number of major problems: the first is that the delay between the initiation of a research project (including securing access to human resources from a biobank) and its conclusion with one or several publications may take several years; the second is the lack of consensus in the research community of the form of acknowledgement of the biobank's contribution (authorship versus mention in one of the sections of the manuscript), which currently makes automatic bibliographic retrieval unreliable: the third is that high quality samples do not ensure high quality research. Equally, it is conceivable for poor quality samples to be used for research that is published in high impact journals. It is therefore necessary for the biobank community to define additional "surrogate" quality indicators, and establish systems of evaluation, in relation to current and future resource requirements. These indicators will help in the realistic assessment of biobanks by institutions and funding bodies and they will help biobanks to demonstrate their value, raise their quality standards and compete for funding. Given that biobanks are expensive structures to maintain, funding issues are particularly important especially in the current economic context. Use of these indicators may also contribute to the development of a biobank impact factor or "bioresource research impact factor" (BRIF). Herein we review four major categories of indicators (describing the quality, the activity, the scientific productivity, and the "visibility" of the biobank) that seem to us to be useful for the evaluation of a HITB. In addition, we propose a scoring system to measure the different items discussed. [START_REF] Cambon-Thomsen | Assessing the impact of biobanks[END_REF][START_REF] Hewitt | Biobanking in a fast moving world: an international perspective[END_REF][START_REF] Womack | Banking human tissue for research: vision to reality[END_REF]. Hospital-integrated tumor biobank (HITB) deliver samples or series of samples for the purpose of better understanding the physiopathology of diseases and/or better defining and validating new diagnostic, pronostic and/or theranostic biomarkers [START_REF] Hewitt | Biobanking: the foundation of personalized medicine[END_REF]. In this regard, the growing number of requests for high quality biological resources, in association with clinical data, requires that HITBs have an efficient turn around time between sample request and sample delivery.

Key

The creation and follow-up of biobank indicators should aim to optimize HITB operations and ensure their sustainability. Potential criteria for biobank evaluation are numerous. Their category and priority need to be defined to guide their introduction into routine practice so that they can be used by the different stakeholders as well as funding agencies.

Proposal of four large categories of indicators for a hospital-integrated tumor biobank

The purpose of the article is to review several potentially useful types of indicators, and to assess their advantages and caveats as tools for HITB evaluation. These indicators have been classified into four broad categories which describe and cover various aspects of HITB operations: 1) indicators related to quality; 2) indicators related to activity; 3) indicators related to scientific productivity and, 4) indicators related to external dissemination and communication.

For items within each of these four categories we have assigned arbitrary scoring coefficients. The list of these items is not exhaustive and many other criteria may be integrated in the future, depending on the strategic orientation of the HITB.

Scoring systems will need to be adjusted to provide comparable assessments of biobanks with different missions and strategic orientations. At one extreme there are biobanks that act purely as service providers for private or public partners. At the other extreme there are biobanks that play an active role in scientific projects and develop their own research.

Depending on its internal organization, its motivation and also on its business plan, an HITB may function using one or a combination of these two "patterns". It is important to measure to what extent, and for which proportion of the research projects, the HITB contributes to the research. This can include performing some of the analytical assays and experiments, the collection and update of clinical data, and the final interpretation of the experimental data, beyond the "simple" delivery of biological resource; in other words, it is important to evaluate the extent and quality of the connections and collaborations established between the HITB and other hospital-based resources and infrastructures (such as the pathology department, the molecular diagnostic department or other) and resources and infrastructures purely dedicated to research activities.

Indicators relating to quality

The different indicators of the quality of an HITB and the corresponding item coefficients are listed in table 1.

The quality of biological resources

-The quality control of the morphology of frozen tissue samples is an essential parameter. This point highlights the obvious necessity to set up a tight collaboration between the pathologists and the biobankers [Bevilacqua et al]. The morphological controls performed must be representative of the frozen sample. This is a critical point since the different analyses performed with frozen tissue (using biochemical and molecular biology technical approaches) have to be done from representative samples of the lesions of interest. This step is particularly important when omic project are developed further, since results can vary considerably depending on the relative proportion of tumor cells, stromal cells and infiltrating inflammatory cells as well as the presence of necrosis. The morphological assessment of tissue samples can be done in various ways depending on the laboratory practice, and each method has advantages and disadvantages. One method is to obtain a formaldehyde fixed paraffin embedded (FFPE) tissue sample to mirror the sample dedicated to the freezing procedure, and to stain sections for assessment and archiving by the biobank. The disadvantage of this approach is that the FFPE tissue sample may not accurately represent the whole frozen tissue sample. However, this method allows in parallel performance of immunohistochemical studies on whole sections and secondary tissue microarrays. It is probably good practice to keep these FFPE tissue blocks at 4°C for collection of high quality and well preserved FFPE tissue blocks (in particular to plan in the long-term molecular biology analyses from these fixed tissues). Another method is to perform imprint cytology of the tissue sample before freezing. This method is rapid and allows one to check whether the tumor lesion is really present and whether there is a sufficient number of tumor cells before freezing. However, quality control of the morphology is only partially reliable since the architecture is not available on these imprints. Moreover, a potential risk of external contamination exists for tissue specimens when using this procedure. Finally, another method is to cut a frozen section of the selected tissue immediately before nucleic acid and/or protein extraction. This approach is also called the « sandwich technique », since tissue sections for morphological analysis have to be cut on either side of the section cut for nucleic acid and/or protein extraction. This method allows for excellent quality control of the frozen lesion morphology (percentage of tumor cells, area of necrosis, stroma component). However, the disadvantage of this method is that it raises the temperature of the whole frozen tissue sample from -80°C or below up to at least -20°C (the temperature of the cryostat). This can be a disadvantage if the remainder of the tissue sample needs to be returned to a lower temperature for future projects. Moreover, external contamination can occur using this procedure.

Whatever the laboratory choice for control of morphology, it is critical to archive the corresponding images using software that allows comparison of histology with the biochemical and/or the molecular data, obtained from the corresponding frozen specimen.

-It is important to assess the quality of the nucleic acids obtained by extraction of the frozen sample). DNA is more « resistant » than the RNA and proteins to the time of warm and cold ischemia, and also to formalin fixation [Ma et al, 2012]. In this regard, it is important to note that even if the pre-analytical time is not optimal, certain DNA samples may be used successfully to detect for genomic alterations in tumor samples.

Conversely, other research projects, in particular those using RNA, need to be done from high quality frozen samples and the RNA quality must then be controlled on a bioanalyser. It is widely claimed that samples must have an RNA Integrating Number (RIN) above 7 for most transcriptomic projects. However, this assumption needs to be questioned because some tumor pathologies are often associated with necrotic areas or with a large number of hypoxic cells and so a cut-off RIN value of 7 may be inappropriate for some human tissue samples. An elevated RIN (above 7) is indicative of good quality control for cell culture, but an elevated RIN does not reflect the reality of most of the tumor's "quality status" even before surgical resection. In this regard, a large number of tumors (for example some lung, pancreatic and central nervous system tumors) will have an exceptionally lowered RIN even in association with a short time of warm and cold ischemia before freezing [Ma et al, 2012]. Whatever, the requirements and the needs of a research project, it is critical for a HITB to demonstrate the efficacy and the management of the different pre-analytical steps and parameters (recording of the time of cold ischemia, and if possible of the time of warm ischemia, length of freezing or duration of the formalin fixation before paraffin embedding, archive period).

-The the number of specimens and quantity of tissue available is an indicator and the gross weight of the frozen tissue samples in the cryotubes should be evaluated before providing samples for a research project. All cryotubes containing a tissue sample should be weighed with a precision balance before freezing. In this regard, a number of HITBs only provide extracted nucleic acids and/or proteins to their partners in order to better control the quantity of sample dispensed.

-For the same cohort of patients, the availability of samples of different origins such as tissues (frozen and/or FFPE tissues), nucleic acids (somatic and germinal DNA, RNA, microRNA) and proteins, biological fluids (whole blood, plasma/sera, pleural liquid, urine, salivary fluid, etc.), and/or primary cell cultures, can provide added value for research projects. For example, projects targeting the discovery and/or validation of biomarkers can use data obtained from both tissues and biological fluids. Moreover, the possibility of obtaining frozen and fixed tissues (and potentially tissue microarrays) from the same population of patients can be useful to validate protein expression.

Finally, the possibility of developing primary cell cultures in the HITB would be useful for pre-clinical research projects using mouse xenograft models or for in vitro cellular drug toxicity tests. However, it is critical for all collections to obtain optimal sample quality control tools [START_REF] Betsou | Identification of Evidence-Based Biospecimen Quality-Control Tools: A Report of the International Society for Biological and Environmental Repositories (ISBER) Biospecimen Science Working Group[END_REF].

-Frozen matched « healthy » tissue (or at least matched non tumor tissue) together with a tumor tissue sample is often used in transcriptomic projects. The availability of such control tissue is another quality indicator for HITBs.

Quality of clinical data associated with bioresources

-Apart from calibration and metrology projects developed for biological test evaluation or validation, all translational and clinical research projects require clinical, pathological and/or biological data associated with the bioresources. For tumor tissue samples, pathological data may relate to the gross morphology and the histological results (in particular the pTNM staging determined according to the updated WHO classification).

For histological data, the minimum data set should include the type of the tumor (according to the latest international classification of tumors), and the codification (Cim-10 and CIMO codification). A "transcodification" table must be made available and used by the biobank software according to the codification system, which can be employed at the national level. The percentage of tumor cells and the percentage of necrotic areas should be registered.

-For some projects, the status of genomic alterations (mutations, translocations, etc.) associated with the tumors should be registered and made available.

-The minimum clinical data set linked to the bioresources must include basic demographic information (age, sex, place of birth) and some supplementary clinical data that add value to the collection and to the pathology. For instance this additional data could include the place of birth of the parents of the patient or the ethnicity (according to the laws of the country), some clinical data more specific of a pathology (for example work exposure or tobacco status for lung cancer patients), the follow-up of patients (specific disease survival, overall survival, progression free survival) and the different treatments received.

-The centralization of all the available information for each patient through a secure and searchable database (including a security access code and a secure server environment) will contribute to the optimal efficacy of a HITB.

-Setting up a quality management system, in particular for the follow-up of the clinicobiological data (by creating a dynamic system for data recording) is critical for the sustainability of updating data. Moreover, software for biostatistical analysis must be integrated into this management system.

Ethics

-Patient informed consent must be obtained before using a human bioresource for a research project. This is mandatory in most but not in all countries [Riegman et al].

However, this requirement has been discussed only recently in certain countries (such as in France) and unfortunately is not required in all countries. Moreover, the laws in this field are changing rapidly, and for example in France it has been mandatory since 2004 to give detailed information to the patient before taking samples for research. Moreover, a patient can refuse that his/her biological resources be used for research. In this regard, the demonstration that formal procedures have been set up to systematically obtain informed consent before collecting patient samples for research is a strong indicator of good practice.

-The success rate of the consent procedure is an important indicator. The strategy set out to obtain the informed consent has also to be evaluated.

-Collection and storage of the signed consent in a secure place has to be formalized: hard copies signed at least twice must be stored in separate locations and/or scanned and registered in a secure hospital database. This patient informed consent must be checked before using samples for a research project.

-The formulation of terms used on the informed consent sheet must be appropriate. The hospital's ethics committee must check the form. The use of broad consent for several research projects is possible, even though this eventuality is controversial in certain countries [Hanson et al, 2006;[START_REF] Hofmann | Broadening consent--and diluting ethics?[END_REF][START_REF] Steinsbekk | Broad consent versus dynamic consent in biobank research: Is passive participation an ethical problem?[END_REF].

-Anonymized personal data: The HITB must demonstrate its ability to protect the personal data of the patients and to show that the biological and clinical data shared with partners does not reveal a patient's identity [START_REF] Malin | Identifiability in biobanks: models, measures, and mitigation strategies[END_REF].

Miscellaneous parameters related to quality criteria

-The risk status of patients for human immunodeficiency virus, hepatitis B and hepatitis C infection is a frequent request when establishing a contract, in particular with industrial partners. However, viral serological testing is not mandatory for all hospitalized patients and can lead to a supplementary cost to some research projects.

-The existence of back-up collections at different locations may also be used as an indicator. These may be fully or partially comprehensive and are particularly important for collections of rare tumours. If backup collections are held by a different HITB, this second HITB needs to show the same level of certification or accreditation as the first.

For example these HITB need to be certified according to the NF S96-900 in France.

-The efficacy in locating samples and the associated data in the database, and thus a good turn around time between the request and delivery of samples needs to be evaluated.

Coefficients

The coefficients assigned to each main item described above in table 1 have been given arbitrarily. We would argue that the criteria corresponding to the « informed consent » should have at least the same coefficient as those concerning the « intrinsic quality » of the samples.

Indicators related to activity

The different indicators related to the activity of an HITB and the proposed coefficients for the items are listed in table 2. The term "activity" does not concern an analytical count only, but includes other miscellaneous criteria. -The criteria used to measure the ratios between the storage and supply are dependent on a number of issues: 1) the type of collection being considered (organ, pathology) 2) the type of samples (tissue, nucleic acids, biological fluids, etc.), or, 3) the global activity of the HITB. The stored data needs to include the number of collected samples for each patient. In France, it is possible to use the budgetary nomenclature set up in Montpellier to evaluate this activity [htpp://www.chu-montpellier.fr/publications/rubrique.jsp]].

Storage and supply activity

Different activities can thus be evaluated, such as the number of tissue samples, of aliquots of plasma/sera, of paraffin sections, of patient tissue specimens included in tissue microarrays, etc. This meticulous work is in fact useful to obtain an objective evaluation of the global activity performed in a HITB.

-Strategic planning taking into account the different results has to be set out at least annually to reduce or to increase the number of samples for storage in the HITB. This strategic approach has to be linked to the number of projects developed each year using the same collection and also to the available annual HITB budget.

-In the extreme situation, it may be decided to destroy certain stored collections if there has been no sample transfer for a long period time.

Management of HITB team workers

-The required number and type of HITB team workers can be directly determined from previously defined criteria for evaluation of activity. The sample turnover (which is objective proof that samples stored in the HITB are used in research projects), is useful for anticipation of workload and planning purposes. The absence of specific expertise in management of the staff (pathologist, biologist, technician, data manager, secretary) can lead to a slowdown in the HITB activity despite growing demands for samples.

Biological resource pricing and setting up a business plan model

-The pricing of human samples is difficult to evaluate and depends on the organization of the HITB. However, setting up a pricing policy for a HITB is a key factor in determining where and how investments will be made. This point is critical in optimizing the running of the HITB and also in maintaining the infrastructure of the HITB [htpp://www.e-cancer.fr/recherche/les-ressources-biologiques].

-The pricing policies developed by the HITB have to be approved by the hospital management. This pricing must be clearly stated in the contract before the formal request of samples and before setting up a research project.

-A clear business model is necessary to anticipate the sustainability of the expenses for manpower (can be maintained, reduced or increased), for the maintenance of the equipment of the HITB and for purchase of consumables.

Turn around time for transferring biological resources

-The turn around time (TAT) between the request for samples and their transfer to the researcher/partner is an indicator of the efficiency of the whole HITB system, including not only the HITB's team (general manager, data manager, pathologist, biologist, technician, secretary), but also the scientific committee and the hospital administration (for contract validation and signature of the material transfer agreement).

-The TAT efficiency is evaluated according to the nature of the inquiry: number and type of samples, the different origin of the biological resources (tissue plus plasma plus RNA for the same patients for example), the number and type of clinical data associated with samples.

-In this regard, it is certainly advisable to give the different TAT which depend on the request and thus to provide the necessary information concerning these TAT in the contract.

Dynamic monitoring indicators

-Selected and miscellaneous indicators can be included here, such as the number of contracts signed per year (number of contracts with private and/or public partners). The level of collaboration with local, regional, national and/or international academic and/or industrial partners should also be monitored.

-Material transfer agreements and contracts made with foreign countries require particular attention to ensure enforcement of the laws for sample transfer.

Demonstrating the sustainability of the quality of the management of the HITB is thus an important guarantee for the different partners [START_REF] Kiehntopf | Biobanking and international interoperability: samples[END_REF].

-The management of the nonconformities that occur in the HITB: The kind of preventive and corrective measures made and their effectiveness should be recorded..

-Regular statistical tests to check the consistency of data on the central HITB database must be done to assess the number of mismatches.

Coefficients

Sample transfer, the establishment of pricing for samples and good management of dynamic indicators are major items of this category.

Indicators related to scientific productivity

The indicators related to scientific productivity are listed in table 3. It is critical that public hospital biobanks take into account these indicators. The integration of these indicators depends on the goals of the specific biobank. If the main role of a given biobank is to transfer human biological resources of high quality to academic and/or private partners and in exchange to obtain funding, then scientific productivity is not a relevant or critical indicator. Conversely, scientific productivity is very important in the evaluation of academic biobanks. In this case, the scientific productivity can also include the team's expertise in research and development.

Development of translational research activities within the biobank gives added value to the structure and motivates the HITB team by giving better external visibility. For example, the system called SIGAPS (a software system documenting the scientific publications according to different criteria) has been set up in France in order to assess the hospital departments (which can include the HITB). According to the number of attributed points, more or less funding can be allocated to the different teams. The different items related to scientific productivity are detailed below.

Scientific publications

-This item must be well defined since it is quite often difficult to know the precise contribution of the HITB to a publication. Moreover, the use and final outcome of biological resources after transfer from the HITB to scientist can be difficult to follow by biobankers. The contribution of the HITB can take different forms. Biobankers can be listed as co-authors of the publication. In this case it will be of interest to check whether the biobanker is the principal investigator in the research work or if he/she is an associated contributor of the publication. The biobank member should then be listed in association with the name of the biobank.

-The contribution of the biobanker (s) listed as an author (s) of a publication has to be clearly indicated (as required currently by some scientific journals at the end of the publication) and in general this work should not be limited to transferring samples.

-A biobank member (manager, pathologist, biologist, technician, etc.) can be cited in the "Acknowledgments" section of the publication and the HITB partnership should appear in this section. The HITB itself can also be cited in this section.

-The HITB must be listed in the "Materials and methods" section of the publication, if the samples provided were used to obtain results for the publication.

-The BRIF working group is currently developing a framework for: i/ creating a tool for calculating research impact of bioresources based on a metric (algorithm) and a unique digital resource identifier, ii/ assessing requirements for citation/acknowledgement of bioresources in order to trace their use in research [START_REF] Cambon-Thomsen | BRIF workshop group. The role of a Bioresource Research Impact Factor as an incentive to share human bioresources[END_REF]. Each collection of a biobank would be assigned a digital object identifier (DOI). Thus for each submitted publication (in which the work or part of the scientific work used biological resources), this DOI would be systematically referred to when submitting a manuscript for review.

Impact factor

-The quality and the value of the scientific work is mostly linked to the current « scientific world system » and to the reputation of the journal in which this work is published. Each journal has an impact factor, which is higher in the more prestigious scientific journals. Although other criteria can exist (such as the citation index of the publication), the impact factor of the journal is the indicator the most frequently used by the different evaluators of the members, teams, and larger structures (departments, hospitals, universities). A cumulative value of impact factors per year can then be calculated in different ways (according to the presence or not of a biobanker in the list of the authors, according to the position among the authors of a biobanker member, etc.). For each collection this impact factor may also be calculated in a similar way. The same approach could be used to indicate the quality and the richness of a specific collection stored in a HITB and this could be used to justify strategies aimed at increasing the number of stored samples corresponding to a specific pathology or organ.

Patents, scientific communications at meetings and reports

-It is necessary to distinguish between the patents obtained subsequent to research performed in the HITB (such as an innovative test for sample quality evaluation) and patents obtained by research teams using samples transferred from the HITB.

-Books and chapters of books in the field of biobanking and popular science publications can be listed.

-Participation in scientific committees organizing conferences on biobanking themes, and invitations to give lectures at conferences are indicators of scientific activity.

-Oral presentations and posters at meetings (at the national or international level) can be taken into consideration (provided the author (s) is (are) members (s) of the HITB and/or the HITB is listed in the abstract).

Grants

-Success in obtaining research grants is an important indicator for a HITB. National and international grants must then be recognized [START_REF] Wescott | Grant writing tips for translational research[END_REF]. Further distinction should be made between grants obtained by the HITB itself or by team researchers associated with the HITB (and using samples transferred from the HITB)

Coefficients

The coefficients could be attributed to the cumulated impact factor per year and to the grants obtained.

Indicators of HITB reputation

This group of indicators is listed in table 4. It contains heterogeneous items aimed at ensuring the visibility of the HITB at the local, regional, national and international level. As the number of HITB all around the world is increasing, creating a competitive environment, visibility is an essential part of a HITB's work.

Certification, accreditation and different labels

-The certification of a HITB is mostly related to the use of biological resources for research projects (not for immediate health care of patients). A biobank can be certified according to different types of certification such as the ISO 9001 certification. The certification according to the norm S96-900 is specific to biobank certification in France. This latter norm includes a management quality system, as well as some other specific business requirements in the biobanking field. This norm could be upgraded in the future to become an ISO norm.

-A couple of accreditations, such as the ISO17025 accreditation norm, can be used by the HITB to establish transfer of calibrated products of excellent quality. In addition, certain accreditations are more appropriate for medical biology laboratories, such as the ISO 15189 accreditation, which can be attributed to a HITB if samples are dedicated to diagnostics, prognostics and/or theranostics of the hospitalized patients.

-Other labels for HITB can exist, such as, the "IBISA" label in France. The latter label certifies that the biobanks have a working technological platform and develops innovative projects using biological samples (for example the improvement of nucleic acid extraction, etc.)

National and international networking

-The participation of the HITB in national and international networks demonstrates recognition and involvement of the HITB members in the biobanking field [START_REF] Hewitt | Biobanking in a fast moving world: an international perspective[END_REF]. A large number of HITB networks exist all around the world. In France different thematic networks have been set up for different biological samples and concern liver or lung cancers, lymphomas and sarcomas or mesotheliomas -Networks of HITB working on the same pathology in association with research projects can be set up. Through these networks, an optimal number of samples of rare pathologies can be obtained for a specific research project [Lochmulle and Schneiderat, 2010].

Membership to biobanking scientific societies and international biobanking groups

-As an example, in France the INCa has set up a group of experts working at the national level to promote good practice for the use of biological samples. This group regularly provides detailed guidance in different areas of biobanking such as pricing and cost recovery evaluation. This guidance is transmitted to the HITB managers as well as to the hospital authorities.

-Different international organizations in the biobanking world have been set up in recent years, such as the Biobanking and Biomolecular Resource Research Infrastructure (BBMRI), the International Society for Biological and Environmental Repositories (ISBER) and the European, Middle East and Africa Society for Biopreservation and Biobanking (ESBB). Through the organization of symposia and meetings, or through the diffusion of guidelines, these different organizations share procedures and ideas to improve the activities of the HITB [START_REF] Kiehntopf | Biobanking and international interoperability: samples[END_REF][START_REF] Yuille | Biobanking for Europe[END_REF]]. Belonging to one or more of these societies allows managers and staff to stay in touch with the latest developments in the field.

Educational programs and dissemination of the information

The development of HITBs and the specificities of the work involved has let to the development of a new job description. It is obvious that the management of a HITB has to be done by a "biobanker" who has gained the knowledge and technical skills necessary to succeed in this specific job [START_REF] Morente | Biobanking: old activity or young discipline?[END_REF]. However, people working in HITBs have a number of different professional backgrounds (pathologist, biologist, technician, data manager, scientist, quality controller, statistician, etc.) and each actor brings a specific contribution.

HITB managers and staff benefit from a comprehensive understanding HITB work including quality control procedures, data management, setting up of contracts and material transfer agreements, business plan development, etc. For this reason, it is critical to be able to offer to HITB managers and staff with opportunities for continuing professional training -The professional training can be done at different levels: 1) in the HITB through the organization of different internal meetings, 2) in the faculties (faculty of medicine or faculty of sciences) through different diplomas such as the master's degree) and 3) in the hospitals in different departments. In this regard, the creation of a Master's degree dedicated to biobank management has been set up in France [http://www.estbb].

Competence of the HITB team

HITB training course attendance and diplomas provide evidence of the competence of HITB personnel. It is important to take into account any complimentary competence of the HITB members.

Integrated technical platforms

A number of different technical platforms can be developed in a HITB, including: 1) a platform for nucleic acids extraction and quality control (spectrophotometer, bioanalyser), 2) a biopathology platform (paraffin embedded tissues, tissue micro arrays, immunohistochemistry, in situ hybridization), 3) a molecular biology platform (DNA cycler, sequencing), 4) a transcriptomic platform (scanner for different chips, bioinformatic expertise), and/or 5) other more specialized platforms including laser capture microdissection, primary cell cultures, and proteomic analysis. These different platforms can be integrated and located in the HITB or can be associated with the HITB through different contracts or partnerships. This item does not concern HITBs that only work as secure storage areas for biological samples and do not participate in translational and clinical research projects.

Marketing activity

Increasing the visibility of the biobank to the community can be done through different forms of marketing. Indeed, having a website, a HITB brochure, and organizing meetings or publishing articles for the general public about the activity of the HITB can all be part of the marketing activity.

Patient involvement

Active participation of patients and patient representatives in some HITB committees should to be considered.

Partnerships with Industry

This is most certainly one of the current most important indicators attesting to the attractiveness of the HITB in showing its capability to rapidly provide high quality samples. This indicator also provides evidence of the sustainability and capacity to obtain private funding. Partnerships with industry can be set up through scientific collaboration (patents, communications, publications) or through contracts for sample transfer, but without any scientific collaboration.

Coefficients

The aim of HITB certification is to obtain a high coefficient. Certification is the guarantee of a highly organised collection and the supply of biological samples of high quality. The HITB's involvement in international networks and scientific collaborations with industrial partners should also obtain high coefficients.

Toward a new system of appraisal of performance of HITB using the coefficients assigned to each category?

Ratings systems for evaluation are never perfect and they can sometimes be considered as an arbitrary means of arriving at a conclusion. However, the establishment of different coefficients based on various items classified into large categories, as described above, can give an objective idea of the efficacy of a HITB. The most sensitive point probably lies in determining the value of each coefficient according to the considered item. The coefficients given here are very informative but may be improved in the future. According to the total value obtained in each of the four large categories of indicators, 5 different ratings could be proposed; for example for a HITB: A+ or "excellent" (>200), A or "very good (150-200), B or "good" (150-200), C or "moderate" (120-150), and D or "weak" (<120) (figure 1).

Conclusion

The establishment of "monitoring indicators" for HITBs aims to maintain the quality of the different procedures, in particular those set up during the time prior to certification or accreditation. These indicators can participate in achieving durable optimization of the HITB.

The indicators detailed above can also evaluate other criteria of the running of the HITB, such as the added value of the infrastructure through scientific publications. The list of items described above is not definitively or rigidly fixed and we hope to be able to add other criteria in the future that could be of potential interest for HITB evaluation. HITBs usually have no scientific evaluation by the different institutions (for example, in France the research institutions Inserm or CNRS do not perform any evaluation). So currently, there is no rating system leading to a "label of excellence" and thus it is not easy to obtain funding through this kind of notation. One reason for this could be the actual absence of an evaluation grid for HITBs that includes objective criteria. In this regard, establishment of indicators could be of interest to set up this evaluation process. The different attributed coefficients outlined in this review are open to discussion and can be modified in the future, in particular when taking into account the "type" and the aim of the HITB, and the different objectives of the HITB. Indeed, some HITBs may not be involved at all in scientific research projects and may have as their unique goal the collection, storage and transfer of biological samples to public and private partners. In this latter case, the indicators concerning the scientific productivity of the biobank are not applicable.

Rating into categories A+, A, B, C or D may be welcomed by the "field workers", and thus may give a reductionist view of the HITB's activity. Different actors may perceive the rating system in a negative way. However, the multiplicity of HITB all around the world, has increased the overall cost of these infrastructures and the need to ensure the sustainability of the staff working in the HITB. This has brought on an urgent need to evaluate the HITB to at least check their efficacy in delivering samples for translational and clinical research. The consequences of such an evaluation may lead to an improvement in the functioning of these infrastructures in different ways, in particular by the optimization of certain targeted collections. In this regard, some synergistic programs involving different HITBs could be set up to obtain a high number of samples with high quality and thus develop excellent research projects.

  Words: Biobank, hospital-integrated tumor biobank, indicators, BRIF, translational research Introduction: New challenges in biobanking and consequences for the hospital-integrated biobanks When considering the high number of biobanks in Europe and other parts of the world and the increase in competition between these research infrastructures, it is important to define performance indicators in order to evaluate to what extent they meet the needs of different private and public partners

-

  This item corresponds to analytical count criteria taking into account the number of samples collected per year (tissues, biological fluids, etc.) and the number of samples supplied per year for use in research projects. As an example, at a national level, this item is a strong parameter, which is taken into account in the HITB evaluation process by the French National Cancer Institute (INCa) in France [http://www.ecancer.fr/recherche].

[

  htpp://www.e-cancer.fr/recherche].

  The research activity of a HITB can be evaluated in different ways: Based on assessment of resulting translational and clinical research and also based on additional indicators such as patents, consulting activities and different expertise, organization of national or international symposiums or meetings, etc. Implementation of the BRIF project [http://www.gen2phen.org/groups/brif-bioresource-impact-factor] has rapidly defined indicators for HITB [http://www.gen; Cambon-Thomsen et al, 2011]. In a complementary manner, transmission of an annual activity report (for example, the requirement set out by the INCa in France in the last two years) is another indicator of HITB activity over time.

Figure 1 .

 1 Figure 1. Global proposal for a HITB evaluation according to the coefficient rating of the

  Monitoring procedures (non-compliances and effectiveness of the corrective actions)Material transfer agreement and contractsConsistency statistical tests in the data base

  Figure 1

Table 1 .

 1 Indicators targeting the HITB quality and corresponding coefficients

Table 2 .

 2 Indicators targeting the HITB activity and corresponding coefficients

Table 3 .

 3 Indicators targeting the HITB scientific productivity and corresponding coefficients

Table 4 .

 4 Indicators targeting the evaluation that aims to raise the profile of a HITB and

Table 2 Table 3

 23

Acknowledgements:

The authors wish to thank the BRIF group for helpful discussion during the preparation of the manuscript

Conflict of interest:

The authors declare no conflict of interest


G Machado

G Chagnon

D Favier
email: denis.favier@grenoble-inp.fr

ANISOTROPY OF THE MULLINS EFFECT IN PARTICLE-REINFORCED SILICONE RUBBER

Keywords: Silicone rubber, Mullins effect, anisotropy, optical methods

INTRODUCTION

Like many filled rubber-like materials, as well as soft biological tissues and other biomaterials, filled silicones exhibit highly non-linear mechanical behavior. This non-linearity is commonly characterized by large strain levels under static conditions, a nonlinear stress-strain response and strain rate dependence. Finally, under cyclic loading conditions, hysteresis and stresssoftening behaviors are observed on both filled and unfilled elastomers. For the last half century all these cyclic phenomena were evidenced and modeled to support the most widely engineering applications. However, their microscopic mechanisms (breaking of weak chains, breaking of links, desabsorption of chains, etc.) explanation remains non-unanimous. Hysteresis is rather related to the dissipative nature of material, i.e., related with viscoelasticity [START_REF] Bergstrom | Large strain time-dependent behavior of filled elastomers[END_REF] and viscoplasticity [START_REF] Miehe | Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation[END_REF] behaviors. It is characterized as the difference between loading and unloading paths during a stabilized cycle. On the other hand the stress-softening phenomenon, also called the Mullins effect (see [START_REF] Mullins | Softening of rubber by deformation[END_REF]), can be described as a softer behavior of the second loading after a first loading. It can be idealized as an instantaneous and irreversible softening of the stress-strain curve, due to rearrangements in the microstructure of the material that occurs whenever the load increases beyond its prior all-time maximum stretch value. At times when the load is less than a prior maximum, nonlinear elastic behavior prevails. One time the previous maximum stretch is reached the loading path turns up and follows the primary curve again up to a new maximum. Through the years, the Mullins effect has experimentally been observed in different deformation states and numerous models have been proposed, but experimental data concerning the influence of loading cycles in one direction on the stress-softening in other directions are quite scarce. [START_REF] Mullins | Effect of stretching on the properties of rubber[END_REF] has alluded that the degree of softening was not the same in all directions for natural rubber samples cut both along and perpendicular to the direction of the previous preconditioning stretch; and thus some anisotropic stress-strain properties were developed. This evidence, for example, can be found in a homogeneous planestrain compression experiment by Pawelski (2001) and in a simple shear experiment performed by Muhr (1999) where simple shear loadings in different directions produce different responses. Other experimental results can be seen in Laraba-Abbes (2003) using a carbon-black filled natural rubber, Diani (2006) for the commercial elastomer filled black (EPDM) and [START_REF] Itskov | Experimental observation of the deformation induced anisotropy of the Mullins effect in rubber[END_REF] for carbon-black filled acrylate rubber (ACM). All these experimental results point out the strain-induced anisotropy in orthogonal directions due to some in-plane preconditioning test procedure. Within that context, the aims of this work are to characterize and understand the mechanical behavior of a filled silicone. The objective is to focus on the straininduced anisotropy by studying the influence of loading direction on the Mullins effect.

EXPERIMENTAL SETUP

Preparation of the Silicone Specimens

The samples used in the experiments were made of a filled silicone rubber called Rhodorsil®RTV3428 supplied as two liquid components: the uncured silicone and the curing agent. The final material is produced by a polyaddition, curing at room temperature. The liquid mixture is injected in a mold to obtain a sheet with constant thickness. Specimens used for each of the experiments were made using the same protocol of elaboration, in order to obtain specimens with reproducible mechanical properties, as follow: (i) mixing the components with a 10/1 mass ratio, (ii) putting the mixture under vacuum for 20 minutes in order to eliminate undesirable entrapped air bubbles, (iii) sheet molding injection, (iv) putting mold inside an oven at 70ºC for 4 hours in order to accelerate the curing process and assure a sufficient cross-linking density; (v) sheet demolding after 1 hour exposed at ambient temperature.

Testing procedures

All the quasi-static experiments were conducted on a MTS 4M universal testing machine with an Entran ELPM-T2±250N load cell. The images were recorded at 0.5Hz with a Jai TM-4200GE CCD camera using a reduced scan of 2048×1000 pixels. Simple tensile tests were performed on rectangular samples having an initial gauge length lo=40, width wo=13 mm and a thickness eo=2 mm. Since the experiment was not intended to fail the specimen, there was no need to use a dumbbell shaped specimen commonly used to prevent specimen failure nearby the clamps. But knowing that the effects of clamps create an indeterminate state of stress and strain in the region surrounding the clamps, due to the process of gripping, the initial gauge length was adopted as being less than the real physical size of the samples. For all tests, homogeneity of strain fields in the gauge region has been verified and elongations are averaged values.

Strain field measurement

The DIC technique like a non-contact method is of-ten used to characterize rubber-like materials, see for example [START_REF] Meunier | Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber[END_REF] and [START_REF] Sasso | Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods[END_REF]. At each testing time step, one image of the sample deformation was recorded using a CCD camera. The DIC technique allows surface reconstruction of the deformed samples and determination of the full-field surface displacements. For the in-plane displacement an accuracy of 10 -2 pixels or better can be reached. For point-to-point strain, the accuracy value lies around 10 -4 . The DIC method is preferred because there is no change in sample stiffness resulting from the presence of an attached sensor (classical extensiometry) and for being insensitive to ambient vibrations and rigid body motions (speckle pattern interferometry). Moreover the method is able to deal with high strain levels, what is a very desirable feature given the high strain level experienced by the tested material. Also the DIC allows demonstrating and measuring a heterogeneous deformation field. See [START_REF] Sutton | Digital Image Correlation for Shape and Deformation Measurements[END_REF] for further explanation about digital image correlation method.

RESULTS

Simple tensile strain state

During the test, using an elongation rate of   =1.60×10 -2 s -1 , the nominal stress tensor P (First Piola-Kirchhoff stress tensor) is assumed to be homogeneous within the gauge region as well as the deformation gradient tensor F. Since the actual thickness is not measured, the material is assumed to be incompressible, i.e., det(F)=1 for convenience. In the central zone, the deformation gradient, considering that the direction 1 is the tensile loading one, is given by

    3 3 2 2 1 1 2 / 1 E e E e E e F          (1)
and the nominal stress tensor

  1 1 11 E e   P P (2)
where (E1, E2, E3) and (e1, e2, e3) are the orthonormal basis used for the initial and current configurations, respectively.

In a second time, a tensile specimen has been subjected to a load/unload sequence at different elongation rates   =25×10 -4 s -1 to   =125×10 -2 s -1 in order to verify the rate-dependence influence. No noticeable difference between stress-strain responses was observed at the considered strain rate range. Consequently the RTV3428 behavior can be assumed independent of the rate of deformation for the observed ranges. A cyclic tensile loading test was realized, the results are presented in Figure 1. Different phenomena are highlighted, first a large Mullins effect appears by comparing the two first loadings at each strain level, but with very little residual elongation. Moreover, a little hysteresis (difference between second and subsequent loadings and unloadings) is observed. MPa at   =1.60×10 -2 s -1 .

Directional Influence

In order to study the anisotropy induced by the Mullins effect, two identical large specimens lo=100 mm, width wo=70 mm and eo=2 mm of thickness were submitted to one cycle of stretch, at λ=2.45 in uniaxial tension along a principal direction referred to 0º. Then, a set of smaller specimens was cut from each of these preconditioned large samples along four different directions 0º (first loading direction), 30º, 45º and 90º (orthogonal direction). An illustration is presented in Figure 2(a). All the cut specimens have been submitted to the same initial strain state (this has been verified thanks to the DIC measures). Figure 2(b) presents the second loading and unloading curves for the different cut specimens. It clearly appears that all these second loading curves come back on the first loading curve at the same maximum elongation. Moreover, the subsequent unloading curves are almost independent of the history. The main difference is the shape of the second loading curve, the amount of stress-softening can be relied to the angle between the two loading directions.

As represented by [START_REF] Shariff | An anisotropic model of the Mullins effect[END_REF] and Diani (2006b), Figure 3 shows the stress ratio between the first virgin load curve and the set of sub-samples orientated at 0º, 30º, 45º and 90º directions. The curves highlight that there is no proportionality between the different curves, moreover there is no easy link between the second loading curves. It appears that the function evolves from a maximum of stress-softening, when the two loadings are in the same direction and a minimum, close to zero, when the directions are orthogonal. That means that, at least, two parameters are necessary to describe the Mullins effect: the maximum stretch criteria and the angle between the first and second loading.

CONCLUSION

In the present work we have conducted an experimental campaign to build evidence showing that the Mullins effect in filled silicone rubbers is, in general, non-isotropic. The reproducibility and accuracy of measurements were evaluated through several successive tests. Results have shown that our protocol to manufacture the silicone specimens without any pre-existent anisotropy and our experimental methodology work well and provide a precise experimental characterization of softening phenomena. Using the DIC method as a non-contact full-field optical measurement, a large strain level was achieved. The results have shown that tensile cycles in one direction hardly cause any softening in the perpendicular direction. In addition, the results with respect to the influence of Mullins effect in the intermediate directions provide valuable information for testing and calibrating numerical models. Finally, the anisotropy of the Mullins effect becomes clearly evident and should be taken into account in the constitutive modeling of filled elastomers.

Figure 1 .

 1 Figure 1. Cyclic loading-unloading tensile test with increasing maximum stress: 0.2, 0.4, 0.6 and 0.8 MPa at   =1.60×10 -2 s -1 .

Figure 2 .

 2 Figure 2. (a) The large preconditioned sample and the different observed orientations. (b) Anisotropy induced by Mullins effect of a filled silicone RTV3428, superposed uniaxial stress-strain responses (load-unload).

Figure 3 .

 3 Figure 3. (a) Stress ratio between the first virgin load curve and the set of sub-samples, for sub-samples orientated at 0 º, 30 º, 45 º and 90º (perpendicular) directions. (b) Ratio of the energy loss for an angle loading to the enrgy loss at 0° Figure 3(b) presents the evolution of the loss energy by Mullins effect according to the loading angle. Experimental points are fitted using the periodic function given by ) 2 cos( ) cos( 2 1 o a a a    


Camille Linardon

Jean-Sébastien Affagard

Grégory Chagnon
email: gregory.chagnon@grenoble-inp.fr

Denis Favier

Benoit Gruez

Simulation of Drawing of Small Stainless Steel Platinum Medical Tubes -Influence of the Tool Parameters on the Forming Limit

Keywords: Tube drawing, Metal forming, Drawability, Jonhson Cook, Cockroft & Latham PACS: 62.20.F

Tube cold drawing processes are used to reduce tube diameters and thickness, while pulling them through a conical converging die with or without inner plug. An accurate modelling of the material deformation and friction behaviour is required in order to well describe these processes. The study concerns a stainless steel platinum alloy. The material behaviour is characterised through tensile tests at strain rates as close as possible to the high strain rates reached during the drawing process. The results are fitted with an isotropic temperatureindependent Johnson Cook constitutive equation. The modelling of floating plug drawing is performed on a ABAQUS/Explicit model. Friction coefficient is difficult to estimate with mechanical experimental tests, thus an inverse analysis is carried out to fit this parameter thanks to finite element simulation and experimental drawing tests. Drawing force measurements are recorded during the forming process. The Cockroft-Latham criterion is applied to understand the different process parameters influence on tube drawing and its accuracy for drawing process is evaluated.

INTRODUCTION

Tube drawing is a forming process used to reduce tube section. The outer diameter reduction is controlled by a die while the inner diameter is controlled either by a mandrel or a floating plug depending on the tube dimensions as illustrated in figure 1. The interest of cold drawing compared to conventional hot drawing is its ability to obtain tubes with thin walls, good surface finish and enhanced mechanical properties. Dies are generally made of tungsten carbide for mandrel drawing and polycrystalline diamond (PCD) for floating plug drawing. In the industry, several drawing passes are always required to reach final tube dimensions. In order to reduce time consumption during processing it is important to know the maximum plastic deformation a tube can undergo. The modelling of tube drawing process was previously studied in [START_REF] Palengat | Tube Brawing Process Modelling by a Finite Element Analysis[END_REF]. The originality of this work is first the material of study, a steel platinum alloy, and its particular mechanical behaviour including strain rate dependency. Second it focuses on the floating plug drawing process and the concept of drawability limit is introduced. The tube drawability limit is linked to several parameters such as tube material, tools geometry, friction coefficient and strain rate. The drawabitity limit is reached when ductile fracture initiates in the tube and so relies on a failure criterion. Numerous theoretical failure criteria have been proposed to estimate the initiation of ductile fracture [START_REF] Rao | A comparative evaluation of the theoretical failure criteria for workability in cold forging[END_REF]. The aim of this study is to apply one of those criteria to estimate the drawability limits of tubes made of a stainless steel platinum alloy drawn on floating plug.

MECHANICAL CHARACTERISATION

The tube drawing process is realised at various speeds depending on the passes. Thus the mechanical behaviour of the material must be known for different strain rates. In this way, tensile tests are performed on tubes.

Tube Tensile Tests

The tubes are 200mm long with an effective length of 100mm. Two mandrels are inserted at the edges of the tube in order to prevent deformation inhomogeneities. Industrial strain rates (up to 100s -1 ) cannot be reached experimentally thus experimental tensile tests are performed at strain rates ranging from 0.005s -1 to 5s -1 . True stress versus true strain curves are plotted for each strain rate in figure 2. The curves highlight the strain rate dependency of stress and justify the use of a viscoplastic model.

Johnson Cook Plasticity Model

Most of the viscoplastic materials are greatly influenced by the temperature: a temperature increase is known to lower the admissible stresses. The Johnson Cook model [START_REF] Johnson | A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[END_REF] enables to model the strain rate dependence and the thermal softening:

                                            m m eq eq n eq eq T T T T C B A 0 0 0 1 ln 1 ) (     (1)
where ε eq is the equivalent plastic strain, eq   the equivalent plastic strain rate, T the current temperature, T 0 a reference temperature and T m a reference melt temperature. A, B, C, n and m are material constants. During the drawing process, it was observed [START_REF] Palengat | Modelisation des couplages multiphysiques materiaux-produits-procedes lors de l'étirage de tubes[END_REF] that temperature increase due to plastic deformation and friction would not exceed 100°C. According to Laheurte [START_REF] Laheurte | Application de la théorie du second gradient a la coupe des matériaux[END_REF] and [START_REF] Palengat | Modelisation des couplages multiphysiques materiaux-produits-procedes lors de l'étirage de tubes[END_REF] thermal softening effects can be neglected and Johnson Cook model can be written as:

                         0 ln 1 ) ( eq eq n eq eq C B A     (2)

Determination of the Johnson Cook Material Parameters

The material Young's modulus is calculated from the elastic part of the stress-strain curves and set to 155 GPa. Poisson's ratio is supposed to be equal to 0.3. Due to the lack of information regarding the Poisson's ratio of the alloy, a sensitivity study about its influence on the simulation will be presented in a further part. The singularities observed at the beginning of the plastic zone on the stress-strain curve are identified as Lüders behaviour. Piobert [START_REF] Piobert | Commission des principes du tir[END_REF] and Lüders [START_REF] Lüders | Über die äusserung der elasticität an stahlartigen eisenstaben und stahlstäben, und über eine beim biegen solcher stäbe beobachtete molecularbewegung[END_REF] first reported the phenomenon of plastic strain localization observed in some alloys.

The material constant A represents the yield stress at temperatures below T 0 . The determination of the other parameters must be done considering that the Johnson Cook law cannot fit perfectly the experimental data. The errors between experimental data and Johnson Cook model must be minimised. In this study, the choice was made to minimise the errors for large deformations i.e. for strains larger than 0.2. The fitted parameters are detailed in Table 1. The fit of the model is presented in figures 3 and 4.

MODELING OF DRAWING

The drawing process is studied through an ABAQUS Explicit model. The tube length is chosen long enough so that steady states conditions are reached. Die and floating plug are also modelled. The tube is considered to have a perfect coaxiality; thus the geometry of the model is simplified into an axisymmetric configuration as illustrated in figure 5. All the geometrical elements are meshed with four-noded linear elements with reduced integration. The stainless steel platinum alloy behaviour which is isotropic, viscoplastic, rate-dependent and temperature-independent is modelled by a Johnson Cook law. Die and floating plug materials are considered to be isotropic elastic, their Young's modulus are set to 950 MPa and 650 MPa respectively and the Poisson's ratio is equal to 0.2. All the thermal effects are neglected and the materials are modelled as temperature-independent. The model was validated thanks to surface temperature and drawing force measurements during experimental drawing tests.

The initial tube with dimensions of 1.80×2.07 mm is reduced to 1.39×1.60 mm. Simulations were done for several tools with different geometrical parameters which are presented in figure 6. Two different dies with semiangle α and two different bearing lengths L were used. Concerning the floating plug, two semi-cone angles β with two different cone nose angles γ where used. All the parameters are listed in table 2, a total of 16 combinations of geometrical parameters were explored. The process is performed at ambient temperature at a drawing speed of 11.4 m/min.

SIMULATION ANALYSIS Contact Modeling

Signorini [START_REF] Signorini | Sopra akune questioni di elastostatica Atti della Societa Italiana per il Progresso delle Scienze[END_REF] proposed a physical contact model for deformable bodies interacting with rigid static bodies. The contact is supposed to behave following a Coulomb friction law. Friction coefficient is dependent upon several parameters among which the most important are material roughness, interface temperature and lubricant. The influence of these parameters on friction behaviour is not easily identifiable and measurable. Thus friction coefficient values are determined by inverse analysis [START_REF] Palengat | Tube Brawing Process Modelling by a Finite Element Analysis[END_REF]. To carry out such an analysis a load cell is put at the die exit and drawing forces are recorded during drawing tests. Friction between tube/plug and tube/die are supposed to have the same characteristics. A drawing force of 420 daN is experimentally measured during a drawing pass with a section reduction of 39%. A friction coefficient value is then chosen so that the simulated drawing force curve fits with the measured force. The value of 0,055 is allocated to the friction coefficient.

Parametric Study

Some of the material properties are determined with incertitude since only little information is available from literature and few experimental tests have been conducted on the alloy. Thus it is important to evaluate the model sensitivity towards those parameters to evaluate its accuracy. Poisson's ratio is set to 0,3 according to values found in the literature. A variation of +/-16% around the mean value was investigated and reveals that the computed drawing force is not affected by such variations. The variation of Young's modulus of +/-15% around the 155GPa value (determined through tensile tests) results in a variation of the stress distribution across tube wall and the average computed drawing force is unchanged.

TUBE DRAWABILITY

Cockroft-Latham Criterion Applied to Tube Drawing

The estimation of workability limits during tube drawing is of importance to understand the conditions leading to tube fracture during processing. Cockroft and Latham [START_REF] Cockcroft | Ductility and the workability of metals[END_REF] established a criterion based on the observation that ductile fracture is more likely to occur in regions of largest tensile stress. The criterion is based on the calculation of a workability parameter C process defined as:

(

) 3
where σ max is the highest tensile principal stress , dε the equivalent plastic strain rate and ε f the equivalent plastic fracture strain. When C process reaches a maximum value called C max the material is likely to fracture. C max is a material constant defined from the tensile stress-strain curve up to fracture (Fig. 7). The experimentally found C max value for the stainless steel platinum alloy is 262 N.mm -2 .

Influence of the Die Geometry

Two geometrical parameters of the die are investigated: α and L. In a general way, C process values are higher for the nodes located on the outer surface. C process values are lower and more homogeneous for the nodes located on the inside of the tube (Fig. 8). The highest C process values on the external part of the tube are explained by greater material distortion and higher shear stress due to the die angle. Figure 8.a presents C process values computed for α=12° and 19° respectively combined to β=10° and 17°. The other geometrical parameters are kept constant: L=0.16 mm and γ=0.17°. A simultaneous increase of α and β leads to a more heterogeneous stress distribution through tube wall: inner stresses are lowered while outer stresses are increased. As a result, when increasing α and β the C process may exceed the C max value and according to the Cockroft-Latham criterion the drawability limit is reached. Fracture may initiate at the outer part of the tube and propagate inward.

Influence of the Plug Geometry

The consequences of a plug nose cone angle variation depend on the die angle α (Fig. 9). For α=12° an increase of γ results in a translation of the plotted curves toward lower values of C process (Fig. 9.a). For α=19° the consequences are slightly different: an increase in γ results in a decrease of the C process for the nodes located on the inside of the tube while the computed value for the external node is almost unchanged (Fig. 9.b). Thus the consequences of the variation of the plug nose cone angle are dependent on the die geometry and can hardly be predicted.

CONCLUSION

Numerical methods such as FEM combined with failure criteria are expected to be a powerful tool to predict ductile fracture and formability limit for tube drawing. The Cockroft-Latham criterion is not perfectly suited for tube drawing and other criteria should be explored for this special forming process. Nevertheless this parametric study permits to highlight the importance of small variation of the tools geometric parameters. To diminish the stress submitted to the tube it is important to use dies and plugs with small semi cone angles (12° and 10° respectively). A plug with higher nose cone angle e.g. 1° enables to lower the stresses in the tubes. Such a geometrical configuration permits to have a more homogeneous stress distribution across the tube wall and it lowers the risk of rupture.

FIGURE 1 .

 1 FIGURE 1. Drawing techniques: (a) mandrel drawing, (b) Floating plug drawing

1 FIGURE 2 .

 12 FIGURE 2. Stress-strain curves of tubes for different strain rates

3 .

 3 : Comparison of the stress calculated by Johnson Cook model and experimental values

FIGURE 4 .

 4 FIGURE 4. : Error between experimental data and Johnson Cook model

FIGURE 5 .

 5 FIGURE 5. : Two-dimensional FE-model for tube drawing process FIGURE 6. : Geometrical parameters of the die and the floating plug

FIGURE 7 .

 7 FIGURE 7. : Evaluation of C process during a tensile test and determination of C max

Figure 8 .FIGURE 8 .

 88 FIGURE 8. : Variation of Cockroft-Latham (C process ) parameter along the tube thickness for (a) die semi-cone angle variation, (b) die bearing length variation

FIGURE 9 .

 9 FIGURE 9. : Variation of Cockroft-Latham (C process ) parameter along the tube thickness for a plug nose cone angle variation for a die with a semi-angle of (a) 12°and (b) 19°

TABLE 1 .

 1 Values of the Johnson Cook parameters for the stainless steel platinum alloy

	A (MPa)	B (MPa)	C	n	0 eq  (s -1 ) 
	376	1315	0.00597	0.608	0.005

TABLE 2 .

 2 Values of the geometrical parameters of the tools

	Die		Plug
	Semi cone	Bearing	Semi cone	Nose cone
	angle	Length	angle	angle
	α (°)	L (mm)	β (°)	γ (°)
	12	0.16	10	0.17
	19	0.56	17	1


G Machado

D Favier

G Chagnon

From the experimental determination of stress-strain full fields during a bulge test thanks to 3D-DIC technique to the characterization of anisotropic Mullins effect

The bulge test is usually mostly used to analyze equibiaxial tensile stress state at the pole of inflated isotropic membranes. Three-dimensional digital image correlation (3D-DIC) technique allows the determination of three-dimensional surface displacements and strain fields. A method is proposed to calculate from these experimental data the membrane curvature tensor at each surface point of the bulge specimen. Curvature tensor fields are then used to investigate axisymmetry of the test; in the axisymmetric case, membrane stress tensor fields are determined from meridional and circumferential curvatures combined with the measurement of the inflating pressure. Stress strain state is then known at any surface point which enriches greatly experimental data deduced from bulge tests. This method is then used to treat an experimental bulge test on a filled silicone rubber membrane. The results highlight that a global membrane with a very heterogeneous strain history is obtained, from equibiaxial behavior at the center of the membrane until a planar (pure) shear state at the periphery of the bulge. Next, different small tensile specimens are cut from the pre-stretched silicone membrane. Identical cyclic tensile tests are realized on all these specimens. The curves are compared and highlight the difference of the stress-softening according to the place of the cut specimen and according to its orientation with respect to the circumferential or meridional direction.

INTRODUCTION

Rubber-like materials exhibit a significant stress softening after a first loading. This phenomenon called Mullins effect has been observed in different paths of deformation during the last six decades. A detailed review for experimental references in different deformations states like uniaxial tension, uniaxial compression, hydrostatic tension, simple shear and equibiaxial tension is given in [START_REF] Diani | A review on the Mullins effect[END_REF].

More recently the evidence that stress softening is an inherently anisotropic phenomenon can be found for different rubber-like materials under different load cases. However, these investigations are almost restricted to simple deformation histories. Tension tests performed successively in two orthogonal directions have been the most usual method to point out the strain-induced anisotropy. Results can be seen in [START_REF] Laraba-Abbes | A new tailor-made methodology for the mechanical behaviour analysis of rubber-like materials: II. Application to the hyperelastic behaviour characterization of a carbon-black filled natural rubber vulcanizate[END_REF] for a carbon-black filled natural rubber as material, [START_REF] Diani | Observation and modeling of the anisotropic viscohyperelastic behavior of a rubberlike material[END_REF] for filled black ethylene propylene diene (EPDM), [START_REF] Itskov | Experimental observation of the deformation induced anisotropy of the Mullins effect in rubber[END_REF] for carbon-black filled acrylate rubber (ACM), [START_REF] Hanson | Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect[END_REF] for a silica-filled polydimethyl-siloxane (PDMS) and [START_REF] Muhr | Anisotropy in gum and black filled sbr and nr vulcanizates due to large deformation[END_REF] for different compositions of black filled styrene-butadiene rubber (SBR) and sulfur-cured carbon black filled natural rubber (NR). Simple shear experiments were performed by [START_REF] Muhr | Experimental determination of model for liquid silicone rubber: Hyperelasticity and Mullins effect[END_REF], they noticed that strain softening of polysiloxane polymer investigated is smaller in directions orthogonal to the strain cycle causing the softening. Similarly under simple shear, [START_REF] Besdo | Modelling inelastic stress-strain phenomena and a scheme for efficient experimental characterization[END_REF] showed that a prior loading, generated by a cyclic one-side shear, lead to a material anisotropy verified during a symmetric loading, i.e., both-sided shear. [START_REF] Pawelski | Softening behaviour of elastomeric media after loading in changing directions. Constitutive models for rubber[END_REF] carried out two tests, first, a homogeneous plane-strain compression using a cubic sample of an elastomeric material (VLGQ-rubber) rotated and rotated back by 90 • with respect to the first preloaded configuration. Here a special procedure was required to correct the original measurements since compression is accompanied by friction which spoils the experimental data. Second, for a polyurethane material, a modified biaxial tension with tensile tests on secondary specimens afterward, was used in a way to find an evidence for more complex memory behavior of the material. Some models aiming to describe the anisotropy of the stress softening are proposed in the literature (see for example, [START_REF] Diani | Directional model isotropic and anisotropic hyperelastic rubber-like materials[END_REF][START_REF] Göktepe | A micro-macro approach to rubber-like materials. Part III: The microsphere model of anisotropic Mullins-type damage[END_REF][START_REF] Shariff | An anisotropic model of the Mullins effect[END_REF][START_REF] Diani | Observation and modeling of the anisotropic viscohyperelastic behavior of a rubberlike material[END_REF][START_REF] Ehret | Modeling of anisotropic softening phenomena: Aplication to soft biological tissues[END_REF]. All these models provide a solid theoretical basis for mathematical description of the stress softening, like an anisotropic phenomenon, in rubber-like materials. However, the predictive capabilities of models describing the anisotropic Mullins effect are mainly restricted to the uniaxial load case. [START_REF] Horgan | A theory of stress softening of elastomers based on finite chain extensibility[END_REF] reported that the anisotropic model cannot be validated since suitable experimental data are not available. [START_REF] Pawelski | Softening behaviour of elastomeric media after loading in changing directions. Constitutive models for rubber[END_REF] advised that further experimental works are necessary before one can decide how complex a material constitutive equation for rubber-like material should be. [START_REF] Itskov | Experimental observation of the deformation induced anisotropy of the Mullins effect in rubber[END_REF] pointed out that additional experiments regarding other load cases are needed. This allows to study further the influence of loading cycles with complex deformation states on the appearance and evolution of the Mullins effect in the case of changing principal stretch directions.

Within this context, the aim of this work is to quantify clearly the induced anisotropy according to the applied strain history. The objective is to focus on the strain-induced anisotropy study by verifying the influence of loading cycles in distinct directions using the bulge test to generate different biaxial deformation histories, and cut specimens from the original plate are thus submitted to tensile tests.

EXPERIMENTAL STUDY AND ANALYSIS

The induced anisotropy by stress softening was experimentally studied. For this purpose, samples were made of a filled silicone rubber called Rhodorsil RTV3428. Supplied as two liquid components, the uncured silicone and the curing agent, this liquid mixture is molded by injection to obtain a sheet with constant thickness [START_REF] Meunier | Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber[END_REF]. The final samples are produced by a polyaddition, curing at 70 • C for 4 h in order to accelerate the curing process and assure a sufficient cross-linking density. This material exhibits a pronounced stress softening under different load cases, as reported in [START_REF] Machado | Analysis of the isotropic models of the Mullins effect based on filled silicone rubber experimental results[END_REF]. In the same work, the manufacture procedure of specimens without any pre-existent anisotropy and testing methods details using three-dimensional image correlation (3D-DIC) are also described. With the 3D-DIC technique, it is possible to determine the 3D contour and the in-plane strain fields of the object surface. This process is carried out by correlation of the images, taken by two cameras in the deformed state with their original reference images. The bulge test were used to precondition the samples, i.e., to induce some primary stress-softening. Thus, subsequent uniaxial tensile tests were conducted on preconditioned specimens.

The objective is to propose an experimental test that permits to analyze second tensile load curves in a material that experienced a more complex first load path.

A biaxial tensile pre-stretch can be used to generate a complex in-plane deformation history, under incompressibility assumption. The complexity of this deformation history is given by the biaxiality ratio (µ), that can be expressed as a relation between principal inplane stretches (λ max ,λ min ) in the form µ = ln(λ min ) ln(λ max ) .

(1)

Thus, biaxiality ratio is very useful to characterize the first history imprinted in the material at the first loading. Note that in the uniaxial tensile pre-stretch [START_REF] Machado | Experimental observation of induced anisotropy of the mullins effect in particle-reinforced silicone rubber[END_REF]), the contractive stretches are the minimal principal directions, then the biaxiality ratio is fixed in µ = -0.5.

In this work the bulge test is proposed as an original way to yield very different biaxial strain-histories for first load path. As pointed in [START_REF] Machado | Membrane curvatures and stress-strain full fields of bulge tests from 3D-DIC measurements. Theory, validation and experimental results on a silicone elastomer[END_REF] bulge test is able to provide more information than the traditional application to determine the material equibiaxial response. It can be used to generate different biaxial states along a radial path of specimen from the equibiaxial state (µ = 1) at the pole until the planar (pure) shear (µ = 0), i.e., a large biaxiality ratio interval (µ ∈ [0, 1]).

Using the 3D-DIC technique, it is possible to determine the three-dimensional surface displacements and the principal stretches (λ m , λ c ) in the meridional and circumferential directions, as schematized in Fig. 1. From this point forward, these directions will be denoted by the subscripts m and c respectively. Nevertheless, in the axisymmetric case, deformed membrane principal stresses (σ m , σ c ) are determined from principal curvatures (κ m , κ c ) combined with the measurement of the inflating pressure (p). These fields are related as follow

σ m = p 2h κ c
(2)

σ c = p 2h κ c ( 2 - κ m κ c ) , ( 3
)
where h is the current thickness calculated using the incompressibility assumption. κ m and κ c are deduced from 3D-DIC measurements. Thus, the stress-strain state is then known at any surface point which enriches greatly experimental data deduced from bulge tests. For a comprehensive explanation see [START_REF] Machado | Membrane curvatures and stress-strain full fields of bulge tests from 3D-DIC measurements. Theory, validation and experimental results on a silicone elastomer[END_REF].

The specimen geometry consists in thin circular plate, of initial radius R = 90 mm with a thickness h 0 = 2 mm. The circular plate is simply supported and subjected to an uniform inflating pressure acting perpendicular to the current configuration. Using the 3D-DIC strain field measures, a set of interest points are specified along the radius of undeformed membrane permitting to know the stress and strain histories for every point over the deformed membrane surface. This set of points is represented in the Fig. 1, where each point can be regarded as a small specimen in view of 3D-DIC as a full field strain measure method. Point a corresponds to the membrane center and the other points (b to j) are 10 mm equidistant through the meridional direction.

Fig. 2 presents the first loading strain and stress history of the points a and h in function of the load pressure. Note that each inflation state involves a heterogeneous stress-strain state that evolves from an equibiaxial state at the pole (R = 0 mm -point a) tending to planar (pure) shear stretching nearest the clamp (R = 90 mm -point j). [START_REF] Machado | Membrane curvatures and stress-strain full fields of bulge tests from 3D-DIC measurements. Theory, validation and experimental results on a silicone elastomer[END_REF] pointed out the experimental difficulty concerning the mea-surements on the overall membrane surface and the region near the clamp simultaneously. For materials that experience high displacements a self-shadow effect is observed in this last region.

Fig. 3 presents the mean value and the range of the biaxiality ratio (µ) for all pressure load steps in each point a to i. The measured ratio is almost constant at a given point and variations between the different pressure load steps can be disregarded. Due to the experimental difficulties concerning the measurements near the clamp, the curves in Fig. 3 were extrapolated for the points i and j using polynomial approximation and represented by dotted lines.

After a recovery time of 1 h, a set of tensile test specimens are cut. Two series of samples are defined as follows: samples aligned to the meridional direction denoted by 0 o and samples tangent to the circum-Figure 3: Mean value and range of biaxiality ratio (µ) during all pressure load steps. Points i and j were extrapolated using a polynomial approximation (dotted lines). ferential direction (or perpendicular to the meridional direction) denoted by 90 o . Both series are illustrated in Fig. 1(b).

At first, the samples aligned to the meridional direction (0 o ) were submitted to a uniaxial tension test. The loading consists of a simple load unload cycle, where the upper limit overpass the maximum value reached, in the biaxial pre-stretch by the major principal (λ m ). It appears that all the curves are different. The figure highlights that closer the sample is from the bulge pole, more stress-softening is observed. Two aspects are observed, the difference between the reference curve (vir) and second load is increasing and the strain-hardening for the return point (RP ) on the reference curve appears later. These results are in consistency with the first maximal deformation level presented in Fig. 3(a).

Second, the samples cut at the points perpendicularly to the meridional direction (90 o ) are tested. However, the second load-unload curves corresponding to points a and g are presented for both directions (0 o and 90 o ) in Fig. 5 and compared to the virgin load curve (vir). The deformation is evaluated locally, using DIC, in a small zone located in the samples center. It clearly appears that the second load curves, for both directions, come back on the first loading curve at that same maximal deformation but with different levels of stress-softening. A stress softening appears in the orthogonal directions as the material was also stretched in this direction during the preconditioning path. This is due to the biaxial pre-loading where the directional intensity of the stress softening depends on the biaxiality ratio (µ). This emphasizes that subsequent directional behavior is strongly influenced by how the maximal pre-loading is applied.

Figure 4: Influence of the biaxial first loading on tensile test response. Uniaxial traction performed at 0 o with respect to the meridional direction for the subsamples a, e, f, g, h, i, and j.

CONCLUSIONS

The use of bulge test, as a biaxial preconditioning test, was originally proposed to find an evidence for an even more complex memory behavior of the material. The measurements made along the meridian of the inflated membrane provide unprecedented information about the history of principal stress and principal strain directions without an explicit dependency of any constitutive equation. Results showed that the induced anisotropy is dependent on the pre-stretch biaxiality ratio. The return on the first load reference curve of all second load curves occurs at the same point, independently of the second load direction. Note also that the form and intensity of the anisotropy of the Mullins effect could depend on the elastomer type, the properties of filler particles, and their mass and volume proportion in the polymeric matrix.

Figure 1 :

 1 Figure 1: Schematic representation of biaxial preconditioning method and principal stretches: (a) axisymmetric representation of the bulge test with the interest points; (b) Illustration of the cut subsamples over two different directions in the circular membrane.

Figure 2 :

 2 Figure 2: Bulge test deformation history for the points a to h. Principal stretches (λ m ,λ c ) and current principal stresses (σ m ,σ c ) are presented respectively on left and right axis according to the inflating pressure (p).

  Fig. 4 presents the second load curves for the different specimens and a virgin uniaxial tensile load curve (vir) as reference. The load curves of the points b, c and d are quasi superposed, thus they are not represented in the figure keeping clear the results visualization.

ACKNOWLEDGE

We would like to thank the French ANR for supporting this work through the project RAAMO ("Robot Anguille Autonome pour Milieux Opaques")


Andri Andriyana
email: andri.andriyana@um.edu.my

Mei Sze Loo

Erwan Verron
email: cerwan.verron@ec-nantes.fr

Grégory Chagnon
email: gregory.chagnon@grenoble-inp.fr

Continuum mechanical model for the Mullins effect in swollen rubber

Keywords: Rubber, Mullins effect, constitutive modeling, swelling, continuum damage mechanics

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

Introduction

Rubbers are widely used in engineering application such as vibration isolator, seals, gaskets, pipe, etc. During the service, they are subjecting to fluctuating mechanical loading which can lead to fatigue failure. Moreover, in engineering applications involving the contamination of aggressive liquids into the rubber components, swelling becomes a major issue since it decreases significantly the mechanical properties of rubber [START_REF] Haseeb | Compatibility of elastomers in palm biodiesel[END_REF]. Thus, the understanding of the mechanical response of swollen rubber is essential for durability analysis of such components.

In the present paper, the continuum mechanical modeling of Mullins effect in swollen rubbers under cyclic loading conditions is addressed. More precisely, the concept of Continuum Damage Mechanics is adopted and extended in order to account for swelling level. For this purpose, the mechanical testing probing the Mullins effect in swollen rubber is conducted. The data is subsequently used to construct the damage function describing Mullins effect.

Continuum Mechanical Framework

Experimental Observation. The stress-strain responses of dry and swollen rubbers under cyclic loading at different maximum strains are presented in Fig. 1. In this figure, the secondary curves correspond to the reloading paths. The stress level during primary curve becomes lower as the swelling level increases. Moreover, as in dry rubber, it is observed that the swollen rubber also exhibits Mullins effect. However, their amount depends on the swelling level [START_REF] Andriyana | Interaction between diffusion of palm biodiesel and large strain in rubber: Effect on stress-softening during cyclic loading[END_REF].

Constitutive Equation. At a continuum scale, swollen rubber is considered as homogeneous, isotropic and hyperelastic. Moreover, it is subjected to isotropic damage due to Mullins effect [START_REF] Chagnon | On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers[END_REF]. Since the volume of swollen rubber does not significantly change during the deformation, the material is assumed to be incompressible. Thus, the mechanical response of the swollen rubber can be entirely characterized by the existence of a strain energy function W S which depends on the two invariants I 1 and I 2 of the left Cauchy-Green strain tensor B relative to the swollen-unstrained configuration, on ( )

s S S J d I I W W , , , 2 1 = (1)
Following the concept of Damage Mechanics by Lemaitre and Chaboche [START_REF] Lemaitre | Mécanique des Matériaux Solides[END_REF], W S can be considered as the product of the surface reducing parameter 1d and the strain energy function of the hypothetically virgin undamaged (due to Mullins effect) swollen material W OS ( ) ( )

s OS S J I I W d W , , 1 2 1 ⋅ - = (2)
It is important to note that the damage that we address in the present work corresponds to the Mullins effect only. Considering the second law of thermodynamics, it can be shown that the Cauchy stress tensor in the incompressible swollen rubber is given by:

( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∂ ∂ - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ ⋅ - + - = 2 2 2 1 1 2 2 1 B I W B I W I I W d I p OS OS OS σ (3)
where the scalar p is the Lagrange multiplier due to incompressibility assumptions and is to be determined from the equilibrium equations and boundary conditions. Classically, it is mainly recognized that the Mullins effect exclusively depends on the maximum deformation endured by the material during its history [START_REF] Mullins | Softening of rubber by deformation[END_REF]. Therefore, a scalar measure of the deformation state and its maximum which depends on the deformation history should be defined. Simo [START_REF] Simo | On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects[END_REF] and Miehe [START_REF] Miehe | Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials[END_REF] used the virgin strain energy density while [START_REF] Chagnon | On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers[END_REF] adopted the elongation of polymeric chain issued from 8-chain model as the measure of deformation state. In the present study, following [START_REF] Chagnon | On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers[END_REF] and [START_REF] Miehe | Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials[END_REF], we adopt the discontinuous exponential-like damage function to desribe Mullins effect. Moreover, the damage function is extended in order to account for the swelling level. For this purpose, the following phenomenological damage function is proposed:

( ) ( ) ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - ⋅ = = s S s S s J J d J d d η α α exp 1 , (4)
where:

( ) ( ) 2 1 1 - + = = s OS s S S J d d J d d and
( ) ( )

1 1 - + = = s OS s S S J J η η η η (5)
In the above equation, d OS , d 1 , η OS and η 1 are material parameters. In the case of dry rubber, i.e. when J s =1, d OS and η OS correspond to the dimensionless maximum (possible) damage and the damage saturation parameter respectively [START_REF] Holzapfel | Nonlinear Solid Mechanics. A Continuum Approach for Engineering[END_REF]. α is the maximum value of deformation measure in the loading history. By choosing polymeric 8-chain elongation as the measure of deformation state, its maximum is defined by:

( ) ] ] ( ) [ ] τ α α τ t t , max ∞ - ∈ = and
( ) ( )

1 3 1 - = t I t α (6)
According to Treloar [START_REF] Treloar | The Physics of Rubber Elasticity[END_REF], swelling of rubber in liquid molecules is a purely physical mixing or interdiffusion process in which the two components may be regarded as chemically neutral. Consequently, from the standpoint of mechanical response, the only effect of the swelling is to reduce the modulus in inverse proportion of the swelling ratio. However, our previous investigation revealed a deviation from the Treloar's theory [START_REF] Chai | Development of a compression test device for investigating interaction between diffusion of biodiesel and large deformation in rubber[END_REF]. Thus, we propose the following generalized Treloar's theory which relates the hyperelastic strain energy functions of dry W OD and swollen one W OS :

( ) ( ) ( ) 2 1 2 1 , , , I I W J J I I W OD n s s OS ⋅ = - ( 7
)
where n is a constant.

Results and Discussion

Special Case of Uniaxial Extension. Without losing generality, we focus our attention on the case of uniaxial extension. Considering the general form of the stress-strain curve, it appears that the Ogden strain energy density function fits well [START_REF] Ogden | Large deformation isotropic elasticity: on correlation of theory and experiment for compressible rubberlike solids[END_REF]:

( ) ( ) ( ) ∑ = - + + ⋅ = 3 1 3 2 1 3 2 1 , , , p p p n s s OS p p p J J W α α α λ λ λ α μ λ λ λ (8)
where λ 1 , λ 2 , λ 3 are the three principal stretches while μ p and α p are material parameters. By considering the boundary conditions to determine the Lagrange multiplier p, the analytical expression for the first Piola-Kirchhoff stress (engineering stress) is:

( ) ( ) ∑ = - - - - ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - ⋅ ⋅ - = 3 1 2 2 1 1 1 1 1 p p n s p p J d P α α λ λ μ (9)
where d is given by Eqs. ( 4) and [START_REF] Mullins | Softening of rubber by deformation[END_REF]. By fitting simultaneously the experimental data, the following material parameters are obtained: Comparison with Experimental Data. Fig. 2 illustrates the comparison between the model and experimental data. In general, the model gives qualitatively good agreements with experimental data. The stress-softening is well described by the model for dry rubber and for swollen rubbers, in particularly at relatively low strain. More discrepancies are observed in swollen rubber for a larger strain level. Indeed, the model appears to overestimate the stress response. The effect of swelling is well described as shown by the primary curves where the model is capable to predict the general stress response of swollen rubbers.

The discrepancies observed between the model and experimental data in large strain range (where strong reinforcement due to strain hardening occurs) can be explained by the limitation of the model itself. Indeed, as highlighted in [START_REF] Chagnon | On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers[END_REF], this limitation is inherent in the choice of the damage mechanism: since the damage variable is written in terms of a maximum deformation state, theoretical secondary curves are proportional. This proportionality is not satisfied at large strain when the reinforcement becomes apparent.

Conclusions

In the present work, the modeling of Mullins effect (stress-softening) in swollen rubber under cyclic loading was addressed. In order to describe the damage in material resulting to stress-softening, an extension version of CDM model developed by Chagnon et al. [START_REF] Chagnon | On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers[END_REF] was considered. More precisely, the damage parameter is enriched by including the effect of swelling on the stress-softening. Results show that the model gives qualitatively good agreements with experimental data.

Fig. 1 .

 1 Fig. 1. Mullins effect observed in dry and swollen rubbers.

Fig. 2 .

 2 Fig. 2. Comparison between the model and experimental data.

Acknowledgements

The authors greatly appreciate the financial support of this research from the Ministry of Higher Education Malaysia through High Impact Research Grant HIR-MOHE D000008-16001.